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 321-330 of 600 questions.
What is the ratio of the sums of the first (45) and first (30) natural numbers?
A. (69:31)
\(S_{45}:S_{30}=1035:465=69:31\)। अनुपात को सबसे छोटे रूप में घटाएं। / \(S_{45}:S_{30}=1035:465=69:31\). Reduce the ratio to its lowest form.
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If \(S_n-S_{n-2}=101\), what is the value of \(S_n\)?
B. (1326)
\(S_n-S_{n-2}=2n-1\), इसलिए (2n-1=101) से (n=51)। अतः \(S_{51}=1326\)। / \(S_n-S_{n-2}=2n-1\), so (2n-1=101) gives (n=51). Hence \(S_{51}=1326\).
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What is the sum of natural numbers from (15) to (45)?
B. (930)
योग \(S_{45}-S_{14}=1035-105=930\) है। (15) से शुरू हो तो (14) तक का योग घटाएं। / The sum is \(S_{45}-S_{14}=1035-105=930\). If it starts from (15), subtract the sum up to (14).
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If the sum of the first (n) natural numbers is \(S_n\), what is \(S_{n+1}-S_{n-1}\) equal to?
B. (2n+1)
(S_{n+1}-S_{n-1}=n+(n+1)=2n+1)। बीच के कटे हुए पदों को पहचानें। / (S_{n+1}-S_{n-1}=n+(n+1)=2n+1). Identify the terms left after cancellation.
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What is the difference between the sums of the first (72) and first (48) natural numbers?
A. (1452)
\(S_{72}-S_{48}=2628-1176=1452\)। यह (49) से (72) तक का योग है। / \(S_{72}-S_{48}=2628-1176=1452\). This is the sum from (49) to (72).
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If \(S_n=4005\), what is the value of (n)?
C. (89)
\(\frac{89\cdot90}{2}=4005\), इसलिए (n=89)। सम संख्या को आधा कर गुणा करें। / \(\frac{89\cdot90}{2}=4005\), so (n=89). Halve the even number and multiply.
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If \(S_n=1081\), what is the value of \(S_{n+4}-S_n\)?
A. (194)
\(1081=S_{46}\), इसलिए अंतर (47+48+49+50=194) है। अगले चार पद जोड़ें। / \(1081=S_{46}\), so the difference is (47+48+49+50=194). Add the next four terms.
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What will be the sum of natural numbers from (40) to (80)?
B. (2460)
योग \(S_{80}-S_{39}=3240-780=2460\) है। (40) से शुरू हो तो (39) तक का योग घटाएं। / The sum is \(S_{80}-S_{39}=3240-780=2460\). If it starts from (40), subtract the sum up to (39).
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If \(S_n-S_{50}=1575\), what is the value of (n)?
B. (75)
\(S_{75}-S_{50}=2850-1275=1575\), इसलिए (n=75)। दिए अंतर को \(S_n-S_k\) से मिलाएं। / \(S_{75}-S_{50}=2850-1275=1575\), so (n=75). Match the given difference with \(S_n-S_k\).
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What is the sum of the sums of the first (18) and first (12) natural numbers?
B. (249)
\(S_{18}+S_{12}=171+78=249\)। दोनों आंशिक योग अलग निकालें। / \(S_{18}+S_{12}=171+78=249\). Find both partial sums separately.
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