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Class 9 Mathematics - Sequences and Progressions - Sequences Hard Quiz

Mathematics Sequences and Progressions Sequences Hard Class 9 Topic Quiz

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Question 1/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(7,12,17,22,\ldots\) का (15)वाँ पद क्या होगा?

What will be the (15)th term of \(7,12,17,22,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (77)

Explanation

Simple Explanation

पहला पद (7) और समान अंतर (5) है। (15)वाँ पद \(7+14\times5=77\) है। / The first term is (7) and the common difference is (5). The (15)th term is \(7+14\times5=77\).

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Question 2/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(120,111,102,93,\ldots\) का (10)वाँ पद क्या है?

What is the (10)th term of \(120,111,102,93,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (39)

Explanation

Simple Explanation

हर बार (9) घट रहा है। (10)वाँ पद \(120-9\times9=39\) है। / Each term decreases by (9). The (10)th term is \(120-9\times9=39\).

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Question 3/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_n=3n^2-2n\) है, तो \(a_6\) का मान क्या होगा?

If \(a_n=3n^2-2n\), what will be the value of \(a_6\)?

Explanation opens after your attempt
Correct Answer

D. (96)

Explanation

Simple Explanation

(n=6) रखने पर (a_6=3\(6^2\)-2(6)=96) है। घात और गुणा को सही क्रम में करें। / Putting (n=6), (a_6=3\(6^2\)-2(6)=96). Handle powers and multiplication in the correct order.

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Question 4/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_n=n^3+n\) है, तो \(a_4\) क्या होगा?

If \(a_n=n^3+n\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

C. (68)

Explanation

Simple Explanation

(n=4) रखने पर \(a_4=4^3+4=68\) है। पहले घन निकालें, फिर जोड़ करें। / Putting (n=4), \(a_4=4^3+4=68\). First find the cube, then add.

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Question 5/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(4,11,18,\Box,32\) में खाली स्थान का मान क्या है?

What is the missing value in \(4,11,18,\Box,32\)?

Explanation opens after your attempt
Correct Answer

C. (25)

Explanation

Simple Explanation

हर बार (7) जोड़ा जा रहा है। (18+7=25), इसलिए खाली स्थान (25) है। / Each term increases by (7). Since (18+7=25), the missing value is (25).

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Question 6/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(150,\Box,126,114,102\) में खाली स्थान कौन सा है?

Which value fills the blank in \(150,\Box,126,114,102\)?

Explanation opens after your attempt
Correct Answer

C. (138)

Explanation

Simple Explanation

क्रम में हर बार (12) घट रहा है। (150-12=138), इसलिए खाली स्थान (138) है। / The sequence decreases by (12) each time. (150-12=138), so the blank is (138).

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Question 7/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(6,11,19,30,44,\ldots\) का अगला पद क्या है?

What is the next term of \(6,11,19,30,44,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (61)

Explanation

Simple Explanation

अंतर (5,8,11,14) हैं और वे (3) से बढ़ रहे हैं। अगला अंतर (17) होगा, इसलिए (44+17=61)। / The differences are (5,8,11,14), increasing by (3). The next difference is (17), so (44+17=61).

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Question 8/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(200,197,191,182,170,\ldots\) का अगला पद क्या होगा?

What will be the next term of \(200,197,191,182,170,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (155)

Explanation

Simple Explanation

घटाव (3,6,9,12) हैं। अगला घटाव (15) होगा, इसलिए (170-15=155)। / The subtractions are (3,6,9,12). The next subtraction is (15), so (170-15=155).

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Question 9/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(4,12,36,108,\ldots\) का (7)वाँ पद क्या है?

What is the (7)th term of \(4,12,36,108,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (2916)

Explanation

Simple Explanation

हर पद पिछले पद का (3) गुना है। (4,12,36,108,324,972,2916) में (7)वाँ पद (2916) है। / Each term is (3) times the previous term. In (4,12,36,108,324,972,2916), the (7)th term is (2916).

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Question 10/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(1024,256,64,16,\ldots\) का अगला पद क्या है?

What is the next term of \(1024,256,64,16,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

हर पद पिछले पद को (4) से भाग देकर मिलता है। \(16\div4=4\) अगला पद है। / Each term is obtained by dividing the previous term by (4). \(16\div4=4\) is the next term.

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Question 11/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(9,16,25,36,49,\ldots\) का (9)वाँ पद क्या होगा?

What will be the (9)th term of \(9,16,25,36,49,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (121)

Explanation

Simple Explanation

यह \(3^2,4^2,5^2,\ldots\) का क्रम है। (9)वाँ पद \(11^2=121\) होगा। / This is the sequence \(3^2,4^2,5^2,\ldots\). The (9)th term will be \(11^2=121\).

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Question 12/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(27,64,125,216,\ldots\) का (6)ठा पद क्या है?

What is the (6)th term of \(27,64,125,216,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (512)

Explanation

Simple Explanation

यह \(3^3,4^3,5^3,6^3,\ldots\) का क्रम है। (6)ठा पद \(8^3=512\) है। / This is the sequence \(3^3,4^3,5^3,6^3,\ldots\). The (6)th term is \(8^3=512\).

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Question 13/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(4,7,11,16,22,\ldots\) का (9)वाँ पद क्या है?

What is the (9)th term of \(4,7,11,16,22,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (49)

Explanation

Simple Explanation

अंतर \(3,4,5,6,\ldots\) हैं। आगे (7,8,9,10) जोड़ने पर (9)वाँ पद (49) है। / The differences are \(3,4,5,6,\ldots\). Adding (7,8,9,10) next gives the (9)th term (49).

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Question 14/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(2,9,11,20,31,\ldots\) का अगला पद क्या है यदि हर नया पद पिछले दो पदों का योग है?

What is the next term of \(2,9,11,20,31,\ldots\) if each new term is the sum of the previous two terms?

Explanation opens after your attempt
Correct Answer

C. (51)

Explanation

Simple Explanation

यहाँ (11=2+9), (20=9+11) और (31=11+20) है। अगला पद (20+31=51) होगा। / Here (11=2+9), (20=9+11), and (31=11+20). The next term will be (20+31=51).

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Question 15/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(6,10,16,26,42,\ldots\) का अगला पद क्या होगा?

What will be the next term of \(6,10,16,26,42,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (68)

Explanation

Simple Explanation

हर पद पिछले दो पदों का योग है। (26+42=68), इसलिए अगला पद (68) है। / Each term is the sum of the previous two terms. (26+42=68), so the next term is (68).

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Question 16/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(5,20,80,320,\ldots\) में (1280) कौन सा पद है?

In \(5,20,80,320,\ldots\), which term is (1280)?

Explanation opens after your attempt
Correct Answer

B. (5)वाँ(5)th

Explanation

Simple Explanation

क्रम (5,20,80,320,1280) है। इसलिए (1280) (5)वाँ पद है। / The sequence is (5,20,80,320,1280). So (1280) is the (5)th term.

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Question 17/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(11,19,27,35,\ldots\) में (83) कौन सा पद होगा?

In \(11,19,27,35,\ldots\), which term will (83) be?

