अनुक्रम \(18,23,28,33,\ldots\) का सार्व अंतर क्या है?
What is the common difference of the sequence \(18,23,28,33,\ldots\)?
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A (4)
B (5)
C (6)
D (10)
Explanation opens after your attempt
Step 1
Concept
The common difference is (23-18=5), and the same difference continues. In exams always check the difference of consecutive terms.
Step 2
Why this answer is correct
The correct answer is B. (5). The common difference is (23-18=5), and the same difference continues. In exams always check the difference of consecutive terms.
Step 3
Exam Tip
सार्व अंतर (23-18=5) है और आगे भी यही अंतर है। परीक्षा में दो क्रमागत पदों का अंतर जरूर जांचें।
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यदि \(4,k,14,19,\ldots\) एक अंकगणितीय श्रेणी है तो (k) का मान क्या होगा?
If \(4,k,14,19,\ldots\) is an arithmetic progression, what is the value of (k)?
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The difference from (14) to (19) is (5), so (k=14-5=9). Use the equal difference rule for missing terms.
Step 2
Why this answer is correct
The correct answer is D. (9). The difference from (14) to (19) is (5), so (k=14-5=9). Use the equal difference rule for missing terms.
Step 3
Exam Tip
यहां (14) से (19) तक अंतर (5) है इसलिए (k=14-5=9)। खाली पद में भी समान अंतर का नियम लगाएं।
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अनुक्रम \(-2,3,8,13,\ldots\) में (a) और (d) क्रमशः क्या हैं?
In the sequence \(-2,3,8,13,\ldots\), what are (a) and (d) respectively?
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A (-2) और (5) / (-2) and (5)
B (3) और (5) / (3) and (5)
C (-2) और (-5) / (-2) and (-5)
D (5) और (-2) / (5) and (-2)
Explanation opens after your attempt
Correct Answer
A. (-2) और (5) / (-2) and (5)
Step 1
Concept
The first term is (-2) and (3-(-2)=5). Be careful while subtracting negative terms.
Step 2
Why this answer is correct
The correct answer is A. (-2) और (5) / (-2) and (5). The first term is (-2) and (3-(-2)=5). Be careful while subtracting negative terms.
Step 3
Exam Tip
पहला पद (-2) है और (3-(-2)=5) है। ऋणात्मक पदों में घटाव सावधानी से करें।
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निम्न में से कौन सा अनुक्रम अंकगणितीय श्रेणी है?
Which of the following sequences is an arithmetic progression?
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A \(3,6,12,24,\ldots\)
B \(1,4,9,16,\ldots\)
C \(5,9,13,17,\ldots\)
D \(2,5,9,14,\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(5,9,13,17,\ldots\)
Step 1
Concept
In \(5,9,13,17,\ldots\), every difference is (4). Choose only the option with equal differences.
Step 2
Why this answer is correct
The correct answer is C. \(5,9,13,17,\ldots\). In \(5,9,13,17,\ldots\), every difference is (4). Choose only the option with equal differences.
Step 3
Exam Tip
\(5,9,13,17,\ldots\) में हर अंतर (4) है। केवल समान अंतर वाला विकल्प चुनें।
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अनुक्रम \(2,6,12,20,\ldots\) अंकगणितीय श्रेणी क्यों नहीं है?
Why is the sequence \(2,6,12,20,\ldots\) not an arithmetic progression?
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A क्योंकि पहला पद (2) है / Because the first term is (2)
B क्योंकि पद बढ़ रहे हैं / Because the terms are increasing
C क्योंकि पद धनात्मक हैं / Because the terms are positive
D क्योंकि क्रमागत अंतर समान नहीं हैं / Because consecutive differences are not equal
Explanation opens after your attempt
Correct Answer
D. क्योंकि क्रमागत अंतर समान नहीं हैं / Because consecutive differences are not equal
Step 1
Concept
The differences are (4,6,8), which are not equal. Increasing terms alone are not enough for an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is D. क्योंकि क्रमागत अंतर समान नहीं हैं / Because consecutive differences are not equal. The differences are (4,6,8), which are not equal. Increasing terms alone are not enough for an arithmetic progression.
Step 3
Exam Tip
अंतर (4,6,8) हैं जो समान नहीं हैं। बढ़ते पद होना ही अंकगणितीय श्रेणी के लिए पर्याप्त नहीं है।
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यदि (a=7) और (d=-3) है तो तीसरा पद क्या होगा?
If (a=7) and (d=-3), what will be the third term?
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A (4)
B (1)
C (10)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The first three terms are (7,4,1), so the third term is (1). When (d) is negative, terms decrease.
Step 2
Why this answer is correct
The correct answer is B. (1). The first three terms are (7,4,1), so the third term is (1). When (d) is negative, terms decrease.
Step 3
Exam Tip
पहले तीन पद (7,4,1) हैं इसलिए तीसरा पद (1) है। ऋणात्मक (d) होने पर पद घटते हैं।
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अनुक्रम \(5x,5x+2,5x+4,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(5x,5x+2,5x+4,\ldots\)?
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A (2)
B (5x)
C (5x+2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The common difference is ((5x+2)-5x=2). For algebraic terms also subtract the first term from the second.
Step 2
Why this answer is correct
The correct answer is A. (2). The common difference is ((5x+2)-5x=2). For algebraic terms also subtract the first term from the second.
Step 3
Exam Tip
सार्व अंतर ((5x+2)-5x=2) है। बीजगणितीय पदों में भी दूसरे पद में से पहला पद घटाएं।
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यदि \(p,11,15,19,\ldots\) एक अंकगणितीय श्रेणी है तो (p) का मान क्या है?
If \(p,11,15,19,\ldots\) is an arithmetic progression, what is the value of (p)?
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A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
The common difference in (11,15,19) is (4), so (p=11-4=7). For the first term move backward by subtracting (d).
Step 2
Why this answer is correct
The correct answer is C. (7). The common difference in (11,15,19) is (4), so (p=11-4=7). For the first term move backward by subtracting (d).
Step 3
Exam Tip
(11,15,19) में सार्व अंतर (4) है इसलिए (p=11-4=7)। पहले पद के लिए पीछे की ओर (d) घटाएं।
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अनुक्रम \(31,27,23,19,\ldots\) में (d) का मान क्या है?
What is the value of (d) in the sequence \(31,27,23,19,\ldots\)?
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A (4)
B (31)
C (-8)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(d=27-31=-4). In a decreasing progression the common difference is written as negative.
Step 2
Why this answer is correct
The correct answer is D. (-4). (d=27-31=-4). In a decreasing progression the common difference is written as negative.
Step 3
Exam Tip
(d=27-31=-4) है। घटती श्रेणी में सार्व अंतर ऋणात्मक लिखा जाता है।
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यदि (3,m,11) किसी अंकगणितीय श्रेणी के क्रमागत तीन पद हैं तो (m) क्या है?
If (3,m,11) are three consecutive terms of an arithmetic progression, what is (m)?
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A (7)
B (6)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The middle term is the average of (3) and (11), so \(m=\frac{3+11}{2}=7\). In three consecutive terms the middle term is the average.
Step 2
Why this answer is correct
The correct answer is A. (7). The middle term is the average of (3) and (11), so \(m=\frac{3+11}{2}=7\). In three consecutive terms the middle term is the average.
Step 3
Exam Tip
बीच का पद (3) और (11) का औसत है इसलिए \(m=\frac{3+11}{2}=7\)। तीन क्रमागत पदों में मध्य पद औसत होता है।
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कौन सा अनुक्रम (d=-6) वाली अंकगणितीय श्रेणी है?
Which sequence is an arithmetic progression with (d=-6)?
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A \(6,12,18,24,\ldots\)
B \(40,34,28,22,\ldots\)
C \(30,24,20,14,\ldots\)
D \(12,6,3,-3,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(40,34,28,22,\ldots\)
Step 1
Concept
(34-40=-6), (28-34=-6), and (22-28=-6). All differences must be equal to (-6).
Step 2
Why this answer is correct
The correct answer is B. \(40,34,28,22,\ldots\). (34-40=-6), (28-34=-6), and (22-28=-6). All differences must be equal to (-6).
Step 3
Exam Tip
(34-40=-6), (28-34=-6) और (22-28=-6) हैं। सभी अंतर समान और (-6) होने चाहिए।
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अनुक्रम \(\frac{3}{4},1,\frac{5}{4},\frac{3}{2},\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(\frac{3}{4},1,\frac{5}{4},\frac{3}{2},\ldots\)?
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A \(\frac{1}{2}\)
B \(\frac{3}{4}\)
C \(\frac{1}{4}\)
D \(\frac{5}{4}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{1}{4}\)
Step 1
Concept
\(1-\frac{3}{4}=\frac{1}{4}\) and \(\frac{5}{4}-1=\frac{1}{4}\). For fractions subtract using common denominators.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{1}{4}\). \(1-\frac{3}{4}=\frac{1}{4}\) and \(\frac{5}{4}-1=\frac{1}{4}\). For fractions subtract using common denominators.
Step 3
Exam Tip
\(1-\frac{3}{4}=\frac{1}{4}\) और \(\frac{5}{4}-1=\frac{1}{4}\) है। भिन्नों में समान हर बनाकर घटाएं।
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यदि (a=-5) और (d=4) है तो पहले चार पद कौन से हैं?
If (a=-5) and (d=4), what are the first four terms?
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A (-5,-2,1,4)
B (-5,0,5,10)
C (-5,-1,2,6)
D (-5,-1,3,7)
Explanation opens after your attempt
Correct Answer
D. (-5,-1,3,7)
Step 1
Concept
Adding (4) each time gives (-5,-1,3,7). Do not forget to add (d) repeatedly.
Step 2
Why this answer is correct
The correct answer is D. (-5,-1,3,7). Adding (4) each time gives (-5,-1,3,7). Do not forget to add (d) repeatedly.
Step 3
Exam Tip
हर बार (4) जोड़ने पर (-5,-1,3,7) मिलते हैं। (d) को लगातार जोड़ना न भूलें।
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अनुक्रम \(0.2,0.5,0.8,1.1,\ldots\) का सार्व अंतर क्या है?
What is the common difference of the sequence \(0.2,0.5,0.8,1.1,\ldots\)?
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A (0.3)
B (0.2)
C (0.5)
D (0.8)
Explanation opens after your attempt
Step 1
Concept
The common difference is (0.5-0.2=0.3). In decimal questions pay attention to place value.
Step 2
Why this answer is correct
The correct answer is A. (0.3). The common difference is (0.5-0.2=0.3). In decimal questions pay attention to place value.
Step 3
Exam Tip
सार्व अंतर (0.5-0.2=0.3) है। दशमलव वाले प्रश्नों में स्थान मान का ध्यान रखें।
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यदि किसी अंकगणितीय श्रेणी में लगातार पद (12) और (17) हैं तो (d) क्या है?
If two consecutive terms in an arithmetic progression are (12) and (17), what is (d)?
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A (29)
B (12)
C (5)
D (17)
Explanation opens after your attempt
Step 1
Concept
The common difference is (17-12=5). When consecutive terms are given, subtract the earlier term from the later term.
Step 2
Why this answer is correct
The correct answer is C. (5). The common difference is (17-12=5). When consecutive terms are given, subtract the earlier term from the later term.
Step 3
Exam Tip
सार्व अंतर (17-12=5) है। लगातार पद दिए हों तो बाद वाला पद घटा पहले वाला पद करें।
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अनुक्रम \(8,13,18,23,\ldots\) में (23) के बाद अगला पद क्या होगा?
In the sequence \(8,13,18,23,\ldots\), what will be the next term after (23)?
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A (26)
B (28)
C (30)
D (31)
Explanation opens after your attempt
Step 1
Concept
The common difference is (5), so the next term is (23+5=28). Identify (d) before finding the next term.
Step 2
Why this answer is correct
The correct answer is B. (28). The common difference is (5), so the next term is (23+5=28). Identify (d) before finding the next term.
Step 3
Exam Tip
सार्व अंतर (5) है इसलिए अगला पद (23+5=28) होगा। अगला पद निकालने से पहले (d) पहचानें।
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यदि (6,10,n,18) अंकगणितीय श्रेणी के क्रमागत पद हैं तो (n) क्या है?
If (6,10,n,18) are consecutive terms of an arithmetic progression, what is (n)?
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A (12)
B (13)
C (15)
D (14)
Explanation opens after your attempt
Step 1
Concept
The common difference is (10-6=4), so (n=10+4=14). It is easy to find (d) from the first two terms.
Step 2
Why this answer is correct
The correct answer is D. (14). The common difference is (10-6=4), so (n=10+4=14). It is easy to find (d) from the first two terms.
Step 3
Exam Tip
सार्व अंतर (10-6=4) है इसलिए (n=10+4=14)। पहले दो पदों से (d) निकालना आसान होता है।
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किस विकल्प में (a=9) और (d=3) है?
Which option has (a=9) and (d=3)?
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A \(3,6,9,12,\ldots\)
B \(9,12,15,18,\ldots\)
C \(9,11,13,15,\ldots\)
D \(12,15,18,21,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(9,12,15,18,\ldots\)
Step 1
Concept
In \(9,12,15,18,\ldots\), the first term is (9) and the difference is (3). Check both (a) and (d) together.
Step 2
Why this answer is correct
The correct answer is B. \(9,12,15,18,\ldots\). In \(9,12,15,18,\ldots\), the first term is (9) and the difference is (3). Check both (a) and (d) together.
Step 3
Exam Tip
\(9,12,15,18,\ldots\) में पहला पद (9) और अंतर (3) है। (a) और (d) दोनों शर्तें एक साथ जांचें।
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अनुक्रम \(42,39,36,33,\ldots\) में तीसरा और चौथा पद का अंतर क्या है?
What is the difference between the third and fourth terms of \(42,39,36,33,\ldots\)?
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A (6)
B (-3)
C (3)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The third term is (36) and the fourth is (33), so (33-36=-3). While finding the difference subtract the previous term from the next term.
Step 2
Why this answer is correct
The correct answer is B. (-3). The third term is (36) and the fourth is (33), so (33-36=-3). While finding the difference subtract the previous term from the next term.
Step 3
Exam Tip
तीसरा पद (36) और चौथा (33) है इसलिए (33-36=-3)। अंतर निकालते समय बाद वाला पद घटा पहले वाला पद करें।
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यदि (a=2.5) और (d=1.5) है तो दूसरा पद क्या है?
If (a=2.5) and (d=1.5), what is the second term?
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A (3.0)
B (3.5)
C (4.0)
D (5.0)
Explanation opens after your attempt
Step 1
Concept
The second term is (a+d=2.5+1.5=4.0). Align digits carefully when adding decimals.
Step 2
Why this answer is correct
The correct answer is C. (4.0). The second term is (a+d=2.5+1.5=4.0). Align digits carefully when adding decimals.
Step 3
Exam Tip
दूसरा पद (a+d=2.5+1.5=4.0) है। दशमलव जोड़ते समय अंकों को ठीक से मिलाएं।
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किस अनुक्रम में सार्व अंतर (0) है?
Which sequence has common difference (0)?
