अनुक्रम \(2,5,8,11,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(2,5,8,11,\ldots\)?
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The difference of consecutive terms is (5-2=3). In exams, subtract the first term from the second term.
Step 2
Why this answer is correct
The correct answer is B. (3). The difference of consecutive terms is (5-2=3). In exams, subtract the first term from the second term.
Step 3
Exam Tip
लगातार पदों का अंतर (5-2=3) है। परीक्षा में दूसरे पद में से पहला पद घटाएँ।
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अनुक्रम \(7,12,17,22,\ldots\) का अगला पद क्या होगा?
What will be the next term of the sequence \(7,12,17,22,\ldots\)?
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A (25)
B (26)
C (27)
D (28)
Explanation opens after your attempt
Step 1
Concept
(5) is added each time, so the next term is (22+5=27). In exams, first identify the common difference.
Step 2
Why this answer is correct
The correct answer is C. (27). (5) is added each time, so the next term is (22+5=27). In exams, first identify the common difference.
Step 3
Exam Tip
हर बार (5) जोड़ा जा रहा है, इसलिए अगला पद (22+5=27) है। परीक्षा में पहले सार्व अंतर पहचानें।
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यदि समांतर श्रेणी में पहला पद (4) और सार्व अंतर (6) है, तो दूसरा पद क्या होगा?
If an arithmetic progression has first term (4) and common difference (6), what is the second term?
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A (8)
B (9)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
The second term is (4+6=10). In exams, add the common difference to get the next term.
Step 2
Why this answer is correct
The correct answer is C. (10). The second term is (4+6=10). In exams, add the common difference to get the next term.
Step 3
Exam Tip
दूसरा पद (4+6=10) होगा। परीक्षा में अगले पद के लिए सार्व अंतर जोड़ें।
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अनुक्रम \(15,11,7,3,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(15,11,7,3,\ldots\)?
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A (4)
B (-4)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Each term decreases by (4), so the common difference is (-4). In exams, a decreasing sequence has a negative difference.
Step 2
Why this answer is correct
The correct answer is B. (-4). Each term decreases by (4), so the common difference is (-4). In exams, a decreasing sequence has a negative difference.
Step 3
Exam Tip
हर पद में (4) घट रहा है, इसलिए सार्व अंतर (-4) है। परीक्षा में घटते अनुक्रम में अंतर ऋणात्मक होता है।
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क्या अनुक्रम \(3,6,9,12,\ldots\) एक समांतर श्रेणी है?
Is the sequence \(3,6,9,12,\ldots\) an arithmetic progression?
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A हाँ, सार्व अंतर (3) है / Yes, common difference is (3)
B हाँ, सार्व अंतर (6) है / Yes, common difference is (6)
C नहीं, अंतर समान नहीं है / No, differences are not equal
D नहीं, पद घट रहे हैं / No, terms are decreasing
Explanation opens after your attempt
Correct Answer
A. हाँ, सार्व अंतर (3) है / Yes, common difference is (3)
Step 1
Concept
All consecutive terms have difference (3). In exams, check equal differences for an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. हाँ, सार्व अंतर (3) है / Yes, common difference is (3). All consecutive terms have difference (3). In exams, check equal differences for an arithmetic progression.
Step 3
Exam Tip
सभी लगातार पदों का अंतर (3) है। परीक्षा में समांतर श्रेणी के लिए समान अंतर जाँचें।
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अनुक्रम \(1,4,9,16,\ldots\) समांतर श्रेणी क्यों नहीं है?
Why is the sequence \(1,4,9,16,\ldots\) not an arithmetic progression?
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A पद समान हैं / Terms are equal
B पहला पद शून्य नहीं है / First term is not zero
C अंतर समान नहीं हैं / Differences are not equal
D सभी पद धनात्मक हैं / All terms are positive
Explanation opens after your attempt
Correct Answer
C. अंतर समान नहीं हैं / Differences are not equal
Step 1
Concept
The differences are (3,5,7), which are not equal. In exams, only check consecutive differences.
Step 2
Why this answer is correct
The correct answer is C. अंतर समान नहीं हैं / Differences are not equal. The differences are (3,5,7), which are not equal. In exams, only check consecutive differences.
Step 3
Exam Tip
अंतर (3,5,7) हैं, जो समान नहीं हैं। परीक्षा में केवल लगातार अंतरों को देखें।
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समांतर श्रेणी \(9,14,19,24,\ldots\) में पहला पद क्या है?
What is the first term in the arithmetic progression \(9,14,19,24,\ldots\)?
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A (5)
B (9)
C (14)
D (19)
Explanation opens after your attempt
Step 1
Concept
The first written term of the sequence is (9). In exams, take the first term (a) directly from the sequence.