Explanation opens after your attempt
Correct Answer

C. (10)वाँ(10)th

Explanation

Simple Explanation

पहला पद (11) और अंतर (8) है। (11+(n-1)8=83) से (n=10) मिलता है। / The first term is (11) and the difference is (8). From (11+(n-1)8=83), (n=10).

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Question 18/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(140,131,122,113,\ldots\) में (77) कौन सा पद है?

In \(140,131,122,113,\ldots\), which term is (77)?

Explanation opens after your attempt
Correct Answer

B. (8)वाँ(8)th

Explanation

Simple Explanation

हर बार (9) घट रहा है। (140-(n-1)9=77) से (n=8) है। / Each term decreases by (9). From (140-(n-1)9=77), (n=8).

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Question 19/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि किसी क्रम के पहले चार पद (6,15,24,33) हैं, तो \(a_n\) का सरल नियम क्या हो सकता है?

If the first four terms of a sequence are (6,15,24,33), what can be a simple rule for \(a_n\)?

Explanation opens after your attempt
Correct Answer

A. \(a_n=9n-3\)

Explanation

Simple Explanation

पहला पद (6) और अंतर (9) है। \(a_n=9n-3\) से वही क्रम मिलता है। / The first term is (6) and the difference is (9). \(a_n=9n-3\) gives the same sequence.

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Question 20/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(13,21,29,37,\ldots\) के लिए सही \(a_n\) नियम कौन सा है?

Which \(a_n\) rule is correct for \(13,21,29,37,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(a_n=8n+5\)

Explanation

Simple Explanation

पहला पद (13) और अंतर (8) है। \(a_n=8n+5\) से \(13,21,29,\ldots\) मिलते हैं। / The first term is (13) and the difference is (8). \(a_n=8n+5\) gives \(13,21,29,\ldots\).

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Question 21/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

नियम \(a_n=7n-4\) से बनने वाले पहले चार पद कौन से हैं?

What are the first four terms formed by \(a_n=7n-4\)?

Explanation opens after your attempt
Correct Answer

A. (3,10,17,24)

Explanation

Simple Explanation

(n=1,2,3,4) रखने पर (3,10,17,24) मिलते हैं। पहले पद के लिए (n=1) से शुरू करें। / Putting (n=1,2,3,4) gives (3,10,17,24). Start with (n=1) for the first term.

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Question 22/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

नियम \(a_n=2n^2+5n\) से \(a_5\) क्या होगा?

What will \(a_5\) be for the rule \(a_n=2n^2+5n\)?

Explanation opens after your attempt
Correct Answer

C. (75)

Explanation

Simple Explanation

(n=5) रखने पर (a_5=2\(5^2\)+5(5)=75) है। वर्ग और गुणा दोनों सावधानी से करें। / Putting (n=5), (a_5=2\(5^2\)+5(5)=75). Handle both the square and multiplication carefully.

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Question 23/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

नियम \(a_n=100-6n\) से बनने वाला (7)वाँ पद क्या है?

What is the (7)th term formed by \(a_n=100-6n\)?

Explanation opens after your attempt
Correct Answer

C. (58)

Explanation

Simple Explanation

(n=7) रखने पर \(a_7=100-42=58\) है। घटाव वाले नियम में चिन्ह पर ध्यान दें। / Putting (n=7), \(a_7=100-42=58\). Pay attention to the sign in subtraction rules.

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Question 24/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

कौन सा क्रम \(a_n=6n^2\) से बनता है?

Which sequence is formed by \(a_n=6n^2\)?

Explanation opens after your attempt
Correct Answer

B. (6,24,54,96)

Explanation

Simple Explanation

(n=1,2,3,4) रखने पर (6,24,54,96) मिलते हैं। \(n^2\) को (6) से गुणा करें। / Putting (n=1,2,3,4) gives (6,24,54,96). Multiply \(n^2\) by (6).

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Question 25/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

कौन सा क्रम \(a_n=2^n+n\) से बने पहले चार पद दिखाता है?

Which sequence shows the first four terms of \(a_n=2^n+n\)?

Explanation opens after your attempt
Correct Answer

A. (3,6,11,20)

Explanation

Simple Explanation

\(2^1+1=3\), \(2^2+2=6\), \(2^3+3=11\), \(2^4+4=20\)। घात के बाद (n) जोड़ें। / \(2^1+1=3\), \(2^2+2=6\), \(2^3+3=11\), and \(2^4+4=20\). Add (n) after evaluating the power.

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Question 26/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(5,11,17,23,\ldots\) और \(2,8,14,20,\ldots\) के (10)वें पदों का अंतर क्या है?

What is the difference between the (10)th terms of \(5,11,17,23,\ldots\) and \(2,8,14,20,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (3)

Explanation

Simple Explanation

दोनों क्रमों का समान अंतर (6) है, इसलिए पदों का अंतर हमेशा (3) रहेगा। (10)वें पदों में भी यही अंतर है। / Both sequences have common difference (6), so the term difference always remains (3). The (10)th terms also differ by (3).

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Question 27/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(18,25,32,\ldots\) का (8)वाँ पद और \(9,16,23,\ldots\) का (8)वाँ पद किस प्रकार संबंधित हैं?

How are the (8)th term of \(18,25,32,\ldots\) and the (8)th term of \(9,16,23,\ldots\) related?

Explanation opens after your attempt
Correct Answer

B. पहला (9) अधिक हैThe first is greater by (9)

Explanation

Simple Explanation

दोनों क्रमों का अंतर (7) है और पहले पदों का अंतर (9) है। इसलिए (8)वें पदों का अंतर भी (9) होगा। / Both sequences have difference (7), and their first terms differ by (9). So their (8)th terms also differ by (9).

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Question 28/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(7,14,21,\ldots\) के पहले (8) पदों का योग क्या है?

What is the sum of the first (8) terms of \(7,14,21,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (252)

Explanation

Simple Explanation

पहले (8) पद (7,14,21,28,35,42,49,56) हैं। इनका योग (252) है। / The first (8) terms are (7,14,21,28,35,42,49,56). Their sum is (252).

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Question 29/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(96,88,80,\ldots\) के पहले (6) पदों का योग क्या है?

What is the sum of the first (6) terms of \(96,88,80,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (456)

Explanation

Simple Explanation

पहले (6) पद (96,88,80,72,64,56) हैं। इनका योग (456) है। / The first (6) terms are (96,88,80,72,64,56). Their sum is (456).

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Question 30/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(6,13,20,27,\ldots\) में कौन सा पद (76) है?

Which term is (76) in \(6,13,20,27,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (11)वाँ(11)th

Explanation

Simple Explanation

पहला पद (6) और अंतर (7) है। (6+(n-1)7=76) से (n=11) मिलता है। / The first term is (6) and the difference is (7). From (6+(n-1)7=76), (n=11).

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Question 31/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(9,14,19,24,\ldots\) में \(a_7+a_8\) का मान क्या है?

