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Mathematics Quiz - Class 9 Mathematics Expert Level 59 Quiz

Question 1/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (92) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (92) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (4278)

Step 1

Concept

\(S_{92}=\frac{92\times93}{2}=4278\). For large (n), halve the even number first.

Step 2

Why this answer is correct

The correct answer is C. (4278). \(S_{92}=\frac{92\times93}{2}=4278\). For large (n), halve the even number first.

Step 3

Exam Tip

\(S_{92}=\frac{92\times93}{2}=4278\) है। बड़े (n) में पहले सम संख्या को आधा करें।

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Question 2/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि पहली (n) प्राकृतिक संख्याओं का योग (4950) है तो (n) का मान क्या है?

If the sum of the first (n) natural numbers is (4950), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (99)

Step 1

Concept

\(S_{99}=\frac{99\times100}{2}=4950\), so (n=99). Match \(2S_n\) with the product of two consecutive numbers.

Step 2

Why this answer is correct

The correct answer is C. (99). \(S_{99}=\frac{99\times100}{2}=4950\), so (n=99). Match \(2S_n\) with the product of two consecutive numbers.

Step 3

Exam Tip

\(S_{99}=\frac{99\times100}{2}=4950\) इसलिए (n=99) है। \(2S_n\) को दो क्रमागत संख्याओं के गुणनफल से मिलाएं।

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Question 3/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

(61) से (125) तक की प्राकृतिक संख्याओं का योग कितना है?

What is the sum of natural numbers from (61) to (125)?

Explanation opens after your attempt

Correct Answer

B. (6045)

Step 1

Concept

The sum is \(S_{125}-S_{60}=7875-1830=6045\). For a middle range, subtract the sum before the starting point.

Step 2

Why this answer is correct

The correct answer is B. (6045). The sum is \(S_{125}-S_{60}=7875-1830=6045\). For a middle range, subtract the sum before the starting point.

Step 3

Exam Tip

योग \(S_{125}-S_{60}=7875-1830=6045\) है। बीच की श्रेणी के लिए शुरुआत से पहले का योग घटाएं।

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Question 4/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{150}-S_{140}\) का मान क्या होगा?

What will be the value of \(S_{150}-S_{140}\)?

Explanation opens after your attempt

Correct Answer

C. (1455)

Step 1

Concept

\(S_{150}-S_{140}=141+142+\cdots+150=1455\). The difference of nearby sums is the sum of the terms in between.

Step 2

Why this answer is correct

The correct answer is C. (1455). \(S_{150}-S_{140}=141+142+\cdots+150=1455\). The difference of nearby sums is the sum of the terms in between.

Step 3

Exam Tip

\(S_{150}-S_{140}=141+142+\cdots+150=1455\) है। पास के योगों का अंतर बीच के पदों का योग होता है।

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Question 5/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n=2080\) है तो \(S_{n+9}\) का मान क्या होगा?

If \(S_n=2080\), what will be the value of \(S_{n+9}\)?

Explanation opens after your attempt

Correct Answer

C. (2701)

Step 1

Concept

\(S_{64}=2080\), so \(S_{73}=2701\). Identify (n) first and then use the new index.

Step 2

Why this answer is correct

The correct answer is C. (2701). \(S_{64}=2080\), so \(S_{73}=2701\). Identify (n) first and then use the new index.

Step 3

Exam Tip

\(S_{64}=2080\) इसलिए \(S_{73}=2701\) होगा। पहले (n) पहचानें फिर नया सूचकांक लगाएं।

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Question 6/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{88}+S_{90}-2S_{89}\) का मान क्या है?

What is the value of \(S_{88}+S_{90}-2S_{89}\)?

Explanation opens after your attempt

Correct Answer

B. (1)

Step 1

Concept

\(S_{90}=S_{89}+90\) and \(S_{88}=S_{89}-89\), so the value is (1). Use differences of consecutive sums.

Step 2

Why this answer is correct

The correct answer is B. (1). \(S_{90}=S_{89}+90\) and \(S_{88}=S_{89}-89\), so the value is (1). Use differences of consecutive sums.

Step 3

Exam Tip

\(S_{90}=S_{89}+90\) और \(S_{88}=S_{89}-89\) है इसलिए मान (1) है। लगातार योगों के अंतर का उपयोग करें।

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Question 7/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (120) प्राकृतिक संख्याओं का योग पहली (60) प्राकृतिक संख्याओं के योग से कितना अधिक है?

How much greater is the sum of the first (120) natural numbers than the sum of the first (60) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (5430)

Step 1

Concept

The difference is \(S_{120}-S_{60}=7260-1830=5430\). In comparison questions, find both sums separately.

Step 2

Why this answer is correct

The correct answer is C. (5430). The difference is \(S_{120}-S_{60}=7260-1830=5430\). In comparison questions, find both sums separately.

