Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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What is the sum of the first (6) terms of the sequence \(3,7,13,21,31,\ldots\)?
B. (114)
छठा पद (43) है और योग (3+7+13+21+31+43=118) नहीं बल्कि (118) है। विकल्पों में (118) सही है। / The sixth term is (43), and the sum is (3+7+13+21+31+43=118). Therefore (118) is correct.
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What is the correct sum of the first (6) terms of the sequence \(3,7,13,21,31,\ldots\)?
D. (118)
छठा पद (43) है और योग (3+7+13+21+31+43=118) है। योग में सभी (6) पद शामिल करें। / The sixth term is (43), and the sum is (3+7+13+21+31+43=118). Exam tip: include all (6) terms in the sum.
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If (a_n=n(n+4)), which term is (165)?
C. (11)वाँ(11)th
(11(11+4)=165) इसलिए यह (11)वाँ पद है। गुणनफल वाले सूत्र में विकल्प सीधे रखें। / (11(11+4)=165), so it is the (11)th term. Exam tip: substitute options directly in product-form formulas.
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B. (11)वाँ(11)th
\(\frac{1}{10^2}=\frac{1}{100}\) छोटा नहीं है और \(\frac{1}{11^2}<\frac{1}{100}\) है। इसलिए पहला पद (11)वाँ है। / \(\frac{1}{10^2}=\frac{1}{100}\) is not smaller, and \(\frac{1}{11^2}<\frac{1}{100}\). So the first term is the (11)th.
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If \(a_n=\frac{n}{2n-1}\), which is the first term less than \(\frac{3}{5}\)?
B. (4)वाँ(4)th
\(\frac{n}{2n-1}<\frac{3}{5}\) से (5n<6n-3) और (n>3) मिलता है। पहला पूर्णांक (4) है। / From \(\frac{n}{2n-1}<\frac{3}{5}\), (5n<6n-3), so (n>3). The first integer is (4).
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What is the average of the first (5) terms of the sequence \(8,16,32,64,\ldots\)?
B. (49.6)
पहले (5) पदों का योग (8+16+32+64+128=248) है। औसत \(\frac{248}{5}=49.6\) होगा। / The sum of the first (5) terms is (8+16+32+64+128=248). The average is \(\frac{248}{5}=49.6\).
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If (a_n=6n-(-1)^n), what will be the value of \(a_{12}-a_{11}\)?
A. (4)
\(a_{12}=71\) और \(a_{11}=67\) इसलिए अंतर (4) है। चिह्न बदलने वाले भाग को अलग जाँचें। / \(a_{12}=71\) and \(a_{11}=67\), so the difference is (4). Exam tip: check the sign-changing part separately.
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In a sequence with equal differences, \(a_6=41\) and \(a_{15}=104\). What will \(a_1\) be?
C. (6)
(9) अंतरों का योग (104-41=63) है इसलिए अंतर (7) है। \(a_1=41-5\times7=6\) होगा। / The sum of (9) differences is (104-41=63), so the difference is (7). Thus \(a_1=41-5\times7=6\).
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If \(a_n=3n^2-2n+5\), what will be the value of \(a_{12}+a_{13}\)?
B. (886)
\(a_{12}=413\) और \(a_{13}=473\) है इसलिए योग (886) है। दोनों पद अलग-अलग निकालें। / \(a_{12}=413\) and \(a_{13}=473\), so the sum is (886). Exam tip: calculate both terms separately.
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In the sequence \(5,10,20,40,\ldots\), which term is (5120)?
B. (11)वाँ(11)th
\(5\times2^{10}=5120\) है इसलिए यह (11)वाँ पद है। पहले पद से गिनते समय घात (n-1) होती है। / \(5\times2^{10}=5120\), so it is the (11)th term. Exam tip: from the first term, the exponent is (n-1).
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