किसी सूची में क्रमागत पदों का अंतर समान हो तो उस सूची को क्या कहते हैं?
What is a list called when the difference between consecutive terms is constant?
#arithmetic progression
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A अंकगणितीय श्रेणी / Arithmetic progression
B ज्यामितीय श्रेणी / Geometric progression
C समुच्चय / Set
D समीकरण / Equation
Explanation opens after your attempt
Correct Answer
A. अंकगणितीय श्रेणी / Arithmetic progression
Step 1
Concept
A constant difference between consecutive terms is the key sign of an arithmetic progression. In exams first check the differences.
Step 2
Why this answer is correct
The correct answer is A. अंकगणितीय श्रेणी / Arithmetic progression. A constant difference between consecutive terms is the key sign of an arithmetic progression. In exams first check the differences.
Step 3
Exam Tip
क्रमागत पदों का समान अंतर अंकगणितीय श्रेणी की मुख्य पहचान है। परीक्षा में पहले अंतर जांचें।
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अनुक्रम \(5,9,13,17,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(5,9,13,17,\ldots\)?
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Here (9-5=4) and (13-9=4). In exams subtract any two consecutive terms.
Step 2
Why this answer is correct
The correct answer is C. (4). Here (9-5=4) and (13-9=4). In exams subtract any two consecutive terms.
Step 3
Exam Tip
यहां (9-5=4) और (13-9=4) है। परीक्षा में किसी भी दो क्रमागत पदों को घटाएं।
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अनुक्रम \(12,10,8,6,\ldots\) का सार्व अंतर क्या है?
What is the common difference of the sequence \(12,10,8,6,\ldots\)?
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A (2)
B (-2)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The common difference is (10-12=-2). A decreasing progression can have a negative difference.
Step 2
Why this answer is correct
The correct answer is B. (-2). The common difference is (10-12=-2). A decreasing progression can have a negative difference.
Step 3
Exam Tip
सार्व अंतर (10-12=-2) है। घटती श्रेणी में अंतर ऋणात्मक हो सकता है।
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क्या \(3,6,9,12,\ldots\) एक अंकगणितीय श्रेणी है?
Is \(3,6,9,12,\ldots\) an arithmetic progression?
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A नहीं क्योंकि पद घट रहे हैं / No because terms decrease
B हां क्योंकि सार्व अंतर (3) है / Yes because common difference is (3)
C नहीं क्योंकि पहला पद (3) है / No because first term is (3)
D हां क्योंकि सभी पद विषम हैं / Yes because all terms are odd
Explanation opens after your attempt
Correct Answer
B. हां क्योंकि सार्व अंतर (3) है / Yes because common difference is (3)
Step 1
Concept
Each time (3) is added so it is an arithmetic progression. Equal difference is the main test.
Step 2
Why this answer is correct
The correct answer is B. हां क्योंकि सार्व अंतर (3) है / Yes because common difference is (3). Each time (3) is added so it is an arithmetic progression. Equal difference is the main test.
Step 3
Exam Tip
हर बार (3) जोड़ा जा रहा है इसलिए यह अंकगणितीय श्रेणी है। समान अंतर ही मुख्य कसौटी है।
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अनुक्रम \(2,5,10,17,\ldots\) के बारे में सही कथन कौन सा है?
Which statement is correct about the sequence \(2,5,10,17,\ldots\)?
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A यह अंकगणितीय श्रेणी है / It is an arithmetic progression
B इसका सार्व अंतर (5) है / Its common difference is (5)
C यह अंकगणितीय श्रेणी नहीं है / It is not an arithmetic progression
D इसका पहला पद (5) है / Its first term is (5)
Explanation opens after your attempt
Correct Answer
C. यह अंकगणितीय श्रेणी नहीं है / It is not an arithmetic progression
Step 1
Concept
The differences are (3,5,7) which are not equal. In exams check differences not only terms.
Step 2
Why this answer is correct
The correct answer is C. यह अंकगणितीय श्रेणी नहीं है / It is not an arithmetic progression. The differences are (3,5,7) which are not equal. In exams check differences not only terms.
Step 3
Exam Tip
अंतर (3,5,7) हैं जो समान नहीं हैं। परीक्षा में केवल पद नहीं बल्कि उनके अंतर देखें।
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यदि किसी अंकगणितीय श्रेणी का पहला पद (7) और सार्व अंतर (2) है तो दूसरा पद क्या होगा?
If the first term of an arithmetic progression is (7) and the common difference is (2), what is the second term?
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A (5)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The second term is (7+2=9). Add the common difference to get the next term.
Step 2
Why this answer is correct
The correct answer is D. (9). The second term is (7+2=9). Add the common difference to get the next term.
Step 3
Exam Tip
दूसरा पद (7+2=9) होगा। अगला पद पाने के लिए सार्व अंतर जोड़ें।
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अनुक्रम \(20,15,10,5,\ldots\) में पहला पद और सार्व अंतर क्रमशः क्या हैं?
