(251) से (300) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of natural numbers from (251) to (300).
Explanation opens after your attempt
Correct Answer
B. (13775)
Step 1
Concept
The sum is \(S_{300}-S_{250}=45150-31375=13775\). The \(S_b-S_{a-1}\) method is fast for large intervals.
Step 2
Why this answer is correct
The correct answer is B. (13775). The sum is \(S_{300}-S_{250}=45150-31375=13775\). The \(S_b-S_{a-1}\) method is fast for large intervals.
Step 3
Exam Tip
योग \(S_{300}-S_{250}=45150-31375=13775\) है। \(S_b-S_{a-1}\) विधि बड़े अंतराल में तेज रहती है।
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यदि \(S_n-S_{n-8}=1228\), तो (n) का मान क्या होगा?
If \(S_n-S_{n-8}=1228\), what will be the value of (n)?
Explanation opens after your attempt
Step 1
Concept
(S_n-S_{n-8}=(n-7)+(n-6)+\cdots+n=8n-28). From (8n-28=1228), (n=157).
Step 2
Why this answer is correct
The correct answer is C. (157). (S_n-S_{n-8}=(n-7)+(n-6)+\cdots+n=8n-28). From (8n-28=1228), (n=157).
Step 3
Exam Tip
(S_n-S_{n-8}=(n-7)+(n-6)+\cdots+n=8n-28) होता है। (8n-28=1228) से (n=157)।
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यदि \(S_n=31375\), तो \(S_{n-12}\) का मान क्या है?
If \(S_n=31375\), what is the value of \(S_{n-12}\)?
Explanation opens after your attempt
Correct Answer
C. (28441)
Step 1
Concept
\(31375=S_{250}\), so \(S_{238}=\frac{238\cdot239}{2}=28441\). Identify (n) first and reduce it by (12).
Step 2
Why this answer is correct
The correct answer is C. (28441). \(31375=S_{250}\), so \(S_{238}=\frac{238\cdot239}{2}=28441\). Identify (n) first and reduce it by (12).
Step 3
Exam Tip
\(31375=S_{250}\), इसलिए \(S_{238}=\frac{238\cdot239}{2}=28441\)। पहले (n) पहचानकर (12) कम करें।
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यदि \(S_n-S_{n-1}=225\), तो \(S_{n+1}\) का मान क्या होगा?
If \(S_n-S_{n-1}=225\), what will be the value of \(S_{n+1}\)?
Explanation opens after your attempt
Correct Answer
B. (25651)
Step 1
Concept
\(S_n-S_{n-1}=n\), so (n=225) and \(S_{226}=25651\). For the next sum, take (n+1).
Step 2
Why this answer is correct
The correct answer is B. (25651). \(S_n-S_{n-1}=n\), so (n=225) and \(S_{226}=25651\). For the next sum, take (n+1).
Step 3
Exam Tip
\(S_n-S_{n-1}=n\), इसलिए (n=225) और \(S_{226}=25651\)। अगले योग के लिए (n+1) लें।
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(401) से (450) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (401) to (450)?
Explanation opens after your attempt
Correct Answer
A. (21275)
Step 1
Concept
The sum is \(S_{450}-S_{400}=101475-80200=21275\). Use the subtraction method for large intervals.
Step 2
Why this answer is correct
The correct answer is A. (21275). The sum is \(S_{450}-S_{400}=101475-80200=21275\). Use the subtraction method for large intervals.
Step 3
Exam Tip
योग \(S_{450}-S_{400}=101475-80200=21275\) है। बड़े अंतराल में घटाव विधि उपयोग करें।
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यदि \(S_n=2145\), तो \(S_{2n}-S_n\) का मान क्या होगा?
If \(S_n=2145\), what will be the value of \(S_{2n}-S_n\)?
Explanation opens after your attempt
Step 1
Concept
\(2145=S_{65}\), so \(S_{2n}-S_n=S_{130}-S_{65}=8515-2145=6370\). Identify (n) first.
