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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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A (6)
B (12)
C (18)
D (24)
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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 \(5m,5m-4,5m-8,5m-12,\ldots\)?
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#algebraic-ap
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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)?
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#common-difference-check
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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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