What is the value of \(a_7+a_8\) in \(9,14,19,24,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (87)

Explanation

Simple Explanation

\(a_7=39\) और \(a_8=44\) है। इसलिए \(a_7+a_8=83\), अतः विकल्प (A) सही होता। / \(a_7=39\) and \(a_8=44\). Therefore \(a_7+a_8=83\), so option (A) would be correct.

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Question 32/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(20,29,38,47,\ldots\) में \(a_8-a_3\) क्या है?

What is \(a_8-a_3\) in \(20,29,38,47,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (45)

Explanation

Simple Explanation

\(a_8=83\) और \(a_3=38\) है। इसलिए \(a_8-a_3=45\) है। / \(a_8=83\) and \(a_3=38\). Therefore \(a_8-a_3=45\).

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Question 33/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(15,21,27,33,\ldots\) में \(a_9\) और \(a_4\) का अंतर क्या है?

What is the difference between \(a_9\) and \(a_4\) in \(15,21,27,33,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (30)

Explanation

Simple Explanation

समान अंतर (6) है और स्थानों का अंतर (5) है। इसलिए अंतर \(5\times6=30\) है। / The common difference is (6), and the gap in positions is (5). So the difference is \(5\times6=30\).

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Question 34/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_1=14\) और हर अगले पद में (8) जोड़ा जाता है, तो \(a_{11}\) क्या होगा?

If \(a_1=14\) and (8) is added to each next term, what is \(a_{11}\)?

Explanation opens after your attempt
Correct Answer

C. (94)

Explanation

Simple Explanation

\(a_{11}=14+10\times8=94\) है। (11)वें पद तक पहुँचने के लिए (10) बार अंतर जोड़ा जाता है। / \(a_{11}=14+10\times8=94\). To reach the (11)th term, the difference is added (10) times.

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Question 35/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_1=130\) और हर अगले पद में (11) घटाया जाता है, तो \(a_9\) क्या होगा?

If \(a_1=130\) and (11) is subtracted for each next term, what is \(a_9\)?

Explanation opens after your attempt
Correct Answer

B. (42)

Explanation

Simple Explanation

\(a_9=130-8\times11=42\) है। (9)वें पद तक (8) बार घटाव होगा। / \(a_9=130-8\times11=42\). There are (8) subtractions before the (9)th term.

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Question 36/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(3,11,35,107,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (3) गुना करके (2) जोड़ना है?

What is the next term in \(3,11,35,107,\ldots\) if the rule is triple the previous term and add (2)?

Explanation opens after your attempt
Correct Answer

C. (323)

Explanation

Simple Explanation

नियम के अनुसार \(107\times3+2=323\) है। अंतिम पद पर दिया गया नियम लगाएँ। / By the rule, \(107\times3+2=323\). Apply the given rule to the last term.

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Question 37/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(128,63,30.5,14.25,\ldots\) में अगला पद क्या है यदि नियम पिछले पद को (2) से भाग देकर (1) घटाना है?

What is the next term in \(128,63,30.5,14.25,\ldots\) if the rule is divide the previous term by (2) and subtract (1)?

Explanation opens after your attempt
Correct Answer

B. (6.125)

Explanation

Simple Explanation

\(14.25\div2-1=6.125\) है। पहले भाग दें और फिर (1) घटाएँ। / \(14.25\div2-1=6.125\). Divide first and then subtract (1).

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Question 38/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(8,14,26,44,68,\ldots\) में अगला पद क्या है?

What is the next term in \(8,14,26,44,68,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (98)

Explanation

Simple Explanation

अंतर (6,12,18,24) हैं। अगला अंतर (30) होगा, इसलिए (68+30=98)। / The differences are (6,12,18,24). The next difference is (30), so (68+30=98).

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Question 39/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(300,288,264,228,180,\ldots\) में अगला पद क्या होगा?

What will be the next term in \(300,288,264,228,180,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (120)

Explanation

Simple Explanation

घटाव (12,24,36,48) है। अगला घटाव (60) होगा, इसलिए (180-60=120)। / The subtractions are (12,24,36,48). The next subtraction is (60), so (180-60=120).

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Question 40/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(4,8,24,96,\ldots\) का अगला पद क्या है?

What is the next term of \(4,8,24,96,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (480)

Explanation

Simple Explanation

यहाँ क्रमशः (2,3,4) से गुणा किया गया है। अगला गुणक (5) होगा, इसलिए \(96\times5=480\)। / The terms are multiplied by (2,3,4) successively. The next multiplier is (5), so \(96\times5=480\).

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Question 41/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(6,30,150,\ldots\) और \(8,40,200,\ldots\) के (3)रे पदों का अनुपात क्या है?

What is the ratio of the (3)rd terms of \(6,30,150,\ldots\) and \(8,40,200,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (3:4)

Explanation

Simple Explanation

तीसरे पद (150) और (200) हैं। उनका अनुपात (150:200=3:4) है। / The third terms are (150) and (200). Their ratio is (150:200=3:4).

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Question 42/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(10,18,26,34,\ldots\) में पहले कितने पदों का योग (130) है?

How many first terms of \(10,18,26,34,\ldots\) have sum (130)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

पहले (5) पद (10,18,26,34,42) हैं। उनका योग (130) है। / The first (5) terms are (10,18,26,34,42). Their sum is (130).

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Question 43/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(12,21,30,\ldots\) में कौन सा पद (75) से ठीक पहले आता है?

In \(12,21,30,\ldots\), which term comes just before (75)?

Explanation opens after your attempt
Correct Answer

C. (66)

Explanation

Simple Explanation

क्रम (12,21,30,39,48,57,66,75) है। (75) से ठीक पहले (66) आता है। / The sequence is (12,21,30,39,48,57,66,75). The term just before (75) is (66).

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Question 44/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(384,192,96,48,\ldots\) में (12) से ठीक पहले कौन सा पद आता है?

In \(384,192,96,48,\ldots\), which term comes just before (12)?

Explanation opens after your attempt
Correct Answer

C. (24)

Explanation

Simple Explanation

हर बार आधा हो रहा है। क्रम (384,192,96,48,24,12) है, इसलिए (12) से पहले (24) है। / Each term is halved. The sequence is (384,192,96,48,24,12), so (24) comes before (12).

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Question 45/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(17,23,29,\ldots\) के (n)वें पद के लिए सही कथन कौन सा है?

Which statement is correct for the (n)th term of \(17,23,29,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. यह (6n+11) हैIt is (6n+11)

Explanation

Simple Explanation

(n=1) पर (6(1)+11=17) और अंतर (6) मिलता है। इसलिए सही नियम (6n+11) है। / At (n=1), (6(1)+11=17), and the difference is (6). So the correct rule is (6n+11).

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Question 46/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(108,99,90,\ldots\) के (n)वें पद का सही नियम कौन सा है?

Which is the correct rule for the (n)th term of \(108,99,90,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(a_n=117-9n\)

Explanation

Simple Explanation

(n=1) रखने पर (117-9=108) मिलता है। यह हर बार (9) घटाने वाला नियम है। / Putting (n=1) gives (117-9=108). This rule decreases by (9) each time.

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Question 47/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_1=8\), \(a_2=13\) और हर अगला पद पिछले दो पदों का योग है, तो \(a_6\) क्या होगा?