Step 2
Why this answer is correct
The correct answer is C. (6370). \(2145=S_{65}\), so \(S_{2n}-S_n=S_{130}-S_{65}=8515-2145=6370\). Identify (n) first.
Step 3
Exam Tip
\(2145=S_{65}\), इसलिए \(S_{2n}-S_n=S_{130}-S_{65}=8515-2145=6370\)। पहले (n) पहचानें।
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पहले (180) और पहले (120) प्राकृतिक संख्याओं के योगों का अंतर क्या है?
What is the difference between the sums of the first (180) and first (120) natural numbers?
Explanation opens after your attempt
Step 1
Concept
\(S_{180}-S_{120}=16290-7260=9030\). This is the sum from (121) to (180).
Step 2
Why this answer is correct
The correct answer is B. (9030). \(S_{180}-S_{120}=16290-7260=9030\). This is the sum from (121) to (180).
Step 3
Exam Tip
\(S_{180}-S_{120}=16290-7260=9030\)। यह (121) से (180) तक का योग है।
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यदि \(S_{n+5}-S_{n-5}=1205\), तो (n) का मान क्या होगा?
If \(S_{n+5}-S_{n-5}=1205\), what will be the value of (n)?
Explanation opens after your attempt
Step 1
Concept
This difference is ((n-4)+(n-3)+\cdots+(n+5)=10n+5). From (10n+5=1205), (n=120).
Step 2
Why this answer is correct
The correct answer is A. (120). This difference is ((n-4)+(n-3)+\cdots+(n+5)=10n+5). From (10n+5=1205), (n=120).
Step 3
Exam Tip
यह अंतर ((n-4)+(n-3)+\cdots+(n+5)=10n+5) है। (10n+5=1205) से (n=120)।
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यदि \(S_n=13041\), तो (n) का मान क्या है?
If \(S_n=13041\), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{161\cdot162}{2}=13041\), so (n=161). Check the options in the formula.
Step 2
Why this answer is correct
The correct answer is D. (161). \(\frac{161\cdot162}{2}=13041\), so (n=161). Check the options in the formula.
Step 3
Exam Tip
\(\frac{161\cdot162}{2}=13041\), इसलिए (n=161)। विकल्पों को सूत्र में रखकर जांचें।
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यदि \(S_n-S_{n-2}=199\), तो \(S_n\) का मान क्या होगा?
If \(S_n-S_{n-2}=199\), what will be the value of \(S_n\)?
Explanation opens after your attempt
Step 1
Concept
\(S_n-S_{n-2}=2n-1\). From (2n-1=199), (n=100), so \(S_n=5050\).
Step 2
Why this answer is correct
The correct answer is C. (5050). \(S_n-S_{n-2}=2n-1\). From (2n-1=199), (n=100), so \(S_n=5050\).
Step 3
Exam Tip
\(S_n-S_{n-2}=2n-1\) है। (2n-1=199) से (n=100), इसलिए \(S_n=5050\)।
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(301) से (350) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of natural numbers from (301) to (350).
Explanation opens after your attempt
Correct Answer
B. (16275)
Step 1
Concept
The sum is \(S_{350}-S_{300}=61425-45150=16275\). If it starts from (301), subtract the sum up to (300).
Step 2
Why this answer is correct
The correct answer is B. (16275). The sum is \(S_{350}-S_{300}=61425-45150=16275\). If it starts from (301), subtract the sum up to (300).
Step 3
Exam Tip
योग \(S_{350}-S_{300}=61425-45150=16275\) है। (301) से शुरू हो तो (300) तक का योग घटाएं।
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यदि (n=50), तो \(S_{2n}-S_n\) का मान क्या है?
If (n=50), what is the value of \(S_{2n}-S_n\)?
Explanation opens after your attempt
Step 1
Concept
\(S_{2n}-S_n=S_{100}-S_{50}=5050-1275=3775\). Find (2n) first.