Step 2
Why this answer is correct
The correct answer is B. (9). The first written term of the sequence is (9). In exams, take the first term (a) directly from the sequence.
Step 3
Exam Tip
अनुक्रम का पहला लिखा हुआ पद (9) है। परीक्षा में पहला पद (a) सीधे पहले पद से लें।
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यदि (a=5) और (d=2) है, तो समांतर श्रेणी का तीसरा पद क्या होगा?
If (a=5) and (d=2), what is the third term of the arithmetic progression?
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A (7)
B (8)
C (9)
D (11)
Explanation opens after your attempt
Step 1
Concept
The third term is (a+2d=5+4=9). In exams, add the difference twice for the third term.
Step 2
Why this answer is correct
The correct answer is C. (9). The third term is (a+2d=5+4=9). In exams, add the difference twice for the third term.
Step 3
Exam Tip
तीसरा पद (a+2d=5+4=9) है। परीक्षा में तीसरे पद के लिए दो बार अंतर जोड़ें।
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समांतर श्रेणी \(20,18,16,14,\ldots\) का अगला पद क्या होगा?
What is the next term of the arithmetic progression \(20,18,16,14,\ldots\)?
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A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
The common difference is (-2), so the next term is (14-2=12). In exams, apply the negative difference for decreasing terms.
Step 2
Why this answer is correct
The correct answer is C. (12). The common difference is (-2), so the next term is (14-2=12). In exams, apply the negative difference for decreasing terms.
Step 3
Exam Tip
सार्व अंतर (-2) है, इसलिए अगला पद (14-2=12) है। परीक्षा में घटते पदों में अंतर घटाकर लगाएँ।
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समांतर श्रेणी \(6,10,14,18,\ldots\) में पाँचवाँ पद क्या है?
What is the fifth term in the arithmetic progression \(6,10,14,18,\ldots\)?
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A (20)
B (21)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
The common difference is (4), so the fifth term is (18+4=22). In exams, extend the terms in order.
Step 2
Why this answer is correct
The correct answer is C. (22). The common difference is (4), so the fifth term is (18+4=22). In exams, extend the terms in order.
Step 3
Exam Tip
सार्व अंतर (4) है, इसलिए पाँचवाँ पद (18+4=22) है। परीक्षा में पदों को क्रम से आगे बढ़ाएँ।
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यदि समांतर श्रेणी \(2,,\Box,,8,11,\ldots\) है, तो रिक्त स्थान में कौन-सा पद होगा?
If \(2,,\Box,,8,11,\ldots\) is an arithmetic progression, what term fills the blank?
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The difference between (8) and (11) is (3), so the blank term is (2+3=5). In exams, identify the difference from nearby known terms.
Step 2
Why this answer is correct
The correct answer is B. (5). The difference between (8) and (11) is (3), so the blank term is (2+3=5). In exams, identify the difference from nearby known terms.
Step 3
Exam Tip
(8) और (11) का अंतर (3) है, इसलिए रिक्त पद (2+3=5) है। परीक्षा में पास के ज्ञात पदों से अंतर पहचानें।
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समांतर श्रेणी \(4,8,12,16,\ldots\) का सामान्य पद क्या है?
What is the general term of the arithmetic progression \(4,8,12,16,\ldots\)?
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A \(a_n=4n\)
B \(a_n=n+4\)
C \(a_n=4n+1\)
D \(a_n=8n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4n\)
Step 1
Concept
This is a sequence of multiples of (4), so \(a_n=4n\). In exams, identify multiple-based progressions as (kn).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4n\). This is a sequence of multiples of (4), so \(a_n=4n\). In exams, identify multiple-based progressions as (kn).
Step 3
Exam Tip
यह (4) के गुणजों की श्रेणी है, इसलिए \(a_n=4n\) है। परीक्षा में गुणजों वाली श्रेणी को (kn) से पहचानें।
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यदि \(a_n=3n+1\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=3n+1\), what is the value of \(a_4\)?
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A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
\(a_4=3\times4+1=13\). In exams, replace (n) with the term number.
Step 2
Why this answer is correct
The correct answer is D. (13). \(a_4=3\times4+1=13\). In exams, replace (n) with the term number.
Step 3
Exam Tip
\(a_4=3\times4+1=13\) है। परीक्षा में (n) की जगह पद संख्या रखें।
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समांतर श्रेणी \(5,9,13,17,\ldots\) का सामान्य पद कौन-सा है?
Which is the general term of the arithmetic progression \(5,9,13,17,\ldots\)?