Step 3

Exam Tip

अंतर \(S_{120}-S_{60}=7260-1830=5430\) है। तुलना में दोनों योगों को अलग-अलग निकालें।

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Question 8/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

किस (n) पर \(S_n\) पहली बार (12000) से अधिक होगा?

At which (n) will \(S_n\) first become greater than (12000)?

Explanation opens after your attempt

Correct Answer

C. (155)

Step 1

Concept

\(S_{154}=11935\) and \(S_{155}=12090\), so it first exceeds (12000) at (n=155). In boundary questions, check nearby values.

Step 2

Why this answer is correct

The correct answer is C. (155). \(S_{154}=11935\) and \(S_{155}=12090\), so it first exceeds (12000) at (n=155). In boundary questions, check nearby values.

Step 3

Exam Tip

\(S_{154}=11935\) और \(S_{155}=12090\) है इसलिए पहली बार (n=155) पर योग (12000) से अधिक होगा। सीमा प्रश्न में आसपास के मान जांचें।

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Question 9/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{90}\) और \(S_{45}\) का अनुपात क्या है?

What is the ratio of \(S_{90}\) to \(S_{45}\)?

Explanation opens after your attempt

Correct Answer

A. (91:23)

Step 1

Concept

\(S_{90}:S_{45}=4095:1035=91:23\). Simplify the ratio by the greatest common factor.

Step 2

Why this answer is correct

The correct answer is A. (91:23). \(S_{90}:S_{45}=4095:1035=91:23\). Simplify the ratio by the greatest common factor.

Step 3

Exam Tip

\(S_{90}:S_{45}=4095:1035=91:23\) है। अनुपात को सबसे बड़े समान गुणक से सरल करें।

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Question 10/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

किस (n) के लिए \(S_n-S_{n-5}=535\) होगा?

For which (n) will \(S_n-S_{n-5}=535\)?

Explanation opens after your attempt

Correct Answer

C. (109)

Step 1

Concept

The difference is ((n-4)+(n-3)+(n-2)+(n-1)+n=5n-10), and (5n-10=535) gives (n=109). Form the sum of the last five terms.

Step 2

Why this answer is correct

The correct answer is C. (109). The difference is ((n-4)+(n-3)+(n-2)+(n-1)+n=5n-10), and (5n-10=535) gives (n=109). Form the sum of the last five terms.

Step 3

Exam Tip

अंतर ((n-4)+(n-3)+(n-2)+(n-1)+n=5n-10) है और (5n-10=535) से (n=109)। अंतिम पांच पदों का योग बनाएं।

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Question 11/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

एक सीढ़ीनुमा आकृति में कुल (3160) ब्लॉक हैं और (r)वीं पंक्ति में (r) ब्लॉक हैं। पंक्तियों की संख्या क्या है?

A staircase figure has (3160) blocks in total, and the (r)th row has (r) blocks. What is the number of rows?

Explanation opens after your attempt

Correct Answer

C. (79)

Step 1

Concept

Total blocks are \(S_r=3160\), and \(S_{79}=3160\), so there are (79) rows. Such figures form a triangular number.

Step 2

Why this answer is correct

The correct answer is C. (79). Total blocks are \(S_r=3160\), and \(S_{79}=3160\), so there are (79) rows. Such figures form a triangular number.

Step 3

Exam Tip

कुल ब्लॉक \(S_r=3160\) हैं और \(S_{79}=3160\), इसलिए पंक्तियां (79) हैं। ऐसी आकृति में कुल वस्तुएं त्रिभुज संख्या बनाती हैं।

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Question 12/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_a=3003\) और \(S_b=5050\) है तो (b-a) का मान क्या होगा?

If \(S_a=3003\) and \(S_b=5050\), what will be the value of (b-a)?

Explanation opens after your attempt

Correct Answer

C. (23)

Step 1

Concept

\(S_{77}=3003\) and \(S_{100}=5050\), so (b-a=23). Identifying both indices first is necessary.

Step 2

Why this answer is correct

The correct answer is C. (23). \(S_{77}=3003\) and \(S_{100}=5050\), so (b-a=23). Identifying both indices first is necessary.

Step 3

Exam Tip

\(S_{77}=3003\) और \(S_{100}=5050\), इसलिए (b-a=23)। पहले दोनों सूचकांक पहचानना जरूरी है।

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Question 13/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(86+87+88+\cdots+140\) का योग कितना है?

What is the sum of \(86+87+88+\cdots+140\)?

Explanation opens after your attempt

Correct Answer

B. (6215)

Step 1

Concept

The sum is \(S_{140}-S_{85}=9870-3655=6215\). When starting from (86), subtract the sum up to (85).

Step 2

Why this answer is correct

The correct answer is B. (6215). The sum is \(S_{140}-S_{85}=9870-3655=6215\). When starting from (86), subtract the sum up to (85).

Step 3

Exam Tip

योग \(S_{140}-S_{85}=9870-3655=6215\) है। (86) से शुरू होने पर (85) तक का योग घटाएं।

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Question 14/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_{m+3}-S_m=282\) है तो (m) का मान क्या है?