Step 2
Why this answer is correct
The correct answer is A. (3775). \(S_{2n}-S_n=S_{100}-S_{50}=5050-1275=3775\). Find (2n) first.
Step 3
Exam Tip
\(S_{2n}-S_n=S_{100}-S_{50}=5050-1275=3775\)। पहले (2n) निकालें।
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यदि \(S_n=11175\), तो \(S_n-S_{n-4}\) क्या होगा?
If \(S_n=11175\), what will be \(S_n-S_{n-4}\)?
Explanation opens after your attempt
Step 1
Concept
\(11175=S_{149}\), so the difference is (146+147+148+149=590). Add the last four terms.
Step 2
Why this answer is correct
The correct answer is D. (590). \(11175=S_{149}\), so the difference is (146+147+148+149=590). Add the last four terms.
Step 3
Exam Tip
\(11175=S_{149}\), इसलिए अंतर (146+147+148+149=590) है। अंतिम चार पद जोड़ें।
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पहले (100) और पहले (50) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?
What is the ratio of the sums of the first (100) and first (50) natural numbers?
Explanation opens after your attempt
Correct Answer
C. (202:51)
Step 1
Concept
\(S_{100}:S_{50}=5050:1275=202:51\). Simplify the ratio fully.
Step 2
Why this answer is correct
The correct answer is C. (202:51). \(S_{100}:S_{50}=5050:1275=202:51\). Simplify the ratio fully.
Step 3
Exam Tip
\(S_{100}:S_{50}=5050:1275=202:51\)। अनुपात को पूरी तरह सरल करें।
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(211) से (260) तक प्राकृतिक संख्याओं का योग कितना है?
How much is the sum of natural numbers from (211) to (260)?
Explanation opens after your attempt
Correct Answer
B. (11775)
Step 1
Concept
The sum is \(S_{260}-S_{210}=33930-22155=11775\). For large intervals, use \(S_b-S_{a-1}\).
Step 2
Why this answer is correct
The correct answer is B. (11775). The sum is \(S_{260}-S_{210}=33930-22155=11775\). For large intervals, use \(S_b-S_{a-1}\).
Step 3
Exam Tip
योग \(S_{260}-S_{210}=33930-22155=11775\) है। बड़े अंतराल में \(S_b-S_{a-1}\) प्रयोग करें।
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यदि \(S_n-S_{n-7}=1330\), तो (n) का मान क्या होगा?
If \(S_n-S_{n-7}=1330\), what will be the value of (n)?
Explanation opens after your attempt
Step 1
Concept
\(S_n-S_{n-7}=7n-21\). From (7n-21=1330), (n=193).
Step 2
Why this answer is correct
The correct answer is A. (193). \(S_n-S_{n-7}=7n-21\). From (7n-21=1330), (n=193).
Step 3
Exam Tip
\(S_n-S_{n-7}=7n-21\) होता है। (7n-21=1330) से (n=193)।
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यदि \(S_n=19900\), तो (n) का मान क्या है?
If \(S_n=19900\), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{199\cdot200}{2}=19900\), so (n=199). Halve the even number and multiply.
Step 2
Why this answer is correct
The correct answer is D. (199). \(\frac{199\cdot200}{2}=19900\), so (n=199). Halve the even number and multiply.
Step 3
Exam Tip
\(\frac{199\cdot200}{2}=19900\), इसलिए (n=199)। सम संख्या को आधा करके गुणा करें।
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पहले (175) प्राकृतिक संख्याओं के योग का (40%) कितना है?
What is (40%) of the sum of the first (175) natural numbers?
Explanation opens after your attempt
Step 1
Concept
\(S_{175}=15400\) and \(40%=\frac{2}{5}\), so the value is (6160). Convert the percentage into a fraction.
Step 2
Why this answer is correct
The correct answer is C. (6160). \(S_{175}=15400\) and \(40%=\frac{2}{5}\), so the value is (6160). Convert the percentage into a fraction.