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A \(0,1,2,3,\ldots\)
B \(5,0,-5,-10,\ldots\)
C \(7,14,21,28,\ldots\)
D \(11,11,11,11,\ldots\)
Explanation opens after your attempt
Correct Answer
D. \(11,11,11,11,\ldots\)
Step 1
Concept
All terms are equal, so (d=0). A constant sequence is also considered an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is D. \(11,11,11,11,\ldots\). All terms are equal, so (d=0). A constant sequence is also considered an arithmetic progression.
Step 3
Exam Tip
सभी पद समान हैं इसलिए (d=0) है। स्थिर अनुक्रम भी अंकगणितीय श्रेणी माना जाता है।
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यदि \(x, x+7, x+14,\ldots\) अंकगणितीय श्रेणी है तो दूसरा और पहला पद का अंतर क्या है?
If \(x, x+7, x+14,\ldots\) is an arithmetic progression, what is the difference between the second and first terms?
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#medium
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A (x+7)
B (7)
C (14)
D (x)
Explanation opens after your attempt
Step 1
Concept
((x+7)-x=7), so the difference is (7). The equal added number is (d).
Step 2
Why this answer is correct
The correct answer is B. (7). ((x+7)-x=7), so the difference is (7). The equal added number is (d).
Step 3
Exam Tip
((x+7)-x=7) है इसलिए अंतर (7) है। समान जोड़ी गई संख्या ही (d) होती है।
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अनुक्रम \(16,20,24,28,\ldots\) में (a+d) का मान क्या है?
In the sequence \(16,20,24,28,\ldots\), what is the value of (a+d)?
#ap
#a plus d
#second term
#medium
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A (16)
B (18)
C (20)
D (24)
Explanation opens after your attempt
Step 1
Concept
Here (a=16) and (d=4), so (a+d=20). (a+d) is actually the second term.
Step 2
Why this answer is correct
The correct answer is C. (20). Here (a=16) and (d=4), so (a+d=20). (a+d) is actually the second term.
Step 3
Exam Tip
यहां (a=16) और (d=4), इसलिए (a+d=20)। (a+d) वास्तव में दूसरा पद होता है।
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यदि \(21,18,q,12,\ldots\) अंकगणितीय श्रेणी है तो (q) का मान क्या है?
If \(21,18,q,12,\ldots\) is an arithmetic progression, what is the value of (q)?
#ap
#missing term
#decreasing sequence
#medium
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A (13)
B (14)
C (16)
D (15)
Explanation opens after your attempt
Step 1
Concept
The common difference is (18-21=-3), so (q=18-3=15). Keep (d) negative in a decreasing progression.
Step 2
Why this answer is correct
The correct answer is D. (15). The common difference is (18-21=-3), so (q=18-3=15). Keep (d) negative in a decreasing progression.
Step 3
Exam Tip
सार्व अंतर (18-21=-3) है इसलिए (q=18-3=15)। घटती श्रेणी में (d) को ऋणात्मक रखें।
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कौन सा कथन \(4,9,14,19,\ldots\) के लिए सही है?
Which statement is correct for \(4,9,14,19,\ldots\)?
#ap
#identify statement
#common difference
#medium
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A यह अंकगणितीय श्रेणी है और (d=5) है / It is an arithmetic progression and (d=5)
B यह अंकगणितीय श्रेणी है और (d=4) है / It is an arithmetic progression and (d=4)
C यह अंकगणितीय श्रेणी नहीं है / It is not an arithmetic progression
D यह ज्यामितीय श्रेणी है / It is a geometric progression
Explanation opens after your attempt
Correct Answer
A. यह अंकगणितीय श्रेणी है और (d=5) है / It is an arithmetic progression and (d=5)
Step 1
Concept
Every consecutive difference is (5), so it is an arithmetic progression. While choosing the statement check both type and (d).
Step 2
Why this answer is correct
The correct answer is A. यह अंकगणितीय श्रेणी है और (d=5) है / It is an arithmetic progression and (d=5). Every consecutive difference is (5), so it is an arithmetic progression. While choosing the statement check both type and (d).
Step 3
Exam Tip
हर क्रमागत अंतर (5) है इसलिए यह अंकगणितीय श्रेणी है। सही कथन चुनते समय प्रकार और (d) दोनों जांचें।
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एक अंकगणितीय श्रेणी में पहला पद (13) और दूसरा पद (8) है। (d) क्या है?
In an arithmetic progression, the first term is (13) and the second term is (8). What is (d)?
#ap
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#negative difference
#medium
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A (5)
B (-5)
C (21)
D (-21)
Explanation opens after your attempt
Step 1
Concept
(d=8-13=-5). If the second term is smaller, (d) will be negative.
Step 2
Why this answer is correct
The correct answer is B. (-5). (d=8-13=-5). If the second term is smaller, (d) will be negative.
Step 3
Exam Tip
(d=8-13=-5) है। दूसरा पद छोटा हो तो (d) ऋणात्मक होगा।
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यदि (a=6) और (d=2) है तो (a+2d) किस पद को दर्शाता है?
If (a=6) and (d=2), which term does (a+2d) represent?
#ap
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#third term
#medium
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A पहला पद / First term
B दूसरा पद / Second term
C तीसरा पद / Third term
D चौथा पद / Fourth term
Explanation opens after your attempt
Correct Answer
C. तीसरा पद / Third term
Step 1
Concept
In the general form \(a,a+d,a+2d,\ldots\), (a+2d) is the third term. Remembering the general form makes term identification easier.
Step 2
Why this answer is correct
The correct answer is C. तीसरा पद / Third term. In the general form \(a,a+d,a+2d,\ldots\), (a+2d) is the third term. Remembering the general form makes term identification easier.
Step 3
Exam Tip
सामान्य रूप \(a,a+d,a+2d,\ldots\) में (a+2d) तीसरा पद है। सामान्य रूप याद रखने से पद पहचानना आसान होता है।
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यदि \(2,5,8,r,\ldots\) अंकगणितीय श्रेणी है तो (r) क्या होगा?
If \(2,5,8,r,\ldots\) is an arithmetic progression, what will (r) be?
#ap
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#common difference
#medium
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A (9)
B (10)
C (12)
D (11)
Explanation opens after your attempt
Step 1
Concept
The common difference is (3), so (r=8+3=11). Add (d) to the previous term to get the next term.
Step 2
Why this answer is correct
The correct answer is D. (11). The common difference is (3), so (r=8+3=11). Add (d) to the previous term to get the next term.
Step 3
Exam Tip
सार्व अंतर (3) है इसलिए (r=8+3=11)। अगला पद पाने के लिए पिछले पद में (d) जोड़ें।
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निम्न में से किस अनुक्रम में (a=-4) और (d=6) है?
Which of the following sequences has (a=-4) and (d=6)?
#ap
#first term
#identify ap
#medium
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A \(-4,0,4,8,\ldots\)
B \(-4,2,8,14,\ldots\)
C \(4,10,16,22,\ldots\)
D \(-6,0,6,12,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(-4,2,8,14,\ldots\)
Step 1
Concept
In \(-4,2,8,14,\ldots\), the first term is (-4) and the difference is (6). Both conditions must match.
Step 2
Why this answer is correct
The correct answer is B. \(-4,2,8,14,\ldots\). In \(-4,2,8,14,\ldots\), the first term is (-4) and the difference is (6). Both conditions must match.
Step 3
Exam Tip
\(-4,2,8,14,\ldots\) में पहला पद (-4) और अंतर (6) है। दोनों शर्तें मिलनी चाहिए।
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अनुक्रम \(1,\frac{3}{2},2,\frac{5}{2},\ldots\) का अगला पद क्या होगा?
What will be the next term of the sequence \(1,\frac{3}{2},2,\frac{5}{2},\ldots\)?
#ap
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#next term
#medium
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A (3)
B \(\frac{7}{2}\)
C \(\frac{9}{2}\)
D (4)
Explanation opens after your attempt
Step 1
Concept
The common difference is \(\frac{1}{2}\), so the next term is \(\frac{5}{2}+\frac{1}{2}=3\). Keep denominators common when adding fractions.
Step 2
Why this answer is correct
The correct answer is A. (3). The common difference is \(\frac{1}{2}\), so the next term is \(\frac{5}{2}+\frac{1}{2}=3\). Keep denominators common when adding fractions.
Step 3
Exam Tip
सार्व अंतर \(\frac{1}{2}\) है इसलिए अगला पद \(\frac{5}{2}+\frac{1}{2}=3\) है। भिन्नों को जोड़ते समय हर समान रखें।
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यदि \(5,5+s,5+2s,\ldots\) एक अंकगणितीय श्रेणी है तो इसका सार्व अंतर क्या है?
If \(5,5+s,5+2s,\ldots\) is an arithmetic progression, what is its common difference?
#ap
#algebraic common difference
#medium
#class ten
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A (5)
B (5+s)
C (s)
D (2s)
Explanation opens after your attempt
Step 1
Concept
The common difference is ((5+s)-5=s). In algebraic sequences also look at the equal added part.
Step 2
Why this answer is correct
The correct answer is C. (s). The common difference is ((5+s)-5=s). In algebraic sequences also look at the equal added part.
Step 3
Exam Tip
सार्व अंतर ((5+s)-5=s) है। अक्षर वाले अनुक्रम में भी समान जोड़ा गया भाग देखें।
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एक पार्किंग शुल्क हर घंटे (20) रुपये बढ़ता है। शुल्क \(30,50,70,90,\ldots\) हैं तो (d) क्या है?
A parking fee increases by (20) rupees every hour. The fees are \(30,50,70,90,\ldots\). What is (d)?
#ap
#word problem
#parking fee
#common difference
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A (30)
B (20)
C (50)
D (90)
Explanation opens after your attempt
Step 1
Concept
The equal hourly increase is (20) rupees, so (d=20). In word problems treat the equal increase as the common difference.
Step 2
Why this answer is correct
The correct answer is B. (20). The equal hourly increase is (20) rupees, so (d=20). In word problems treat the equal increase as the common difference.
Step 3
Exam Tip
हर घंटे समान वृद्धि (20) रुपये है इसलिए (d=20)। शब्द प्रश्नों में समान वृद्धि को सार्व अंतर मानें।
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किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-2) नहीं है?
In which sequence are the terms decreasing by an equal amount but (d) is not (-2)?
#ap
#decreasing sequence
#negative difference
#medium
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A \(20,17,14,11,\ldots\)
B \(9,7,5,3,\ldots\)
C \(8,6,4,2,\ldots\)
D \(5,3,1,-1,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(20,17,14,11,\ldots\)
Step 1
Concept
In \(20,17,14,11,\ldots\), (d=-3), not (-2). Check both sign and value in options.
Step 2
Why this answer is correct
The correct answer is A. \(20,17,14,11,\ldots\). In \(20,17,14,11,\ldots\), (d=-3), not (-2). Check both sign and value in options.
Step 3
Exam Tip
\(20,17,14,11,\ldots\) में (d=-3) है, (-2) नहीं। विकल्पों में चिह्न और मान दोनों जांचें।
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यदि (a=10) और (d=0) है तो चौथा पद क्या होगा?
If (a=10) and (d=0), what will be the fourth term?
#ap
#zero d
#fourth term
#medium
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A (0)
B (20)
C (30)
D (10)
Explanation opens after your attempt
Step 1
Concept
When (d=0), all terms remain (10). In a constant progression there is no increase or decrease.
Step 2
Why this answer is correct
The correct answer is D. (10). When (d=0), all terms remain (10). In a constant progression there is no increase or decrease.
Step 3
Exam Tip
(d=0) होने पर सभी पद (10) रहते हैं। स्थिर श्रेणी में कोई वृद्धि या कमी नहीं होती।
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अनुक्रम \(3,8,13,18,\ldots\) में (a+2d) का मान क्या है?
In the sequence \(3,8,13,18,\ldots\), what is the value of (a+2d)?
#ap
#a plus 2d
#third term
#medium
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A (8)
B (18)
C (13)
D (5)
Explanation opens after your attempt
Step 1
Concept
Here (a=3) and (d=5), so (a+2d=3+10=13). (a+2d) equals the third term.
Step 2
Why this answer is correct
The correct answer is C. (13). Here (a=3) and (d=5), so (a+2d=3+10=13). (a+2d) equals the third term.
Step 3
Exam Tip
यहां (a=3) और (d=5), इसलिए (a+2d=3+10=13)। (a+2d) तीसरे पद के बराबर होता है।
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यदि \(y-2,y+1,y+4,\ldots\) अंकगणितीय श्रेणी है तो (d) क्या है?
If \(y-2,y+1,y+4,\ldots\) is an arithmetic progression, what is (d)?
#ap
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#find d
#medium
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A (y)
B (3)
C (y+1)
D (6)
Explanation opens after your attempt
Step 1
Concept
(d=(y+1)-(y-2)=3). When variables cancel, the constant difference remains.
Step 2
Why this answer is correct
The correct answer is B. (3). (d=(y+1)-(y-2)=3). When variables cancel, the constant difference remains.
Step 3
Exam Tip
(d=(y+1)-(y-2)=3) है। चर कट जाने पर स्थिर अंतर मिलता है।
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अनुक्रम \(50,45,40,35,\ldots\) में अगला पद और (d) क्रमशः क्या हैं?
In the sequence \(50,45,40,35,\ldots\), what are the next term and (d) respectively?
#ap
#next term
#negative d
#medium
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A (30) और (5) / (30) and (5)
B (40) और (-5) / (40) and (-5)
C (35) और (-5) / (35) and (-5)
D (30) और (-5) / (30) and (-5)
Explanation opens after your attempt
Correct Answer
D. (30) और (-5) / (30) and (-5)
Step 1
Concept
The common difference is (-5), and the next term is (35-5=30). Do not change the order when answering respectively.
Step 2
Why this answer is correct
The correct answer is D. (30) और (-5) / (30) and (-5). The common difference is (-5), and the next term is (35-5=30). Do not change the order when answering respectively.
Step 3
Exam Tip
सार्व अंतर (-5) है और अगला पद (35-5=30) है। क्रमशः में उत्तर का क्रम न बदलें।
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यदि (a=12) और (d=-4) है तो पहले तीन पदों का सही क्रम कौन सा है?
If (a=12) and (d=-4), which is the correct order of the first three terms?
#ap
#first three terms
#negative difference
#medium
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A (12,8,4)
B (12,16,20)
C (8,4,0)
D (12,4,-4)
Explanation opens after your attempt
Correct Answer
A. (12,8,4)
Step 1
Concept
Adding (-4) each time gives (12,8,4). Understand negative difference as subtraction.
Step 2
Why this answer is correct
The correct answer is A. (12,8,4). Adding (-4) each time gives (12,8,4). Understand negative difference as subtraction.
Step 3
Exam Tip
हर बार (-4) जोड़ने पर (12,8,4) मिलता है। ऋणात्मक अंतर को घटाव की तरह समझें।
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अनुक्रम \(0,-3,-6,-9,\ldots\) में (a) और (d) क्रमशः क्या हैं?
In the sequence \(0,-3,-6,-9,\ldots\), what are (a) and (d) respectively?