In the sequence \(20,15,10,5,\ldots\), what are the first term and common difference respectively?
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A (20) और (-5) / (20) and (-5)
B (15) और (5) / (15) and (5)
C (20) और (5) / (20) and (5)
D (5) और (-5) / (5) and (-5)
Explanation opens after your attempt
Correct Answer
A. (20) और (-5) / (20) and (-5)
Step 1
Concept
The first term is (20) and (15-20=-5). When asked respectively keep the order in mind.
Step 2
Why this answer is correct
The correct answer is A. (20) और (-5) / (20) and (-5). The first term is (20) and (15-20=-5). When asked respectively keep the order in mind.
Step 3
Exam Tip
पहला पद (20) है और (15-20=-5) है। क्रमशः पूछे जाने पर क्रम का ध्यान रखें।
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यदि (a=4) और (d=6) है तो अंकगणितीय श्रेणी के पहले तीन पद कौन से हैं?
If (a=4) and (d=6), what are the first three terms of the arithmetic progression?
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A (4,8,12)
B (4,10,16)
C (6,10,14)
D (10,16,22)
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Correct Answer
B. (4,10,16)
Step 1
Concept
The first three terms are (4,4+6,4+12). Add (d) each time while forming terms.
Step 2
Why this answer is correct
The correct answer is B. (4,10,16). The first three terms are (4,4+6,4+12). Add (d) each time while forming terms.
Step 3
Exam Tip
पहले तीन पद (4,4+6,4+12) हैं। पद बनाते समय हर बार (d) जोड़ें।
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अनुक्रम \(1,4,7,10,\ldots\) में कौन सा पद अगला होगा?
What will be the next term in the sequence \(1,4,7,10,\ldots\)?
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A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
The common difference is (3), so the next term is (10+3=13). The next term is found by adding (d) to the previous term.
Step 2
Why this answer is correct
The correct answer is C. (13). The common difference is (3), so the next term is (10+3=13). The next term is found by adding (d) to the previous term.
Step 3
Exam Tip
सार्व अंतर (3) है इसलिए अगला पद (10+3=13) होगा। अगला पद हमेशा पिछले पद में (d) जोड़कर मिलता है।
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अनुक्रम \(-3,0,3,6,\ldots\) का सार्व अंतर क्या है?
What is the common difference of the sequence \(-3,0,3,6,\ldots\)?
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A (6)
B (-3)
C (3)
D (0)
Explanation opens after your attempt
Step 1
Concept
The common difference is (0-(-3)=3). Be careful while subtracting negative terms.
Step 2
Why this answer is correct
The correct answer is C. (3). The common difference is (0-(-3)=3). Be careful while subtracting negative terms.
Step 3
Exam Tip
सार्व अंतर (0-(-3)=3) है। ऋणात्मक पदों में घटाव सावधानी से करें।
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यदि सार्व अंतर (0) हो तो अंकगणितीय श्रेणी कैसी होती है?
If the common difference is (0), what type of arithmetic progression is formed?
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A सभी पद समान होते हैं / All terms are equal
B सभी पद शून्य होते हैं / All terms are zero
C सभी पद ऋणात्मक होते हैं / All terms are negative
D सभी पद भिन्न होते हैं / All terms are different
Explanation opens after your attempt
Correct Answer
A. सभी पद समान होते हैं / All terms are equal
Step 1
Concept
When (d=0), each next term remains the same. This can also be an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. सभी पद समान होते हैं / All terms are equal. When (d=0), each next term remains the same. This can also be an arithmetic progression.
Step 3
Exam Tip
(d=0) होने पर प्रत्येक अगला पद पहले जैसा रहता है। यह भी अंकगणितीय श्रेणी हो सकती है।
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अनुक्रम \(8,8,8,8,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(8,8,8,8,\ldots\)?
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A (8)
B (0)
C (1)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The common difference is (8-8=0). A sequence with equal terms has difference (0).
Step 2
Why this answer is correct
The correct answer is B. (0). The common difference is (8-8=0). A sequence with equal terms has difference (0).
Step 3
Exam Tip
सार्व अंतर (8-8=0) है। समान पदों वाली श्रेणी में अंतर (0) होता है।
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एक अंकगणितीय श्रेणी में (d) किसे दर्शाता है?
In an arithmetic progression, what does (d) represent?
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A अंतिम पद / Last term
B पदों की संख्या / Number of terms
C सार्व अंतर / Common difference
D पहला पद / First term
Explanation opens after your attempt
Correct Answer
C. सार्व अंतर / Common difference
Step 1
Concept
(d) represents the common difference. In exams identify (a) and (d) separately.
Step 2
Why this answer is correct
The correct answer is C. सार्व अंतर / Common difference. (d) represents the common difference. In exams identify (a) and (d) separately.