If \(a_1=8\), \(a_2=13\), and each next term is the sum of the previous two terms, what is \(a_6\)?

Explanation opens after your attempt
Correct Answer

C. (76)

Explanation

Simple Explanation

क्रम (8,13,21,34,55,89) बनेगा। इसलिए \(a_6=89\), अतः दिए गए विकल्पों में सही मान नहीं है। / The sequence becomes (8,13,21,34,55,89). Therefore \(a_6=89\), so the correct value is not in the options.

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Question 48/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि क्रम \(6,24,96,384,\ldots\) में \(a_n=1536\) है, तो (n) क्या है?

If \(a_n=1536\) in the sequence \(6,24,96,384,\ldots\), what is (n)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

क्रम (6,24,96,384,1536) है। (1536) पाँचवाँ पद है, इसलिए (n=5)। / The sequence is (6,24,96,384,1536). (1536) is the fifth term, so (n=5).

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Question 49/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

यदि \(a_n=4n^2-3n+2\) है, तो \(a_5-a_2\) का मान क्या होगा?

If \(a_n=4n^2-3n+2\), what is the value of \(a_5-a_2\)?

Explanation opens after your attempt
Correct Answer

B. (78)

Explanation

Simple Explanation

(a_5=4\(5^2\)-3(5)+2=87) और (a_2=4\(2^2\)-3(2)+2=9) है। इसलिए अंतर (87-9=78) है। / (a_5=4\(5^2\)-3(5)+2=87) and (a_2=4\(2^2\)-3(2)+2=9). Therefore the difference is (87-9=78).

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Question 50/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 42

क्रम \(3,7,15,31,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (2) गुना करके (1) जोड़ना है?

What is the next term in \(3,7,15,31,\ldots\) if the rule is double the previous term and add (1)?

Explanation opens after your attempt
Correct Answer

C. (63)

Explanation

Simple Explanation

नियम के अनुसार \(31\times2+1=63\) है। अंतिम पद पर नियम लगाकर अगला पद निकालें। / By the rule, \(31\times2+1=63\). Apply the rule to the last term to get the next term.

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Question 51/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(8,14,20,26,\ldots\) का (16)वाँ पद क्या होगा?

What will be the (16)th term of \(8,14,20,26,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (98)

Explanation

Simple Explanation

पहला पद (8) और समान अंतर (6) है। (16)वाँ पद \(8+15\times6=98\) है। / The first term is (8) and the common difference is (6). The (16)th term is \(8+15\times6=98\).

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Question 52/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(160,148,136,124,\ldots\) का (11)वाँ पद क्या है?

What is the (11)th term of \(160,148,136,124,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (40)

Explanation

Simple Explanation

हर बार (12) घट रहा है। (11)वाँ पद \(160-10\times12=40\) है। / Each term decreases by (12). The (11)th term is \(160-10\times12=40\).

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Question 53/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=4n^2-3n\) है, तो \(a_7\) का मान क्या होगा?

If \(a_n=4n^2-3n\), what will be the value of \(a_7\)?

Explanation opens after your attempt
Correct Answer

B. (175)

Explanation

Simple Explanation

(n=7) रखने पर (a_7=4\(7^2\)-3(7)=175) है। पहले वर्ग निकालें फिर गुणा और घटाव करें। / Putting (n=7), (a_7=4\(7^2\)-3(7)=175). Square first, then multiply and subtract.

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Question 54/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=n^3-2n\) है, तो \(a_5\) क्या होगा?

If \(a_n=n^3-2n\), what is \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (115)

Explanation

Simple Explanation

(n=5) रखने पर (a_5=53-2(5)=115) है। घन और गुणा दोनों सावधानी से करें। / Putting (n=5), (a_5=53-2(5)=115). Handle the cube and multiplication carefully.

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Question 55/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(9,18,27,\Box,45\) में खाली स्थान का मान क्या है?

What is the missing value in \(9,18,27,\Box,45\)?

Explanation opens after your attempt
Correct Answer

C. (36)

Explanation

Simple Explanation

हर बार (9) जोड़ा जा रहा है। (27+9=36) इसलिए खाली स्थान (36) है। / Each term increases by (9). Since (27+9=36), the missing value is (36).

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Question 56/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(180,\Box,152,138,124\) में खाली स्थान कौन सा है?

Which value fills the blank in \(180,\Box,152,138,124\)?

Explanation opens after your attempt
Correct Answer

C. (166)

Explanation

Simple Explanation

क्रम में हर बार (14) घट रहा है। (180-14=166) होगा। / The sequence decreases by (14) each time. (180-14=166).

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Question 57/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(5,12,22,35,51,\ldots\) का अगला पद क्या है?

What is the next term of \(5,12,22,35,51,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (70)

Explanation

Simple Explanation

अंतर (7,10,13,16) हैं और वे (3) से बढ़ रहे हैं। अगला अंतर (19) होगा इसलिए (51+19=70)। / The differences are (7,10,13,16), increasing by (3). The next difference is (19), so (51+19=70).

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Question 58/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(250,245,235,220,200,\ldots\) का अगला पद क्या होगा?

What will be the next term of \(250,245,235,220,200,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (175)

Explanation

Simple Explanation

घटाव (5,10,15,20) हैं। अगला घटाव (25) होगा इसलिए (200-25=175)। / The subtractions are (5,10,15,20). The next subtraction is (25), so (200-25=175).

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Question 59/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(6,24,96,384,\ldots\) का (6)ठा पद क्या है?

What is the (6)th term of \(6,24,96,384,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. (6144)

Explanation

Simple Explanation

हर पद पिछले पद का (4) गुना है। (5)वाँ पद (1536) और (6)ठा पद (6144) है। / Each term is (4) times the previous term. The (5)th term is (1536) and the (6)th term is (6144).

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Question 60/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(729,243,81,27,\ldots\) का अगला पद क्या है?

What is the next term of \(729,243,81,27,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (9)

Explanation

Simple Explanation

हर पद पिछले पद को (3) से भाग देकर मिलता है। \(27\div3=9\) अगला पद है। / Each term is obtained by dividing the previous term by (3). \(27\div3=9\) is the next term.

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Question 61/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(16,25,36,49,64,\ldots\) का (8)वाँ पद क्या होगा?

What will be the (8)th term of \(16,25,36,49,64,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (121)

Explanation

Simple Explanation

यह \(4^2,5^2,6^2,\ldots\) का क्रम है। (8)वाँ पद \(11^2=121\) होगा। / This is the sequence \(4^2,5^2,6^2,\ldots\). The (8)th term will be \(11^2=121\).

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Question 62/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(64,125,216,343,\ldots\) का (6)ठा पद क्या है?

What is the (6)th term of \(64,125,216,343,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (729)

Explanation

Simple Explanation

यह \(4^3,5^3,6^3,7^3,\ldots\) का क्रम है। (6)ठा पद \(9^3=729\) है। / This is the sequence \(4^3,5^3,6^3,7^3,\ldots\). The (6)th term is \(9^3=729\).