#ap
#zero first term
#negative d
#medium
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A (0) और (3) / (0) and (3)
B (-3) और (-3) / (-3) and (-3)
C (0) और (-3) / (0) and (-3)
D (-9) और (0) / (-9) and (0)
Explanation opens after your attempt
Correct Answer
C. (0) और (-3) / (0) and (-3)
Step 1
Concept
The first term is (0), and (d=-3-0=-3). Zero can also be the first term.
Step 2
Why this answer is correct
The correct answer is C. (0) और (-3) / (0) and (-3). The first term is (0), and (d=-3-0=-3). Zero can also be the first term.
Step 3
Exam Tip
पहला पद (0) है और (d=-3-0=-3) है। शून्य भी पहला पद हो सकता है।
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एक मशीन हर घंटे (15) वस्तुएं अधिक बनाती है। उत्पादन \(20,35,50,65,\ldots\) है तो तीसरे और पहले पद का अंतर क्या है?
A machine produces (15) more items each hour. The production is \(20,35,50,65,\ldots\). What is the difference between the third and first terms?
#ap
#word problem
#term difference
#medium
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A (15)
B (20)
C (35)
D (30)
Explanation opens after your attempt
Step 1
Concept
The third term is (50) and the first is (20), so the difference is (30). It equals (2d).
Step 2
Why this answer is correct
The correct answer is D. (30). The third term is (50) and the first is (20), so the difference is (30). It equals (2d).
Step 3
Exam Tip
तीसरा पद (50) और पहला (20) है इसलिए अंतर (30) है। यह (2d) के बराबर है।
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यदि \(4,9,14,19,\ldots\) में प्रत्येक पद में (2) जोड़ दिया जाए तो नए अनुक्रम का (d) क्या होगा?
If (2) is added to each term of \(4,9,14,19,\ldots\), what will be (d) of the new sequence?
#ap
#common difference
#transformed sequence
#medium
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A (2)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
Adding the same (2) to each term does not change the difference, so (d=5). Equal change in all terms does not change (d).
Step 2
Why this answer is correct
The correct answer is B. (5). Adding the same (2) to each term does not change the difference, so (d=5). Equal change in all terms does not change (d).
Step 3
Exam Tip
हर पद में समान (2) जोड़ने से अंतर नहीं बदलता, इसलिए (d=5) रहेगा। सभी पदों में समान बदलाव (d) को नहीं बदलता।
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यदि किसी अंकगणितीय श्रेणी के पहले दो पद (-7) और (-2) हैं तो तीसरा पद क्या होगा?
If the first two terms of an arithmetic progression are (-7) and (-2), what will be the third term?
#ap
#first two terms
#third term
#medium
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A (3)
B (-5)
C (5)
D (-12)
Explanation opens after your attempt
Step 1
Concept
The common difference is (-2-(-7)=5), so the third term is (-2+5=3). Watch signs carefully with negative numbers.
Step 2
Why this answer is correct
The correct answer is A. (3). The common difference is (-2-(-7)=5), so the third term is (-2+5=3). Watch signs carefully with negative numbers.
Step 3
Exam Tip
सार्व अंतर (-2-(-7)=5) है इसलिए तीसरा पद (-2+5=3) है। ऋणात्मक संख्याओं में चिह्न सावधानी से देखें।
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अनुक्रम \(2a,2a-5,2a-10,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(2a,2a-5,2a-10,\ldots\)?
#ap
#algebraic sequence
#negative d
#medium
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A (5)
B (2a)
C (2a-5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
(d=(2a-5)-2a=-5). In a decreasing algebraic sequence (d) can be negative.
Step 2
Why this answer is correct
The correct answer is D. (-5). (d=(2a-5)-2a=-5). In a decreasing algebraic sequence (d) can be negative.
Step 3
Exam Tip
(d=(2a-5)-2a=-5) है। घटते बीजगणितीय अनुक्रम में (d) ऋणात्मक हो सकता है।
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यदि (9,b,21) अंकगणितीय श्रेणी के क्रमागत पद हैं तो (b) का मान क्या है?
If (9,b,21) are consecutive terms of an arithmetic progression, what is the value of (b)?
#ap
#middle term
#missing value
#medium
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A (12)
B (13)
C (15)
D (18)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(b=\frac{9+21}{2}=15\). In three consecutive terms the middle term is the average.
Step 2
Why this answer is correct
The correct answer is C. (15). The middle term is \(b=\frac{9+21}{2}=15\). In three consecutive terms the middle term is the average.
Step 3
Exam Tip
मध्य पद \(b=\frac{9+21}{2}=15\) है। तीन क्रमागत पदों में बीच वाला पद औसत होता है।
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किस अनुक्रम में \(d=\frac{2}{3}\) है?
Which sequence has \(d=\frac{2}{3}\)?
#ap
#fraction common difference
#identify sequence
#medium
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A \(1,\frac{4}{3},\frac{5}{3},2,\ldots\)
B \(\frac{1}{3},1,\frac{5}{3},\frac{7}{3},\ldots\)
C \(2,\frac{8}{3},3,\frac{10}{3},\ldots\)
D \(\frac{2}{3},1,\frac{4}{3},\frac{5}{3},\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{3},1,\frac{5}{3},\frac{7}{3},\ldots\)
Step 1
Concept
In \(\frac{1}{3},1,\frac{5}{3},\frac{7}{3},\ldots\), every difference is \(\frac{2}{3}\). Check fractions using common denominators.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{3},1,\frac{5}{3},\frac{7}{3},\ldots\). In \(\frac{1}{3},1,\frac{5}{3},\frac{7}{3},\ldots\), every difference is \(\frac{2}{3}\). Check fractions using common denominators.
Step 3
Exam Tip
\(\frac{1}{3},1,\frac{5}{3},\frac{7}{3},\ldots\) में हर अंतर \(\frac{2}{3}\) है। भिन्नों में हर समान करके जांचें।
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यदि (a=3) और दूसरा पद (10) है तो (d) क्या है?
If (a=3) and the second term is (10), what is (d)?
#ap
#find d
#second term
#medium
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A (13)
B (10)
C (7)
D (3)
Explanation opens after your attempt
Step 1
Concept
(d=10-3=7). Find the common difference by subtracting the first term from the second term.
Step 2
Why this answer is correct
The correct answer is C. (7). (d=10-3=7). Find the common difference by subtracting the first term from the second term.
Step 3
Exam Tip
(d=10-3=7) है। दूसरे पद में से पहले पद को घटाकर सार्व अंतर पाएं।
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अनुक्रम \(6,6.8,7.6,8.4,\ldots\) में (d) क्या है?
What is (d) in the sequence \(6,6.8,7.6,8.4,\ldots\)?
#ap
#decimal d
#common difference
#medium
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A (0.6)
B (0.8)
C (1.2)
D (6.8)
Explanation opens after your attempt
Step 1
Concept
(d=6.8-6=0.8), and the same difference continues. In decimal subtraction use zeros if needed.
Step 2
Why this answer is correct
The correct answer is B. (0.8). (d=6.8-6=0.8), and the same difference continues. In decimal subtraction use zeros if needed.
Step 3
Exam Tip
(d=6.8-6=0.8) है और आगे भी यही अंतर है। दशमलव घटाव में शून्य लगाकर गणना करें।
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यदि \(15,10,5,0,\ldots\) में (d) ज्ञात करना हो तो सही गणना कौन सी है?
If (d) is to be found in \(15,10,5,0,\ldots\), which calculation is correct?
#ap
#correct calculation
#negative d
#medium
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A (15-10=5)
B (15+10=25)
C (10-15=-5)
D \(15\times10=150\)
Explanation opens after your attempt
Correct Answer
C. (10-15=-5)
Step 1
Concept
The common difference is next term minus previous term, so (10-15=-5). In a decreasing sequence the order of subtraction is very important.
Step 2
Why this answer is correct
The correct answer is C. (10-15=-5). The common difference is next term minus previous term, so (10-15=-5). In a decreasing sequence the order of subtraction is very important.
Step 3
Exam Tip
सार्व अंतर बाद वाला पद घटा पहले वाला पद है इसलिए (10-15=-5)। घटते अनुक्रम में घटाव का क्रम बहुत जरूरी है।
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एक अंकगणितीय श्रेणी में (d=4) है और दूसरा पद (11) है। पहला पद क्या होगा?
In an arithmetic progression, (d=4) and the second term is (11). What is the first term?
#ap
#find first term
#common difference
#medium
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A (7)
B (11)
C (15)
D (4)
Explanation opens after your attempt
Step 1
Concept
The first term is (11-4=7). Subtract (d) from the second term to get the first term.
Step 2
Why this answer is correct
The correct answer is A. (7). The first term is (11-4=7). Subtract (d) from the second term to get the first term.
Step 3
Exam Tip
पहला पद (11-4=7) है। दूसरे पद से (d) घटाकर पहला पद मिलता है।
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यदि \(6,u,18,24,\ldots\) एक अंकगणितीय श्रेणी है तो (u) का मान क्या होगा?
If \(6,u,18,24,\ldots\) is an arithmetic progression, what will be the value of (u)?
#ap
#missing term
#common difference
#medium
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A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
The difference from (18) to (24) is (6), so (u=18-6=12). While finding a missing term use the same difference forward and backward.
Step 2
Why this answer is correct
The correct answer is B. (12). The difference from (18) to (24) is (6), so (u=18-6=12). While finding a missing term use the same difference forward and backward.
Step 3
Exam Tip
(18) से (24) तक अंतर (6) है इसलिए (u=18-6=12)। खाली पद निकालते समय समान अंतर को आगे और पीछे दोनों तरफ लगाएं।
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अनुक्रम \(8,13,18,23,\ldots\) का सार्व अंतर क्या है?
What is the common difference of the sequence \(8,13,18,23,\ldots\)?
#arithmetic-progression
#common-difference
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A (4)
B (5)
C (8)
D (13)
Explanation opens after your attempt
Step 1
Concept
The common difference is (13-8=5). Always check the difference of two consecutive terms.
Step 2
Why this answer is correct
The correct answer is B. (5). The common difference is (13-8=5). Always check the difference of two consecutive terms.
Step 3
Exam Tip
सार्व अंतर (13-8=5) है। हमेशा लगातार दो पदों का अंतर जाँचें।
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अनुक्रम \(42,36,30,24,\ldots\) में सार्व अंतर क्या होगा?
What will be the common difference in \(42,36,30,24,\ldots\)?
#arithmetic-progression
#negative-difference
#class10
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A (6)
B (-6)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
The common difference is (36-42=-6). Always check the sign in a decreasing progression.
Step 2
Why this answer is correct
The correct answer is B. (-6). The common difference is (36-42=-6). Always check the sign in a decreasing progression.
Step 3
Exam Tip
सार्व अंतर (36-42=-6) है। घटती श्रेढ़ी में चिन्ह जरूर जाँचें।
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अनुक्रम \(6,10,14,\Box,22,\ldots\) में रिक्त स्थान का मान क्या है?
What is the missing value in \(6,10,14,\Box,22,\ldots\)?
#arithmetic-progression
#missing-term
#class10
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A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
The common difference is (4). Therefore, (14+4=18) fills the blank.
Step 2
Why this answer is correct
The correct answer is C. (18). The common difference is (4). Therefore, (14+4=18) fills the blank.
Step 3
Exam Tip
यहाँ सार्व अंतर (4) है। इसलिए (14+4=18) रिक्त स्थान में आएगा।
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यदि समांतर श्रेढ़ी का प्रथम पद (a=12) और सार्व अंतर (d=5) है, तो पहले चार पद कौन-से होंगे?
If the first term of an arithmetic progression is (a=12) and the common difference is (d=5), what are the first four terms?
#arithmetic-progression
#construct-ap
#class10
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A (12,17,22,27)
B (5,12,19,26)
C (12,18,24,30)
D (17,22,27,32)
Explanation opens after your attempt
Correct Answer
A. (12,17,22,27)
Step 1
Concept
The first term is (12) and (5) is added each time. Hence the terms are (12,17,22,27).
Step 2
Why this answer is correct
The correct answer is A. (12,17,22,27). The first term is (12) and (5) is added each time. Hence the terms are (12,17,22,27).
Step 3
Exam Tip
पहला पद (12) है और हर बार (5) जोड़ना है। इसलिए पद (12,17,22,27) होंगे।
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अनुक्रम \(-5,-1,3,7,\ldots\) में (a) और (d) क्रमशः क्या हैं?
In the sequence \(-5,-1,3,7,\ldots\), what are (a) and (d) respectively?
#arithmetic-progression
#first-term-common-difference
#class10
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A (a=4,\ d=-5)
B (a=-5,\ d=4)
C (a=-1,\ d=4)
D (a=-5,\ d=-4)
Explanation opens after your attempt
Correct Answer
B. (a=-5,\ d=4)
Step 1
Concept
The first term is (-5) and (-1-(-5)=4). Do not change the order of asked values.
Step 2
Why this answer is correct
The correct answer is B. (a=-5,\ d=4). The first term is (-5) and (-1-(-5)=4). Do not change the order of asked values.
Step 3
Exam Tip
पहला पद (-5) है और (-1-(-5)=4) है। क्रमशः पूछे गए मानों का क्रम न बदलें।
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समांतर श्रेढ़ी \(31,27,23,19,\ldots\) में अगला पद क्या होगा?
What will be the next term in the arithmetic progression \(31,27,23,19,\ldots\)?
#arithmetic-progression
#next-term
#class10
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A (16)
B (15)
C (14)
D (13)
Explanation opens after your attempt
Step 1
Concept
Here (d=-4). Therefore, the next term is (19-4=15).
Step 2
Why this answer is correct
The correct answer is B. (15). Here (d=-4). Therefore, the next term is (19-4=15).
Step 3
Exam Tip
यहाँ (d=-4) है। इसलिए अगला पद (19-4=15) होगा।
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यदि किसी समांतर श्रेढ़ी के लगातार दो पद (18) और (25) हैं, तो सार्व अंतर क्या है?
If two consecutive terms of an arithmetic progression are (18) and (25), what is the common difference?
#arithmetic-progression
#consecutive-terms
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A (5)
B (6)
C (7)
D (43)
Explanation opens after your attempt
Step 1
Concept
The common difference is (25-18=7). When consecutive terms are given, subtract directly.
Step 2
Why this answer is correct
The correct answer is C. (7). The common difference is (25-18=7). When consecutive terms are given, subtract directly.
Step 3
Exam Tip
सार्व अंतर (25-18=7) है। लगातार पद दिए हों तो सीधे घटाव करें।
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अनुक्रम \(\frac{3}{2},2,\frac{5}{2},3,\ldots\) का सार्व अंतर क्या है?
What is the common difference of \(\frac{3}{2},2,\frac{5}{2},3,\ldots\)?
#arithmetic-progression
#fraction-ap
#class10
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A \(\frac{1}{2}\)
B (1)
C \(\frac{3}{2}\)
D (2)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
\(2-\frac{3}{2}=\frac{1}{2}\). For fractions also, take the difference of consecutive terms.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). \(2-\frac{3}{2}=\frac{1}{2}\). For fractions also, take the difference of consecutive terms.