Step 3
Exam Tip
(d) सार्व अंतर को दर्शाता है। परीक्षा में (a) और (d) की पहचान अलग रखें।
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एक अंकगणितीय श्रेणी में (a) सामान्यतः किसे दर्शाता है?
In an arithmetic progression, what does (a) usually represent?
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A सार्व अंतर / Common difference
B दूसरा पद / Second term
C अंतिम पद / Last term
D पहला पद / First term
Explanation opens after your attempt
Correct Answer
D. पहला पद / First term
Step 1
Concept
(a) usually represents the first term. Identify (a) and (d) before using formulas.
Step 2
Why this answer is correct
The correct answer is D. पहला पद / First term. (a) usually represents the first term. Identify (a) and (d) before using formulas.
Step 3
Exam Tip
(a) सामान्यतः पहला पद होता है। सूत्र लगाने से पहले (a) और (d) पहचानें।
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अनुक्रम \(4,7,10,13,\ldots\) में (d) का मान क्या है?
What is the value of (d) in the sequence \(4,7,10,13,\ldots\)?
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A (3)
B (4)
C (7)
D (10)
Explanation opens after your attempt
Step 1
Concept
Here (d=7-4=3). Find (d) by subtracting the first term from the second term.
Step 2
Why this answer is correct
The correct answer is A. (3). Here (d=7-4=3). Find (d) by subtracting the first term from the second term.
Step 3
Exam Tip
यहां (d=7-4=3) है। (d) हमेशा दूसरा पद घटा पहला पद से निकालें।
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अनुक्रम \(11,14,17,20,\ldots\) में (a) का मान क्या है?
What is the value of (a) in the sequence \(11,14,17,20,\ldots\)?
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A (3)
B (11)
C (14)
D (20)
Explanation opens after your attempt
Step 1
Concept
The first term is (11), so (a=11). For (a), look at the first term of the list.
Step 2
Why this answer is correct
The correct answer is B. (11). The first term is (11), so (a=11). For (a), look at the first term of the list.
Step 3
Exam Tip
पहला पद (11) है इसलिए (a=11) है। (a) के लिए सूची का पहला पद देखें।
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अनुक्रम \(6,12,18,24,\ldots\) में चौथा पद क्या है?
What is the fourth term in the sequence \(6,12,18,24,\ldots\)?
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A (12)
B (18)
C (24)
D (30)
Explanation opens after your attempt
Step 1
Concept
The fourth term in the given terms is (24). Start counting from (6) as the first term.
Step 2
Why this answer is correct
The correct answer is C. (24). The fourth term in the given terms is (24). Start counting from (6) as the first term.
Step 3
Exam Tip
दिए गए पदों में चौथा पद (24) है। क्रम गिनते समय पहला पद (6) से शुरू करें।
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अनुक्रम \(9,7,5,3,\ldots\) में तीसरा पद क्या है?
What is the third term in the sequence \(9,7,5,3,\ldots\)?
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A (9)
B (7)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
The terms are (9,7,5,3), so the third term is (5). Do not rush while counting term positions.
Step 2
Why this answer is correct
The correct answer is D. (5). The terms are (9,7,5,3), so the third term is (5). Do not rush while counting term positions.
Step 3
Exam Tip
पद क्रम से (9,7,5,3) हैं इसलिए तीसरा पद (5) है। पद संख्या गिनने में जल्दबाजी न करें।
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यदि किसी अंकगणितीय श्रेणी में (a=10) और (d=-1) है तो पहले चार पद कौन से हैं?
If an arithmetic progression has (a=10) and (d=-1), what are the first four terms?
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A (10,9,8,7)
B (10,11,12,13)
C (9,8,7,6)
D (10,8,6,4)
Explanation opens after your attempt
Correct Answer
A. (10,9,8,7)
Step 1
Concept
Adding (-1) each time gives (10,9,8,7). Negative (d) means the terms decrease.
Step 2
Why this answer is correct
The correct answer is A. (10,9,8,7). Adding (-1) each time gives (10,9,8,7). Negative (d) means the terms decrease.
Step 3
Exam Tip
हर बार (-1) जोड़ने पर (10,9,8,7) मिलता है। ऋणात्मक (d) का अर्थ घटते पद हैं।
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निम्न में से किस अनुक्रम का सार्व अंतर (7) है?
Which of the following sequences has common difference (7)?
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A \(4,9,14,19,\ldots\)
B \(2,9,16,23,\ldots\)
C \(7,14,28,35,\ldots\)
D \(1,8,14,21,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(2,9,16,23,\ldots\)
Step 1
Concept
(9-2=7), (16-9=7), and (23-16=7). All consecutive differences must be equal.
Step 2
Why this answer is correct
The correct answer is B. \(2,9,16,23,\ldots\). (9-2=7), (16-9=7), and (23-16=7). All consecutive differences must be equal.
Step 3
Exam Tip
(9-2=7), (16-9=7) और (23-16=7) हैं। सभी क्रमागत अंतर समान होने चाहिए।
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अनुक्रम \(100,90,80,70,\ldots\) में सार्व अंतर कितना है?
