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 sum of the first (150) natural numbers?
B. (11325)
\(S_{150}=\frac{150\times151}{2}=11325\) है। बड़े (n) में पहले (150) को (75) बनाएं। / \(S_{150}=\frac{150\times151}{2}=11325\). For large (n), first change (150) to (75).
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Find the value of \(S_{100}-S_{90}+S_{10}\).
A. (1010)
(5050-4095+55=1010) है। पहले घटाव करें फिर छोटे योग को जोड़ें। / (5050-4095+55=1010). First subtract and then add the smaller sum.
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If \(S_{3k}=1176\), what will be the value of (k)?
C. (16)
\(S_{48}=1176\) इसलिए (3k=48) और (k=16)। पहले (S) के सूचकांक को पहचानें। / \(S_{48}=1176\), so (3k=48) and (k=16). First identify the index of (S).
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What is the sum of \(71+72+73+\cdots+100\)?
B. (2565)
योग \(S_{100}-S_{70}=5050-2485=2565\) है। (71) से शुरू होने पर (70) तक का योग घटाएं। / The sum is \(S_{100}-S_{70}=5050-2485=2565\). When starting from (71), subtract the sum up to (70).
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If \(S_n=1830\), what is the value of \(S_{n+10}-S_n\)?
B. (655)
\(S_{60}=1830\) इसलिए अंतर \(61+62+\cdots+70=655\) है। आगे के (10) पदों का योग अलग से निकालें। / \(S_{60}=1830\), so the difference is \(61+62+\cdots+70=655\). Find the sum of the next (10) terms separately.
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At which (n) will \(S_n\) first become greater than (5000)?
C. (100)
\(S_{99}=4950\) और \(S_{100}=5050\), इसलिए पहली बार (n=100) पर (5000) से अधिक है। सीमा प्रश्न में आसपास के मान जांचें। / \(S_{99}=4950\) and \(S_{100}=5050\), so it first exceeds (5000) at (n=100). In boundary questions, check nearby values.
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B. (1640)
कुल वाहन \(2S_{40}=2\times820=1640\) हैं। (2r) जैसा पैटर्न हो तो (2) को बाहर लें। / Total vehicles are \(2S_{40}=2\times820=1640\). For a pattern like (2r), take (2) outside.
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If \(S_x=2278\), what is the value of (x)?
B. (67)
\(S_{67}=\frac{67\times68}{2}=2278\) इसलिए (x=67) है। \(2S_x\) करके क्रमागत गुणनफल ढूंढें। / \(S_{67}=\frac{67\times68}{2}=2278\), so (x=67). Use \(2S_x\) to find the consecutive product.
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What is the value of \(S_{33}+S_{66}-S_{22}\)?
B. (2496)
(561+2211-253=2519) है। प्रत्येक योग को सही लिखना सबसे जरूरी है। / (561+2211-253=2519). Writing each sum correctly is the most important step.
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D. (4060)
अंतर \(S_{120}-S_{80}=7260-3240=4020\) है। यह (81) से (120) तक का योग है। / The difference is \(S_{120}-S_{80}=7260-3240=4020\). It is the sum from (81) to (120).
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