Step 3
Exam Tip
\(2-\frac{3}{2}=\frac{1}{2}\) है। भिन्नों में भी लगातार पदों का अंतर लें।
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यदि (a=20) और (d=-3) है, तो समांतर श्रेढ़ी का तीसरा पद क्या होगा?
If (a=20) and (d=-3), what is the third term of the arithmetic progression?
#arithmetic-progression
#third-term
#class10
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A (14)
B (17)
C (20)
D (23)
Explanation opens after your attempt
Step 1
Concept
The first three terms are (20,17,14). With negative (d), subtraction occurs each time.
Step 2
Why this answer is correct
The correct answer is A. (14). The first three terms are (20,17,14). With negative (d), subtraction occurs each time.
Step 3
Exam Tip
पहले तीन पद (20,17,14) होंगे। ऋणात्मक (d) में हर बार घटाव होता है।
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कौन-सा अनुक्रम (a=9) और (d=-2) से बनता है?
Which sequence is formed with (a=9) and (d=-2)?
#arithmetic-progression
#construct-ap
#class10
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A \(9,11,13,15,\ldots\)
B \(9,7,5,3,\ldots\)
C \(2,7,12,17,\ldots\)
D \(7,5,3,1,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(9,7,5,3,\ldots\)
Step 1
Concept
The first term is (9) and (2) is subtracted each time. Hence the sequence is \(9,7,5,3,\ldots\).
Step 2
Why this answer is correct
The correct answer is B. \(9,7,5,3,\ldots\). The first term is (9) and (2) is subtracted each time. Hence the sequence is \(9,7,5,3,\ldots\).
Step 3
Exam Tip
पहला पद (9) है और हर बार (2) घटता है। इसलिए अनुक्रम \(9,7,5,3,\ldots\) बनेगा।
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अनुक्रम \(1.2,1.8,2.4,3.0,\ldots\) का सार्व अंतर क्या है?
What is the common difference of \(1.2,1.8,2.4,3.0,\ldots\)?
#arithmetic-progression
#decimal-ap
#class10
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A (0.4)
B (0.5)
C (0.6)
D (1.2)
Explanation opens after your attempt
Step 1
Concept
The common difference is (1.8-1.2=0.6). For decimals also, check the difference of consecutive terms.
Step 2
Why this answer is correct
The correct answer is C. (0.6). The common difference is (1.8-1.2=0.6). For decimals also, check the difference of consecutive terms.
Step 3
Exam Tip
सार्व अंतर (1.8-1.2=0.6) है। दशमलव में भी लगातार पदों का अंतर देखें।
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अनुक्रम \(2,8,14,20,\ldots\) में पाँचवाँ पद क्या होगा?
What will be the fifth term in \(2,8,14,20,\ldots\)?
#arithmetic-progression
#fifth-term
#class10
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A (24)
B (25)
C (26)
D (28)
Explanation opens after your attempt
Step 1
Concept
Here (d=6). The fifth term will be (20+6=26).
Step 2
Why this answer is correct
The correct answer is C. (26). Here (d=6). The fifth term will be (20+6=26).
Step 3
Exam Tip
यहाँ (d=6) है। पाँचवाँ पद (20+6=26) होगा।
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समांतर श्रेढ़ी \(4,4,4,4,\ldots\) के बारे में कौन-सा कथन सही है?
Which statement is correct about the arithmetic progression \(4,4,4,4,\ldots\)?
#arithmetic-progression
#zero-difference
#class10
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A इसका (d=4) है / Its (d=4)
B इसका (d=0) है / Its (d=0)
C यह समांतर श्रेढ़ी नहीं है / It is not an arithmetic progression
D इसका प्रथम पद (0) है / Its first term is (0)
Explanation opens after your attempt
Correct Answer
B. इसका (d=0) है / Its (d=0)
Step 1
Concept
The difference of consecutive terms is (4-4=0). A constant-term progression has (d=0).
Step 2
Why this answer is correct
The correct answer is B. इसका (d=0) है / Its (d=0). The difference of consecutive terms is (4-4=0). A constant-term progression has (d=0).
Step 3
Exam Tip
लगातार पदों का अंतर (4-4=0) है। समान पदों वाली श्रेढ़ी में (d=0) होता है।
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यदि किसी अनुक्रम में अंतर (3,3,3) है, तो वह किस प्रकार का अनुक्रम है?
If the differences in a sequence are (3,3,3), what type of sequence is it?
#arithmetic-progression
#ap-test
#class10
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A समांतर श्रेढ़ी / Arithmetic progression
B गुणोत्तर श्रेढ़ी / Geometric progression
C असमान अंतर वाला अनुक्रम / Sequence with unequal differences
D केवल स्थिर अनुक्रम / Only constant sequence
Explanation opens after your attempt
Correct Answer
A. समांतर श्रेढ़ी / Arithmetic progression
Step 1
Concept
The consecutive differences are equal, so the sequence is an arithmetic progression. In exams, first check equality of differences.
Step 2
Why this answer is correct
The correct answer is A. समांतर श्रेढ़ी / Arithmetic progression. The consecutive differences are equal, so the sequence is an arithmetic progression. In exams, first check equality of differences.
Step 3
Exam Tip
लगातार अंतर समान हैं इसलिए अनुक्रम समांतर श्रेढ़ी है। परीक्षा में पहले अंतरों की समानता जाँचें।
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अनुक्रम \(100,92,84,76,\ldots\) में अगले दो पद कौन-से होंगे?
What are the next two terms in \(100,92,84,76,\ldots\)?
#arithmetic-progression
#next-two-terms
#class10
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A (70,64)
B (68,60)
C (69,62)
D (72,68)
Explanation opens after your attempt
Correct Answer
B. (68,60)
Step 1
Concept
Here (d=-8). Therefore, (76-8=68) and (68-8=60).
Step 2
Why this answer is correct
The correct answer is B. (68,60). Here (d=-8). Therefore, (76-8=68) and (68-8=60).
Step 3
Exam Tip
यहाँ (d=-8) है। इसलिए (76-8=68) और (68-8=60) होंगे।
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किस अनुक्रम में सार्व अंतर (7) है?
Which sequence has common difference (7)?
#arithmetic-progression
#identify-d
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A \(5,12,19,26,\ldots\)
B \(7,12,17,22,\ldots\)
C \(14,7,0,-7,\ldots\)
D \(2,7,14,23,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(5,12,19,26,\ldots\)
Step 1
Concept
(12-5=7), and the same difference continues. A sequence with equal (d) is an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. \(5,12,19,26,\ldots\). (12-5=7), and the same difference continues. A sequence with equal (d) is an arithmetic progression.
Step 3
Exam Tip
(12-5=7) और आगे भी यही अंतर है। समान (d) वाला अनुक्रम समांतर श्रेढ़ी है।
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यदि समांतर श्रेढ़ी \(x,x+4,x+8,x+12,\ldots\) है, तो सार्व अंतर क्या है?
If the arithmetic progression is \(x,x+4,x+8,x+12,\ldots\), what is the common difference?
#arithmetic-progression
#algebraic-ap
#class10
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A (x)
B (2x)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The difference of consecutive terms is ((x+4)-x=4). The same rule applies to algebraic terms.
Step 2
Why this answer is correct
The correct answer is C. (4). The difference of consecutive terms is ((x+4)-x=4). The same rule applies to algebraic terms.
Step 3
Exam Tip
लगातार पदों का अंतर ((x+4)-x=4) है। अक्षर वाले पदों में भी वही नियम लगता है।
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अनुक्रम \(11,16,22,29,\ldots\) समांतर श्रेढ़ी क्यों नहीं है?
Why is \(11,16,22,29,\ldots\) not an arithmetic progression?
#arithmetic-progression
#non-ap-reason
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A क्योंकि पहला पद (11) है / Because the first term is (11)
B क्योंकि पद बढ़ रहे हैं / Because the terms are increasing
C क्योंकि अंतर (5,6,7) समान नहीं हैं / Because the differences (5,6,7) are not equal
D क्योंकि सभी पद धनात्मक हैं / Because all terms are positive
Explanation opens after your attempt
Correct Answer
C. क्योंकि अंतर (5,6,7) समान नहीं हैं / Because the differences (5,6,7) are not equal
Step 1
Concept
In an arithmetic progression, consecutive differences are equal. Here the differences change, so it is not an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि अंतर (5,6,7) समान नहीं हैं / Because the differences (5,6,7) are not equal. In an arithmetic progression, consecutive differences are equal. Here the differences change, so it is not an arithmetic progression.
Step 3
Exam Tip
समांतर श्रेढ़ी में लगातार अंतर समान होते हैं। यहाँ अंतर बदल रहे हैं इसलिए यह समांतर श्रेढ़ी नहीं है।
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एक दुकानदार रोज़ पिछले दिन से (15) रुपये अधिक बचाता है। यदि पहले दिन (50) रुपये बचाए, तो बचत का अनुक्रम क्या होगा?
A shopkeeper saves (15) rupees more than the previous day. If he saved (50) rupees on the first day, what will be the savings sequence?
#arithmetic-progression
#word-problem
#class10
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A \(50,60,70,80,\ldots\)
B \(15,50,85,120,\ldots\)
C \(50,65,80,95,\ldots\)
D \(65,80,95,110,\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(50,65,80,95,\ldots\)
Step 1
Concept
The first term is (50), and (15) is added each time. Hence the sequence is \(50,65,80,95,\ldots\).
Step 2
Why this answer is correct
The correct answer is C. \(50,65,80,95,\ldots\). The first term is (50), and (15) is added each time. Hence the sequence is \(50,65,80,95,\ldots\).
Step 3
Exam Tip
पहला पद (50) है और हर बार (15) जोड़ना है। इसलिए अनुक्रम \(50,65,80,95,\ldots\) होगा।
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समांतर श्रेढ़ी \(3,9,15,21,\ldots\) में (a) और (d) का योग क्या है?
In the arithmetic progression \(3,9,15,21,\ldots\), what is the sum of (a) and (d)?
#arithmetic-progression
#first-term-common-difference
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A (6)
B (9)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
Here (a=3) and (d=6). Therefore, (a+d=9).
Step 2
Why this answer is correct
The correct answer is B. (9). Here (a=3) and (d=6). Therefore, (a+d=9).
Step 3
Exam Tip
यहाँ (a=3) और (d=6) है। इसलिए (a+d=9) होगा।
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यदि \(a_1=35\) और \(a_2=29\) हैं, तो सार्व अंतर (d) क्या है?
If \(a_1=35\) and \(a_2=29\), what is the common difference (d)?
#arithmetic-progression
#common-difference-formula
#class10
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A (6)
B (-6)
C (29)
D (64)
Explanation opens after your attempt
Step 1
Concept
\(d=a_2-a_1=29-35=-6\). Subtract the first term from the second term.
Step 2
Why this answer is correct
The correct answer is B. (-6). \(d=a_2-a_1=29-35=-6\). Subtract the first term from the second term.
Step 3
Exam Tip
\(d=a_2-a_1=29-35=-6\) है। दूसरे पद से पहले पद को घटाएँ।
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अनुक्रम \(\frac{5}{4},\frac{7}{4},\frac{9}{4},\frac{11}{4},\ldots\) में चौथा पद क्या है?
What is the fourth term in \(\frac{5}{4},\frac{7}{4},\frac{9}{4},\frac{11}{4},\ldots\)?
#arithmetic-progression
#term-position
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A \(\frac{5}{4}\)
B \(\frac{7}{4}\)
C \(\frac{9}{4}\)
D \(\frac{11}{4}\)
Explanation opens after your attempt
Correct Answer
D. \(\frac{11}{4}\)
Step 1
Concept
In the written order, the fourth term is \(\frac{11}{4}\). Include the first term while counting positions.
Step 2
Why this answer is correct
The correct answer is D. \(\frac{11}{4}\). In the written order, the fourth term is \(\frac{11}{4}\). Include the first term while counting positions.
Step 3
Exam Tip
लिखे क्रम में चौथा पद \(\frac{11}{4}\) है। पद संख्या गिनते समय पहला पद शामिल करें।
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कौन-सा अनुक्रम (d=-5) वाली समांतर श्रेढ़ी है?
Which sequence is an arithmetic progression with (d=-5)?
#arithmetic-progression
#negative-difference
#class10
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A \(10,15,20,25,\ldots\)
B \(40,35,30,25,\ldots\)
C \(5,0,-6,-13,\ldots\)
D \(25,20,10,5,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(40,35,30,25,\ldots\)
Step 1
Concept
(35-40=-5), and the same difference continues. Equal negative difference forms a decreasing arithmetic progression.
Step 2
Why this answer is correct
The correct answer is B. \(40,35,30,25,\ldots\). (35-40=-5), and the same difference continues. Equal negative difference forms a decreasing arithmetic progression.
Step 3
Exam Tip
(35-40=-5) और आगे भी यही अंतर है। समान ऋणात्मक अंतर घटती समांतर श्रेढ़ी बनाता है।
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यदि (d>0) है और प्रथम पद धनात्मक है, तो समांतर श्रेढ़ी के पद सामान्यतः कैसे बदलेंगे?
If (d>0) and the first term is positive, how will the terms of an arithmetic progression generally change?
#arithmetic-progression
#positive-difference
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A घटेंगे / They will decrease
B समान रहेंगे / They will remain equal
C बढ़ेंगे / They will increase
D अनियमित होंगे / They will be irregular
Explanation opens after your attempt
Correct Answer
C. बढ़ेंगे / They will increase
Step 1
Concept
Positive (d) means adding each time. Therefore, the terms generally keep increasing.
Step 2
Why this answer is correct
The correct answer is C. बढ़ेंगे / They will increase. Positive (d) means adding each time. Therefore, the terms generally keep increasing.
Step 3
Exam Tip
धनात्मक (d) का अर्थ हर बार जोड़ना है। इसलिए पद सामान्यतः बढ़ते जाते हैं।
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अनुक्रम \(0,5,10,15,\ldots\) में (d) और (a) क्रमशः क्या हैं?
In \(0,5,10,15,\ldots\), what are (d) and (a) respectively?
#arithmetic-progression
#zero-first-term
#class10
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A (d=0,\ a=5)
B (d=5,\ a=0)
C (d=10,\ a=0)
D (d=5,\ a=5)
Explanation opens after your attempt
Correct Answer
B. (d=5,\ a=0)
Step 1
Concept
The common difference is (5-0=5), and the first term is (0). The question asks in the order (d) then (a).
Step 2
Why this answer is correct
The correct answer is B. (d=5,\ a=0). The common difference is (5-0=5), and the first term is (0). The question asks in the order (d) then (a).
Step 3
Exam Tip
सार्व अंतर (5-0=5) और पहला पद (0) है। प्रश्न में क्रम (d) फिर (a) दिया है।
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यदि (a=6) और दूसरा पद (10) है, तो सार्व अंतर क्या होगा?
If (a=6) and the second term is (10), what is the common difference?
#arithmetic-progression
#find-d
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A (2)
B (3)
C (4)
D (16)
Explanation opens after your attempt
Step 1
Concept
The second term is (a+d). Therefore, (d=10-6=4).
