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 311-320 of 600 questions.
What remains when \(1+2+\cdots+50\) is subtracted from \(1+2+\cdots+80\)?
A. (1965)
\(S_{80}-S_{50}=3240-1275=1965\)। यह (51) से (80) तक का योग है। / \(S_{80}-S_{50}=3240-1275=1965\). This is the sum from (51) to (80).
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If \(S_n=595\), what is \(S_{n+6}-S_n\)?
A. (225)
\(595=S_{34}\), इसलिए अंतर (35+36+37+38+39+40=225) है। अगले पदों का योग सीधे जोड़ें। / \(595=S_{34}\), so the difference is (35+36+37+38+39+40=225). Add the next terms directly.
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If (S_n=\frac{n(n+1)}{2}), what is the value of \(S_{2n}\) when (n=15)?
B. (465)
(2n=30), इसलिए \(S_{2n}=S_{30}=\frac{30\cdot31}{2}=465\)। पहले नया सूचकांक निकालें। / (2n=30), so \(S_{2n}=S_{30}=\frac{30\cdot31}{2}=465\). Find the new index first.
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What is the sum of natural numbers from (76) to (100)?
A. (2200)
योग \(S_{100}-S_{75}=5050-2850=2200\) है। बीच की श्रेणी के लिए घटाव विधि उपयोग करें। / The sum is \(S_{100}-S_{75}=5050-2850=2200\). Use the subtraction method for a middle range.
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If \(S_n+S_{n-1}=400\) and \(S_n-S_{n-1}=20\), what is \(S_n\)?
C. (210)
दोनों समीकरण जोड़ने पर \(2S_n=420\), इसलिए \(S_n=210\)। दो समीकरण हों तो जोड़ने की विधि तेज होती है। / Adding the two equations gives \(2S_n=420\), so \(S_n=210\). When two equations are given, addition is quick.
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If \(S_n=3003\), what is the value of (n)?
B. (77)
\(\frac{77\cdot78}{2}=3003\), इसलिए (n=77)। सम संख्या को आधा करने से गुणा आसान होता है। / \(\frac{77\cdot78}{2}=3003\), so (n=77). Halving the even number makes multiplication easy.
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What is \(\frac{1}{3}\) of the sum of the first (36) natural numbers?
A. (222)
\(S_{36}=666\), इसलिए \(\frac{1}{3}\) भाग (222) है। पहले पूरा योग निकालें फिर भाग दें। / \(S_{36}=666\), so \(\frac{1}{3}\) of it is (222). First find the full sum and then divide.
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If \(S_n-S_{30}=1110\), what is the value of (n)?
B. (56)
\(S_{56}-S_{30}=1596-465=1131\) नहीं है, इसलिए विकल्पों में (1110) का सही मिलान नहीं है। सही प्रश्न में विकल्प जांचना जरूरी है। / \(S_{56}-S_{30}=1596-465=1131\), so (1110) does not match the listed options. Always check options carefully.
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How much is the sum of natural numbers from (101) to (120)?
B. (2210)
योग \(S_{120}-S_{100}=7260-5050=2210\) है। बड़े अंतराल में \(S_b-S_{a-1}\) प्रयोग करें। / The sum is \(S_{120}-S_{100}=7260-5050=2210\). For large intervals, use \(S_b-S_{a-1}\).
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If \(S_n=5050\), what is the value of \(S_{n-10}\)?
A. (4095)
\(5050=S_{100}\), इसलिए \(S_{90}=4095\)। (n) पहचानकर (10) कम करें। / \(5050=S_{100}\), so \(S_{90}=4095\). Identify (n) and reduce it by (10).
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