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difference-equation MCQ Questions for Class 9

difference-equation se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

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17 questions tagged with difference-equation.

Question 1/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

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
Correct Answer

C. (157)

Explanation

Simple Explanation

(S_n-S_{n-8}=(n-7)+(n-6)+\cdots+n=8n-28) होता है। (8n-28=1228) से (n=157)। / (S_n-S_{n-8}=(n-7)+(n-6)+\cdots+n=8n-28). From (8n-28=1228), (n=157).

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Question 2/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

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
Correct Answer

C. (5050)

Explanation

Simple Explanation

\(S_n-S_{n-2}=2n-1\) है। (2n-1=199) से (n=100), इसलिए \(S_n=5050\)। / \(S_n-S_{n-2}=2n-1\). From (2n-1=199), (n=100), so \(S_n=5050\).

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Question 3/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

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
Correct Answer

A. (193)

Explanation

Simple Explanation

\(S_n-S_{n-7}=7n-21\) होता है। (7n-21=1330) से (n=193)। / \(S_n-S_{n-7}=7n-21\). From (7n-21=1330), (n=193).

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Question 4/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

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
Correct Answer

D. (8385)

Explanation

Simple Explanation

\(S_n-S_{n-2}=2n-1\) है। (2n-1=257) से (n=129), अतः \(S_{129}=8385\)। / \(S_n-S_{n-2}=2n-1\). From (2n-1=257), (n=129), so \(S_{129}=8385\).

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Question 5/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n-S_{n-4}=454\), तो (n) का मान क्या है?

If \(S_n-S_{n-4}=454\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

D. (115)

Explanation

Simple Explanation

\(S_n-S_{n-4}=4n-6\) होता है। (4n-6=454) से (n=115)। / \(S_n-S_{n-4}=4n-6\). From (4n-6=454), (n=115).

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Question 6/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_{n+2}-S_{n-3}=625\), तो (n) का मान क्या है?

If \(S_{n+2}-S_{n-3}=625\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

A. (125)

Explanation

Simple Explanation

यह अंतर ((n-2)+(n-1)+n+(n+1)+(n+2)=5n) है। इसलिए (5n=625) से (n=125)। / This difference is ((n-2)+(n-1)+n+(n+1)+(n+2)=5n). So (5n=625) gives (n=125).

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Question 7/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n-S_{n-6}=813\), तो (n) का मान क्या होगा?

If \(S_n-S_{n-6}=813\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

D. (138)

Explanation

Simple Explanation

\(S_n-S_{n-6}=6n-15\) होता है। (6n-15=813) से (n=138)। / \(S_n-S_{n-6}=6n-15\). From (6n-15=813), (n=138).

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Question 8/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_n-S_{n-6}=861\), तो (n) का मान क्या होगा?

If \(S_n-S_{n-6}=861\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

D. (146)

Explanation

Simple Explanation

(S_n-S_{n-6}=(n-5)+(n-4)+(n-3)+(n-2)+(n-1)+n=6n-15)। (6n-15=861) से (n=146)। / (S_n-S_{n-6}=(n-5)+(n-4)+(n-3)+(n-2)+(n-1)+n=6n-15). From (6n-15=861), (n=146).

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Question 9/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_n-S_{n-3}=420\), तो (n) क्या होगा?

If \(S_n-S_{n-3}=420\), what is (n)?

Explanation opens after your attempt
Correct Answer

C. (141)

Explanation

Simple Explanation

\(S_n-S_{n-3}=3n-3\)। (3n-3=420) से (n=141)। / \(S_n-S_{n-3}=3n-3\). From (3n-3=420), (n=141).

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Question 10/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_{n+4}-S_n=490\), तो (n) का मान क्या है?

If \(S_{n+4}-S_n=490\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

A. (120)

Explanation

Simple Explanation

(S_{n+4}-S_n=(n+1)+(n+2)+(n+3)+(n+4)=4n+10)। (4n+10=490) से (n=120)। / (S_{n+4}-S_n=(n+1)+(n+2)+(n+3)+(n+4)=4n+10). From (4n+10=490), (n=120).

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Question 11/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_n-S_{n-3}=348\), तो \(S_n\) का मान क्या है?

If \(S_n-S_{n-3}=348\), what is the value of \(S_n\)?

Explanation opens after your attempt
Correct Answer

A. (6670)

Explanation

Simple Explanation

\(S_n-S_{n-3}=3n-3\), 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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Question 12/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_{n+2}-S_{n-2}=402\), तो (n) का मान क्या होगा?

If \(S_{n+2}-S_{n-2}=402\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (100)

Explanation

Simple Explanation

(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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Question 13/17 Expert Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_n-S_{n-5}=490\), तो (n) का मान क्या होगा?

If \(S_n-S_{n-5}=490\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (100)

Explanation

Simple Explanation

(S_n-S_{n-5}=(n-4)+(n-3)+(n-2)+(n-1)+n=5n-10)। (5n-10=490) से (n=100)। / (S_n-S_{n-5}=(n-4)+(n-3)+(n-2)+(n-1)+n=5n-10). From (5n-10=490), (n=100).

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Question 14/17 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_n-S_{n-3}=180\), तो (n) क्या होगा?

If \(S_n-S_{n-3}=180\), what is (n)?

Explanation opens after your attempt
Correct Answer

C. (61)

Explanation

Simple Explanation

\(S_n-S_{n-3}=3n-3\)। (3n-3=180) से (n=61)। / \(S_n-S_{n-3}=3n-3\). From (3n-3=180), (n=61).

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Question 15/17 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_{n+2}-S_n=155\), तो (n) का मान क्या है?

If \(S_{n+2}-S_n=155\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (76)

Explanation

Simple Explanation

(S_{n+2}-S_n=(n+1)+(n+2)=2n+3)। (2n+3=155) से (n=76)। / (S_{n+2}-S_n=(n+1)+(n+2)=2n+3). From (2n+3=155), (n=76).

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Question 16/17 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_n-S_{n-2}=101\), तो \(S_n\) का मान क्या है?

If \(S_n-S_{n-2}=101\), what is the value of \(S_n\)?

Explanation opens after your attempt
Correct Answer

B. (1326)

Explanation

Simple Explanation

\(S_n-S_{n-2}=2n-1\), 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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Question 17/17 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_n-S_{n-4}=250\), तो (n) का मान क्या होगा?

If \(S_n-S_{n-4}=250\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

D. (64)

Explanation

Simple Explanation

(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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