What is the common difference in the sequence \(100,90,80,70,\ldots\)?
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A (10)
B (90)
C (-10)
D (-90)
Explanation opens after your attempt
Step 1
Concept
The common difference is (90-100=-10). In a decreasing sequence carefully check the sign.
Step 2
Why this answer is correct
The correct answer is C. (-10). The common difference is (90-100=-10). In a decreasing sequence carefully check the sign.
Step 3
Exam Tip
सार्व अंतर (90-100=-10) है। घटते अनुक्रम में उत्तर का चिह्न जरूर देखें।
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कौन सा कथन अंकगणितीय श्रेणी के लिए सही है?
Which statement is true for an arithmetic progression?
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A हर पद पिछले पद से गुणा करके मिलता है / Each term is obtained by multiplying the previous term
B हर पद पिछले पद से भाग देकर मिलता है / Each term is obtained by dividing the previous term
C पदों का योग हमेशा (0) होता है / Sum of terms is always (0)
D हर अगला पद पिछले पद में समान संख्या जोड़कर मिलता है / Each next term is obtained by adding the same number to the previous term
Explanation opens after your attempt
Correct Answer
D. हर अगला पद पिछले पद में समान संख्या जोड़कर मिलता है / Each next term is obtained by adding the same number to the previous term
Step 1
Concept
In an arithmetic progression the same number is added. This number is called the common difference.
Step 2
Why this answer is correct
The correct answer is D. हर अगला पद पिछले पद में समान संख्या जोड़कर मिलता है / Each next term is obtained by adding the same number to the previous term. In an arithmetic progression the same number is added. This number is called the common difference.
Step 3
Exam Tip
अंकगणितीय श्रेणी में समान संख्या जोड़ी जाती है। यही संख्या सार्व अंतर कहलाती है।
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अनुक्रम \(15,18,21,24,\ldots\) में (a) और (d) क्रमशः क्या हैं?
In the sequence \(15,18,21,24,\ldots\), what are (a) and (d) respectively?
#ap
#first term
#common difference
#easy
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A (15) और (3) / (15) and (3)
B (18) और (3) / (18) and (3)
C (15) और (18) / (15) and (18)
D (3) और (15) / (3) and (15)
Explanation opens after your attempt
Correct Answer
A. (15) और (3) / (15) and (3)
Step 1
Concept
The first term is (15) and (18-15=3). Respectively means answer in the same order.
Step 2
Why this answer is correct
The correct answer is A. (15) और (3) / (15) and (3). The first term is (15) and (18-15=3). Respectively means answer in the same order.
Step 3
Exam Tip
पहला पद (15) है और (18-15=3) है। क्रमशः का अर्थ उसी क्रम में उत्तर देना है।
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अनुक्रम \(0,5,10,15,\ldots\) में अगला पद क्या है?
What is the next term in the sequence \(0,5,10,15,\ldots\)?
#ap
#next term
#zero first term
#class ten
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A (16)
B (20)
C (25)
D (30)
Explanation opens after your attempt
Step 1
Concept
The common difference is (5), so (15+5=20). Zero can be the first term.
Step 2
Why this answer is correct
The correct answer is B. (20). The common difference is (5), so (15+5=20). Zero can be the first term.
Step 3
Exam Tip
सार्व अंतर (5) है इसलिए (15+5=20) होगा। शून्य पहला पद हो सकता है।
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अनुक्रम \(1,3,6,10,\ldots\) अंकगणितीय श्रेणी क्यों नहीं है?
Why is \(1,3,6,10,\ldots\) not an arithmetic progression?
#ap
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#common difference
#easy
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A क्योंकि पहला पद (1) है / Because the first term is (1)
B क्योंकि पद बढ़ रहे हैं / Because terms are increasing
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 (2,3,4), which are not equal. Increasing terms alone do not make an arithmetic progression.
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 (2,3,4), which are not equal. Increasing terms alone do not make an arithmetic progression.
Step 3
Exam Tip
अंतर (2,3,4) हैं जो समान नहीं हैं। बढ़ते पद होने से ही अंकगणितीय श्रेणी नहीं बनती।
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यदि (a=2) और पहला अगला पद (5) है तो (d) क्या है?
If (a=2) and the next term is (5), what is (d)?
#ap
#find d
#two terms
#class ten
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A (2)
B (5)
C (7)
D (3)
Explanation opens after your attempt
Step 1
Concept
The common difference is (5-2=3). Subtract the first term from the second term.
Step 2
Why this answer is correct
The correct answer is D. (3). The common difference is (5-2=3). Subtract the first term from the second term.
Step 3
Exam Tip
सार्व अंतर (5-2=3) है। दूसरे पद में से पहले पद को घटाएं।
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निम्न में से कौन सा अनुक्रम घटती अंकगणितीय श्रेणी है?
Which of the following is a decreasing arithmetic progression?