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A \(a_n=5n\)
B \(a_n=4n+1\)
C \(a_n=4n-1\)
D \(a_n=n+4\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=4n+1\)
Step 1
Concept
The first term is (5) and the difference is (4), so \(a_n=4n+1\). In exams, use (a_n=a+(n-1)d).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=4n+1\). The first term is (5) and the difference is (4), so \(a_n=4n+1\). In exams, use (a_n=a+(n-1)d).
Step 3
Exam Tip
पहला पद (5) और अंतर (4) है, इसलिए \(a_n=4n+1\) है। परीक्षा में (a_n=a+(n-1)d) लगाएँ।
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यदि समांतर श्रेणी का पहला पद (10) और सार्व अंतर (-3) है, तो दूसरा पद क्या होगा?
If the first term of an arithmetic progression is (10) and the common difference is (-3), what is the second term?
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A (7)
B (8)
C (13)
D (6)
Explanation opens after your attempt
Step 1
Concept
The second term is (10+(-3)=7). In exams, be careful with signs when adding a negative difference.
Step 2
Why this answer is correct
The correct answer is A. (7). The second term is (10+(-3)=7). In exams, be careful with signs when adding a negative difference.
Step 3
Exam Tip
दूसरा पद (10+(-3)=7) है। परीक्षा में ऋणात्मक अंतर को जोड़ते समय चिह्न ध्यान रखें।
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अनुक्रम \(2,4,8,16,\ldots\) समांतर श्रेणी क्यों नहीं है?
Why is the sequence \(2,4,8,16,\ldots\) not an arithmetic progression?
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A क्योंकि पद बढ़ते हैं / Because terms increase
B क्योंकि पहला पद (2) है / Because first term is (2)
C क्योंकि लगातार अंतर समान नहीं हैं / Because consecutive differences are not equal
D क्योंकि सभी पद सम हैं / Because all terms are even
Explanation opens after your attempt
Correct Answer
C. क्योंकि लगातार अंतर समान नहीं हैं / Because consecutive differences are not equal
Step 1
Concept
The differences are (2,4,8), which are not equal. In exams, equal difference is necessary for an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि लगातार अंतर समान नहीं हैं / Because consecutive differences are not equal. The differences are (2,4,8), which are not equal. In exams, equal difference is necessary for an arithmetic progression.
Step 3
Exam Tip
अंतर (2,4,8) हैं, जो समान नहीं हैं। परीक्षा में समांतर श्रेणी के लिए समान अंतर आवश्यक है।
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समांतर श्रेणी \(3,7,11,15,\ldots\) में (d) का मान क्या है?
What is the value of (d) in the arithmetic progression \(3,7,11,15,\ldots\)?
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A (3)
B (4)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
The common difference is (d=7-3=4). In exams, subtract the first term from the second term for (d).
Step 2
Why this answer is correct
The correct answer is B. (4). The common difference is (d=7-3=4). In exams, subtract the first term from the second term for (d).
Step 3
Exam Tip
सार्व अंतर (d=7-3=4) है। परीक्षा में (d) के लिए दूसरे पद में से पहला पद घटाएँ।
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यदि (a=12) और (d=5) है, तो समांतर श्रेणी का चौथा पद क्या होगा?
If (a=12) and (d=5), what is the fourth term of the arithmetic progression?
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A (22)
B (24)
C (27)
D (32)
Explanation opens after your attempt
Step 1
Concept
The fourth term is (a+3d=12+15=27). In exams, add the difference three times for the fourth term.
Step 2
Why this answer is correct
The correct answer is C. (27). The fourth term is (a+3d=12+15=27). In exams, add the difference three times for the fourth term.
Step 3
Exam Tip
चौथा पद (a+3d=12+15=27) है। परीक्षा में चौथे पद के लिए तीन बार अंतर जोड़ें।
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समांतर श्रेणी \(30,25,20,15,\ldots\) में छठा पद क्या है?
What is the sixth term in the arithmetic progression \(30,25,20,15,\ldots\)?
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A (10)
B (5)
C (0)
D (15)
Explanation opens after your attempt
Step 1
Concept
The difference is (-5), so the terms are (30,25,20,15,10,5). In exams, include the first term while counting.
Step 2
Why this answer is correct
The correct answer is B. (5). The difference is (-5), so the terms are (30,25,20,15,10,5). In exams, include the first term while counting.
Step 3
Exam Tip
अंतर (-5) है, इसलिए पद (30,25,20,15,10,5) हैं। परीक्षा में पद संख्या गिनते समय पहला पद भी गिनें।
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समांतर श्रेणी \(1,6,11,16,\ldots\) में (21) कौन-सा पद है?