Step 2
Why this answer is correct
The correct answer is C. (4). The second term is (a+d). Therefore, (d=10-6=4).
Step 3
Exam Tip
दूसरा पद (a+d) होता है। इसलिए (d=10-6=4) है।
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अनुक्रम \(14,20,26,32,\ldots\) में (20) कौन-सा पद है?
In the sequence \(14,20,26,32,\ldots\), which term is (20)?
#arithmetic-progression
#term-number
#class10
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A पहला पद / First term
B दूसरा पद / Second term
C तीसरा पद / Third term
D चौथा पद / Fourth term
Explanation opens after your attempt
Correct Answer
B. दूसरा पद / Second term
Step 1
Concept
In the written order, (14) is the first term and (20) is the second term. Count in order to find the term number.
Step 2
Why this answer is correct
The correct answer is B. दूसरा पद / Second term. In the written order, (14) is the first term and (20) is the second term. Count in order to find the term number.
Step 3
Exam Tip
लिखे क्रम में (14) पहला और (20) दूसरा पद है। पद संख्या के लिए क्रम से गिनें।
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समांतर श्रेढ़ी \(17,13,9,5,\ldots\) में पहले पद और सार्व अंतर का गुणनफल क्या है?
In the arithmetic progression \(17,13,9,5,\ldots\), what is the product of the first term and the common difference?
#arithmetic-progression
#first-term-common-difference
#class10
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A (68)
B (-68)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
Here the first term is (17) and (d=-4). Therefore, the product is \(17\times(-4)=-68\).
Step 2
Why this answer is correct
The correct answer is B. (-68). Here the first term is (17) and (d=-4). Therefore, the product is \(17\times(-4)=-68\).
Step 3
Exam Tip
यहाँ पहला पद (17) और (d=-4) है। इसलिए गुणनफल \(17\times(-4)=-68\) होगा।
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यदि किसी अनुक्रम के लगातार अंतर (2,4,6) हैं, तो सही निष्कर्ष क्या है?
If the consecutive differences of a sequence are (2,4,6), what is the correct conclusion?
#arithmetic-progression
#ap-check
#class10
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A यह समांतर श्रेढ़ी है / It is an arithmetic progression
B यह समांतर श्रेढ़ी नहीं है / It is not an arithmetic progression
C इसका सार्व अंतर (2) है / Its common difference is (2)
D इसके सभी पद समान हैं / All its terms are equal
Explanation opens after your attempt
Correct Answer
B. यह समांतर श्रेढ़ी नहीं है / It is not an arithmetic progression
Step 1
Concept
The differences are not equal, so the common difference is not constant. Hence it is not an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is B. यह समांतर श्रेढ़ी नहीं है / It is not an arithmetic progression. The differences are not equal, so the common difference is not constant. Hence it is not an arithmetic progression.
Step 3
Exam Tip
अंतर समान नहीं हैं इसलिए सार्व अंतर स्थिर नहीं है। अतः यह समांतर श्रेढ़ी नहीं है।
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अनुक्रम \(5,12,19,26,\ldots\) में पहले दो पदों का अंतर और तीसरे-चौथे पदों का अंतर क्या है?
In \(5,12,19,26,\ldots\), what are the difference of the first two terms and the difference of the third and fourth terms?
#arithmetic-progression
#common-difference-check
#class10
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A (7) और (7) / (7) and (7)
B (5) और (7) / (5) and (7)
C (12) और (26) / (12) and (26)
D (7) और (14) / (7) and (14)
Explanation opens after your attempt
Correct Answer
A. (7) और (7) / (7) and (7)
Step 1
Concept
The first difference is (12-5=7), and the second is (26-19=7). Equal differences confirm an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. (7) और (7) / (7) and (7). The first difference is (12-5=7), and the second is (26-19=7). Equal differences confirm an arithmetic progression.
Step 3
Exam Tip
पहला अंतर (12-5=7) और दूसरा (26-19=7) है। समान अंतर समांतर श्रेढ़ी की पुष्टि करता है।
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किसी समांतर श्रेढ़ी में (a=3) और (d=0) है। पहले तीन पद कौन-से होंगे?
In an arithmetic progression, (a=3) and (d=0). What are the first three terms?
#arithmetic-progression
#zero-difference
#class10
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A (3,0,0)
B (0,3,6)
C (3,3,3)
D (3,6,9)
Explanation opens after your attempt
Correct Answer
C. (3,3,3)
Step 1
Concept
When (d=0), every term remains equal. Therefore, the first three terms are (3,3,3).
Step 2
Why this answer is correct
The correct answer is C. (3,3,3). When (d=0), every term remains equal. Therefore, the first three terms are (3,3,3).
Step 3
Exam Tip
(d=0) होने पर हर पद समान रहता है। इसलिए पहले तीन पद (3,3,3) हैं।
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यदि (a=15) और (d=-4) है, तो पहले चार पद कौन-से हैं?
If (a=15) and (d=-4), what are the first four terms?
#arithmetic-progression
#construct-ap
#class10
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A (15,19,23,27)
B (15,11,7,3)
C (4,8,12,16)
D (11,7,3,-1)
Explanation opens after your attempt
Correct Answer
B. (15,11,7,3)
Step 1
Concept
The first term is (15), and (4) is subtracted each time. Hence the terms are (15,11,7,3).
Step 2
Why this answer is correct
The correct answer is B. (15,11,7,3). The first term is (15), and (4) is subtracted each time. Hence the terms are (15,11,7,3).
Step 3
Exam Tip
पहला पद (15) है और हर बार (4) घटता है। इसलिए पद (15,11,7,3) होंगे।
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अनुक्रम \(2k,2k+3,2k+6,2k+9,\ldots\) का सार्व अंतर क्या है?
What is the common difference of \(2k,2k+3,2k+6,2k+9,\ldots\)?
#arithmetic-progression
#algebraic-ap
#class10
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A (2k)
B (3)
C (6)
D (2k+3)
Explanation opens after your attempt
Step 1
Concept
The difference of consecutive terms is ((2k+3)-2k=3). In algebraic terms, cancel like terms.
Step 2
Why this answer is correct
The correct answer is B. (3). The difference of consecutive terms is ((2k+3)-2k=3). In algebraic terms, cancel like terms.
Step 3
Exam Tip
लगातार पदों का अंतर ((2k+3)-2k=3) है। बीजीय पदों में समान पद काट दें।
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यदि किसी समांतर श्रेढ़ी में (d=-1.5) है और प्रथम पद (10) है, तो दूसरा पद क्या होगा?
If an arithmetic progression has (d=-1.5) and first term (10), what is the second term?
#arithmetic-progression
#decimal-negative-d
#class10
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A (8.5)
B (9.5)
C (11.5)
D (-8.5)
Explanation opens after your attempt
Step 1
Concept
The second term is (10+(-1.5)=8.5). Take care of both decimals and negative signs.
Step 2
Why this answer is correct
The correct answer is A. (8.5). The second term is (10+(-1.5)=8.5). Take care of both decimals and negative signs.
Step 3
Exam Tip
दूसरा पद (10+(-1.5)=8.5) है। दशमलव और ऋणात्मक चिन्ह दोनों का ध्यान रखें।
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समांतर श्रेढ़ी \(\frac{1}{3},\frac{2}{3},1,\frac{4}{3},\ldots\) में (d) क्या है?
What is (d) in the arithmetic progression \(\frac{1}{3},\frac{2}{3},1,\frac{4}{3},\ldots\)?
#arithmetic-progression
#fraction-common-difference
#class10
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A \(\frac{1}{3}\)
B \(\frac{2}{3}\)
C (1)
D \(\frac{4}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{3}\)
Step 1
Concept
\(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\). For fractions, find the difference of the first two terms.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{3}\). \(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\). For fractions, find the difference of the first two terms.
Step 3
Exam Tip
\(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\) है। भिन्नों में पहले दो पदों का अंतर निकालें।
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एक इमारत की मंजिलों पर कमरे \(18,22,26,30,\ldots\) के अनुसार बढ़ते हैं। सार्व अंतर क्या है?
Rooms on the floors of a building increase as \(18,22,26,30,\ldots\). What is the common difference?
#arithmetic-progression
#real-life-ap
#class10
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A (2)
B (4)
C (8)
D (18)
Explanation opens after your attempt
Step 1
Concept
Each next floor has (4) more rooms. Therefore, the common difference is (4).
Step 2
Why this answer is correct
The correct answer is B. (4). Each next floor has (4) more rooms. Therefore, the common difference is (4).
Step 3
Exam Tip
हर अगली मंजिल पर (4) कमरे बढ़ रहे हैं। इसलिए सार्व अंतर (4) है।
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अनुक्रम \(64,57,50,43,\ldots\) में पाँचवाँ पद क्या होगा?
What will be the fifth term in \(64,57,50,43,\ldots\)?
#arithmetic-progression
#fifth-term
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A (36)
B (37)
C (39)
D (40)
Explanation opens after your attempt
Step 1
Concept
Here (d=-7). The fifth term will be (43-7=36).
Step 2
Why this answer is correct
The correct answer is A. (36). Here (d=-7). The fifth term will be (43-7=36).
Step 3
Exam Tip
यहाँ (d=-7) है। पाँचवाँ पद (43-7=36) होगा।
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यदि (a=4) और (a+d=13) है, तो (d) का मान क्या है?
If (a=4) and (a+d=13), what is the value of (d)?
#arithmetic-progression
#find-d
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A (4)
B (9)
C (13)
D (17)
Explanation opens after your attempt
Step 1
Concept
(d=13-4=9). Subtracting the first term from the second term gives the common difference.
Step 2
Why this answer is correct
The correct answer is B. (9). (d=13-4=9). Subtracting the first term from the second term gives the common difference.
Step 3
Exam Tip
(d=13-4=9) है। दूसरे पद से पहले पद को घटाने पर सार्व अंतर मिलता है।
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कौन-सा अनुक्रम (d=0.25) वाली समांतर श्रेढ़ी है?
Which sequence is an arithmetic progression with (d=0.25)?
#arithmetic-progression
#decimal-ap
#class10
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A \(1,1.5,2,2.5,\ldots\)
B \(0.25,0.5,0.75,1.0,\ldots\)
C \(2,2.25,2.75,3.5,\ldots\)
D \(0.25,1,4,16,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(0.25,0.5,0.75,1.0,\ldots\)
Step 1
Concept
(0.5-0.25=0.25), and the same difference continues. Hence this is the correct arithmetic progression.
Step 2
Why this answer is correct
The correct answer is B. \(0.25,0.5,0.75,1.0,\ldots\). (0.5-0.25=0.25), and the same difference continues. Hence this is the correct arithmetic progression.
Step 3
Exam Tip
(0.5-0.25=0.25) और आगे भी यही अंतर है। इसलिए यह सही समांतर श्रेढ़ी है।
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अनुक्रम \(7,7.5,8,8.5,\ldots\) में सार्व अंतर क्या है?
What is the common difference in \(7,7.5,8,8.5,\ldots\)?
#arithmetic-progression
#decimal-common-difference
#class10
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A (0.25)
B (0.5)
C (1)
D (7.5)
Explanation opens after your attempt
Step 1
Concept
The common difference is (7.5-7=0.5). For decimal terms also, check the regular difference.
Step 2
Why this answer is correct
The correct answer is B. (0.5). The common difference is (7.5-7=0.5). For decimal terms also, check the regular difference.
Step 3
Exam Tip
सार्व अंतर (7.5-7=0.5) है। दशमलव पदों में भी नियमित अंतर देखें।
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यदि कोई अनुक्रम \(1,4,7,10,\ldots\) है, तो तीसरे और दूसरे पद का अंतर क्या है?
If a sequence is \(1,4,7,10,\ldots\), what is the difference between the third and second terms?
#arithmetic-progression
#common-difference-check
#class10
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A (2)
B (3)
C (4)
D (7)
Explanation opens after your attempt
Step 1
Concept
The third term is (7) and the second term is (4). Therefore, the difference is (7-4=3).
Step 2
Why this answer is correct
The correct answer is B. (3). The third term is (7) and the second term is (4). Therefore, the difference is (7-4=3).
Step 3
Exam Tip
तीसरा पद (7) और दूसरा पद (4) है। इसलिए अंतर (7-4=3) है।
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समांतर श्रेढ़ी \(a-2,a+1,a+4,a+7,\ldots\) का सार्व अंतर क्या है?
What is the common difference of the arithmetic progression \(a-2,a+1,a+4,a+7,\ldots\)?
#arithmetic-progression
#algebraic-ap
#class10
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A (2)
B (3)
C (a)
D (a+3)
Explanation opens after your attempt
Step 1
Concept
The difference of consecutive terms is ((a+1)-(a-2)=3). Like terms cancel in variable terms.
Step 2
Why this answer is correct
The correct answer is B. (3). The difference of consecutive terms is ((a+1)-(a-2)=3). Like terms cancel in variable terms.
Step 3
Exam Tip
लगातार पदों का अंतर ((a+1)-(a-2)=3) है। चर वाले पदों में समान पद कट जाते हैं।
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किस अनुक्रम में लगातार अंतर बराबर नहीं हैं?
In which sequence are the consecutive differences not equal?
#arithmetic-progression
#not-ap
#class10
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A \(9,14,19,24,\ldots\)
B \(40,36,32,28,\ldots\)
C \(3,3,3,3,\ldots\)
D \(2,3,5,8,\ldots\)
Explanation opens after your attempt
Correct Answer
D. \(2,3,5,8,\ldots\)
Step 1
Concept
In \(2,3,5,8,\ldots\), the differences are (1,2,3). Hence the consecutive differences are not equal.
Step 2
Why this answer is correct
The correct answer is D. \(2,3,5,8,\ldots\). In \(2,3,5,8,\ldots\), the differences are (1,2,3). Hence the consecutive differences are not equal.
Step 3
Exam Tip
\(2,3,5,8,\ldots\) में अंतर (1,2,3) हैं। इसलिए लगातार अंतर बराबर नहीं हैं।
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यदि समांतर श्रेढ़ी का दूसरा पद (18) और पहला पद (11) है, तो (d) क्या होगा?
If the second term of an arithmetic progression is (18) and the first term is (11), what will (d) be?
#arithmetic-progression
#find-d
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A (6)
B (7)
C (18)
D (29)
Explanation opens after your attempt
Step 1
Concept
The common difference is (18-11=7). For (d), subtract the first term from the second term.
Step 2
Why this answer is correct
The correct answer is B. (7). The common difference is (18-11=7). For (d), subtract the first term from the second term.
Step 3
Exam Tip
सार्व अंतर (18-11=7) है। (d) के लिए दूसरा पद घटा पहला पद करें।
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अनुक्रम \(25,21,17,13,\ldots\) में (21) कौन-सा पद है?
In the sequence \(25,21,17,13,\ldots\), which term is (21)?
#arithmetic-progression
#term-position
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A पहला पद / First term
B दूसरा पद / Second term
C तीसरा पद / Third term
D चौथा पद / Fourth term
Explanation opens after your attempt
Correct Answer
B. दूसरा पद / Second term
Step 1
Concept
In the written order, (25) is the first term and (21) is the second term. Count in order to find the position.