#ap
#decreasing ap
#negative difference
#easy
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A \(50,45,40,35,\ldots\)
B \(2,4,8,16,\ldots\)
C \(5,5,5,5,\ldots\)
D \(1,4,9,16,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(50,45,40,35,\ldots\)
Step 1
Concept
In \(50,45,40,35,\ldots\), the equal difference is (-5). A decreasing arithmetic progression has negative (d).
Step 2
Why this answer is correct
The correct answer is A. \(50,45,40,35,\ldots\). In \(50,45,40,35,\ldots\), the equal difference is (-5). A decreasing arithmetic progression has negative (d).
Step 3
Exam Tip
\(50,45,40,35,\ldots\) में समान अंतर (-5) है। घटती अंकगणितीय श्रेणी का (d) ऋणात्मक होता है।
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अनुक्रम \(2.5,3.0,3.5,4.0,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(2.5,3.0,3.5,4.0,\ldots\)?
#ap
#decimal terms
#common difference
#class ten
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A (1.5)
B (0.5)
C (2.5)
D (3.0)
Explanation opens after your attempt
Step 1
Concept
The common difference is (3.0-2.5=0.5). The same rule applies to decimal terms.
Step 2
Why this answer is correct
The correct answer is B. (0.5). The common difference is (3.0-2.5=0.5). The same rule applies to decimal terms.
Step 3
Exam Tip
सार्व अंतर (3.0-2.5=0.5) है। दशमलव पदों में भी वही नियम लागू होता है।
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अनुक्रम \(\frac{1}{2},1,\frac{3}{2},2,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(\frac{1}{2},1,\frac{3}{2},2,\ldots\)?
#ap
#fractions
#common difference
#easy
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A \(\frac{1}{4}\)
B (1)
C \(\frac{1}{2}\)
D (2)
Explanation opens after your attempt
Correct Answer
C. \(\frac{1}{2}\)
Step 1
Concept
The common difference is \(1-\frac{1}{2}=\frac{1}{2}\). For fractions also subtract consecutive terms.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{1}{2}\). The common difference is \(1-\frac{1}{2}=\frac{1}{2}\). For fractions also subtract consecutive terms.
Step 3
Exam Tip
सार्व अंतर \(1-\frac{1}{2}=\frac{1}{2}\) है। भिन्नों में भी क्रमागत पद घटाएं।
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किसी अंकगणितीय श्रेणी \(a,a+d,a+2d,\ldots\) में दूसरा पद कौन सा है?
In an arithmetic progression \(a,a+d,a+2d,\ldots\), which is the second term?
#ap
#general form
#second term
#class ten
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A (a)
B (d)
C (a+2d)
D (a+d)
Explanation opens after your attempt
Step 1
Concept
The second term is (a+d). Remember the order of terms in the general form.
Step 2
Why this answer is correct
The correct answer is D. (a+d). The second term is (a+d). Remember the order of terms in the general form.
Step 3
Exam Tip
दूसरा पद (a+d) होता है। सामान्य रूप में पदों का क्रम याद रखें।
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किसी अंकगणितीय श्रेणी \(a,a+d,a+2d,\ldots\) में तीसरा पद कौन सा है?
In an arithmetic progression \(a,a+d,a+2d,\ldots\), which is the third term?
#ap
#general form
#third term
#easy
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A (a+2d)
B (a+d)
C (2a+d)
D (ad)
Explanation opens after your attempt
Step 1
Concept
The third term is (a+2d). As the term number increases the coefficient of (d) increases.
Step 2
Why this answer is correct
The correct answer is A. (a+2d). The third term is (a+2d). As the term number increases the coefficient of (d) increases.
Step 3
Exam Tip
तीसरा पद (a+2d) है। पद संख्या बढ़ने पर (d) का गुणांक बढ़ता है।
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एक अंकगणितीय श्रेणी \(4,4.5,5,5.5,\ldots\) में अगला पद क्या होगा?
What is the next term in the arithmetic progression \(4,4.5,5,5.5,\ldots\)?
#ap
#next term
#decimal ap
#class ten
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A (5.75)
B (6)
C (6.5)
D (7)
Explanation opens after your attempt
Step 1
Concept
The common difference is (0.5), so (5.5+0.5=6). Add decimals carefully.
Step 2
Why this answer is correct
The correct answer is B. (6). The common difference is (0.5), so (5.5+0.5=6). Add decimals carefully.
Step 3
Exam Tip
सार्व अंतर (0.5) है इसलिए (5.5+0.5=6) होगा। दशमलव में जोड़ सावधानी से करें।
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अनुक्रम \(3,3,3,3,\ldots\) के बारे में सही कथन क्या है?
Which statement is correct about the sequence \(3,3,3,3,\ldots\)?