In the arithmetic progression \(1,6,11,16,\ldots\), which term is (21)?
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A तीसरा पद / (3)rd term
B चौथा पद / (4)th term
C पाँचवाँ पद / (5)th term
D छठा पद / (6)th term
Explanation opens after your attempt
Correct Answer
C. पाँचवाँ पद / (5)th term
Step 1
Concept
The terms are (1,6,11,16,21), so (21) is the fifth term. In exams, list terms in order for a quick check.
Step 2
Why this answer is correct
The correct answer is C. पाँचवाँ पद / (5)th term. The terms are (1,6,11,16,21), so (21) is the fifth term. In exams, list terms in order for a quick check.
Step 3
Exam Tip
पद (1,6,11,16,21) हैं, इसलिए (21) पाँचवाँ पद है। परीक्षा में क्रम से पद लिखकर जल्दी जाँचें।
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यदि \(a_n=2n+5\) है, तो यह किस समांतर श्रेणी के पहले तीन पद देता है?
If \(a_n=2n+5\), which first three terms of an arithmetic progression does it give?
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A (5,7,9)
B (7,9,11)
C (6,8,10)
D (8,10,12)
Explanation opens after your attempt
Correct Answer
B. (7,9,11)
Step 1
Concept
Putting (n=1,2,3) gives (7,9,11). In exams, use small (n) values for the first three terms.
Step 2
Why this answer is correct
The correct answer is B. (7,9,11). Putting (n=1,2,3) gives (7,9,11). In exams, use small (n) values for the first three terms.
Step 3
Exam Tip
(n=1,2,3) रखने पर (7,9,11) मिलते हैं। परीक्षा में पहले तीन पदों के लिए छोटे (n) मान रखें।
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समांतर श्रेणी \(8,13,18,23,\ldots\) का सामान्य पद क्या है?
What is the general term of the arithmetic progression \(8,13,18,23,\ldots\)?
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A \(a_n=5n+3\)
B \(a_n=8n\)
C \(a_n=5n-3\)
D \(a_n=n+7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n+3\)
Step 1
Concept
The first term is (8) and the difference is (5), so \(a_n=5n+3\). In exams, find the constant part from the first term.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n+3\). The first term is (8) and the difference is (5), so \(a_n=5n+3\). In exams, find the constant part from the first term.
Step 3
Exam Tip
पहला पद (8) और अंतर (5) है, इसलिए \(a_n=5n+3\) है। परीक्षा में पहले पद से स्थिर भाग निकालें।
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यदि समांतर श्रेणी \(4,10,16,\Box,\ldots\) है, तो रिक्त स्थान में कौन-सा पद होगा?
If \(4,10,16,\Box,\ldots\) is an arithmetic progression, what term fills the blank?
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A (20)
B (21)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
The common difference is (6), so the next term is (16+6=22). In exams, continue the same difference for the blank term.
Step 2
Why this answer is correct
The correct answer is C. (22). The common difference is (6), so the next term is (16+6=22). In exams, continue the same difference for the blank term.
Step 3
Exam Tip
सार्व अंतर (6) है, इसलिए अगला पद (16+6=22) है। परीक्षा में रिक्त पद के लिए समान अंतर जारी रखें।
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समांतर श्रेणी \(11,8,5,2,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the arithmetic progression \(11,8,5,2,\ldots\)?
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A (3)
B (-3)
C (2)
D (-2)
Explanation opens after your attempt
Step 1
Concept
The difference of consecutive terms is (8-11=-3). In exams, write the difference as negative for a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. (-3). The difference of consecutive terms is (8-11=-3). In exams, write the difference as negative for a decreasing sequence.
Step 3
Exam Tip
लगातार पदों का अंतर (8-11=-3) है। परीक्षा में घटते अनुक्रम में अंतर ऋणात्मक लिखें।
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समांतर श्रेणी \(13,18,23,28,\ldots\) में आठवाँ पद क्या होगा?
What is the eighth term in the arithmetic progression \(13,18,23,28,\ldots\)?
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A (43)
B (45)
C (48)
D (50)
Explanation opens after your attempt
Step 1
Concept
(a=13) and (d=5), so \(a_8=13+7\times5=48\). In exams, use (a+(n-1)d) for the (n)th term.
Step 2
Why this answer is correct
The correct answer is C. (48). (a=13) and (d=5), so \(a_8=13+7\times5=48\). In exams, use (a+(n-1)d) for the (n)th term.
Step 3
Exam Tip
(a=13) और (d=5), इसलिए \(a_8=13+7\times5=48\) है। परीक्षा में (n)वें पद के लिए (a+(n-1)d) लगाएँ।
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क्या \(10,20,30,40,\ldots\) समांतर श्रेणी है?
