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 441-450 of 600 questions.
If \(S_n-S_{n-1}=126\) and \(S_m=1953\), what is (n-m)?
C. (64)
पहले (n=126) और \(S_m=1953\) से (m=62), इसलिए (n-m=64)। लगातार योगों का अंतर सूचकांक देता है। / First (n=126), and \(S_m=1953\) gives (m=62), so (n-m=64). The difference of consecutive sums gives the index.
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Which sum is obtained by adding (116+117+118+119+120) to \(S_{115}\)?
D. \(S_{120}\)
\(S_{115}+116+117+118+119+120=S_{120}\) है। लगातार नए पद जुड़ने पर अंतिम पद नया सूचकांक बनता है। / \(S_{115}+116+117+118+119+120=S_{120}\). When consecutive new terms are added, the last term becomes the new index.
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If \(S_n=7875\), what is the value of (n)?
A. (125)
\(S_{125}=\frac{125\times126}{2}=7875\) इसलिए (n=125) है। बड़े मानों में \(2S_n\) से पहचान आसान होती है। / \(S_{125}=\frac{125\times126}{2}=7875\), so (n=125). For large values, using \(2S_n\) makes identification easier.
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Find the value of \(S_{29}+S_{58}+S_{87}\).
B. (5974)
\(S_{29}=435\), \(S_{58}=1711\) और \(S_{87}=3828\), इसलिए कुल (5974) है। तीन अलग सूचकांकों को ध्यान से जोड़ें। / \(S_{29}=435\), \(S_{58}=1711\), and \(S_{87}=3828\), so the total is (5974). Add the three different indices carefully.
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The sum of the first (n) natural numbers is (10878). What is the value of (n-25)?
C. (122)
\(S_{147}=10878\) इसलिए (n=147) और (n-25=122)। पहले (n) निकालें फिर पूछा गया मान दें। / \(S_{147}=10878\), so (n=147) and (n-25=122). Find (n) first and then answer what is asked.
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If \(S_{n+2}-S_{n-2}=286\), what will be the value of (n)?
D. (71)
अंतर ((n-1)+n+(n+1)+(n+2)=4n+2) है और (4n+2=286) से (n=71)। बीच के चार पदों का योग बनाएं। / The difference is ((n-1)+n+(n+1)+(n+2)=4n+2), and (4n+2=286) gives (n=71). Form the sum of the four middle terms.
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What is the value of \(S_{250}-S_{240}\)?
A. (2455)
अंतर \(241+242+\cdots+250=2455\) है। बड़े सूचकांकों में भी केवल बीच के पद जोड़ने होते हैं। / The difference is \(241+242+\cdots+250=2455\). Even with large indices, only the terms in between need to be added.
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If \(S_n=9180\), what is the value of (n)?
B. (135)
\(S_{135}=\frac{135\times136}{2}=9180\) इसलिए (n=135) है। \(2S_n\) को क्रमागत गुणनफल से मिलाएं। / \(S_{135}=\frac{135\times136}{2}=9180\), so (n=135). Match \(2S_n\) with a consecutive product.
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What is (2) times the difference between \(S_{72}\) and \(S_{36}\)?
C. (3924)
\(S_{72}-S_{36}=2628-666=1962\) और \(2\times1962=3924\) है। पहले अंतर निकालें फिर गुणा करें। / \(S_{72}-S_{36}=2628-666=1962\), and \(2\times1962=3924\). First find the difference and then multiply.
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If \(S_y=7381\), what will be the value of \(S_{y+2}\)?
C. (7626)
\(S_{121}=7381\) है इसलिए \(S_{123}=7381+122+123=7626\)। दो आगे जाने पर अगले दो पद जोड़ें। / \(S_{121}=7381\), so \(S_{123}=7381+122+123=7626\). To move two steps ahead, add the next two terms.
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