#ap
#constant ap
#zero difference
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A यह अंकगणितीय श्रेणी नहीं है / It is not an arithmetic progression
B यह अंकगणितीय श्रेणी है और (d=0) है / It is an arithmetic progression and (d=0)
C इसका (d=3) है / Its (d=3)
D इसका (a=0) है / Its (a=0)
Explanation opens after your attempt
Correct Answer
B. यह अंकगणितीय श्रेणी है और (d=0) है / It is an arithmetic progression and (d=0)
Step 1
Concept
All terms are equal, so the common difference is (0). A constant sequence is also an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is B. यह अंकगणितीय श्रेणी है और (d=0) है / It is an arithmetic progression and (d=0). All terms are equal, so the common difference is (0). A constant sequence is also an arithmetic progression.
Step 3
Exam Tip
सभी पद समान हैं इसलिए सार्व अंतर (0) है। स्थिर अनुक्रम भी अंकगणितीय श्रेणी होता है।
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अनुक्रम \(14,11,8,5,\ldots\) में (d) का मान क्या है?
What is the value of (d) in the sequence \(14,11,8,5,\ldots\)?
#ap
#value of d
#negative common difference
#class ten
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A (3)
B (-6)
C (-3)
D (14)
Explanation opens after your attempt
Step 1
Concept
(d=11-14=-3). The negative sign is an important part of the answer.
Step 2
Why this answer is correct
The correct answer is C. (-3). (d=11-14=-3). The negative sign is an important part of the answer.
Step 3
Exam Tip
(d=11-14=-3) है। ऋण चिह्न उत्तर का जरूरी भाग है।
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एक सीढ़ी पर हर अगला डंडा पिछले से (6) सेमी ऊंचा है। ऊंचाइयां \(10,16,22,28,\ldots\) हैं तो यह क्या बनाती हैं?
On a ladder, each next rung is (6) cm higher than the previous one. The heights are \(10,16,22,28,\ldots\). What do they form?
#ap
#word problem
#equal increase
#class ten
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A ज्यामितीय श्रेणी / Geometric progression
B साधारण सूची / Simple list
C कोई अनुक्रम नहीं / No sequence
D अंकगणितीय श्रेणी / Arithmetic progression
Explanation opens after your attempt
Correct Answer
D. अंकगणितीय श्रेणी / Arithmetic progression
Step 1
Concept
There is an equal increase of (6) each time, so it is an arithmetic progression. In word problems look for equal increase.
Step 2
Why this answer is correct
The correct answer is D. अंकगणितीय श्रेणी / Arithmetic progression. There is an equal increase of (6) each time, so it is an arithmetic progression. In word problems look for equal increase.
Step 3
Exam Tip
हर बार (6) की समान वृद्धि है इसलिए यह अंकगणितीय श्रेणी है। शब्द प्रश्न में समान वृद्धि खोजें।
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यदि बचत राशि हर सप्ताह (50) रुपये बढ़ती है और राशियां \(100,150,200,250,\ldots\) हैं तो सार्व अंतर क्या है?
If savings increase by (50) rupees every week and the amounts are \(100,150,200,250,\ldots\), what is the common difference?
#ap
#word problem
#savings
#common difference
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A (50)
B (100)
C (150)
D (250)
Explanation opens after your attempt
Step 1
Concept
The consecutive difference is (150-100=50). In real-life questions the equal increase is (d).
Step 2
Why this answer is correct
The correct answer is A. (50). The consecutive difference is (150-100=50). In real-life questions the equal increase is (d).
Step 3
Exam Tip
क्रमागत अंतर (150-100=50) है। वास्तविक जीवन के प्रश्नों में समान बढ़ोतरी ही (d) होती है।
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एक पौधे की ऊंचाई हर दिन (2) सेमी बढ़ती है। ऊंचाइयां \(12,14,16,18,\ldots\) हैं तो चौथे दिन की ऊंचाई क्या है?
A plant grows (2) cm every day. The heights are \(12,14,16,18,\ldots\). What is the height on the fourth day?
#ap
#word problem
#term position
#easy
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A (12) सेमी / (12) cm
B (14) सेमी / (14) cm
C (18) सेमी / (18) cm
D (20) सेमी / (20) cm
Explanation opens after your attempt
Correct Answer
C. (18) सेमी / (18) cm
Step 1
Concept
The fourth term in the list is (18). Count the day and term position together.
Step 2
Why this answer is correct
The correct answer is C. (18) सेमी / (18) cm. The fourth term in the list is (18). Count the day and term position together.
Step 3
Exam Tip
सूची में चौथा पद (18) है। दिन और पद संख्या को साथ मिलाकर गिनें।
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यदि टिकटों की कीमतें \(40,45,50,55,\ldots\) हैं तो कीमतों का सार्व अंतर क्या है?
If ticket prices are \(40,45,50,55,\ldots\), what is the common difference of the prices?
#ap
#word problem
#price
#common difference
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A (40)
B (45)
C (10)
D (5)
Explanation opens after your attempt
Step 1
Concept
(45-40=5), and the same difference continues. The equal increase in prices is (d).