Step 2
Why this answer is correct
The correct answer is B. दूसरा पद / Second term. In the written order, (25) is the first term and (21) is the second term. Count in order to find the position.
Step 3
Exam Tip
लिखे क्रम में (25) पहला और (21) दूसरा पद है। पद की स्थिति के लिए क्रम से गिनें।
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यदि (a=2.5) और (d=1.5) है, तो पहले तीन पद कौन-से होंगे?
If (a=2.5) and (d=1.5), what are the first three terms?
#arithmetic-progression
#decimal-ap
#class10
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A (2.5,4.0,5.5)
B (1.5,3.0,4.5)
C (2.5,5.0,7.5)
D (4.0,5.5,7.0)
Explanation opens after your attempt
Correct Answer
A. (2.5,4.0,5.5)
Step 1
Concept
The first term is (2.5), and (1.5) is added each time. Hence the terms are (2.5,4.0,5.5).
Step 2
Why this answer is correct
The correct answer is A. (2.5,4.0,5.5). The first term is (2.5), and (1.5) is added each time. Hence the terms are (2.5,4.0,5.5).
Step 3
Exam Tip
पहला पद (2.5) है और हर बार (1.5) जोड़ना है। इसलिए पद (2.5,4.0,5.5) हैं।
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अनुक्रम \(-18,-12,-6,0,\ldots\) में छठा पद क्या होगा?
What will be the sixth term in \(-18,-12,-6,0,\ldots\)?
#arithmetic-progression
#next-term
#class10
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A (6)
B (12)
C (18)
D (24)
Explanation opens after your attempt
Step 1
Concept
The common difference is (6). The fifth term is (6) and the sixth term is (12).
Step 2
Why this answer is correct
The correct answer is B. (12). The common difference is (6). The fifth term is (6) and the sixth term is (12).
Step 3
Exam Tip
यहाँ सार्व अंतर (6) है। पाँचवाँ पद (6) और छठा पद (12) होगा।
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यदि किसी समांतर श्रेढ़ी में (a=28) और दूसरा पद (19) है, तो सार्व अंतर क्या है?
If an arithmetic progression has (a=28) and second term (19), what is the common difference?
#arithmetic-progression
#find-d
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A (9)
B (-9)
C (19)
D (47)
Explanation opens after your attempt
Step 1
Concept
The common difference is (19-28=-9). Find (d) by subtracting the first term from the second term.
Step 2
Why this answer is correct
The correct answer is B. (-9). The common difference is (19-28=-9). Find (d) by subtracting the first term from the second term.
Step 3
Exam Tip
सार्व अंतर (19-28=-9) है। दूसरे पद से पहले पद को घटाकर (d) निकालें।
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अनुक्रम \(5m,5m-4,5m-8,5m-12,\ldots\) का सार्व अंतर क्या है?
What is the common difference of \(5m,5m-4,5m-8,5m-12,\ldots\)?
#arithmetic-progression
#algebraic-ap
#class10
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A (4)
B (-4)
C (5m)
D (5m-4)
Explanation opens after your attempt
Step 1
Concept
The difference of consecutive terms is ((5m-4)-5m=-4). In algebraic terms, cancel like terms to find the difference.
Step 2
Why this answer is correct
The correct answer is B. (-4). The difference of consecutive terms is ((5m-4)-5m=-4). In algebraic terms, cancel like terms to find the difference.
Step 3
Exam Tip
लगातार पदों का अंतर ((5m-4)-5m=-4) है। बीजीय पदों में समान पद काटकर अंतर निकालें।
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किस अनुक्रम में पहले तीन लगातार अंतर (4,4,4) मिलते हैं?
In which sequence are the first three consecutive differences (4,4,4)?
#arithmetic-progression
#common-difference-check
#class10
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A \(2,6,10,14,\ldots\)
B \(4,8,13,19,\ldots\)
C \(10,8,6,4,\ldots\)
D \(1,4,9,16,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(2,6,10,14,\ldots\)
Step 1
Concept
In \(2,6,10,14,\ldots\), the differences are (4,4,4). Equal differences identify an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. \(2,6,10,14,\ldots\). In \(2,6,10,14,\ldots\), the differences are (4,4,4). Equal differences identify an arithmetic progression.
Step 3
Exam Tip
\(2,6,10,14,\ldots\) में अंतर (4,4,4) हैं। समान अंतर समांतर श्रेढ़ी की पहचान है।
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अनुक्रम \(24,29,34,39,\ldots\) में (d) का मान क्या है?
What is the value of (d) in the sequence \(24,29,34,39,\ldots\)?
#arithmetic progression
#common difference
#medium
#class ten
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A (4)
B (5)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
(d=29-24=5), and the same difference continues. In exams always check the difference of two consecutive terms.
Step 2
Why this answer is correct
The correct answer is B. (5). (d=29-24=5), and the same difference continues. In exams always check the difference of two consecutive terms.
Step 3
Exam Tip
(d=29-24=5) है और आगे भी यही अंतर है। परीक्षा में हमेशा दो क्रमागत पदों का अंतर जांचें।
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यदि \(9,k,23,30,\ldots\) एक अंकगणितीय श्रेणी है तो (k) का मान क्या होगा?
If \(9,k,23,30,\ldots\) is an arithmetic progression, what will be the value of (k)?
#ap
#missing term
#common difference
#medium
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A (14)
B (15)
C (16)
D (17)
Explanation opens after your attempt
Step 1
Concept
The difference from (23) to (30) is (7), so (k=23-7=16). For a missing term use the same difference backward.
Step 2
Why this answer is correct
The correct answer is C. (16). The difference from (23) to (30) is (7), so (k=23-7=16). For a missing term use the same difference backward.
Step 3
Exam Tip
(23) से (30) तक अंतर (7) है इसलिए (k=23-7=16)। खाली पद निकालते समय समान अंतर को पीछे की ओर लगाएं।
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अनुक्रम \(-8,-3,2,7,\ldots\) में (a) और (d) क्रमशः क्या हैं?
In the sequence \(-8,-3,2,7,\ldots\), what are (a) and (d) respectively?
#ap
#first term
#common difference
#integers
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A (-8) और (5) / (-8) and (5)
B (-3) और (5) / (-3) and (5)
C (-8) और (-5) / (-8) and (-5)
D (5) और (-8) / (5) and (-8)
Explanation opens after your attempt
Correct Answer
A. (-8) और (5) / (-8) and (5)
Step 1
Concept
The first term is (-8), and (d=-3-(-8)=5). Pay attention to signs with negative numbers.
Step 2
Why this answer is correct
The correct answer is A. (-8) और (5) / (-8) and (5). The first term is (-8), and (d=-3-(-8)=5). Pay attention to signs with negative numbers.
Step 3
Exam Tip
पहला पद (-8) है और (d=-3-(-8)=5) है। ऋणात्मक संख्याओं में चिह्न पर ध्यान दें।
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अनुक्रम \(3,7,13,21,\ldots\) अंकगणितीय श्रेणी क्यों नहीं है?
Why is \(3,7,13,21,\ldots\) not an arithmetic progression?
#ap
#not ap
#unequal difference
#medium
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A क्योंकि पहला पद (3) है / Because the first term is (3)
B क्योंकि पद धनात्मक हैं / Because the terms are positive
C क्योंकि क्रमागत अंतर समान नहीं हैं / Because consecutive differences are not equal
D क्योंकि अंतिम पद नहीं दिया गया / Because the last term is not given
Explanation opens after your attempt
Correct Answer
C. क्योंकि क्रमागत अंतर समान नहीं हैं / Because consecutive differences are not equal
Step 1
Concept
The differences are (4,6,8), which are not equal. Do not assume arithmetic progression only because terms increase.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि क्रमागत अंतर समान नहीं हैं / Because consecutive differences are not equal. The differences are (4,6,8), which are not equal. Do not assume arithmetic progression only because terms increase.
Step 3
Exam Tip
अंतर (4,6,8) हैं जो समान नहीं हैं। केवल बढ़ते पद देखकर अंकगणितीय श्रेणी न मानें।
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यदि (a=15) और (d=-4) है तो तीसरा पद क्या होगा?
If (a=15) and (d=-4), what will be the third term?
#ap
#third term
#negative difference
#medium
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A (11)
B (7)
C (19)
D (3)
Explanation opens after your attempt
Step 1
Concept
The first three terms are (15,11,7), so the third term is (7). When (d) is negative, terms decrease.
Step 2
Why this answer is correct
The correct answer is B. (7). The first three terms are (15,11,7), so the third term is (7). When (d) is negative, terms decrease.
Step 3
Exam Tip
पहले तीन पद (15,11,7) हैं इसलिए तीसरा पद (7) है। ऋणात्मक (d) होने पर पद घटते हैं।
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अनुक्रम \(4x,4x+3,4x+6,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(4x,4x+3,4x+6,\ldots\)?
#ap
#algebraic terms
#common difference
#medium
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A (4x)
B (6)
C (3)
D (4x+3)
Explanation opens after your attempt
Step 1
Concept
(d=(4x+3)-4x=3). For algebraic terms also subtract the first term from the second term.
Step 2
Why this answer is correct
The correct answer is C. (3). (d=(4x+3)-4x=3). For algebraic terms also subtract the first term from the second term.
Step 3
Exam Tip
(d=(4x+3)-4x=3) है। बीजगणितीय पदों में भी दूसरा पद घटा पहला पद करें।
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यदि \(p,18,25,32,\ldots\) एक अंकगणितीय श्रेणी है तो (p) का मान क्या है?
If \(p,18,25,32,\ldots\) is an arithmetic progression, what is the value of (p)?
#ap
#missing first term
#common difference
#medium
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
The common difference in (18,25,32) is (7), so (p=18-7=11). For the first term subtract (d) backward.
Step 2
Why this answer is correct
The correct answer is C. (11). The common difference in (18,25,32) is (7), so (p=18-7=11). For the first term subtract (d) backward.
Step 3
Exam Tip
(18,25,32) में सार्व अंतर (7) है इसलिए (p=18-7=11)। पहले पद के लिए (d) को पीछे की ओर घटाएं।
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अनुक्रम \(56,51,46,41,\ldots\) में (d) का मान क्या है?
What is the value of (d) in the sequence \(56,51,46,41,\ldots\)?
#ap
#negative d
#decreasing ap
#medium
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A (5)
B (-5)
C (-10)
D (56)
Explanation opens after your attempt
Step 1
Concept
(d=51-56=-5). In a decreasing progression (d) is written as negative.
Step 2
Why this answer is correct
The correct answer is B. (-5). (d=51-56=-5). In a decreasing progression (d) is written as negative.
Step 3
Exam Tip
(d=51-56=-5) है। घटती श्रेणी में (d) ऋणात्मक लिखा जाता है।
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यदि (8,m,20) किसी अंकगणितीय श्रेणी के क्रमागत तीन पद हैं तो (m) क्या है?
If (8,m,20) are three consecutive terms of an arithmetic progression, what is (m)?
#ap
#middle term
#missing term
#medium
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A (12)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(m=\frac{8+20}{2}=14\). In three consecutive terms the middle term is the average.
Step 2
Why this answer is correct
The correct answer is C. (14). The middle term is \(m=\frac{8+20}{2}=14\). In three consecutive terms the middle term is the average.
Step 3
Exam Tip
मध्य पद \(m=\frac{8+20}{2}=14\) है। तीन क्रमागत पदों में बीच वाला पद औसत होता है।
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कौन सा अनुक्रम (d=-7) वाली अंकगणितीय श्रेणी है?
Which sequence is an arithmetic progression with (d=-7)?
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#negative difference
#medium
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A \(60,53,46,39,\ldots\)
B \(21,28,35,42,\ldots\)
C \(50,43,37,30,\ldots\)
D \(14,7,3,-4,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(60,53,46,39,\ldots\)
Step 1
Concept
(53-60=-7), (46-53=-7), and (39-46=-7). All differences must be equal to (-7).
Step 2
Why this answer is correct
The correct answer is A. \(60,53,46,39,\ldots\). (53-60=-7), (46-53=-7), and (39-46=-7). All differences must be equal to (-7).
Step 3
Exam Tip
(53-60=-7), (46-53=-7) और (39-46=-7) हैं। सभी अंतर समान और (-7) होने चाहिए।
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अनुक्रम \(\frac{5}{6},\frac{7}{6},\frac{3}{2},\frac{11}{6},\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(\frac{5}{6},\frac{7}{6},\frac{3}{2},\frac{11}{6},\ldots\)?
#ap
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#common difference
#medium
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A \(\frac{1}{6}\)
B \(\frac{1}{3}\)
C \(\frac{1}{2}\)
D \(\frac{2}{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{3}\)
Step 1
Concept
\(\frac{7}{6}-\frac{5}{6}=\frac{1}{3}\) and \(\frac{3}{2}-\frac{7}{6}=\frac{1}{3}\). For fractions subtract using common denominators.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{3}\). \(\frac{7}{6}-\frac{5}{6}=\frac{1}{3}\) and \(\frac{3}{2}-\frac{7}{6}=\frac{1}{3}\). For fractions subtract using common denominators.
Step 3
Exam Tip
\(\frac{7}{6}-\frac{5}{6}=\frac{1}{3}\) और \(\frac{3}{2}-\frac{7}{6}=\frac{1}{3}\) है। भिन्नों में हर समान करके घटाएं।
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यदि (a=-9) और (d=6) है तो पहले चार पद कौन से हैं?
If (a=-9) and (d=6), what are the first four terms?
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#integers
#medium
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A (-9,-3,3,9)
B (-9,-4,1,6)
C (-9,0,9,18)
D (-9,-15,-21,-27)
Explanation opens after your attempt
Correct Answer
A. (-9,-3,3,9)
Step 1
Concept
Adding (6) each time gives (-9,-3,3,9). Keep adding (d) successively.
Step 2
Why this answer is correct
The correct answer is A. (-9,-3,3,9). Adding (6) each time gives (-9,-3,3,9). Keep adding (d) successively.
Step 3
Exam Tip
हर बार (6) जोड़ने पर (-9,-3,3,9) मिलते हैं। (d) को लगातार जोड़ते जाएं।
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अनुक्रम \(1.4,1.9,2.4,2.9,\ldots\) का सार्व अंतर क्या है?
What is the common difference of the sequence \(1.4,1.9,2.4,2.9,\ldots\)?
#ap
#decimal sequence
#common difference
#medium
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A (0.4)
B (0.5)
C (1.4)
D (1.9)
Explanation opens after your attempt
Step 1
Concept
The common difference is (1.9-1.4=0.5). In decimal subtraction pay attention to place value.
Step 2
Why this answer is correct
The correct answer is B. (0.5). The common difference is (1.9-1.4=0.5). In decimal subtraction pay attention to place value.
Step 3
Exam Tip
सार्व अंतर (1.9-1.4=0.5) है। दशमलव घटाते समय स्थान मान का ध्यान रखें।
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यदि किसी अंकगणितीय श्रेणी में लगातार पद (27) और (35) हैं तो (d) क्या है?
If two consecutive terms in an arithmetic progression are (27) and (35), what is (d)?