Is \(10,20,30,40,\ldots\) an arithmetic progression?
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A हाँ, सार्व अंतर (10) है / Yes, common difference is (10)
B हाँ, सार्व अंतर (20) है / Yes, common difference is (20)
C नहीं, पद समान नहीं हैं / No, terms are not equal
D नहीं, यह घटती श्रेणी है / No, it is decreasing
Explanation opens after your attempt
Correct Answer
A. हाँ, सार्व अंतर (10) है / Yes, common difference is (10)
Step 1
Concept
Each consecutive term differs by (10). In exams, if equal difference appears, treat it as an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. हाँ, सार्व अंतर (10) है / Yes, common difference is (10). Each consecutive term differs by (10). In exams, if equal difference appears, treat it as an arithmetic progression.
Step 3
Exam Tip
हर लगातार पद का अंतर (10) है। परीक्षा में समान अंतर दिखे तो समांतर श्रेणी मानें।
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यदि (a=3) और (d=7) है, तो पहले चार पद कौन-से होंगे?
If (a=3) and (d=7), what are the first four terms?
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A (3,7,14,21)
B (3,10,17,24)
C (7,10,17,24)
D (3,11,19,27)
Explanation opens after your attempt
Correct Answer
B. (3,10,17,24)
Step 1
Concept
Adding (7) each time gives (3,10,17,24). In exams, do not change the first term.
Step 2
Why this answer is correct
The correct answer is B. (3,10,17,24). Adding (7) each time gives (3,10,17,24). In exams, do not change the first term.
Step 3
Exam Tip
हर बार (7) जोड़ने पर (3,10,17,24) मिलते हैं। परीक्षा में पहला पद न बदलें।
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समांतर श्रेणी \(25,20,15,10,\ldots\) का सामान्य पद कौन-सा है?
Which is the general term of the arithmetic progression \(25,20,15,10,\ldots\)?
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A \(a_n=25-5n\)
B \(a_n=30-5n\)
C \(a_n=5n+20\)
D \(a_n=25+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=30-5n\)
Step 1
Concept
At (n=1) it gives (25), and at (n=2) it gives (20), so \(a_n=30-5n\). In exams, check a decreasing rule with the first term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=30-5n\). At (n=1) it gives (25), and at (n=2) it gives (20), so \(a_n=30-5n\). In exams, check a decreasing rule with the first term.
Step 3
Exam Tip
(n=1) पर (25) और (n=2) पर (20) मिलता है, इसलिए \(a_n=30-5n\) है। परीक्षा में घटते नियम को पहले पद से जाँचें।
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यदि \(a_n=30-5n\) है, तो \(a_4\) का मान क्या होगा?
If \(a_n=30-5n\), what is the value of \(a_4\)?
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A (5)
B (10)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(a_4=30-20=10\). In exams, calculate (5n) first and then subtract.
Step 2
Why this answer is correct
The correct answer is B. (10). \(a_4=30-20=10\). In exams, calculate (5n) first and then subtract.
Step 3
Exam Tip
\(a_4=30-20=10\) है। परीक्षा में पहले (5n) निकालें और फिर घटाएँ।
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समांतर श्रेणी \(2,9,16,23,\ldots\) में (a) और (d) क्या हैं?
What are (a) and (d) in the arithmetic progression \(2,9,16,23,\ldots\)?
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A (a=2,d=7)
B (a=7,d=2)
C (a=2,d=9)
D (a=9,d=7)
Explanation opens after your attempt
Correct Answer
A. (a=2,d=7)
Step 1
Concept
The first term is (2), and the difference is (9-2=7). In exams, identify (a) and (d) separately.
Step 2
Why this answer is correct
The correct answer is A. (a=2,d=7). The first term is (2), and the difference is (9-2=7). In exams, identify (a) and (d) separately.
Step 3
Exam Tip
पहला पद (2) है और अंतर (9-2=7) है। परीक्षा में (a) और (d) अलग-अलग पहचानें।
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यदि किसी समांतर श्रेणी में (a=6) और (d=4) है, तो पाँचवाँ पद क्या होगा?
If an arithmetic progression has (a=6) and (d=4), what is the fifth term?
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A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
\(a_5=6+4\times4=22\). In exams, put (n=5) in (a_n=a+(n-1)d).
Step 2
Why this answer is correct
The correct answer is C. (22). \(a_5=6+4\times4=22\). In exams, put (n=5) in (a_n=a+(n-1)d).
Step 3
Exam Tip
\(a_5=6+4\times4=22\) है। परीक्षा में (a_n=a+(n-1)d) में (n=5) रखें।
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अनुक्रम \(4,7,10,13,\ldots\) में (19) कौन-सा पद है?