Step 3
Exam Tip
\(S_{175}=15400\) और \(40%=\frac{2}{5}\), इसलिए मान (6160) है। प्रतिशत को भिन्न में बदलें।
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(90) से (150) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (90) to (150)?
Explanation opens after your attempt
Step 1
Concept
The sum is \(S_{150}-S_{89}=11325-4005=7320\). If it starts from (90), subtract the sum up to (89).
Step 2
Why this answer is correct
The correct answer is B. (7320). The sum is \(S_{150}-S_{89}=11325-4005=7320\). If it starts from (90), subtract the sum up to (89).
Step 3
Exam Tip
योग \(S_{150}-S_{89}=11325-4005=7320\) है। (90) से शुरू हो तो (89) तक का योग घटाएं।
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यदि \(S_{n+3}-S_{n-2}=760\), तो (n) का मान क्या है?
If \(S_{n+3}-S_{n-2}=760\), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
This difference is ((n-1)+n+(n+1)+(n+2)+(n+3)=5n+5). From (5n+5=760), (n=151).
Step 2
Why this answer is correct
The correct answer is A. (151). This difference is ((n-1)+n+(n+1)+(n+2)+(n+3)=5n+5). From (5n+5=760), (n=151).
Step 3
Exam Tip
यह अंतर ((n-1)+n+(n+1)+(n+2)+(n+3)=5n+5) है। (5n+5=760) से (n=151)।
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यदि \(S_n=1830\), तो \(S_{3n}\) का मान क्या होगा?
If \(S_n=1830\), what will be the value of \(S_{3n}\)?
Explanation opens after your attempt
Correct Answer
D. (16290)
Step 1
Concept
\(1830=S_{60}\), so (3n=180) and \(S_{180}=16290\). Identify (n) first.
Step 2
Why this answer is correct
The correct answer is D. (16290). \(1830=S_{60}\), so (3n=180) and \(S_{180}=16290\). Identify (n) first.
Step 3
Exam Tip
\(1830=S_{60}\), इसलिए (3n=180) और \(S_{180}=16290\)। पहले (n) पहचानें।
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यदि \(S_n+S_{n-1}=12544\) और \(S_n-S_{n-1}=112\), तो \(S_n\) का मान क्या है?
If \(S_n+S_{n-1}=12544\) and \(S_n-S_{n-1}=112\), what is the value of \(S_n\)?
Explanation opens after your attempt
Step 1
Concept
Adding the two equations gives \(2S_n=12656\), so \(S_n=6328\). Adding the equations is the fastest way.
Step 2
Why this answer is correct
The correct answer is C. (6328). Adding the two equations gives \(2S_n=12656\), so \(S_n=6328\). Adding the equations is the fastest way.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर \(2S_n=12656\), इसलिए \(S_n=6328\)। समीकरणों को जोड़ना सबसे तेज है।
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यदि \(S_n=8256\), तो \(S_{n+5}-S_n\) क्या होगा?
If \(S_n=8256\), what will be \(S_{n+5}-S_n\)?
Explanation opens after your attempt
Step 1
Concept
\(8256=S_{128}\), so the difference is (129+130+131+132+133=655). Add the next five terms.
Step 2
Why this answer is correct
The correct answer is B. (655). \(8256=S_{128}\), so the difference is (129+130+131+132+133=655). Add the next five terms.
Step 3
Exam Tip
\(8256=S_{128}\), इसलिए अंतर (129+130+131+132+133=655) है। अगले पांच पदों को जोड़ें।
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पहले (128) और पहले (64) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?
What is the ratio of the sums of the first (128) and first (64) natural numbers?
Explanation opens after your attempt
Correct Answer
C. (258:65)
Step 1
Concept
\(S_{128}:S_{64}=8256:2080=258:65\). Write the ratio in simplest form.
Step 2
Why this answer is correct
The correct answer is C. (258:65). \(S_{128}:S_{64}=8256:2080=258:65\). Write the ratio in simplest form.