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Question 63/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(6,10,15,21,28,\ldots\) का (10)वाँ पद क्या है?

What is the (10)th term of \(6,10,15,21,28,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (64)

Explanation

Simple Explanation

अंतर \(4,5,6,7,\ldots\) हैं। (10)वें पद तक बढ़ने पर मान (64) मिलता है। / The differences are \(4,5,6,7,\ldots\). Extending to the (10)th term gives (64).

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Question 64/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(4,10,14,24,38,\ldots\) का अगला पद क्या है यदि हर नया पद पिछले दो पदों का योग है?

What is the next term of \(4,10,14,24,38,\ldots\) if each new term is the sum of the previous two terms?

Explanation opens after your attempt
Correct Answer

C. (62)

Explanation

Simple Explanation

यहाँ (14=4+10), (24=10+14) और (38=14+24) है। अगला पद (24+38=62) होगा। / Here (14=4+10), (24=10+14), and (38=14+24). The next term will be (24+38=62).

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Question 65/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(9,27,81,243,\ldots\) में (729) कौन सा पद है?

In \(9,27,81,243,\ldots\), which term is (729)?

Explanation opens after your attempt
Correct Answer

B. (5)वाँ(5)th

Explanation

Simple Explanation

क्रम (9,27,81,243,729) है। इसलिए (729) (5)वाँ पद है। / The sequence is (9,27,81,243,729). So (729) is the (5)th term.

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Question 66/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(15,24,33,42,\ldots\) में (105) कौन सा पद होगा?

In \(15,24,33,42,\ldots\), which term will (105) be?

Explanation opens after your attempt
Correct Answer

C. (11)वाँ(11)th

Explanation

Simple Explanation

पहला पद (15) और अंतर (9) है। (15+(n-1)9=105) से (n=11) मिलता है। / The first term is (15) and the difference is (9). From (15+(n-1)9=105), (n=11).

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Question 67/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(170,158,146,134,\ldots\) में (74) कौन सा पद है?

In \(170,158,146,134,\ldots\), which term is (74)?

Explanation opens after your attempt
Correct Answer

C. (9)वाँ(9)th

Explanation

Simple Explanation

हर बार (12) घट रहा है। (170-(n-1)12=74) से (n=9) है। / Each term decreases by (12). From (170-(n-1)12=74), (n=9).

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Question 68/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि किसी क्रम के पहले चार पद (9,20,31,42) हैं, तो \(a_n\) का सरल नियम क्या हो सकता है?

If the first four terms of a sequence are (9,20,31,42), what can be a simple rule for \(a_n\)?

Explanation opens after your attempt
Correct Answer

A. \(a_n=11n-2\)

Explanation

Simple Explanation

पहला पद (9) और अंतर (11) है। \(a_n=11n-2\) से वही क्रम मिलता है। / The first term is (9) and the difference is (11). \(a_n=11n-2\) gives the same sequence.

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Question 69/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(16,25,34,43,\ldots\) के लिए सही \(a_n\) नियम कौन सा है?

Which \(a_n\) rule is correct for \(16,25,34,43,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(a_n=9n+7\)

Explanation

Simple Explanation

पहला पद (16) और अंतर (9) है। \(a_n=9n+7\) से \(16,25,34,\ldots\) मिलते हैं। / The first term is (16) and the difference is (9). \(a_n=9n+7\) gives \(16,25,34,\ldots\).

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Question 70/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

नियम \(a_n=8n-5\) से बनने वाले पहले चार पद कौन से हैं?

What are the first four terms formed by \(a_n=8n-5\)?

Explanation opens after your attempt
Correct Answer

A. (3,11,19,27)

Explanation

Simple Explanation

(n=1,2,3,4) रखने पर (3,11,19,27) मिलते हैं। पहले पद के लिए (n=1) से शुरू करें। / Putting (n=1,2,3,4) gives (3,11,19,27). Start with (n=1) for the first term.

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Question 71/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

नियम \(a_n=3n^2+4n\) से \(a_6\) क्या होगा?

What will \(a_6\) be for the rule \(a_n=3n^2+4n\)?

Explanation opens after your attempt
Correct Answer

C. (132)

Explanation

Simple Explanation

(n=6) रखने पर (a_6=3\(6^2\)+4(6)=132) है। वर्ग और गुणा दोनों सावधानी से करें। / Putting (n=6), (a_6=3\(6^2\)+4(6)=132). Handle both the square and multiplication carefully.

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Question 72/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

नियम \(a_n=140-9n\) से बनने वाला (8)वाँ पद क्या है?

What is the (8)th term formed by \(a_n=140-9n\)?

Explanation opens after your attempt
Correct Answer

C. (68)

Explanation

Simple Explanation

(n=8) रखने पर \(a_8=140-72=68\) है। घटाव वाले नियम में चिन्ह पर ध्यान दें। / Putting (n=8), \(a_8=140-72=68\). Pay attention to the sign in subtraction rules.

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Question 73/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

कौन सा क्रम \(a_n=7n^2\) से बनता है?

Which sequence is formed by \(a_n=7n^2\)?

Explanation opens after your attempt
Correct Answer

B. (7,28,63,112)

Explanation

Simple Explanation

(n=1,2,3,4) रखने पर (7,28,63,112) मिलते हैं। \(n^2\) को (7) से गुणा करें। / Putting (n=1,2,3,4) gives (7,28,63,112). Multiply \(n^2\) by (7).

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Question 74/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

कौन सा क्रम \(a_n=3^n+n\) से बने पहले चार पद दिखाता है?

Which sequence shows the first four terms of \(a_n=3^n+n\)?

Explanation opens after your attempt
Correct Answer

A. (4,11,30,85)

Explanation

Simple Explanation

\(3^1+1=4\), \(3^2+2=11\), \(3^3+3=30\), \(3^4+4=85\)। घात के बाद (n) जोड़ें। / \(3^1+1=4\), \(3^2+2=11\), \(3^3+3=30\), and \(3^4+4=85\). Add (n) after evaluating the power.

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Question 75/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(7,14,21,28,\ldots\) और \(3,10,17,24,\ldots\) के (12)वें पदों का अंतर क्या है?

What is the difference between the (12)th terms of \(7,14,21,28,\ldots\) and \(3,10,17,24,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

दोनों क्रमों का समान अंतर (7) है इसलिए पदों का अंतर हमेशा (4) रहेगा। (12)वें पदों में भी यही अंतर है। / Both sequences have common difference (7), so the term difference always remains (4). The (12)th terms also differ by (4).

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Question 76/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(22,30,38,\ldots\) का (9)वाँ पद और \(13,21,29,\ldots\) का (9)वाँ पद किस प्रकार संबंधित हैं?

How are the (9)th term of \(22,30,38,\ldots\) and the (9)th term of \(13,21,29,\ldots\) related?

Explanation opens after your attempt
Correct Answer

B. पहला (9) अधिक हैThe first is greater by (9)

Explanation

Simple Explanation

दोनों क्रमों का अंतर (8) है और पहले पदों का अंतर (9) है। इसलिए (9)वें पदों का अंतर भी (9) होगा। / Both sequences have difference (8), and their first terms differ by (9). So their (9)th terms also differ by (9).