In the sequence \(4,7,10,13,\ldots\), which term is (19)?
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A चौथा पद / (4)th term
B पाँचवाँ पद / (5)th term
C छठा पद / (6)th term
D सातवाँ पद / (7)th term
Explanation opens after your attempt
Correct Answer
C. छठा पद / (6)th term
Step 1
Concept
The terms are (4,7,10,13,16,19), so (19) is the sixth term. In exams, include the first term while counting.
Step 2
Why this answer is correct
The correct answer is C. छठा पद / (6)th term. The terms are (4,7,10,13,16,19), so (19) is the sixth term. In exams, include the first term while counting.
Step 3
Exam Tip
पद (4,7,10,13,16,19) हैं, इसलिए (19) छठा पद है। परीक्षा में पदों को गिनते समय पहला पद शामिल करें।
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यदि समांतर श्रेणी का \(a_1=8\) और \(a_2=14\) है, तो सार्व अंतर क्या होगा?
If an arithmetic progression has \(a_1=8\) and \(a_2=14\), what is the common difference?
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The common difference is \(a_2-a_1=14-8=6\). In exams, take the difference of two consecutive terms.
Step 2
Why this answer is correct
The correct answer is C. (6). The common difference is \(a_2-a_1=14-8=6\). In exams, take the difference of two consecutive terms.
Step 3
Exam Tip
सार्व अंतर \(a_2-a_1=14-8=6\) है। परीक्षा में दो लगातार पदों का अंतर लें।
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समांतर श्रेणी \(17,21,25,29,\ldots\) का अगला पद क्या है?
What is the next term of the arithmetic progression \(17,21,25,29,\ldots\)?
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A (31)
B (32)
C (33)
D (34)
Explanation opens after your attempt
Step 1
Concept
The common difference is (4), so the next term is (29+4=33). In exams, add the difference to the last known term.
Step 2
Why this answer is correct
The correct answer is C. (33). The common difference is (4), so the next term is (29+4=33). In exams, add the difference to the last known term.
Step 3
Exam Tip
सार्व अंतर (4) है, इसलिए अगला पद (29+4=33) है। परीक्षा में अंतिम ज्ञात पद में अंतर जोड़ें।
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किस विकल्प में समांतर श्रेणी दी गई है?
Which option shows an arithmetic progression?
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A (2,4,8,16)
B (1,3,6,10)
C (5,10,15,20)
D (1,4,9,16)
Explanation opens after your attempt
Correct Answer
C. (5,10,15,20)
Step 1
Concept
In (5,10,15,20), the consecutive difference is (5). In exams, look for equal differences in the options.
Step 2
Why this answer is correct
The correct answer is C. (5,10,15,20). In (5,10,15,20), the consecutive difference is (5). In exams, look for equal differences in the options.
Step 3
Exam Tip
(5,10,15,20) में लगातार अंतर (5) है। परीक्षा में विकल्पों में समान अंतर खोजें।
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समांतर श्रेणी \(100,90,80,70,\ldots\) में पाँचवाँ पद क्या है?
What is the fifth term in the arithmetic progression \(100,90,80,70,\ldots\)?
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A (50)
B (60)
C (70)
D (80)
Explanation opens after your attempt
Step 1
Concept
The common difference is (-10), so the fifth term is (60). In exams, count in the correct direction for decreasing terms.
Step 2
Why this answer is correct
The correct answer is B. (60). The common difference is (-10), so the fifth term is (60). In exams, count in the correct direction for decreasing terms.
Step 3
Exam Tip
सार्व अंतर (-10) है, इसलिए पाँचवाँ पद (60) है। परीक्षा में घटते पदों में सही दिशा में गिनें।
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यदि समांतर श्रेणी \(x,,x+4,,x+8,\ldots\) है, तो सार्व अंतर क्या है?
If \(x,,x+4,,x+8,\ldots\) is an arithmetic progression, what is the common difference?
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A (x)
B (2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The difference between the second and first terms is ((x+4)-x=4). In exams, subtract even with algebraic terms.
Step 2
Why this answer is correct
The correct answer is C. (4). The difference between the second and first terms is ((x+4)-x=4). In exams, subtract even with algebraic terms.
Step 3
Exam Tip
दूसरे पद और पहले पद का अंतर ((x+4)-x=4) है। परीक्षा में बीजीय पदों में भी घटाव करें।
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समांतर श्रेणी \(3,3,3,3,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the arithmetic progression \(3,3,3,3,\ldots\)?