If \(S_{m+3}-S_m=282\), what is the value of (m)?

Explanation opens after your attempt

Correct Answer

B. (93)

Step 1

Concept

(S_{m+3}-S_m=(m+1)+(m+2)+(m+3)=3m+6), so (m=92). In a three-step difference, add the next three terms.

Step 2

Why this answer is correct

The correct answer is B. (93). (S_{m+3}-S_m=(m+1)+(m+2)+(m+3)=3m+6), so (m=92). In a three-step difference, add the next three terms.

Step 3

Exam Tip

(S_{m+3}-S_m=(m+1)+(m+2)+(m+3)=3m+6) है इसलिए (m=92)। तीन आगे के अंतर में अगले तीन पद जोड़ें।

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Question 15/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (200) प्राकृतिक संख्याओं के योग में से पहली (160) प्राकृतिक संख्याओं का योग घटाने पर क्या मिलेगा?

What is obtained by subtracting the sum of the first (160) natural numbers from the sum of the first (200) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (7220)

Step 1

Concept

The difference is \(S_{200}-S_{160}=20100-12880=7220\). It is the sum from (161) to (200).

Step 2

Why this answer is correct

The correct answer is C. (7220). The difference is \(S_{200}-S_{160}=20100-12880=7220\). It is the sum from (161) to (200).

Step 3

Exam Tip

अंतर \(S_{200}-S_{160}=20100-12880=7220\) है। यह (161) से (200) तक के पदों का योग है।

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Question 16/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

किस (n) पर \(S_n\) पहली बार (15000) से अधिक होगा?

At which (n) will \(S_n\) first become greater than (15000)?

Explanation opens after your attempt

Correct Answer

B. (173)

Step 1

Concept

\(S_{172}=14878\) and \(S_{173}=15051\), so it first exceeds (15000) at (n=173). In boundary questions, check the previous and next sums.

Step 2

Why this answer is correct

The correct answer is B. (173). \(S_{172}=14878\) and \(S_{173}=15051\), so it first exceeds (15000) at (n=173). In boundary questions, check the previous and next sums.

Step 3

Exam Tip

\(S_{172}=14878\) और \(S_{173}=15051\) है इसलिए पहली बार (n=173) पर योग (15000) से अधिक होगा। सीमा वाले प्रश्न में पिछले और अगले योग की जांच करें।

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Question 17/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{42}+S_{84}+S_{126}\) का मान क्या है?

What is the value of \(S_{42}+S_{84}+S_{126}\)?

Explanation opens after your attempt

Correct Answer

B. (12484)

Step 1

Concept

\(S_{42}=903\), \(S_{84}=3570\), and \(S_{126}=8001\), so the total is (12474). Write all three sums separately and add.

Step 2

Why this answer is correct

The correct answer is B. (12484). \(S_{42}=903\), \(S_{84}=3570\), and \(S_{126}=8001\), so the total is (12474). Write all three sums separately and add.

Step 3

Exam Tip

\(S_{42}=903\), \(S_{84}=3570\) और \(S_{126}=8001\), इसलिए कुल (12474) है। तीनों योग अलग-अलग लिखकर जोड़ें।

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Question 18/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n=5995\) है तो \(S_{n-8}\) का मान क्या होगा?

If \(S_n=5995\), what will be the value of \(S_{n-8}\)?

Explanation opens after your attempt

Correct Answer

C. (5253)

Step 1

Concept

\(S_{109}=5995\), so \(S_{101}=5151\). Identify (n) first and then use (n-8).

Step 2

Why this answer is correct

The correct answer is C. (5253). \(S_{109}=5995\), so \(S_{101}=5151\). Identify (n) first and then use (n-8).

Step 3

Exam Tip

\(S_{109}=5995\) है इसलिए \(S_{101}=5151\) होगा। पहले (n) पहचानें फिर (n-8) लगाएं।

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Question 19/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (132) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (132) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (8778)

Step 1

Concept

\(S_{132}=\frac{132\times133}{2}=8778\). Halve (132) and calculate \(66\times133\).

Step 2

Why this answer is correct

The correct answer is A. (8778). \(S_{132}=\frac{132\times133}{2}=8778\). Halve (132) and calculate \(66\times133\).

Step 3

Exam Tip

\(S_{132}=\frac{132\times133}{2}=8778\) है। (132) को आधा करके \(66\times133\) करें।

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Question 20/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{81}+S_{108}-S_{54}\) का मान ज्ञात कीजिए।

Find the value of \(S_{81}+S_{108}-S_{54}\).

Explanation opens after your attempt

Correct Answer

B. (7722)

Step 1

Concept

\(S_{81}=3321\), \(S_{108}=5886\), and \(S_{54}=1485\), so the value is (7722). In mixed sums, write each \(S_n\) separately.

