Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 381-390 of 600 questions.
What is the general term of the sequence \(1,2,5,10,\ldots\)?
A. \(a_n=n^2-2n+2\)
\(n^2-2n+2\) से (1,2,5,10) मिलते हैं। बढ़ते अंतर वाले क्रम में द्विघात विकल्प जांचें। / \(n^2-2n+2\) gives (1,2,5,10). In a sequence with increasing differences, check quadratic options.
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If \(a_n=\frac{2n+3}{n+1}\), what is \(a_4\)?
C. \(\frac{11}{5}\)
(a_4=\frac{2(4)+3}{4+1}=\frac{11}{5})। भिन्न वाले नियम में अंश और हर दोनों में (n) रखें। / (a_4=\frac{2(4)+3}{4+1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.
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What is the general term of the sequence \(8,27,64,125,\ldots\)?
B. (a_n=(n+1)3)
यह \(2^3,3^3,4^3,5^3,\ldots\) है इसलिए (a_n=(n+1)3)। घन अनुक्रम में आधार संख्या पहचानें। / This is \(2^3,3^3,4^3,5^3,\ldots\), so (a_n=(n+1)3). In cube sequences identify the base number.
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Which is the correct rule for the sequence \(6,14,24,36,\ldots\)?
D. \(a_n=n^2+5n\)
\(n^2+5n\) से (6,14,24,36) मिलते हैं। विकल्पों को (n=1,2,3) से जांचें। / \(n^2+5n\) gives (6,14,24,36). Check the options using (n=1,2,3).
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If \(a_n=7-3n\), what is the common difference of this sequence?
A. (-3)
रैखिक नियम में (n) का गुणांक (-3) है इसलिए समान अंतर (-3) है। \(a_n\) के गुणांक को ध्यान से पढ़ें। / In a linear rule the coefficient of (n) is (-3), so the common difference is (-3). Read the coefficient of \(a_n\) carefully.
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If \(a_n=4n^2-1\), what is the value of \(a_5+a_1\)?
C. (102)
\(a_5=99\) और \(a_1=3\), इसलिए योग (102) है। दोनों पद निकालकर ही जोड़ें। / \(a_5=99\) and \(a_1=3\), so the sum is (102). Find both terms before adding.
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In the sequence \(45,40,35,30,\ldots\), which term is (0)?
B. (10)वाँ(10)th
सामान्य पद \(a_n=50-5n\) है और (50-5n=0) से (n=10)। घटते अनुक्रम में भी पद-संख्या प्राकृतिक रहती है। / The general term is \(a_n=50-5n\), and (50-5n=0) gives (n=10). Even in a decreasing sequence the position remains natural.
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If \(a_n=2n^2+2n+1\), what are the first three terms?
D. (5,13,25)
(n=1,2,3) रखने पर (5,13,25) मिलते हैं। द्विघात नियम में हर पद की गणना सावधानी से करें। / Putting (n=1,2,3) gives (5,13,25). Calculate each term carefully in a quadratic rule.
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A. \(a_n=\frac{n^2+1}{n+2}\)
अंश \(n^2+1\) और हर (n+2) है इसलिए \(a_n=\frac{n^2+1}{n+2}\)। भिन्न अनुक्रम में अंश का अलग पैटर्न पहचानें। / The numerator is \(n^2+1\) and the denominator is (n+2), so \(a_n=\frac{n^2+1}{n+2}\). In a fractional sequence identify the numerator pattern separately.
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C. \(a_n=\frac{n}{2n+1}\)
अंश (n) और हर (2n+1) है इसलिए \(a_n=\frac{n}{2n+1}\)। भिन्नों में हर की बढ़त को ध्यान से देखें। / The numerator is (n) and the denominator is (2n+1), so \(a_n=\frac{n}{2n+1}\). In fractions observe the denominator growth carefully.
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