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A (0)
B (1)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Consecutive terms are equal, so the difference is (3-3=0). In exams, a constant sequence can also be an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. (0). Consecutive terms are equal, so the difference is (3-3=0). In exams, a constant sequence can also be an arithmetic progression.
Step 3
Exam Tip
लगातार पद समान हैं, इसलिए अंतर (3-3=0) है। परीक्षा में स्थिर श्रेणी भी समांतर श्रेणी हो सकती है।
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यदि (a=9) और (d=0) है, तो पहले तीन पद क्या होंगे?
If (a=9) and (d=0), what are the first three terms?
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A (9,0,9)
B (0,9,18)
C (9,9,9)
D (9,18,27)
Explanation opens after your attempt
Correct Answer
C. (9,9,9)
Step 1
Concept
When the common difference is (0), all terms remain (9). In exams, (d=0) means a constant sequence.
Step 2
Why this answer is correct
The correct answer is C. (9,9,9). When the common difference is (0), all terms remain (9). In exams, (d=0) means a constant sequence.
Step 3
Exam Tip
सार्व अंतर (0) होने पर सभी पद (9) रहेंगे। परीक्षा में (d=0) का मतलब स्थिर श्रेणी है।
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समांतर श्रेणी \(2,\Box,10,14,\ldots\) में रिक्त पद क्या होगा?
What is the missing term in the arithmetic progression \(2,\Box,10,14,\ldots\)?
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The difference between (10) and (14) is (4), so the missing term is (10-4=6). In exams, apply the common difference backward too.
Step 2
Why this answer is correct
The correct answer is C. (6). The difference between (10) and (14) is (4), so the missing term is (10-4=6). In exams, apply the common difference backward too.
Step 3
Exam Tip
(10) और (14) का अंतर (4) है, इसलिए रिक्त पद (10-4=6) है। परीक्षा में पीछे की ओर भी सार्व अंतर लगाएँ।
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यदि \(a_n=5n-2\) है, तो इस समांतर श्रेणी का सार्व अंतर क्या है?
If \(a_n=5n-2\), what is the common difference of this arithmetic progression?
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A (2)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
In the linear rule \(a_n=5n-2\), the coefficient of (n) is the difference (5). In exams, take (k) as (d) in (kn+c).
Step 2
Why this answer is correct
The correct answer is C. (5). In the linear rule \(a_n=5n-2\), the coefficient of (n) is the difference (5). In exams, take (k) as (d) in (kn+c).
Step 3
Exam Tip
रैखिक नियम \(a_n=5n-2\) में (n) का गुणांक (5) ही अंतर है। परीक्षा में (kn+c) में (k) को (d) मानें।
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समांतर श्रेणी \(12,15,18,21,\ldots\) का \(a_6\) क्या है?
What is \(a_6\) of the arithmetic progression \(12,15,18,21,\ldots\)?
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A (24)
B (27)
C (30)
D (33)
Explanation opens after your attempt
Step 1
Concept
(a=12) and (d=3), so \(a_6=12+5\times3=27\). In exams, keep (n-1) correct.
Step 2
Why this answer is correct
The correct answer is B. (27). (a=12) and (d=3), so \(a_6=12+5\times3=27\). In exams, keep (n-1) correct.
Step 3
Exam Tip
(a=12) और (d=3), इसलिए \(a_6=12+5\times3=27\) है। परीक्षा में (n-1) को सही रखें।
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यदि समांतर श्रेणी में \(a_1=5\) और (d=10) है, तो \(a_4\) क्या होगा?
If an arithmetic progression has \(a_1=5\) and (d=10), what is \(a_4\)?
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A (25)
B (30)
C (35)
D (40)
Explanation opens after your attempt
Step 1
Concept
\(a_4=5+3\times10=35\). In exams, add three differences for the fourth term.
Step 2
Why this answer is correct
The correct answer is C. (35). \(a_4=5+3\times10=35\). In exams, add three differences for the fourth term.
Step 3
Exam Tip
\(a_4=5+3\times10=35\) है। परीक्षा में चौथे पद के लिए तीन अंतर जोड़ें।
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किस अनुक्रम में सार्व अंतर (-2) है?
Which sequence has common difference (-2)?
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A (2,4,6,8)
B (10,8,6,4)
C (5,10,15,20)
D (1,1,1,1)
Explanation opens after your attempt
Correct Answer
B. (10,8,6,4)
Step 1
Concept
In (10,8,6,4), (2) is subtracted each time. In exams, write a decreasing difference as negative.
Step 2
Why this answer is correct
The correct answer is B. (10,8,6,4). In (10,8,6,4), (2) is subtracted each time. In exams, write a decreasing difference as negative.