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Question 77/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(8,16,24,\ldots\) के पहले (9) पदों का योग क्या है?

What is the sum of the first (9) terms of \(8,16,24,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (360)

Explanation

Simple Explanation

पहले (9) पद (8) से (72) तक हैं। उनका योग (360) है। / The first (9) terms run from (8) to (72). Their sum is (360).

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Question 78/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(132,121,110,\ldots\) के पहले (6) पदों का योग क्या है?

What is the sum of the first (6) terms of \(132,121,110,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (627)

Explanation

Simple Explanation

पहले (6) पद (132,121,110,99,88,77) हैं। इनका योग (627) है। / The first (6) terms are (132,121,110,99,88,77). Their sum is (627).

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Question 79/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(10,18,26,34,\ldots\) में कौन सा पद (90) है?

Which term is (90) in \(10,18,26,34,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (11)वाँ(11)th

Explanation

Simple Explanation

पहला पद (10) और अंतर (8) है। (10+(n-1)8=90) से (n=11) मिलता है। / The first term is (10) and the difference is (8). From (10+(n-1)8=90), (n=11).

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Question 80/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(11,17,23,29,\ldots\) में \(a_8+a_9\) का मान क्या है?

What is the value of \(a_8+a_9\) in \(11,17,23,29,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (106)

Explanation

Simple Explanation

\(a_8=53\) और \(a_9=59\) है। इसलिए \(a_8+a_9=112\), अतः विकल्पों में सही मान नहीं है। / \(a_8=53\) and \(a_9=59\). Therefore \(a_8+a_9=112\), so the correct value is not in the options.

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Question 81/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(24,34,44,54,\ldots\) में \(a_9-a_4\) क्या है?

What is \(a_9-a_4\) in \(24,34,44,54,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (50)

Explanation

Simple Explanation

समान अंतर (10) है और स्थानों का अंतर (5) है। इसलिए \(a_9-a_4=5\times10=50\) है। / The common difference is (10), and the gap in positions is (5). Therefore \(a_9-a_4=5\times10=50\).

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Question 82/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(20,27,34,41,\ldots\) में \(a_{10}\) और \(a_5\) का अंतर क्या है?

What is the difference between \(a_{10}\) and \(a_5\) in \(20,27,34,41,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (35)

Explanation

Simple Explanation

समान अंतर (7) है और स्थानों का अंतर (5) है। इसलिए अंतर \(5\times7=35\) है। / The common difference is (7), and the position gap is (5). So the difference is \(5\times7=35\).

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Question 83/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_1=18\) और हर अगले पद में (9) जोड़ा जाता है, तो \(a_{12}\) क्या होगा?

If \(a_1=18\) and (9) is added to each next term, what is \(a_{12}\)?

Explanation opens after your attempt
Correct Answer

B. (117)

Explanation

Simple Explanation

\(a_{12}=18+11\times9=117\) है। (12)वें पद तक पहुँचने के लिए (11) बार अंतर जोड़ा जाता है। / \(a_{12}=18+11\times9=117\). To reach the (12)th term, the difference is added (11) times.

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Question 84/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_1=180\) और हर अगले पद में (13) घटाया जाता है, तो \(a_{10}\) क्या होगा?

If \(a_1=180\) and (13) is subtracted for each next term, what is \(a_{10}\)?

Explanation opens after your attempt
Correct Answer

A. (63)

Explanation

Simple Explanation

\(a_{10}=180-9\times13=63\) है। (10)वें पद तक (9) बार घटाव होगा। / \(a_{10}=180-9\times13=63\). There are (9) subtractions before the (10)th term.

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Question 85/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(5,17,53,161,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (3) गुना करके (2) जोड़ना है?

What is the next term in \(5,17,53,161,\ldots\) if the rule is triple the previous term and add (2)?

Explanation opens after your attempt
Correct Answer

B. (485)

Explanation

Simple Explanation

नियम के अनुसार \(161\times3+2=485\) है। अंतिम पद पर दिया गया नियम लगाएँ। / By the rule, \(161\times3+2=485\). Apply the given rule to the last term.

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Question 86/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(160,79,38.5,18.25,\ldots\) में अगला पद क्या है यदि नियम पिछले पद को (2) से भाग देकर (1) घटाना है?

What is the next term in \(160,79,38.5,18.25,\ldots\) if the rule is divide the previous term by (2) and subtract (1)?

Explanation opens after your attempt
Correct Answer

A. (8.125)

Explanation

Simple Explanation

\(18.25\div2-1=8.125\) है। पहले भाग दें और फिर (1) घटाएँ। / \(18.25\div2-1=8.125\). Divide first and then subtract (1).

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Question 87/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(10,18,34,58,90,\ldots\) में अगला पद क्या है?

What is the next term in \(10,18,34,58,90,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (130)

Explanation

Simple Explanation

अंतर (8,16,24,32) हैं। अगला अंतर (40) होगा इसलिए (90+40=130)। / The differences are (8,16,24,32). The next difference is (40), so (90+40=130).

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Question 88/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(360,345,315,270,210,\ldots\) में अगला पद क्या होगा?

What will be the next term in \(360,345,315,270,210,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (135)

Explanation

Simple Explanation

घटाव (15,30,45,60) है। अगला घटाव (75) होगा इसलिए (210-75=135)। / The subtractions are (15,30,45,60). The next subtraction is (75), so (210-75=135).

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Question 89/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(5,10,30,120,\ldots\) का अगला पद क्या है?

What is the next term of \(5,10,30,120,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (600)

Explanation

Simple Explanation

यहाँ क्रमशः (2,3,4) से गुणा किया गया है। अगला गुणक (5) होगा इसलिए \(120\times5=600\)। / The terms are multiplied by (2,3,4) successively. The next multiplier is (5), so \(120\times5=600\).

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Question 90/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(7,42,252,\ldots\) और \(5,30,180,\ldots\) के (3)रे पदों का अनुपात क्या है?

What is the ratio of the (3)rd terms of \(7,42,252,\ldots\) and \(5,30,180,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (7:5)

Explanation

Simple Explanation

तीसरे पद (252) और (180) हैं। उनका अनुपात (252:180=7:5) है। / The third terms are (252) and (180). Their ratio is (252:180=7:5).

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Question 91/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(12,21,30,39,\ldots\) में पहले कितने पदों का योग (150) है?

How many first terms of \(12,21,30,39,\ldots\) have sum (150)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

पहले (5) पद (12,21,30,39,48) हैं। उनका योग (150) है। / The first (5) terms are (12,21,30,39,48). Their sum is (150).

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Question 92/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(14,25,36,\ldots\) में कौन सा पद (91) से ठीक पहले आता है?

In \(14,25,36,\ldots\), which term comes just before (91)?

Explanation opens after your attempt
Correct Answer

C. (80)

Explanation

Simple Explanation

क्रम (14,25,36,47,58,69,80,91) है। (91) से ठीक पहले (80) आता है। / The sequence is (14,25,36,47,58,69,80,91). The term just before (91) is (80).