#ap
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#find d
#medium
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A (8)
B (27)
C (35)
D (62)
Explanation opens after your attempt
Step 1
Concept
(d=35-27=8). When consecutive terms are given, subtract the earlier term from the later term.
Step 2
Why this answer is correct
The correct answer is A. (8). (d=35-27=8). When consecutive terms are given, subtract the earlier term from the later term.
Step 3
Exam Tip
(d=35-27=8) है। लगातार पद दिए हों तो बाद वाले पद में से पहले वाला पद घटाएं।
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अनुक्रम \(12,19,26,33,\ldots\) में (33) के बाद अगला पद क्या होगा?
In the sequence \(12,19,26,33,\ldots\), what will be the next term after (33)?
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#common difference
#medium
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A (38)
B (39)
C (40)
D (41)
Explanation opens after your attempt
Step 1
Concept
The common difference is (7), so the next term is (33+7=40). Identify (d) before finding the next term.
Step 2
Why this answer is correct
The correct answer is C. (40). The common difference is (7), so the next term is (33+7=40). Identify (d) before finding the next term.
Step 3
Exam Tip
सार्व अंतर (7) है इसलिए अगला पद (33+7=40) होगा। अगला पद निकालने से पहले (d) पहचानें।
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यदि (5,11,n,23) अंकगणितीय श्रेणी के क्रमागत पद हैं तो (n) क्या है?
If (5,11,n,23) are consecutive terms of an arithmetic progression, what is (n)?
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#medium
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A (15)
B (16)
C (17)
D (18)
Explanation opens after your attempt
Step 1
Concept
The common difference is (11-5=6), so (n=11+6=17). It is easy to find (d) from the first two terms.
Step 2
Why this answer is correct
The correct answer is C. (17). The common difference is (11-5=6), so (n=11+6=17). It is easy to find (d) from the first two terms.
Step 3
Exam Tip
सार्व अंतर (11-5=6) है इसलिए (n=11+6=17)। पहले दो पदों से (d) निकालना आसान होता है।
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किस विकल्प में (a=14) और (d=4) है?
Which option has (a=14) and (d=4)?
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#medium
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A \(4,8,12,16,\ldots\)
B \(14,18,22,26,\ldots\)
C \(14,17,20,23,\ldots\)
D \(18,22,26,30,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(14,18,22,26,\ldots\)
Step 1
Concept
In \(14,18,22,26,\ldots\), the first term is (14) and the difference is (4). Check both (a) and (d) together.
Step 2
Why this answer is correct
The correct answer is B. \(14,18,22,26,\ldots\). In \(14,18,22,26,\ldots\), the first term is (14) and the difference is (4). Check both (a) and (d) together.
Step 3
Exam Tip
\(14,18,22,26,\ldots\) में पहला पद (14) और अंतर (4) है। (a) और (d) दोनों शर्तें साथ में जांचें।
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अनुक्रम \(75,69,63,57,\ldots\) में तीसरे और चौथे पद का अंतर क्या है?
What is the difference between the third and fourth terms of \(75,69,63,57,\ldots\)?
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#negative difference
#medium
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A (6)
B (-6)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
The third term is (63) and the fourth is (57), so the difference is (57-63=-6). While finding difference subtract the previous term from the next term.
Step 2
Why this answer is correct
The correct answer is B. (-6). The third term is (63) and the fourth is (57), so the difference is (57-63=-6). While finding difference subtract the previous term from the next term.
Step 3
Exam Tip
तीसरा पद (63) और चौथा (57) है इसलिए अंतर (57-63=-6) है। अंतर निकालते समय अगला पद घटा पिछला पद करें।
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यदि (a=3.5) और (d=2.5) है तो दूसरा पद क्या है?
If (a=3.5) and (d=2.5), what is the second term?
#ap
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#second term
#medium
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A (5.0)
B (5.5)
C (6.0)
D (6.5)
Explanation opens after your attempt
Step 1
Concept
The second term is (a+d=3.5+2.5=6.0). While adding decimals keep digits in proper places.
Step 2
Why this answer is correct
The correct answer is C. (6.0). The second term is (a+d=3.5+2.5=6.0). While adding decimals keep digits in proper places.
Step 3
Exam Tip
दूसरा पद (a+d=3.5+2.5=6.0) है। दशमलव जोड़ते समय अंकों को सही स्थान पर रखें।
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यदि \(t,t+9,t+18,\ldots\) अंकगणितीय श्रेणी है तो दूसरे और पहले पद का अंतर क्या है?
If \(t,t+9,t+18,\ldots\) is an arithmetic progression, what is the difference between the second and first terms?
#ap
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#common difference
#medium
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A (t)
B (9)
C (18)
D (t+9)
Explanation opens after your attempt
Step 1
Concept
((t+9)-t=9), so the difference is (9). The equally added number is (d).
Step 2
Why this answer is correct
The correct answer is B. (9). ((t+9)-t=9), so the difference is (9). The equally added number is (d).
Step 3
Exam Tip
((t+9)-t=9) है इसलिए अंतर (9) है। समान जोड़ी गई संख्या ही (d) होती है।
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अनुक्रम \(21,26,31,36,\ldots\) में (a+d) का मान क्या है?
In the sequence \(21,26,31,36,\ldots\), what is the value of (a+d)?
#ap
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#second term
#medium
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A (21)
B (26)
C (31)
D (36)
Explanation opens after your attempt
Step 1
Concept
Here (a=21) and (d=5), so (a+d=26). (a+d) is the second term.
Step 2
Why this answer is correct
The correct answer is B. (26). Here (a=21) and (d=5), so (a+d=26). (a+d) is the second term.
Step 3
Exam Tip
यहां (a=21) और (d=5), इसलिए (a+d=26) है। (a+d) दूसरा पद होता है।
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यदि \(48,42,q,30,\ldots\) अंकगणितीय श्रेणी है तो (q) का मान क्या है?
If \(48,42,q,30,\ldots\) is an arithmetic progression, what is the value of (q)?
#ap
#missing term
#decreasing sequence
#medium
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A (32)
B (34)
C (36)
D (38)
Explanation opens after your attempt
Step 1
Concept
The common difference is (42-48=-6), so (q=42-6=36). Keep (d) negative in a decreasing progression.
Step 2
Why this answer is correct
The correct answer is C. (36). The common difference is (42-48=-6), so (q=42-6=36). Keep (d) negative in a decreasing progression.
Step 3
Exam Tip
सार्व अंतर (42-48=-6) है इसलिए (q=42-6=36)। घटती श्रेणी में (d) ऋणात्मक रखें।
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कौन सा कथन \(7,13,19,25,\ldots\) के लिए सही है?
Which statement is correct for \(7,13,19,25,\ldots\)?
#ap
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#medium
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A यह अंकगणितीय श्रेणी है और (d=6) है / It is an arithmetic progression and (d=6)
B यह अंकगणितीय श्रेणी है और (d=7) है / It is an arithmetic progression and (d=7)
C यह अंकगणितीय श्रेणी नहीं है / It is not an arithmetic progression
D यह (d=5) वाली श्रेणी है / It is a progression with (d=5)
Explanation opens after your attempt
Correct Answer
A. यह अंकगणितीय श्रेणी है और (d=6) है / It is an arithmetic progression and (d=6)
Step 1
Concept
Every consecutive difference is (6), so it is an arithmetic progression. While choosing a statement check both type and (d).
Step 2
Why this answer is correct
The correct answer is A. यह अंकगणितीय श्रेणी है और (d=6) है / It is an arithmetic progression and (d=6). Every consecutive difference is (6), so it is an arithmetic progression. While choosing a statement check both type and (d).
Step 3
Exam Tip
हर क्रमागत अंतर (6) है इसलिए यह अंकगणितीय श्रेणी है। सही कथन चुनते समय प्रकार और (d) दोनों जांचें।
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एक अंकगणितीय श्रेणी में पहला पद (22) और दूसरा पद (16) है। (d) क्या है?
In an arithmetic progression, the first term is (22) and the second term is (16). What is (d)?
#ap
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#negative difference
#medium
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A (6)
B (-6)
C (38)
D (-38)
Explanation opens after your attempt
Step 1
Concept
(d=16-22=-6). If the second term is smaller, (d) is negative.
Step 2
Why this answer is correct
The correct answer is B. (-6). (d=16-22=-6). If the second term is smaller, (d) is negative.
Step 3
Exam Tip
(d=16-22=-6) है। दूसरा पद छोटा हो तो (d) ऋणात्मक होता है।
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यदि (a=8) और (d=3) है तो (a+2d) किस पद को दर्शाता है?
If (a=8) and (d=3), which term does (a+2d) represent?
#ap
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#medium
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A पहला पद / First term
B दूसरा पद / Second term
C तीसरा पद / Third term
D चौथा पद / Fourth term
Explanation opens after your attempt
Correct Answer
C. तीसरा पद / Third term
Step 1
Concept
In the general form \(a,a+d,a+2d,\ldots\), (a+2d) is the third term. Remember the general form to identify terms.
Step 2
Why this answer is correct
The correct answer is C. तीसरा पद / Third term. In the general form \(a,a+d,a+2d,\ldots\), (a+2d) is the third term. Remember the general form to identify terms.
Step 3
Exam Tip
सामान्य रूप \(a,a+d,a+2d,\ldots\) में (a+2d) तीसरा पद है। पद पहचानने के लिए सामान्य रूप याद रखें।
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यदि \(4,10,16,r,\ldots\) अंकगणितीय श्रेणी है तो (r) क्या होगा?
If \(4,10,16,r,\ldots\) is an arithmetic progression, what will (r) be?
#ap
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#common difference
#medium
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A (20)
B (21)
C (22)
D (23)
Explanation opens after your attempt
Step 1
Concept
The common difference is (6), so (r=16+6=22). Add (d) to the previous term to get the next term.
Step 2
Why this answer is correct
The correct answer is C. (22). The common difference is (6), so (r=16+6=22). Add (d) to the previous term to get the next term.
Step 3
Exam Tip
सार्व अंतर (6) है इसलिए (r=16+6=22)। अगला पद पाने के लिए पिछले पद में (d) जोड़ें।
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निम्न में से किस अनुक्रम में (a=-6) और (d=5) है?
Which of the following sequences has (a=-6) and (d=5)?
#ap
#first term
#identify ap
#medium
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A \(-6,-1,4,9,\ldots\)
B \(-6,0,6,12,\ldots\)
C \(6,11,16,21,\ldots\)
D \(-5,0,5,10,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(-6,-1,4,9,\ldots\)
Step 1
Concept
In \(-6,-1,4,9,\ldots\), the first term is (-6) and the difference is (5). Both conditions must match.
Step 2
Why this answer is correct
The correct answer is A. \(-6,-1,4,9,\ldots\). In \(-6,-1,4,9,\ldots\), the first term is (-6) and the difference is (5). Both conditions must match.
Step 3
Exam Tip
\(-6,-1,4,9,\ldots\) में पहला पद (-6) और अंतर (5) है। दोनों शर्तें मिलनी चाहिए।
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अनुक्रम \(\frac{2}{3},\frac{5}{3},\frac{8}{3},\frac{11}{3},\ldots\) का अगला पद क्या होगा?
What will be the next term of the sequence \(\frac{2}{3},\frac{5}{3},\frac{8}{3},\frac{11}{3},\ldots\)?
#ap
#fractions
#next term
#medium
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A (4)
B \(\frac{13}{3}\)
C \(\frac{14}{3}\)
D (5)
Explanation opens after your attempt
Correct Answer
C. \(\frac{14}{3}\)
Step 1
Concept
The common difference is (1), so the next term is \(\frac{11}{3}+1=\frac{14}{3}\). Use a common denominator when adding an integer to a fraction.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{14}{3}\). The common difference is (1), so the next term is \(\frac{11}{3}+1=\frac{14}{3}\). Use a common denominator when adding an integer to a fraction.
Step 3
Exam Tip
सार्व अंतर (1) है इसलिए अगला पद \(\frac{11}{3}+1=\frac{14}{3}\) है। भिन्न में पूर्णांक जोड़ते समय हर समान करें।
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यदि \(8,8+s,8+2s,\ldots\) एक अंकगणितीय श्रेणी है तो इसका सार्व अंतर क्या है?
If \(8,8+s,8+2s,\ldots\) is an arithmetic progression, what is its common difference?
#ap
#algebraic common difference
#medium
#class ten
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A (8)
B (8+s)
C (s)
D (2s)
Explanation opens after your attempt
Step 1
Concept
The common difference is ((8+s)-8=s). In algebraic sequences also look at the equally added part.
Step 2
Why this answer is correct
The correct answer is C. (s). The common difference is ((8+s)-8=s). In algebraic sequences also look at the equally added part.
Step 3
Exam Tip
सार्व अंतर ((8+s)-8=s) है। अक्षर वाले अनुक्रम में भी समान जोड़ा गया भाग देखें।
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एक मोबाइल रिचार्ज योजना में डाटा हर दिन (1.5) जीबी बढ़ता है। डाटा \(2,3.5,5,6.5,\ldots\) है तो (d) क्या है?
In a mobile recharge plan, data increases by (1.5) GB each day. The data is \(2,3.5,5,6.5,\ldots\). What is (d)?
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#common difference
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A (1)
B (1.5)
C (2)
D (3.5)
Explanation opens after your attempt
Step 1
Concept
The equal daily increase is (1.5), so (d=1.5). In word problems treat the equal increase as the common difference.
Step 2
Why this answer is correct
The correct answer is B. (1.5). The equal daily increase is (1.5), so (d=1.5). In word problems treat the equal increase as the common difference.
Step 3
Exam Tip
हर दिन समान वृद्धि (1.5) है इसलिए (d=1.5)। शब्द प्रश्नों में समान वृद्धि को सार्व अंतर मानें।
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किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-4) नहीं है?
In which sequence are terms decreasing by an equal amount but (d) is not (-4)?
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#negative difference
#medium
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A \(30,26,22,18,\ldots\)
B \(45,40,35,30,\ldots\)
C \(16,12,8,4,\ldots\)
D \(9,5,1,-3,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(45,40,35,30,\ldots\)
Step 1
Concept
In \(45,40,35,30,\ldots\), (d=-5), not (-4). Check both value and sign in the options.
Step 2
Why this answer is correct
The correct answer is B. \(45,40,35,30,\ldots\). In \(45,40,35,30,\ldots\), (d=-5), not (-4). Check both value and sign in the options.
Step 3
Exam Tip
\(45,40,35,30,\ldots\) में (d=-5) है, (-4) नहीं। विकल्पों में मान और चिह्न दोनों जांचें।
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यदि (a=17) और (d=0) है तो चौथा पद क्या होगा?
If (a=17) and (d=0), what will be the fourth term?
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#fourth term
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A (0)
B (17)
C (34)
D (51)
Explanation opens after your attempt
Step 1
Concept
When (d=0), all terms remain (17). In a constant progression there is no increase or decrease.
Step 2
Why this answer is correct
The correct answer is B. (17). When (d=0), all terms remain (17). In a constant progression there is no increase or decrease.
