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 501-510 of 600 questions.
If (S_n=\frac{n(n+1)}{2}) and \(S_n=6670\), what is the value of (n)?
C. (115)
\(\frac{115\cdot116}{2}=6670\), इसलिए (n=115)। बड़े मानों में विकल्पों को सूत्र में रखकर जांचें। / \(\frac{115\cdot116}{2}=6670\), so (n=115). For large values, check options in the formula.
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What is the sum of natural numbers from (41) to (95)?
A. (3740)
योग \(S_{95}-S_{40}=4560-820=3740\) है। सीमा से पहले तक का योग जरूर घटाएं। / The sum is \(S_{95}-S_{40}=4560-820=3740\). Always subtract the sum before the lower limit.
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If \(S_n-S_{n-5}=490\), what will be the value of (n)?
C. (100)
(S_n-S_{n-5}=(n-4)+(n-3)+(n-2)+(n-1)+n=5n-10)। (5n-10=490) से (n=100)। / (S_n-S_{n-5}=(n-4)+(n-3)+(n-2)+(n-1)+n=5n-10). From (5n-10=490), (n=100).
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If \(S_{n+3}-S_n=222\), what is the value of (n)?
B. (72)
(S_{n+3}-S_n=(n+1)+(n+2)+(n+3)=3n+6)। (3n+6=222) से (n=72)। / (S_{n+3}-S_n=(n+1)+(n+2)+(n+3)=3n+6). From (3n+6=222), (n=72).
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What is the difference between the sums of the first (120) and first (85) natural numbers?
C. (3605)
\(S_{120}-S_{85}=7260-3655=3605\)। यह (86) से (120) तक का योग है। / \(S_{120}-S_{85}=7260-3655=3605\). This is the sum from (86) to (120).
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If \(S_n=5050\), what is the value of \(S_{n+4}-S_n\)?
B. (410)
\(5050=S_{100}\), इसलिए अंतर (101+102+103+104=410) है। अगले पदों को सीधे जोड़ें। / \(5050=S_{100}\), so the difference is (101+102+103+104=410). Add the next terms directly.
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What is the ratio of the sums of the first (64) and first (32) natural numbers?
A. (65:33)
\(S_{64}:S_{32}=2080:528=65:33\)। अनुपात को सरलतम रूप में लिखें। / \(S_{64}:S_{32}=2080:528=65:33\). Write the ratio in simplest form.
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If \(S_n+S_{n-1}=4212\) and \(S_n-S_{n-1}=65\), what is the value of \(S_n\)?
A. (2138.5)
दोनों समीकरण जोड़ने पर \(2S_n=4277\), इसलिए \(S_n=2138.5\)। दिए गए आंकड़ों की संगति भी जांचें। / Adding the two equations gives \(2S_n=4277\), so \(S_n=2138.5\). Also check the consistency of the given data.
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Find the sum of natural numbers from (126) to (175).
A. (7525)
योग \(S_{175}-S_{125}=15400-7875=7525\) है। \(S_b-S_{a-1}\) विधि उपयोग करें। / The sum is \(S_{175}-S_{125}=15400-7875=7525\). Use the \(S_b-S_{a-1}\) method.
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If \(S_n=7875\), what is the value of \(S_{n-7}\)?
C. (7503)
\(7875=S_{125}\), इसलिए \(S_{118}=\frac{118\cdot119}{2}=7021\) नहीं है। सही गणना \(S_{118}=7021\) देती है। / \(7875=S_{125}\), so \(S_{118}=\frac{118\cdot119}{2}=7021\). The listed options should be checked carefully.
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