Step 2

Why this answer is correct

The correct answer is B. (7722). \(S_{81}=3321\), \(S_{108}=5886\), and \(S_{54}=1485\), so the value is (7722). In mixed sums, write each \(S_n\) separately.

Step 3

Exam Tip

\(S_{81}=3321\), \(S_{108}=5886\) और \(S_{54}=1485\), इसलिए मान (7722) है। मिश्रित योगों में हर \(S_n\) अलग लिखें।

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Question 21/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_{4p}=7875\) है तो (p) का मान क्या है?

If \(S_{4p}=7875\), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

B. (31)

Step 1

Concept

\(S_{125}=7875\), so (4p=125) gives no integer (p). In such questions, check divisibility of the index too.

Step 2

Why this answer is correct

The correct answer is B. (31). \(S_{125}=7875\), so (4p=125) gives no integer (p). In such questions, check divisibility of the index too.

Step 3

Exam Tip

\(S_{125}=7875\) है इसलिए (4p=125) से पूर्णांक (p) नहीं मिलता। ऐसे प्रश्नों में सूचकांक की विभाज्यता भी जांचें।

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Question 22/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{144}-2S_{72}\) का मान क्या होगा?

What will be the value of \(S_{144}-2S_{72}\)?

Explanation opens after your attempt

Correct Answer

A. (5040)

Step 1

Concept

\(S_{144}=10440\) and \(2S_{72}=5256\), so the value is (5184). Keep the order of multiplication and subtraction clear.

Step 2

Why this answer is correct

The correct answer is A. (5040). \(S_{144}=10440\) and \(2S_{72}=5256\), so the value is (5184). Keep the order of multiplication and subtraction clear.

Step 3

Exam Tip

\(S_{144}=10440\) और \(2S_{72}=5256\), इसलिए मान (5184) है। गुणा और घटाव का क्रम ध्यान से रखें।

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Question 23/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

एक मंच पर (r)वीं पंक्ति में (6r) दीपक हैं। (45) पंक्तियों में कुल दीपक कितने होंगे?

On a stage, the (r)th row has (6r) lamps. How many lamps will there be in (45) rows?

Explanation opens after your attempt

Correct Answer

B. (6210)

Step 1

Concept

Total lamps are \(6S_{45}=6\times1035=6210\). If there is a common multiplier, keep it outside the sum.

Step 2

Why this answer is correct

The correct answer is B. (6210). Total lamps are \(6S_{45}=6\times1035=6210\). If there is a common multiplier, keep it outside the sum.

Step 3

Exam Tip

कुल दीपक \(6S_{45}=6\times1035=6210\) हैं। समान गुणक हो तो उसे योग के बाहर रखें।

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Question 24/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n=7260\) है तो (n) का मान क्या होगा?

If \(S_n=7260\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

\(S_{120}=\frac{120\times121}{2}=7260\), so (n=120). Match \(2S_n\) with the product of consecutive numbers.

Step 2

Why this answer is correct

The correct answer is C. (120). \(S_{120}=\frac{120\times121}{2}=7260\), so (n=120). Match \(2S_n\) with the product of consecutive numbers.

Step 3

Exam Tip

\(S_{120}=\frac{120\times121}{2}=7260\) इसलिए (n=120) है। \(2S_n\) को क्रमागत संख्याओं के गुणनफल से मिलाएं।

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Question 25/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_n-S_{n-2}+S_{n-6}-S_{n-8}\) का मान (312) है। (n) कितना है?

The value of \(S_n-S_{n-2}+S_{n-6}-S_{n-8}\) is (312). What is (n)?

Explanation opens after your attempt

Correct Answer

A. (80)

Step 1

Concept

The expression is ((n-1)+n+(n-7)+(n-6)=4n-14), and (4n-14=312) gives no integer (n). Convert into terms and check parity first.

Step 2

Why this answer is correct

The correct answer is A. (80). The expression is ((n-1)+n+(n-7)+(n-6)=4n-14), and (4n-14=312) gives no integer (n). Convert into terms and check parity first.

Step 3

Exam Tip

व्यंजक ((n-1)+n+(n-7)+(n-6)=4n-14) है और (4n-14=312) से पूर्णांक (n) नहीं मिलता। पहले पदों में बदलकर समता जांचें।

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Question 26/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{95}\) में कौन सी संख्या जोड़ने पर \(S_{105}\) प्राप्त होगा?

Which number should be added to \(S_{95}\) to get \(S_{105}\)?

Explanation opens after your attempt

Correct Answer

A. (1005)

Step 1

Concept

The needed number is \(96+97+\cdots+105=1005\). Add all new terms in between.

Step 2

Why this answer is correct

The correct answer is A. (1005). The needed number is \(96+97+\cdots+105=1005\). Add all new terms in between.

Step 3

Exam Tip

जरूरी संख्या \(96+97+\cdots+105=1005\) है। बीच के सभी नए पद जोड़ें।

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Question 27/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_u=2346\) और \(S_v=6670\) है तो (u+v) का मान क्या है?