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Question 93/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(768,384,192,96,\ldots\) में (24) से ठीक पहले कौन सा पद आता है?

In \(768,384,192,96,\ldots\), which term comes just before (24)?

Explanation opens after your attempt
Correct Answer

C. (48)

Explanation

Simple Explanation

हर बार आधा हो रहा है। क्रम (768,384,192,96,48,24) है इसलिए (24) से पहले (48) है। / Each term is halved. The sequence is (768,384,192,96,48,24), so (48) comes before (24).

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Question 94/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(19,27,35,\ldots\) के (n)वें पद के लिए सही कथन कौन सा है?

Which statement is correct for the (n)th term of \(19,27,35,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. यह (8n+11) हैIt is (8n+11)

Explanation

Simple Explanation

(n=1) पर (8(1)+11=19) और अंतर (8) मिलता है। इसलिए सही नियम (8n+11) है। / At (n=1), (8(1)+11=19), and the difference is (8). So the correct rule is (8n+11).

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Question 95/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(156,144,132,\ldots\) के (n)वें पद का सही नियम कौन सा है?

Which is the correct rule for the (n)th term of \(156,144,132,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(a_n=168-12n\)

Explanation

Simple Explanation

(n=1) रखने पर (168-12=156) मिलता है। यह हर बार (12) घटाने वाला नियम है। / Putting (n=1) gives (168-12=156). This rule decreases by (12) each time.

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Question 96/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_1=9\), \(a_2=16\) और हर अगला पद पिछले दो पदों का योग है, तो \(a_6\) क्या होगा?

If \(a_1=9\), \(a_2=16\), and each next term is the sum of the previous two terms, what is \(a_6\)?

Explanation opens after your attempt
Correct Answer

D. (107)

Explanation

Simple Explanation

क्रम (9,16,25,41,66,107) बनेगा। इसलिए \(a_6=107\) है। / The sequence becomes (9,16,25,41,66,107). Therefore \(a_6=107\).

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Question 97/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि क्रम \(8,40,200,1000,\ldots\) में \(a_n=5000\) है, तो (n) क्या है?

If \(a_n=5000\) in the sequence \(8,40,200,1000,\ldots\), what is (n)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

क्रम (8,40,200,1000,5000) है। (5000) पाँचवाँ पद है इसलिए (n=5)। / The sequence is (8,40,200,1000,5000). (5000) is the fifth term, so (n=5).

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Question 98/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=5n^2-4n+1\) है, तो \(a_6-a_3\) का मान क्या होगा?

If \(a_n=5n^2-4n+1\), what is the value of \(a_6-a_3\)?

Explanation opens after your attempt
Correct Answer

C. (111)

Explanation

Simple Explanation

(a_6=5\(6^2\)-4(6)+1=157) और (a_3=5\(3^2\)-4(3)+1=34) है। इसलिए अंतर (157-34=123) नहीं, विकल्पों में सही मान नहीं है। / (a_6=5\(6^2\)-4(6)+1=157) and (a_3=5\(3^2\)-4(3)+1=34). So the difference is (157-34=123), not listed in the options.

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Question 99/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(6,13,29,61,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (2) गुना करके (1) जोड़ना है?

What is the next term in \(6,13,29,61,\ldots\) if the rule is double the previous term and add (1)?

Explanation opens after your attempt
Correct Answer

C. (123)

Explanation

Simple Explanation

नियम के अनुसार \(61\times2+1=123\) है। अंतिम पद पर नियम लगाकर अगला पद निकालें। / By the rule, \(61\times2+1=123\). Apply the rule to the last term to get the next term.

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Question 100/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 43

क्रम \(20,31,46,65,88,\ldots\) का अगला पद क्या होगा?

What will be the next term of \(20,31,46,65,88,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (115)

Explanation

Simple Explanation

अंतर (11,15,19,23) हैं और वे (4) से बढ़ रहे हैं। अगला अंतर (27) होगा इसलिए (88+27=115)। / The differences are (11,15,19,23), increasing by (4). The next difference is (27), so (88+27=115).

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Question 101/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(3,8,15,24,\ldots\) में (n)वाँ पद \(a_n=n^2+2n\) है। दसवाँ पद क्या होगा?

In the sequence \(3,8,15,24,\ldots\), the (n)th term is \(a_n=n^2+2n\). What is the tenth term?

Explanation opens after your attempt
Correct Answer

C. (120)

Explanation

Simple Explanation

\(a_{10}=10^2+2\times10=120\) इसलिए सही उत्तर (120) है। परीक्षा में (n) की जगह सीधे दिया गया क्रमांक रखें। / \(a_{10}=10^2+2\times10=120\), so the correct answer is (120). Exam tip: substitute the given position directly for (n).

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Question 102/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,6,12,20,\ldots\) का सामान्य पद (a_n=n(n+1)) है। कौन सा पद (72) के बराबर है?

The sequence \(2,6,12,20,\ldots\) has general term (a_n=n(n+1)). Which term is equal to (72)?

Explanation opens after your attempt
Correct Answer

B. (8)वाँ(8)th

Explanation

Simple Explanation

(n(n+1)=72) में \(8\times9=72\) मिलता है। ऐसी स्थिति में आस-पास के गुणनखंड जल्दी जाँचें। / For (n(n+1)=72), \(8\times9=72\). Exam tip: check nearby factor pairs quickly.

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Question 103/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(1,4,9,16,\ldots\) में (15)वें पद और (14)वें पद का अंतर कितना है?

In the sequence \(1,4,9,16,\ldots\), what is the difference between the (15)th term and the (14)th term?

Explanation opens after your attempt
Correct Answer

C. (29)

Explanation

Simple Explanation

वर्गों के अंतर में (152-142=(15-14)(15+14)=29) होता है। परीक्षा में \(a^2-b^2\) का सूत्र याद रखें। / The difference is (152-142=(15-14)(15+14)=29). Exam tip: use the identity \(a^2-b^2\).

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Question 104/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(5,11,19,29,41,\ldots\) में अगला पद क्या होगा?

What is the next term in the sequence \(5,11,19,29,41,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (55)

Explanation

Simple Explanation

अंतर (6,8,10,12) हैं इसलिए अगला अंतर (14) होगा। (41+14=55) मिलता है। / The differences are (6,8,10,12), so the next difference is (14). Thus (41+14=55).

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Question 105/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(4,9,18,31,48,\ldots\) में पदों के अंतर \(5,9,13,17,\ldots\) हैं। अगला पद क्या है?

In the sequence \(4,9,18,31,48,\ldots\), the differences are \(5,9,13,17,\ldots\). What is the next term?

Explanation opens after your attempt
Correct Answer

B. (69)

Explanation

Simple Explanation

अंतर (4) से बढ़ रहे हैं इसलिए अगला अंतर (21) होगा। (48+21=69) सही है। / The differences increase by (4), so the next difference is (21). Therefore (48+21=69).

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Question 106/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,5,10,17,26,\ldots\) का (n)वाँ पद \(a_n=n^2+1\) है। \(a_{12}-a_{10}\) का मान क्या है?