Step 3
Exam Tip
\(S_{128}:S_{64}=8256:2080=258:65\)। अनुपात को सरलतम रूप में लिखें।
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(181) से (240) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of natural numbers from (181) to (240).
Explanation opens after your attempt
Correct Answer
A. (12630)
Step 1
Concept
The sum is \(S_{240}-S_{180}=28920-16290=12630\). The subtraction method is quick for large intervals.
Step 2
Why this answer is correct
The correct answer is A. (12630). The sum is \(S_{240}-S_{180}=28920-16290=12630\). The subtraction method is quick for large intervals.
Step 3
Exam Tip
योग \(S_{240}-S_{180}=28920-16290=12630\) है। बड़े अंतराल में घटाव विधि तेज होती है।
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यदि \(S_n-S_{n-2}=257\), तो \(S_n\) का मान क्या है?
If \(S_n-S_{n-2}=257\), what is the value of \(S_n\)?
Explanation opens after your attempt
Step 1
Concept
\(S_n-S_{n-2}=2n-1\). From (2n-1=257), (n=129), so \(S_{129}=8385\).
Step 2
Why this answer is correct
The correct answer is D. (8385). \(S_n-S_{n-2}=2n-1\). From (2n-1=257), (n=129), so \(S_{129}=8385\).
Step 3
Exam Tip
\(S_n-S_{n-2}=2n-1\) है। (2n-1=257) से (n=129), अतः \(S_{129}=8385\)।
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यदि \(S_n=10440\), तो (n) का मान क्या है?
If \(S_n=10440\), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{144\cdot145}{2}=10440\), so (n=144). Check the answer by substituting options in the formula.
Step 2
Why this answer is correct
The correct answer is C. (144). \(\frac{144\cdot145}{2}=10440\), so (n=144). Check the answer by substituting options in the formula.
Step 3
Exam Tip
\(\frac{144\cdot145}{2}=10440\), इसलिए (n=144)। सूत्र में विकल्प रखकर उत्तर जांचें।
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\(S_{120}-S_{80}+S_{40}\) का मान क्या है?
What is the value of \(S_{120}-S_{80}+S_{40}\)?
Explanation opens after your attempt
Step 1
Concept
\(S_{120}-S_{80}+S_{40}=7260-3240+820=4840\). Write each partial sum separately.
Step 2
Why this answer is correct
The correct answer is B. (4840). \(S_{120}-S_{80}+S_{40}=7260-3240+820=4840\). Write each partial sum separately.
Step 3
Exam Tip
\(S_{120}-S_{80}+S_{40}=7260-3240+820=4840\)। हर आंशिक योग अलग लिखें।
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(75) से (125) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (75) to (125)?
Explanation opens after your attempt
Step 1
Concept
The sum is \(S_{125}-S_{74}=7875-2775=5100\). Subtract the sum before the lower limit.
Step 2
Why this answer is correct
The correct answer is A. (5100). The sum is \(S_{125}-S_{74}=7875-2775=5100\). Subtract the sum before the lower limit.
Step 3
Exam Tip
योग \(S_{125}-S_{74}=7875-2775=5100\) है। निचली सीमा से पहले का योग घटाएं।
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यदि \(S_{n+1}-S_{n-4}=695\), तो (n) का मान क्या होगा?
If \(S_{n+1}-S_{n-4}=695\), what will be the value of (n)?
Explanation opens after your attempt
Step 1
Concept
This difference is ((n-3)+(n-2)+(n-1)+n+(n+1)=5n-5). From (5n-5=695), (n=140).
Step 2
Why this answer is correct
The correct answer is D. (140). This difference is ((n-3)+(n-2)+(n-1)+n+(n+1)=5n-5). From (5n-5=695), (n=140).
Step 3
Exam Tip
यह अंतर ((n-3)+(n-2)+(n-1)+n+(n+1)=5n-5) है। (5n-5=695) से (n=140)।
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