If \(S_u=2346\) and \(S_v=6670\), what is the value of (u+v)?

Explanation opens after your attempt

Correct Answer

B. (182)

Step 1

Concept

\(S_{68}=2346\) and \(S_{115}=6670\), so (u+v=183). Identify the indices of both triangular numbers.

Step 2

Why this answer is correct

The correct answer is B. (182). \(S_{68}=2346\) and \(S_{115}=6670\), so (u+v=183). Identify the indices of both triangular numbers.

Step 3

Exam Tip

\(S_{68}=2346\) और \(S_{115}=6670\), इसलिए (u+v=183) है। दोनों त्रिभुज संख्याओं के सूचकांक पहचानें।

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Question 28/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (144) प्राकृतिक संख्याओं के योग का (12.5%) कितना है?

What is (12.5%) of the sum of the first (144) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (1305)

Step 1

Concept

\(S_{144}=10440\), and \(12.5%=\frac{1}{8}\), so the value is (1305). Converting percent to a fraction makes it easier.

Step 2

Why this answer is correct

The correct answer is B. (1305). \(S_{144}=10440\), and \(12.5%=\frac{1}{8}\), so the value is (1305). Converting percent to a fraction makes it easier.

Step 3

Exam Tip

\(S_{144}=10440\) है और \(12.5%=\frac{1}{8}\), इसलिए मान (1305) है। प्रतिशत को भिन्न में बदलना आसान रहता है।

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Question 29/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{102}+S_{103}-S_{101}\) का मान क्या है?

What is the value of \(S_{102}+S_{103}-S_{101}\)?

Explanation opens after your attempt

Correct Answer

C. (5554)

Step 1

Concept

\(S_{102}=5253\), \(S_{103}=5356\), and \(S_{101}=5151\), so the value is (5458). Subtract carefully with nearby indices.

Step 2

Why this answer is correct

The correct answer is C. (5554). \(S_{102}=5253\), \(S_{103}=5356\), and \(S_{101}=5151\), so the value is (5458). Subtract carefully with nearby indices.

Step 3

Exam Tip

\(S_{102}=5253\), \(S_{103}=5356\) और \(S_{101}=5151\), इसलिए मान (5458) है। निकट सूचकांकों में सावधानी से घटाएं।

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Question 30/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n-S_{n-7}=1001\) है तो (n) का मान क्या होगा?

If \(S_n-S_{n-7}=1001\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (142)

Step 1

Concept

The difference is ((n-6)+(n-5)+\cdots+n=7n-21), and (7n-21=1001) gives (n=146). Form the sum of the last seven terms.

Step 2

Why this answer is correct

The correct answer is C. (142). The difference is ((n-6)+(n-5)+\cdots+n=7n-21), and (7n-21=1001) gives (n=146). Form the sum of the last seven terms.

Step 3

Exam Tip

अंतर ((n-6)+(n-5)+\cdots+n=7n-21) है और (7n-21=1001) से (n=146) मिलता है। अंतिम सात पदों का योग बनाएं।

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Question 31/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (250) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (250) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (31375)

Step 1

Concept

\(S_{250}=\frac{250\times251}{2}=31375\). For large (n), first change (250) to (125).

Step 2

Why this answer is correct

The correct answer is B. (31375). \(S_{250}=\frac{250\times251}{2}=31375\). For large (n), first change (250) to (125).

Step 3

Exam Tip

\(S_{250}=\frac{250\times251}{2}=31375\) है। बड़े (n) में पहले (250) को (125) बनाएं।

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Question 32/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{180}-S_{170}+S_{20}\) का मान ज्ञात कीजिए।

Find the value of \(S_{180}-S_{170}+S_{20}\).

Explanation opens after your attempt

Correct Answer

B. (1975)

Step 1

Concept

(16290-14535+210=1965). First subtract and then add the smaller sum.

Step 2

Why this answer is correct

The correct answer is B. (1975). (16290-14535+210=1965). First subtract and then add the smaller sum.

Step 3

Exam Tip

(16290-14535+210=1965) है। पहले घटाव करें फिर छोटे योग को जोड़ें।

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Question 33/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_{2k+3}=3240\) है तो (k) का मान क्या होगा?

If \(S_{2k+3}=3240\), what will be the value of (k)?

Explanation opens after your attempt

Correct Answer

D. (40)

Step 1

Concept

\(S_{80}=3240\), so (2k+3=80) gives no integer (k). Check the given index condition too.

Step 2

Why this answer is correct

The correct answer is D. (40). \(S_{80}=3240\), so (2k+3=80) gives no integer (k). Check the given index condition too.

Step 3

Exam Tip

\(S_{80}=3240\) इसलिए (2k+3=80) से पूर्णांक (k) नहीं मिलता। सूचकांक में दी गई शर्त को भी जांचें।

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Question 34/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(151+152+153+\cdots+210\) का योग कितना है?