Step 3
Exam Tip
(d=0) होने पर सभी पद (17) रहते हैं। स्थिर श्रेणी में कोई वृद्धि या कमी नहीं होती।
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अनुक्रम \(9,16,23,30,\ldots\) में (a+2d) का मान क्या है?
In the sequence \(9,16,23,30,\ldots\), what is the value of (a+2d)?
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#third term
#medium
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A (16)
B (30)
C (23)
D (7)
Explanation opens after your attempt
Step 1
Concept
Here (a=9) and (d=7), so (a+2d=9+14=23). (a+2d) equals the third term.
Step 2
Why this answer is correct
The correct answer is C. (23). Here (a=9) and (d=7), so (a+2d=9+14=23). (a+2d) equals the third term.
Step 3
Exam Tip
यहां (a=9) और (d=7), इसलिए (a+2d=9+14=23)। (a+2d) तीसरे पद के बराबर होता है।
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यदि \(z-4,z+2,z+8,\ldots\) अंकगणितीय श्रेणी है तो (d) क्या है?
If \(z-4,z+2,z+8,\ldots\) is an arithmetic progression, what is (d)?
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#find d
#medium
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A (z)
B (4)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
(d=(z+2)-(z-4)=6). When variables cancel, the constant difference remains.
Step 2
Why this answer is correct
The correct answer is C. (6). (d=(z+2)-(z-4)=6). When variables cancel, the constant difference remains.
Step 3
Exam Tip
(d=(z+2)-(z-4)=6) है। चर कट जाने पर स्थिर अंतर मिलता है।
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अनुक्रम \(70,64,58,52,\ldots\) में अगला पद और (d) क्रमशः क्या हैं?
In the sequence \(70,64,58,52,\ldots\), what are the next term and (d) respectively?
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A (46) और (-6) / (46) and (-6)
B (46) और (6) / (46) and (6)
C (58) और (-6) / (58) and (-6)
D (52) और (-6) / (52) and (-6)
Explanation opens after your attempt
Correct Answer
A. (46) और (-6) / (46) and (-6)
Step 1
Concept
The common difference is (-6), and the next term is (52-6=46). Do not change the order when answering respectively.
Step 2
Why this answer is correct
The correct answer is A. (46) और (-6) / (46) and (-6). The common difference is (-6), and the next term is (52-6=46). Do not change the order when answering respectively.
Step 3
Exam Tip
सार्व अंतर (-6) है और अगला पद (52-6=46) है। क्रमशः में उत्तर का क्रम न बदलें।
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यदि (a=18) और (d=-5) है तो पहले तीन पदों का सही क्रम कौन सा है?
If (a=18) and (d=-5), which is the correct order of the first three terms?
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#negative difference
#medium
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A (18,23,28)
B (18,13,8)
C (13,8,3)
D (18,8,-2)
Explanation opens after your attempt
Correct Answer
B. (18,13,8)
Step 1
Concept
Adding (-5) each time gives (18,13,8). Understand negative difference as subtraction.
Step 2
Why this answer is correct
The correct answer is B. (18,13,8). Adding (-5) each time gives (18,13,8). Understand negative difference as subtraction.
Step 3
Exam Tip
हर बार (-5) जोड़ने पर (18,13,8) मिलता है। ऋणात्मक अंतर को घटाव की तरह समझें।
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अनुक्रम \(0,-4,-8,-12,\ldots\) में (a) और (d) क्रमशः क्या हैं?
In the sequence \(0,-4,-8,-12,\ldots\), what are (a) and (d) respectively?
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A (0) और (4) / (0) and (4)
B (-4) और (-4) / (-4) and (-4)
C (0) और (-4) / (0) and (-4)
D (-12) और (0) / (-12) and (0)
Explanation opens after your attempt
Correct Answer
C. (0) और (-4) / (0) and (-4)
Step 1
Concept
The first term is (0), and (d=-4-0=-4). Zero can also be the first term.
Step 2
Why this answer is correct
The correct answer is C. (0) और (-4) / (0) and (-4). The first term is (0), and (d=-4-0=-4). Zero can also be the first term.
Step 3
Exam Tip
पहला पद (0) है और (d=-4-0=-4) है। शून्य भी पहला पद हो सकता है।
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एक प्रशिक्षण कार्यक्रम में दौड़ की दूरी हर दिन (0.4) किमी बढ़ती है। दूरियां \(1.2,1.6,2.0,2.4,\ldots\) हैं तो तीसरे और पहले पद का अंतर क्या है?
In a training program, running distance increases by (0.4) km each day. The distances are \(1.2,1.6,2.0,2.4,\ldots\). What is the difference between the third and first terms?
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A (0.4)
B (0.6)
C (0.8)
D (1.2)
Explanation opens after your attempt
Step 1
Concept
The third term is (2.0) and the first is (1.2), so the difference is (0.8). It equals (2d).
Step 2
Why this answer is correct
The correct answer is C. (0.8). The third term is (2.0) and the first is (1.2), so the difference is (0.8). It equals (2d).
Step 3
Exam Tip
तीसरा पद (2.0) और पहला (1.2) है इसलिए अंतर (0.8) है। यह (2d) के बराबर है।
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यदि \(10,16,22,28,\ldots\) में प्रत्येक पद में (3) जोड़ दिया जाए तो नए अनुक्रम का (d) क्या होगा?
If (3) is added to each term of \(10,16,22,28,\ldots\), what will be (d) of the new sequence?
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A (3)
B (6)
C (9)
D (13)
Explanation opens after your attempt
Step 1
Concept
Adding the same (3) to each term does not change the difference, so (d=6). Equal change in all terms does not change (d).
Step 2
Why this answer is correct
The correct answer is B. (6). Adding the same (3) to each term does not change the difference, so (d=6). Equal change in all terms does not change (d).
Step 3
Exam Tip
हर पद में समान (3) जोड़ने से अंतर नहीं बदलता, इसलिए (d=6) रहेगा। सभी पदों में समान बदलाव (d) को नहीं बदलता।
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यदि किसी अंकगणितीय श्रेणी के पहले दो पद (-12) और (-7) हैं तो तीसरा पद क्या होगा?
If the first two terms of an arithmetic progression are (-12) and (-7), what will be the third term?
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A (-2)
B (-5)
C (2)
D (-17)
Explanation opens after your attempt
Step 1
Concept
The common difference is (-7-(-12)=5), so the third term is (-7+5=-2). Watch signs carefully with negative numbers.
Step 2
Why this answer is correct
The correct answer is A. (-2). The common difference is (-7-(-12)=5), so the third term is (-7+5=-2). Watch signs carefully with negative numbers.
Step 3
Exam Tip
सार्व अंतर (-7-(-12)=5) है इसलिए तीसरा पद (-7+5=-2) है। ऋणात्मक संख्याओं में चिह्न सावधानी से देखें।
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अनुक्रम \(3a,3a-4,3a-8,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(3a,3a-4,3a-8,\ldots\)?
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A (4)
B (3a)
C (-4)
D (3a-4)
Explanation opens after your attempt
Step 1
Concept
(d=(3a-4)-3a=-4). In a decreasing algebraic sequence (d) can be negative.
Step 2
Why this answer is correct
The correct answer is C. (-4). (d=(3a-4)-3a=-4). In a decreasing algebraic sequence (d) can be negative.
Step 3
Exam Tip
(d=(3a-4)-3a=-4) है। घटते बीजगणितीय अनुक्रम में (d) ऋणात्मक हो सकता है।
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यदि (13,b,31) अंकगणितीय श्रेणी के क्रमागत पद हैं तो (b) का मान क्या है?
If (13,b,31) are consecutive terms of an arithmetic progression, what is the value of (b)?
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A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
The middle term is \(b=\frac{13+31}{2}=22\). In three consecutive terms the middle term is the average.
Step 2
Why this answer is correct
The correct answer is C. (22). The middle term is \(b=\frac{13+31}{2}=22\). In three consecutive terms the middle term is the average.
Step 3
Exam Tip
मध्य पद \(b=\frac{13+31}{2}=22\) है। तीन क्रमागत पदों में बीच वाला पद औसत होता है।
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किस अनुक्रम में \(d=\frac{3}{4}\) है?
Which sequence has \(d=\frac{3}{4}\)?
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#identify sequence
#medium
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A \(\frac{1}{4},1,\frac{7}{4},\frac{5}{2},\ldots\)
B \(1,\frac{5}{4},\frac{3}{2},\frac{7}{4},\ldots\)
C \(\frac{3}{4},1,\frac{5}{4},\frac{3}{2},\ldots\)
D \(2,\frac{5}{2},3,\frac{7}{2},\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{4},1,\frac{7}{4},\frac{5}{2},\ldots\)
Step 1
Concept
In \(\frac{1}{4},1,\frac{7}{4},\frac{5}{2},\ldots\), every difference is \(\frac{3}{4}\). Check fractions using common denominators.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{4},1,\frac{7}{4},\frac{5}{2},\ldots\). In \(\frac{1}{4},1,\frac{7}{4},\frac{5}{2},\ldots\), every difference is \(\frac{3}{4}\). Check fractions using common denominators.
Step 3
Exam Tip
\(\frac{1}{4},1,\frac{7}{4},\frac{5}{2},\ldots\) में हर अंतर \(\frac{3}{4}\) है। भिन्नों में हर समान करके जांचें।
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यदि (a=5) और दूसरा पद (17) है तो (d) क्या है?
If (a=5) and the second term is (17), what is (d)?
#ap
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#medium
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A (22)
B (17)
C (12)
D (5)
Explanation opens after your attempt
Step 1
Concept
(d=17-5=12). Find the common difference by subtracting the first term from the second term.
Step 2
Why this answer is correct
The correct answer is C. (12). (d=17-5=12). Find the common difference by subtracting the first term from the second term.
Step 3
Exam Tip
(d=17-5=12) है। दूसरे पद में से पहले पद को घटाकर सार्व अंतर पाएं।
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अनुक्रम \(2.2,3.1,4.0,4.9,\ldots\) में (d) क्या है?
What is (d) in the sequence \(2.2,3.1,4.0,4.9,\ldots\)?
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#medium
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A (0.7)
B (0.8)
C (0.9)
D (1.1)
Explanation opens after your attempt
Step 1
Concept
(d=3.1-2.2=0.9), and the same difference continues. Keep place value carefully in decimal subtraction.
Step 2
Why this answer is correct
The correct answer is C. (0.9). (d=3.1-2.2=0.9), and the same difference continues. Keep place value carefully in decimal subtraction.
Step 3
Exam Tip
(d=3.1-2.2=0.9) है और आगे भी यही अंतर है। दशमलव घटाव में स्थान मान सावधानी से रखें।
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यदि \(28,21,14,7,\ldots\) में (d) ज्ञात करना हो तो सही गणना कौन सी है?
If (d) is to be found in \(28,21,14,7,\ldots\), which calculation is correct?
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#negative d
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A (28-21=7)
B (28+21=49)
C (21-28=-7)
D \(28\times21=588\)
Explanation opens after your attempt
Correct Answer
C. (21-28=-7)
Step 1
Concept
The common difference is next term minus previous term, so (21-28=-7). In a decreasing sequence the order of subtraction is very important.
Step 2
Why this answer is correct
The correct answer is C. (21-28=-7). The common difference is next term minus previous term, so (21-28=-7). In a decreasing sequence the order of subtraction is very important.
Step 3
Exam Tip
सार्व अंतर अगला पद घटा पिछला पद है इसलिए (21-28=-7)। घटते अनुक्रम में घटाव का क्रम बहुत जरूरी है।
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एक अंकगणितीय श्रेणी में (d=9) है और दूसरा पद (20) है। पहला पद क्या होगा?
In an arithmetic progression, (d=9) and the second term is (20). What is the first term?
#ap
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#medium
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A (9)
B (11)
C (20)
D (29)
Explanation opens after your attempt
Step 1
Concept
The first term is (20-9=11). Subtract (d) from the second term to get the first term.
Step 2
Why this answer is correct
The correct answer is B. (11). The first term is (20-9=11). Subtract (d) from the second term to get the first term.
Step 3
Exam Tip
पहला पद (20-9=11) है। दूसरे पद से (d) घटाकर पहला पद मिलता है।
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यदि अंकगणितीय श्रेणी \(3,8,13,18,\ldots\) के प्रत्येक पद को (2) से गुणा किया जाए तो नए अनुक्रम का सार्व अंतर क्या होगा?
If each term of the arithmetic progression \(3,8,13,18,\ldots\) is multiplied by (2), what will be the common difference of the new sequence?
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#transformation
#medium
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A (5)
B (8)
C (10)
D (16)
Explanation opens after your attempt
Step 1
Concept
The original common difference is (5), and after multiplying by (2), the new common difference becomes (10). When all terms are multiplied by the same number, (d) is also multiplied by it.
Step 2
Why this answer is correct
The correct answer is C. (10). The original common difference is (5), and after multiplying by (2), the new common difference becomes (10). When all terms are multiplied by the same number, (d) is also multiplied by it.
Step 3
Exam Tip
मूल सार्व अंतर (5) है और (2) से गुणा करने पर नया सार्व अंतर (10) होगा। सभी पदों को समान संख्या से गुणा करने पर (d) भी उसी से गुणा होता है।
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अनुक्रम \(6,12,18,24,\ldots\) को उलटे क्रम में लिखने पर नए अनुक्रम का (d) क्या होगा?
If the sequence \(6,12,18,24,\ldots\) is written in reverse order, what will be (d) of the new sequence?
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#negative difference
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A (6)
B (-6)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
The reverse order is \(24,18,12,6,\ldots\), and (d=18-24=-6). When the order is reversed, the sign of the common difference changes.
Step 2
Why this answer is correct
The correct answer is B. (-6). The reverse order is \(24,18,12,6,\ldots\), and (d=18-24=-6). When the order is reversed, the sign of the common difference changes.
Step 3
Exam Tip
उलटा क्रम \(24,18,12,6,\ldots\) होगा और (d=18-24=-6) है। क्रम उलटने पर सार्व अंतर का चिह्न बदल जाता है।
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यदि (5,x,y,20) अंकगणितीय श्रेणी के क्रमागत पद हैं तो (x) और (y) के मान क्या होंगे?
If (5,x,y,20) are consecutive terms of an arithmetic progression, what will be the values of (x) and (y)?
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#equal gaps
#medium
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A (x=8,y=14)
B (x=10,y=15)
C (x=12,y=16)
D (x=15,y=10)
Explanation opens after your attempt
Correct Answer
B. (x=10,y=15)
Step 1
Concept
There are three equal gaps from (5) to (20), so \(d=\frac{20-5}{3}=5\), hence (x=10) and (y=15). Find missing terms by splitting the total difference into equal gaps.
Step 2
Why this answer is correct
The correct answer is B. (x=10,y=15). There are three equal gaps from (5) to (20), so \(d=\frac{20-5}{3}=5\), hence (x=10) and (y=15). Find missing terms by splitting the total difference into equal gaps.
Step 3
Exam Tip
(5) से (20) तक तीन समान अंतर हैं इसलिए \(d=\frac{20-5}{3}=5\), अतः (x=10) और (y=15)। दो पदों के बीच समान अंतर बांटकर खाली पद निकालें।
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