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 361-370 of 600 questions.
If \(a_n=2n+1\) and \(b_n=n^2-1\), what is \(a_4+b_4\)?
B. (24)
\(a_4=9\) और \(b_4=15\) इसलिए योग (24) है। दो नियम हों तो दोनों में वही (n) रखें। / \(a_4=9\) and \(b_4=15\), so the sum is (24). When there are two rules use the same (n) in both.
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What will be the (8)th term of the sequence \(5,11,19,29,\ldots\)?
D. (89)
इसका नियम \(a_n=n^2+3n+1\) है इसलिए \(a_8=64+24+1=89\)। पहले सामान्य नियम पहचानें फिर पद निकालें। / Its rule is \(a_n=n^2+3n+1\), so \(a_8=64+24+1=89\). First identify the general rule and then find the term.
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Which is the correct rule for the sequence \(2,7,14,23,\ldots\)?
A. \(a_n=n^2+2n-1\)
\(n^2+2n-1\) से (2,7,14,23) मिलते हैं। बढ़ते अंतर दिखें तो द्विघात नियम की जांच करें। / \(n^2+2n-1\) gives (2,7,14,23). When differences increase, check a quadratic rule.
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Which statement about (50) is correct for the sequence \(8,12,16,20,\ldots\)?
C. (50) इस अनुक्रम का पद नहीं है(50) is not a term of this sequence
सामान्य पद \(a_n=4n+4\) है और (4n+4=50) से \(n=\frac{23}{2}\) मिलता है। पद-संख्या प्राकृतिक संख्या न हो तो दिया पद अनुक्रम में नहीं होगा। / The general term is \(a_n=4n+4\), and (4n+4=50) gives \(n=\frac{23}{2}\). If the position is not a natural number, the given number is not a term.
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What is the general term of the sequence \(1,9,25,49,\ldots\)?
B. (a_n=(2n-1)2)
यह विषम संख्याओं के वर्ग \(1^2,3^2,5^2,7^2,\ldots\) हैं इसलिए (a_n=(2n-1)2)। वर्गों में आधार का पैटर्न देखें। / These are squares of odd numbers \(1^2,3^2,5^2,7^2,\ldots\), so (a_n=(2n-1)2). In squares observe the base pattern.
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If \(a_n=5^n\), what is the value of \(a_4\)?
D. (625)
\(a_4=5^4=625\)। घातांक वाले नियम में गुणा बार-बार करना याद रखें। / \(a_4=5^4=625\). In exponential rules remember repeated multiplication.
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What is the general term of the sequence \(\frac{1}{2},\frac{3}{3},\frac{5}{4},\frac{7}{5},\ldots\)?
A. \(a_n=\frac{2n-1}{n+1}\)
अंश (2n-1) और हर (n+1) है इसलिए \(a_n=\frac{2n-1}{n+1}\)। भिन्न अनुक्रम में दोनों भागों का अलग नियम बनाएं। / The numerator is (2n-1) and the denominator is (n+1), so \(a_n=\frac{2n-1}{n+1}\). In a fraction sequence form rules for both parts separately.
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In an arithmetic sequence, \(a_2=7\) and \(a_5=16\). What is its general term?
C. \(a_n=3n+1\)
\(a_5-a_2=9\) और तीन अंतर हैं इसलिए (d=3), फिर \(a_n=3n+1\)। दो दिए पदों से पहले समान अंतर निकालें। / \(a_5-a_2=9\) and there are three gaps, so (d=3), then \(a_n=3n+1\). From two given terms first find the common difference.
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Which option contains the first three terms formed by \(a_n=n^2+3n-1\)?
B. (3,9,17)
(n=1,2,3) रखने पर (3,9,17) मिलते हैं। विकल्प जांचने के लिए शुरुआती पद जल्दी निकालें। / Putting (n=1,2,3) gives (3,9,17). To check options, quickly find the initial terms.
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If \(a_n=kn+2\) and \(a_7=37\), what is the value of (k)?
D. (5)
(7k+2=37) से (7k=35) और (k=5)। अज्ञात गुणांक निकालने के लिए दिया पद substitute करें। / From (7k+2=37), (7k=35) and (k=5). Substitute the given term to find the unknown coefficient.
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