What is the sum of \(151+152+153+\cdots+210\)?

Explanation opens after your attempt

Correct Answer

A. (10830)

Step 1

Concept

The sum is \(S_{210}-S_{150}=22155-11325=10830\). When starting from (151), subtract the sum up to (150).

Step 2

Why this answer is correct

The correct answer is A. (10830). The sum is \(S_{210}-S_{150}=22155-11325=10830\). When starting from (151), subtract the sum up to (150).

Step 3

Exam Tip

योग \(S_{210}-S_{150}=22155-11325=10830\) है। (151) से शुरू होने पर (150) तक का योग घटाएं।

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Question 35/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n=4656\) है तो \(S_{n+12}-S_n\) का मान क्या है?

If \(S_n=4656\), what is the value of \(S_{n+12}-S_n\)?

Explanation opens after your attempt

Correct Answer

A. (1230)

Step 1

Concept

\(S_{96}=4656\), so the difference is \(97+98+\cdots+108=1230\). Find the sum of the next (12) terms separately.

Step 2

Why this answer is correct

The correct answer is A. (1230). \(S_{96}=4656\), so the difference is \(97+98+\cdots+108=1230\). Find the sum of the next (12) terms separately.

Step 3

Exam Tip

\(S_{96}=4656\) इसलिए अंतर \(97+98+\cdots+108=1230\) है। आगे के (12) पदों का योग अलग से निकालें।

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Question 36/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

किस (n) पर \(S_n\) पहली बार (30000) से अधिक होगा?

At which (n) will \(S_n\) first become greater than (30000)?

Explanation opens after your attempt

Correct Answer

B. (245)

Step 1

Concept

\(S_{244}=29890\) and \(S_{245}=30135\), so it first exceeds (30000) at (n=245). Checking nearby values is the safest method.

Step 2

Why this answer is correct

The correct answer is B. (245). \(S_{244}=29890\) and \(S_{245}=30135\), so it first exceeds (30000) at (n=245). Checking nearby values is the safest method.

Step 3

Exam Tip

\(S_{244}=29890\) और \(S_{245}=30135\) है इसलिए पहली बार (n=245) पर योग (30000) से अधिक होगा। आसपास के मान जांचना सबसे सुरक्षित है।

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Question 37/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

एक पार्किंग में (r)वीं पंक्ति में (7r) वाहन हैं। (56) पंक्तियों में कुल वाहन कितने होंगे?

In a parking arrangement, the (r)th row has (7r) vehicles. How many vehicles will there be in (56) rows?

Explanation opens after your attempt

Correct Answer

A. (11172)

Step 1

Concept

Total vehicles are \(7S_{56}=7\times1596=11172\). In a pattern like (7r), take (7) outside the sum.

Step 2

Why this answer is correct

The correct answer is A. (11172). Total vehicles are \(7S_{56}=7\times1596=11172\). In a pattern like (7r), take (7) outside the sum.

Step 3

Exam Tip

कुल वाहन \(7S_{56}=7\times1596=11172\) हैं। (7r) जैसे पैटर्न में (7) को योग के बाहर लें।

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Question 38/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_x=8385\) है तो (x) का मान क्या है?

If \(S_x=8385\), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

B. (129)

Step 1

Concept

\(S_{129}=\frac{129\times130}{2}=8385\), so (x=129). Use \(2S_x\) to find the consecutive product.

Step 2

Why this answer is correct

The correct answer is B. (129). \(S_{129}=\frac{129\times130}{2}=8385\), so (x=129). Use \(2S_x\) to find the consecutive product.

Step 3

Exam Tip

\(S_{129}=\frac{129\times130}{2}=8385\) इसलिए (x=129) है। \(2S_x\) करके क्रमागत गुणनफल खोजें।

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Question 39/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{48}+S_{96}-S_{32}\) का मान क्या है?

What is the value of \(S_{48}+S_{96}-S_{32}\)?

Explanation opens after your attempt

Correct Answer

B. (5294)

Step 1

Concept

(1176+4656-528=5304). Write the value of each \(S_n\) first and then perform the operation.

Step 2

Why this answer is correct

The correct answer is B. (5294). (1176+4656-528=5304). Write the value of each \(S_n\) first and then perform the operation.

Step 3

Exam Tip

(1176+4656-528=5304) है। हर \(S_n\) का मान पहले लिखकर फिर क्रिया करें।

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Question 40/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (175) प्राकृतिक संख्याओं के योग और पहली (125) प्राकृतिक संख्याओं के योग का अंतर क्या है?

What is the difference between the sum of the first (175) natural numbers and the sum of the first (125) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (7525)

Step 1

Concept

The difference is \(S_{175}-S_{125}=15400-7875=7525\). It is the sum from (126) to (175).

Step 2

Why this answer is correct

The correct answer is C. (7525). The difference is \(S_{175}-S_{125}=15400-7875=7525\). It is the sum from (126) to (175).

