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 511-520 of 600 questions.
If \(S_{n+2}-S_{n-2}=402\), what will be the value of (n)?
B. (100)
(S_{n+2}-S_{n-2}=(n-1)+n+(n+1)+(n+2)=4n+2)। (4n+2=402) से (n=100)। / (S_{n+2}-S_{n-2}=(n-1)+n+(n+1)+(n+2)=4n+2). From (4n+2=402), (n=100).
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What is (20%) of the sum of the first (150) natural numbers?
C. (2265)
\(S_{150}=11325\) और \(20%=\frac{1}{5}\), इसलिए मान (2265) है। प्रतिशत को भिन्न में बदलें। / \(S_{150}=11325\) and \(20%=\frac{1}{5}\), so the value is (2265). Convert percentage into a fraction.
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If \(S_n=12246\), what is the value of (n)?
C. (156)
\(\frac{156\cdot157}{2}=12246\), इसलिए (n=156)। सम संख्या को आधा करके गुणा करें। / \(\frac{156\cdot157}{2}=12246\), so (n=156). Halve the even number and multiply.
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If \(S_n-S_{70}=5250\), what is the value of (n)?
B. (125)
\(S_{125}-S_{70}=7875-2485=5390\) नहीं है, इसलिए दिए विकल्पों में (5250) का सही मिलान नहीं है। पहले अंतर की जांच करें। / \(S_{125}-S_{70}=7875-2485=5390\), so none of the listed options matches (5250). Check the difference first.
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What is the difference between the sum from (1) to (200) and the sum from (1) to (150)?
B. (8775)
\(S_{200}-S_{150}=20100-11325=8775\)। यह (151) से (200) तक का योग है। / \(S_{200}-S_{150}=20100-11325=8775\). This is the sum from (151) to (200).
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If \(S_n=20100\), what will be the value of \(S_n-S_{n-8}\)?
A. (1572)
\(20100=S_{200}\), इसलिए अंतर \(193+194+\cdots+200=1572\) है। अंतिम (8) पदों का योग लें। / \(20100=S_{200}\), so the difference is \(193+194+\cdots+200=1572\). Take the sum of the last (8) terms.
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If \(S_{3n}=1770\), what is the value of (n)?
B. (19)
\(1770=S_{59}\), इसलिए (3n=59) होगा जो पूर्णांक (n) नहीं देता। सही निष्कर्ष है कि कोई पूर्णांक (n) नहीं है। / \(1770=S_{59}\), so (3n=59), which does not give an integer (n). The correct conclusion is no integer (n).
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What is the sum of natural numbers from (50) to (150)?
A. (10100)
योग \(S_{150}-S_{49}=11325-1225=10100\) है। निचली सीमा से एक कम तक का योग घटाएं। / The sum is \(S_{150}-S_{49}=11325-1225=10100\). Subtract the sum up to one less than the lower limit.
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If \(S_n-S_{n-3}=348\), what is the value of \(S_n\)?
A. (6670)
\(S_n-S_{n-3}=3n-3\), इसलिए (3n-3=348) से (n=117)। अतः \(S_{117}=6903\) होना चाहिए। / \(S_n-S_{n-3}=3n-3\), so (3n-3=348) gives (n=117). Hence \(S_{117}=6903\).
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What is the ratio of the sums of the first (96) and first (72) natural numbers?
B. (194:109)
\(S_{96}:S_{72}=4656:2628=194:109\)। अनुपात को सरलतम रूप में लिखें। / \(S_{96}:S_{72}=4656:2628=194:109\). Write the ratio in simplest form.
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