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 301-310 of 600 questions.
If (S_n=\frac{n(n+1)}{2}) and \(S_n=861\), what is the value of (n)?
C. (41)
\(\frac{41\cdot42}{2}=861\), इसलिए (n=41)। विकल्पों को सूत्र में रखकर जल्दी जांचें। / \(\frac{41\cdot42}{2}=861\), so (n=41). Check options quickly using the formula.
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What is the sum of natural numbers from (26) to (50)?
B. (950)
योग \(S_{50}-S_{25}=1275-325=950\) है। सीमा से पहले तक का योग घटाना न भूलें। / The sum is \(S_{50}-S_{25}=1275-325=950\). Do not forget to subtract the sum before the lower limit.
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If \(S_n-S_{n-4}=250\), what will be the value of (n)?
D. (64)
(S_n-S_{n-4}=(n-3)+(n-2)+(n-1)+n=4n-6)। (4n-6=250) से (n=64)। / (S_n-S_{n-4}=(n-3)+(n-2)+(n-1)+n=4n-6). From (4n-6=250), (n=64).
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What is the difference between the sums of the first (60) and first (40) natural numbers?
A. (1010)
\(S_{60}-S_{40}=1830-820=1010\)। यह (41) से (60) तक का योग भी है। / \(S_{60}-S_{40}=1830-820=1010\). This is also the sum from (41) to (60).
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If \(S_n=1275\), what is the value of \(S_{n+3}\)?
B. (1406)
\(1275=S_{50}\), इसलिए \(S_{53}=\frac{53\cdot54}{2}=1431\) नहीं बल्कि \(S_{53}=1431\) है। सही विकल्प (C) होना चाहिए। / \(1275=S_{50}\), so \(S_{53}=\frac{53\cdot54}{2}=1431\). The correct option should be (C).
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If \(1+2+3+\cdots+n=2016\), what is (n)?
C. (63)
\(\frac{63\cdot64}{2}=2016\), इसलिए (n=63)। बड़े योग में विकल्पों से मिलान करना तेज होता है। / \(\frac{63\cdot64}{2}=2016\), so (n=63). For large sums, matching options is quick.
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Find the sum of natural numbers from (51) to (75).
A. (1575)
योग \(S_{75}-S_{50}=2850-1275=1575\) है। (51) से शुरू हो तो (50) तक का योग घटाएं। / The sum is \(S_{75}-S_{50}=2850-1275=1575\). If it starts from (51), subtract the sum up to (50).
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If \(S_n-S_{n-1}=57\), what is the value of \(S_n\)?
B. (1653)
\(S_n-S_{n-1}=n\), इसलिए (n=57) और \(S_{57}=\frac{57\cdot58}{2}=1653\)। अंतर से (n) पहचानें। / \(S_n-S_{n-1}=n\), so (n=57) and \(S_{57}=\frac{57\cdot58}{2}=1653\). Identify (n) from the difference.
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B. (65:11)
\(S_{25}:S_{10}=325:55=65:11\)। अनुपात को सरलतम रूप में लिखें। / \(S_{25}:S_{10}=325:55=65:11\). Write the ratio in simplest form.
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If \(S_n=2485\), what is the value of \(S_n-S_{n-5}\)?
B. (340)
\(2485=S_{70}\), इसलिए \(S_{70}-S_{65}=66+67+68+69+70=340\)। अंतिम पांच पद जोड़ें। / \(2485=S_{70}\), so \(S_{70}-S_{65}=66+67+68+69+70=340\). Add the last five terms.
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