Step 3

Exam Tip

अंतर \(S_{175}-S_{125}=15400-7875=7525\) है। यह (126) से (175) तक के पदों का योग है।

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Question 41/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n-S_{n-1}=154\) और \(S_m=7503\) है तो (n-m) कितना है?

If \(S_n-S_{n-1}=154\) and \(S_m=7503\), what is (n-m)?

Explanation opens after your attempt

Correct Answer

B. (31)

Step 1

Concept

First (n=154), and \(S_m=7503\) gives (m=122), so (n-m=32). The difference of consecutive sums gives the index.

Step 2

Why this answer is correct

The correct answer is B. (31). First (n=154), and \(S_m=7503\) gives (m=122), so (n-m=32). The difference of consecutive sums gives the index.

Step 3

Exam Tip

पहले (n=154) और \(S_m=7503\) से (m=122), इसलिए (n-m=32)। लगातार योगों का अंतर सूचकांक देता है।

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Question 42/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{132}\) में \(133+134+\cdots+140\) जोड़ने पर कौन सा योग प्राप्त होगा?

Which sum is obtained by adding \(133+134+\cdots+140\) to \(S_{132}\)?

Explanation opens after your attempt

Correct Answer

C. \(S_{140}\)

Step 1

Concept

\(S_{132}+133+134+\cdots+140=S_{140}\). When consecutive new terms are added, the last term becomes the new index.

Step 2

Why this answer is correct

The correct answer is C. \(S_{140}\). \(S_{132}+133+134+\cdots+140=S_{140}\). When consecutive new terms are added, the last term becomes the new index.

Step 3

Exam Tip

\(S_{132}+133+134+\cdots+140=S_{140}\) है। लगातार नए पद जुड़ने पर अंतिम पद नया सूचकांक बनता है।

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Question 43/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n=11781\) है तो (n) का मान क्या है?

If \(S_n=11781\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (153)

Step 1

Concept

\(S_{153}=\frac{153\times154}{2}=11781\), so (n=153). For large values, using \(2S_n\) makes identification easier.

Step 2

Why this answer is correct

The correct answer is C. (153). \(S_{153}=\frac{153\times154}{2}=11781\), so (n=153). For large values, using \(2S_n\) makes identification easier.

Step 3

Exam Tip

\(S_{153}=\frac{153\times154}{2}=11781\) इसलिए (n=153) है। बड़े मानों में \(2S_n\) से पहचान आसान होती है।

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Question 44/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{37}+S_{74}+S_{111}\) का मान ज्ञात करें।

Find the value of \(S_{37}+S_{74}+S_{111}\).

Explanation opens after your attempt

Correct Answer

A. (9775)

Step 1

Concept

\(S_{37}=703\), \(S_{74}=2775\), and \(S_{111}=6216\), so the total is (9694). Add the three different indices carefully.

Step 2

Why this answer is correct

The correct answer is A. (9775). \(S_{37}=703\), \(S_{74}=2775\), and \(S_{111}=6216\), so the total is (9694). Add the three different indices carefully.

Step 3

Exam Tip

\(S_{37}=703\), \(S_{74}=2775\) और \(S_{111}=6216\), इसलिए कुल (9694) है। तीन अलग सूचकांकों को ध्यान से जोड़ें।

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Question 45/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (n) प्राकृतिक संख्याओं का योग (13695) है। (n-30) का मान क्या होगा?

The sum of the first (n) natural numbers is (13695). What is the value of (n-30)?

Explanation opens after your attempt

Correct Answer

B. (135)

Step 1

Concept

\(S_{165}=13695\), so (n=165) and (n-30=135). Find (n) first and then answer what is asked.

Step 2

Why this answer is correct

The correct answer is B. (135). \(S_{165}=13695\), so (n=165) and (n-30=135). Find (n) first and then answer what is asked.

Step 3

Exam Tip

\(S_{165}=13695\) इसलिए (n=165) और (n-30=135)। पहले (n) निकालें फिर पूछा गया मान दें।

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Question 46/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_{n+3}-S_{n-3}=615\) है तो (n) का मान क्या होगा?

If \(S_{n+3}-S_{n-3}=615\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

D. (102)

Step 1

Concept

The difference is ((n-2)+(n-1)+n+(n+1)+(n+2)+(n+3)=6n+3), and (6n+3=615) gives (n=102). Form the sum of the six middle terms.

Step 2

Why this answer is correct

The correct answer is D. (102). The difference is ((n-2)+(n-1)+n+(n+1)+(n+2)+(n+3)=6n+3), and (6n+3=615) gives (n=102). Form the sum of the six middle terms.

Step 3

Exam Tip

अंतर ((n-2)+(n-1)+n+(n+1)+(n+2)+(n+3)=6n+3) है और (6n+3=615) से (n=102)। बीच के छह पदों का योग बनाएं।

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Question 47/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{300}-S_{285}\) का मान क्या है?

