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 491-500 of 600 questions.
If \(S_n-S_{n-1}=154\) and \(S_m=7503\), what is (n-m)?
B. (31)
पहले (n=154) और \(S_m=7503\) से (m=122), इसलिए (n-m=32)। लगातार योगों का अंतर सूचकांक देता है। / First (n=154), and \(S_m=7503\) gives (m=122), so (n-m=32). The difference of consecutive sums gives the index.
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Which sum is obtained by adding \(133+134+\cdots+140\) to \(S_{132}\)?
C. \(S_{140}\)
\(S_{132}+133+134+\cdots+140=S_{140}\) है। लगातार नए पद जुड़ने पर अंतिम पद नया सूचकांक बनता है। / \(S_{132}+133+134+\cdots+140=S_{140}\). When consecutive new terms are added, the last term becomes the new index.
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If \(S_n=11781\), what is the value of (n)?
C. (153)
\(S_{153}=\frac{153\times154}{2}=11781\) इसलिए (n=153) है। बड़े मानों में \(2S_n\) से पहचान आसान होती है। / \(S_{153}=\frac{153\times154}{2}=11781\), so (n=153). For large values, using \(2S_n\) makes identification easier.
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Find the value of \(S_{37}+S_{74}+S_{111}\).
A. (9775)
\(S_{37}=703\), \(S_{74}=2775\) और \(S_{111}=6216\), इसलिए कुल (9694) है। तीन अलग सूचकांकों को ध्यान से जोड़ें। / \(S_{37}=703\), \(S_{74}=2775\), and \(S_{111}=6216\), so the total is (9694). Add the three different indices carefully.
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The sum of the first (n) natural numbers is (13695). What is the value of (n-30)?
B. (135)
\(S_{165}=13695\) इसलिए (n=165) और (n-30=135)। पहले (n) निकालें फिर पूछा गया मान दें। / \(S_{165}=13695\), so (n=165) and (n-30=135). Find (n) first and then answer what is asked.
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If \(S_{n+3}-S_{n-3}=615\), what will be the value of (n)?
D. (102)
अंतर ((n-2)+(n-1)+n+(n+1)+(n+2)+(n+3)=6n+3) है और (6n+3=615) से (n=102)। बीच के छह पदों का योग बनाएं। / The difference is ((n-2)+(n-1)+n+(n+1)+(n+2)+(n+3)=6n+3), and (6n+3=615) gives (n=102). Form the sum of the six middle terms.
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What is the value of \(S_{300}-S_{285}\)?
B. (4395)
अंतर \(286+287+\cdots+300=4395\) है। बड़े सूचकांकों में भी केवल बीच के पद जोड़ने होते हैं। / The difference is \(286+287+\cdots+300=4395\). Even with large indices, only the terms in between need to be added.
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If \(S_n=20100\), what is the value of (n)?
C. (200)
\(S_{200}=\frac{200\times201}{2}=20100\) इसलिए (n=200) है। \(2S_n\) को क्रमागत गुणनफल से मिलाएं। / \(S_{200}=\frac{200\times201}{2}=20100\), so (n=200). Match \(2S_n\) with a consecutive product.
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What is (4) times the difference between \(S_{96}\) and \(S_{48}\)?
A. (13920)
\(S_{96}-S_{48}=4656-1176=3480\) और \(4\times3480=13920\) है। पहले अंतर निकालें फिर गुणा करें। / \(S_{96}-S_{48}=4656-1176=3480\), and \(4\times3480=13920\). First find the difference and then multiply.
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If \(S_y=15931\), what will be the value of \(S_{y+3}\)?
A. (16435)
\(S_{178}=15931\) है इसलिए \(S_{181}=15931+179+180+181=16471\)। तीन आगे जाने पर अगले तीन पद जोड़ें। / \(S_{178}=15931\), so \(S_{181}=15931+179+180+181=16471\). To move three steps ahead, add the next three terms.
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