Step 2
Why this answer is correct
The correct answer is D. (5). (45-40=5), and the same difference continues. The equal increase in prices is (d).
Step 3
Exam Tip
(45-40=5) है और आगे भी यही अंतर है। कीमतों में समान वृद्धि (d) होती है।
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अनुक्रम \(6,10,14,18,\ldots\) में दूसरा और तीसरा पद का अंतर क्या है?
What is the difference between the second and third terms in \(6,10,14,18,\ldots\)?
#ap
#term difference
#common difference
#class ten
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A (4)
B (6)
C (10)
D (14)
Explanation opens after your attempt
Step 1
Concept
The second term is (10) and the third term is (14), so the difference is (14-10=4). It equals (d).
Step 2
Why this answer is correct
The correct answer is A. (4). The second term is (10) and the third term is (14), so the difference is (14-10=4). It equals (d).
Step 3
Exam Tip
दूसरा पद (10) और तीसरा पद (14) है इसलिए अंतर (14-10=4) है। यह (d) के बराबर है।
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कौन सा अनुक्रम (d=-4) वाली अंकगणितीय श्रेणी है?
Which sequence is an arithmetic progression with (d=-4)?
#ap
#negative d
#identify sequence
#easy
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A \(1,5,9,13,\ldots\)
B \(18,14,10,6,\ldots\)
C \(4,0,-8,-12,\ldots\)
D \(20,16,13,9,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(18,14,10,6,\ldots\)
Step 1
Concept
(14-18=-4), (10-14=-4), and (6-10=-4). All differences must be (-4).
Step 2
Why this answer is correct
The correct answer is B. \(18,14,10,6,\ldots\). (14-18=-4), (10-14=-4), and (6-10=-4). All differences must be (-4).
Step 3
Exam Tip
(14-18=-4), (10-14=-4) और (6-10=-4) हैं। सभी अंतर (-4) होने चाहिए।
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यदि अनुक्रम \(x, x+5, x+10,\ldots\) है तो सार्व अंतर क्या है?
If the sequence is \(x, x+5, x+10,\ldots\), what is the common difference?
#ap
#algebraic sequence
#common difference
#class ten
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A (x)
B (10)
C (5)
D (x+5)
Explanation opens after your attempt
Step 1
Concept
The common difference is ((x+5)-x=5). For algebraic terms also subtract the first term from the second.
Step 2
Why this answer is correct
The correct answer is C. (5). The common difference is ((x+5)-x=5). For algebraic terms also subtract the first term from the second.
Step 3
Exam Tip
सार्व अंतर ((x+5)-x=5) है। अक्षर वाले पदों में भी दूसरा पद घटा पहला पद करें।
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अनुक्रम \(2p,2p+3,2p+6,\ldots\) में (d) क्या है?
What is (d) in the sequence \(2p,2p+3,2p+6,\ldots\)?
#ap
#algebraic terms
#common difference
#easy
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A (2p)
B (3)
C (6)
D (p)
Explanation opens after your attempt
Step 1
Concept
(d=(2p+3)-2p=3). The equal number added is the common difference.
Step 2
Why this answer is correct
The correct answer is B. (3). (d=(2p+3)-2p=3). The equal number added is the common difference.
Step 3
Exam Tip
(d=(2p+3)-2p=3) है। समान जोड़ी गई संख्या ही सार्व अंतर है।
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किस विकल्प में लगातार अंतर समान नहीं है?
In which option are the consecutive differences not equal?
#ap
#not an ap
#identify difference
#class ten
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A \(7,10,13,16,\ldots\)
B \(1,6,11,16,\ldots\)
C \(3,9,15,21,\ldots\)
D \(2,4,7,11,\ldots\)
Explanation opens after your attempt
Correct Answer
D. \(2,4,7,11,\ldots\)
Step 1
Concept
In \(2,4,7,11,\ldots\), the differences are (2,3,4). To identify an arithmetic progression all differences must be equal.
Step 2
Why this answer is correct
The correct answer is D. \(2,4,7,11,\ldots\). In \(2,4,7,11,\ldots\), the differences are (2,3,4). To identify an arithmetic progression all differences must be equal.
Step 3
Exam Tip
\(2,4,7,11,\ldots\) में अंतर (2,3,4) हैं। अंकगणितीय श्रेणी पहचानने के लिए सभी अंतर समान होने चाहिए।
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अनुक्रम \(-10,-7,-4,-1,\ldots\) में अगला पद क्या है?
What is the next term in the sequence \(-10,-7,-4,-1,\ldots\)?
#ap
#integers
#next term
#easy
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A (2)
B (1)
C (-2)
D (3)
Explanation opens after your attempt
Step 1
Concept
The common difference is (3), so (-1+3=2). Handle signs carefully when moving from negative to positive.
Step 2
Why this answer is correct
The correct answer is A. (2). The common difference is (3), so (-1+3=2). Handle signs carefully when moving from negative to positive.