Step 3
Exam Tip
(10,8,6,4) में हर बार (2) घटता है। परीक्षा में घटते अंतर को ऋणात्मक लिखें।
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समांतर श्रेणी \(7,14,21,28,\ldots\) का दसवाँ पद क्या है?
What is the tenth term of the arithmetic progression \(7,14,21,28,\ldots\)?
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A (63)
B (70)
C (77)
D (84)
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Step 1
Concept
This is a sequence of multiples of (7), so the tenth term is (70). In exams, identify multiples quickly.
Step 2
Why this answer is correct
The correct answer is B. (70). This is a sequence of multiples of (7), so the tenth term is (70). In exams, identify multiples quickly.
Step 3
Exam Tip
यह (7) के गुणजों की श्रेणी है, इसलिए दसवाँ पद (70) है। परीक्षा में गुणजों को जल्दी पहचानें।
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यदि \(a_n=11-2n\) है, तो \(a_3\) का मान क्या होगा?
If \(a_n=11-2n\), what is the value of \(a_3\)?
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A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_3=11-6=5\). In exams, subtract (2n) correctly in a decreasing rule.
Step 2
Why this answer is correct
The correct answer is B. (5). \(a_3=11-6=5\). In exams, subtract (2n) correctly in a decreasing rule.
Step 3
Exam Tip
\(a_3=11-6=5\) है। परीक्षा में घटते नियम में (2n) सही घटाएँ।
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समांतर श्रेणी \(9,7,5,3,\ldots\) का सामान्य पद क्या है?
What is the general term of the arithmetic progression \(9,7,5,3,\ldots\)?
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A \(a_n=9-2n\)
B \(a_n=11-2n\)
C \(a_n=2n+7\)
D \(a_n=9+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=11-2n\)
Step 1
Concept
At (n=1) it gives (9), and at (n=2) it gives (7), so \(a_n=11-2n\). In exams, choose the rule after checking the first term.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=11-2n\). At (n=1) it gives (9), and at (n=2) it gives (7), so \(a_n=11-2n\). In exams, choose the rule after checking the first term.
Step 3
Exam Tip
(n=1) पर (9) और (n=2) पर (7) मिलता है, इसलिए \(a_n=11-2n\) है। परीक्षा में पहला पद जाँचकर नियम चुनें।
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यदि समांतर श्रेणी (5,,x,,15) है, तो (x) का मान क्या होगा?
If (5,,x,,15) is an arithmetic progression, what is the value of (x)?
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A (8)
B (9)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
The middle term is the average of (5) and (15), so \(x=\frac{5+15}{2}=10\). In exams, take the average for the middle term in three-term progressions.
Step 2
Why this answer is correct
The correct answer is C. (10). The middle term is the average of (5) and (15), so \(x=\frac{5+15}{2}=10\). In exams, take the average for the middle term in three-term progressions.
Step 3
Exam Tip
बीच का पद (5) और (15) का औसत है, इसलिए \(x=\frac{5+15}{2}=10\) है। परीक्षा में तीन पदों वाली श्रेणी में मध्य पद का औसत लें।
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समांतर श्रेणी \(18,24,30,36,\ldots\) में सातवाँ पद क्या होगा?
What will be the seventh term in the arithmetic progression \(18,24,30,36,\ldots\)?
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A (48)
B (50)
C (52)
D (54)
Explanation opens after your attempt
Step 1
Concept
(a=18) and (d=6), so \(a_7=18+6\times6=54\). In exams, add the difference (n-1) times.
Step 2
Why this answer is correct
The correct answer is D. (54). (a=18) and (d=6), so \(a_7=18+6\times6=54\). In exams, add the difference (n-1) times.
Step 3
Exam Tip
(a=18) और (d=6), इसलिए \(a_7=18+6\times6=54\) है। परीक्षा में (n-1) बार अंतर जोड़ें।
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किस समांतर श्रेणी का पहला पद (6) और सार्व अंतर (4) है?
Which arithmetic progression has first term (6) and common difference (4)?
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A \(6,10,14,18,\ldots\)
B \(4,8,12,16,\ldots\)
C \(6,12,18,24,\ldots\)
D \(10,14,18,22,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(6,10,14,18,\ldots\)
Step 1
Concept
The first term is (6), and (4) is added each time. In exams, match both the first term and the difference.
Step 2
Why this answer is correct
The correct answer is A. \(6,10,14,18,\ldots\). The first term is (6), and (4) is added each time. In exams, match both the first term and the difference.
Step 3
Exam Tip
पहला पद (6) है और हर बार (4) जुड़ रहा है। परीक्षा में पहला पद और अंतर दोनों मिलाएँ।
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