What is the value of \(S_{300}-S_{285}\)?

Explanation opens after your attempt

Correct Answer

B. (4395)

Step 1

Concept

The difference is \(286+287+\cdots+300=4395\). Even with large indices, only the terms in between need to be added.

Step 2

Why this answer is correct

The correct answer is B. (4395). The difference is \(286+287+\cdots+300=4395\). Even with large indices, only the terms in between need to be added.

Step 3

Exam Tip

अंतर \(286+287+\cdots+300=4395\) है। बड़े सूचकांकों में भी केवल बीच के पद जोड़ने होते हैं।

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Question 48/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n=20100\) है तो (n) का मान क्या है?

If \(S_n=20100\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (200)

Step 1

Concept

\(S_{200}=\frac{200\times201}{2}=20100\), so (n=200). Match \(2S_n\) with a consecutive product.

Step 2

Why this answer is correct

The correct answer is C. (200). \(S_{200}=\frac{200\times201}{2}=20100\), so (n=200). Match \(2S_n\) with a consecutive product.

Step 3

Exam Tip

\(S_{200}=\frac{200\times201}{2}=20100\) इसलिए (n=200) है। \(2S_n\) को क्रमागत गुणनफल से मिलाएं।

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Question 49/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{96}\) और \(S_{48}\) के अंतर का (4) गुना कितना है?

What is (4) times the difference between \(S_{96}\) and \(S_{48}\)?

Explanation opens after your attempt

Correct Answer

A. (13920)

Step 1

Concept

\(S_{96}-S_{48}=4656-1176=3480\), and \(4\times3480=13920\). First find the difference and then multiply.

Step 2

Why this answer is correct

The correct answer is A. (13920). \(S_{96}-S_{48}=4656-1176=3480\), and \(4\times3480=13920\). First find the difference and then multiply.

Step 3

Exam Tip

\(S_{96}-S_{48}=4656-1176=3480\) और \(4\times3480=13920\) है। पहले अंतर निकालें फिर गुणा करें।

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Question 50/50 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_y=15931\) है तो \(S_{y+3}\) का मान क्या होगा?

If \(S_y=15931\), what will be the value of \(S_{y+3}\)?

Explanation opens after your attempt

Correct Answer

A. (16435)

Step 1

Concept

\(S_{178}=15931\), so \(S_{181}=15931+179+180+181=16471\). To move three steps ahead, add the next three terms.

Step 2

Why this answer is correct

The correct answer is A. (16435). \(S_{178}=15931\), so \(S_{181}=15931+179+180+181=16471\). To move three steps ahead, add the next three terms.

Step 3

Exam Tip

\(S_{178}=15931\) है इसलिए \(S_{181}=15931+179+180+181=16471\)। तीन आगे जाने पर अगले तीन पद जोड़ें।

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Class 9 Mathematics Expert Quiz

पहली (92) प्राकृतिक संख्याओं का योग कितना है?

Concept

Why this answer is correct

Exam Tip

यदि पहली (n) प्राकृतिक संख्याओं का योग (4950) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(61) से (125) तक की प्राकृतिक संख्याओं का योग कितना है?

Concept

Why this answer is correct

Exam Tip

\(S_{150}-S_{140}\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=2080\) है तो \(S_{n+9}\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

\(S_{88}+S_{90}-2S_{89}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

पहली (120) प्राकृतिक संख्याओं का योग पहली (60) प्राकृतिक संख्याओं के योग से कितना अधिक है?

Concept

Why this answer is correct

Exam Tip

किस (n) पर \(S_n\) पहली बार (12000) से अधिक होगा?

Concept

Why this answer is correct

Exam Tip

\(S_{90}\) और \(S_{45}\) का अनुपात क्या है?

Concept

Why this answer is correct

Exam Tip

किस (n) के लिए \(S_n-S_{n-5}=535\) होगा?

Concept

Why this answer is correct

Exam Tip

एक सीढ़ीनुमा आकृति में कुल (3160) ब्लॉक हैं और (r)वीं पंक्ति में (r) ब्लॉक हैं। पंक्तियों की संख्या क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_a=3003\) और \(S_b=5050\) है तो (b-a) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

\(86+87+88+\cdots+140\) का योग कितना है?

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यदि \(S_{m+3}-S_m=282\) है तो (m) का मान क्या है?

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पहली (200) प्राकृतिक संख्याओं के योग में से पहली (160) प्राकृतिक संख्याओं का योग घटाने पर क्या मिलेगा?

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किस (n) पर \(S_n\) पहली बार (15000) से अधिक होगा?

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\(S_{42}+S_{84}+S_{126}\) का मान क्या है?

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यदि \(S_n=5995\) है तो \(S_{n-8}\) का मान क्या होगा?

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पहली (132) प्राकृतिक संख्याओं का योग कितना है?

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Exam Tip

\(S_{81}+S_{108}-S_{54}\) का मान ज्ञात कीजिए।

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