Step 3
Exam Tip
सार्व अंतर (3) है इसलिए (-1+3=2) होगा। ऋणात्मक और धनात्मक में बदलते समय चिह्न संभालें।
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यदि (d=4) और पहला पद (1) है तो दूसरा पद क्या होगा?
If (d=4) and the first term is (1), what will be the second term?
#ap
#second term
#common difference
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A (3)
B (5)
C (4)
D (1)
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Step 1
Concept
The second term is (1+4=5). Add the common difference to the first term.
Step 2
Why this answer is correct
The correct answer is B. (5). The second term is (1+4=5). Add the common difference to the first term.
Step 3
Exam Tip
दूसरा पद (1+4=5) होगा। पहले पद में सार्व अंतर जोड़ें।
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अनुक्रम \(25,30,35,40,\ldots\) में कितनी समान वृद्धि है?
How much equal increase is there in the sequence \(25,30,35,40,\ldots\)?
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#equal increase
#common difference
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A (25)
B (30)
C (5)
D (10)
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Step 1
Concept
Each next term is (5) more than the previous one. The equal increase is called (d).
Step 2
Why this answer is correct
The correct answer is C. (5). Each next term is (5) more than the previous one. The equal increase is called (d).
Step 3
Exam Tip
हर अगला पद पिछले से (5) अधिक है। समान वृद्धि ही (d) कहलाती है।
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अनुक्रम \(16,12,8,4,\ldots\) में कितनी समान कमी है?
How much equal decrease is there in the sequence \(16,12,8,4,\ldots\)?
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#equal decrease
#negative difference
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A (2)
B (4)
C (8)
D (12)
Explanation opens after your attempt
Step 1
Concept
Each next term is (4) less, so the equal decrease is (4). But as (d), it is (-4).
Step 2
Why this answer is correct
The correct answer is B. (4). Each next term is (4) less, so the equal decrease is (4). But as (d), it is (-4).
Step 3
Exam Tip
हर अगला पद (4) कम है इसलिए समान कमी (4) है। लेकिन (d) के रूप में यह (-4) होगा।
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यदि (a=9) और (d=0) है तो पहले तीन पद कौन से होंगे?
If (a=9) and (d=0), what will be the first three terms?
#ap
#zero difference
#first terms
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A (0,9,18)
B (9,0,-9)
C (9,9,9)
D (9,10,11)
Explanation opens after your attempt
Correct Answer
C. (9,9,9)
Step 1
Concept
When (d=0), terms do not change. Therefore all first three terms will be (9).
Step 2
Why this answer is correct
The correct answer is C. (9,9,9). When (d=0), terms do not change. Therefore all first three terms will be (9).
Step 3
Exam Tip
(d=0) होने पर पद बदलते नहीं हैं। इसलिए सभी पहले तीन पद (9) होंगे।
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एक बस हर स्टॉप पर (8) मिनट के अंतर से पहुंचती है। समय \(6,14,22,30,\ldots\) मिनट हैं तो यह किस प्रकार का अनुक्रम है?
A bus reaches each stop at intervals of (8) minutes. The times are \(6,14,22,30,\ldots\) minutes. What type of sequence is this?
#arithmetic progression
#ap
#word problem
#common difference
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A अंकगणितीय श्रेणी / Arithmetic progression
B ज्यामितीय श्रेणी / Geometric progression
C समानता / Equality
D चर / Variable
Explanation opens after your attempt
Correct Answer
A. अंकगणितीय श्रेणी / Arithmetic progression
Step 1
Concept
Each consecutive time has the same difference of (8), so it is an arithmetic progression. In word problems identify the equal difference.
Step 2
Why this answer is correct
The correct answer is A. अंकगणितीय श्रेणी / Arithmetic progression. Each consecutive time has the same difference of (8), so it is an arithmetic progression. In word problems identify the equal difference.
Step 3
Exam Tip
हर क्रमागत समय में (8) का समान अंतर है इसलिए यह अंकगणितीय श्रेणी है। शब्द प्रश्न में समान अंतर को पहचानें।
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अनुक्रम \(7,11,15,19,\ldots\) में पहले दो पदों से सार्व अंतर कैसे मिलेगा?
How will the common difference be found from the first two terms of \(7,11,15,19,\ldots\)?
#arithmetic progression
#ap
#find common difference
#class ten
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A (7-11=-4)
B (11-7=4)
C (11+7=18)
D \(11\times7=77\)
Explanation opens after your attempt
Correct Answer
B. (11-7=4)
Step 1
Concept
The common difference is second term minus first term, so (11-7=4). In exams do not reverse the order of subtraction.
Step 2
Why this answer is correct
The correct answer is B. (11-7=4). The common difference is second term minus first term, so (11-7=4). In exams do not reverse the order of subtraction.
Step 3
Exam Tip
सार्व अंतर दूसरा पद घटा पहला पद होता है इसलिए (11-7=4) है। परीक्षा में घटाव का क्रम न बदलें।
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