For the sequence \(2,5,10,17,26,\ldots\), the (n)th term is \(a_n=n^2+1\). What is the value of \(a_{12}-a_{10}\)?

Explanation opens after your attempt
Correct Answer

C. (44)

Explanation

Simple Explanation

\(a_{12}=145\) और \(a_{10}=101\) इसलिए अंतर (44) है। पहले दोनों पद अलग-अलग निकालें। / \(a_{12}=145\) and \(a_{10}=101\), so the difference is (44). Exam tip: find both terms separately first.

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Question 107/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(7,14,23,34,47,\ldots\) में पहला अंतर (7) है और हर बार अंतर (2) बढ़ता है। छठा पद क्या होगा?

In the sequence \(7,14,23,34,47,\ldots\), the first difference is (7) and each difference increases by (2). What is the sixth term?

Explanation opens after your attempt
Correct Answer

D. (62)

Explanation

Simple Explanation

अगला अंतर (15) होगा इसलिए छठा पद (47+15=62) है। बदलते अंतरों को अलग पंक्ति में लिखना उपयोगी रहता है। / The next difference is (15), so the sixth term is (47+15=62). Exam tip: write changing differences separately.

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Question 108/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(1,3,6,10,15,\ldots\) में कौन सा पद (45) है?

In the sequence \(1,3,6,10,15,\ldots\), which term is (45)?

Explanation opens after your attempt
Correct Answer

B. (9)वाँ(9)th

Explanation

Simple Explanation

यह त्रिभुजीय अनुक्रम है और (T_n=\frac{n(n+1)}{2}) होता है। \(\frac{9\times10}{2}=45\) इसलिए यह (9)वाँ पद है। / This is a triangular sequence with (T_n=\frac{n(n+1)}{2}). Since \(\frac{9\times10}{2}=45\), it is the (9)th term.

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Question 109/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,4,8,16,\ldots\) में \(a_1=2\) और हर अगला पद पिछले पद का दोगुना है। आठवाँ पद क्या होगा?

In the sequence \(2,4,8,16,\ldots\), \(a_1=2\) and each next term is double the previous term. What is the eighth term?

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Correct Answer

C. (256)

Explanation

Simple Explanation

आठवाँ पद \(2^8=256\) है। दोगुने वाले अनुक्रम में घातों को पहचानें। / The eighth term is \(2^8=256\). Exam tip: identify powers in doubling sequences.

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Question 110/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(81,27,9,3,\ldots\) में प्रत्येक पद पिछले पद का \(\frac{1}{3}\) है। छठा पद क्या होगा?

In the sequence \(81,27,9,3,\ldots\), each term is \(\frac{1}{3}\) of the previous term. What is the sixth term?

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Correct Answer

B. \(\frac{1}{3}\)

Explanation

Simple Explanation

पद हैं \(81,27,9,3,1,\frac{1}{3}\)। क्रम से घटाते समय हर पद को \(\frac{3}{1}\) से न बाँटें बल्कि (3) से बाँटें। / The terms are \(81,27,9,3,1,\frac{1}{3}\). Exam tip: divide each term by (3) step by step.

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Question 111/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(4,7,12,19,28,\ldots\) में \(a_n=n^2+3\) है। कौन सा पद (84) है?

In the sequence \(4,7,12,19,28,\ldots\), \(a_n=n^2+3\). Which term is (84)?

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Correct Answer

B. (9)वाँ(9)th

Explanation

Simple Explanation

\(n^2+3=84\) से \(n^2=81\) और (n=9) मिलता है। वर्ग संख्या पहचानना समय बचाता है। / From \(n^2+3=84\), \(n^2=81\) and (n=9). Exam tip: recognizing perfect squares saves time.

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Question 112/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(6,13,24,39,58,\ldots\) में अगला पद ज्ञात कीजिए।

Find the next term in the sequence \(6,13,24,39,58,\ldots\).

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Correct Answer

D. (81)

Explanation

Simple Explanation

अंतर (7,11,15,19) हैं इसलिए अगला अंतर (23) होगा। (58+23=81) मिलता है। / The differences are (7,11,15,19), so the next difference is (23). Thus (58+23=81).

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Question 113/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(1,8,27,64,\ldots\) में (n)वाँ पद \(n^3\) है। (6)वाँ पद और (5)वाँ पद का अंतर क्या है?

In the sequence \(1,8,27,64,\ldots\), the (n)th term is \(n^3\). What is the difference between the (6)th term and the (5)th term?

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Correct Answer

A. (91)

Explanation

Simple Explanation

\(6^3-5^3=216-125=91\) है। घन अनुक्रम में सीधे घन निकालकर घटाएँ। / \(6^3-5^3=216-125=91\). Exam tip: in cube sequences, calculate the two cubes and subtract.

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Question 114/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(10,8,11,9,12,10,\ldots\) में दो उप-अनुक्रम छिपे हैं। अगला पद क्या होगा?

In the sequence \(10,8,11,9,12,10,\ldots\), two subsequences are hidden. What is the next term?

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Correct Answer

B. (13)

Explanation

Simple Explanation

विषम स्थानों पर \(10,11,12,\ldots\) है इसलिए अगला विषम स्थान (13) होगा। वैकल्पिक अनुक्रम में स्थानों को अलग करें। / Odd positions are \(10,11,12,\ldots\), so the next odd-position term is (13). Exam tip: separate positions in alternating sequences.

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Question 115/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,9,4,16,6,25,\ldots\) में अगला पद क्या है?

What is the next term in the sequence \(2,9,4,16,6,25,\ldots\)?

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Correct Answer

A. (8)

Explanation

Simple Explanation

विषम स्थानों पर \(2,4,6,\ldots\) हैं इसलिए अगला विषम पद (8) है। वैकल्पिक पैटर्न में दोनों धाराएँ अलग देखें। / Odd positions are \(2,4,6,\ldots\), so the next odd-position term is (8). Exam tip: split the two patterns in alternating sequences.

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Question 116/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(3,6,11,18,27,\ldots\) में \(a_n=n^2+2\) है। \(a_9\) का मान क्या है?

In the sequence \(3,6,11,18,27,\ldots\), \(a_n=n^2+2\). What is \(a_9\)?

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Correct Answer

C. (83)

Explanation

Simple Explanation

\(a_9=9^2+2=83\) है। सामान्य पद मिलने पर अनुमान नहीं लगाना चाहिए। / \(a_9=9^2+2=83\). Exam tip: when the general term is given, avoid guessing.

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Question 117/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(12,17,22,27,\ldots\) में कितने पद (60) से छोटे हैं?

How many terms of the sequence \(12,17,22,27,\ldots\) are less than (60)?

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Correct Answer

C. (10)

Explanation

Simple Explanation

यहाँ (a_n=12+5(n-1)) और (12+5(n-1)<60) से (n<10.6) मिलता है। इसलिए (10) पद छोटे हैं। / Here (a_n=12+5(n-1)), and (12+5(n-1)<60) gives (n<10.6). So (10) terms are less than (60).

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Question 118/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(100,93,86,79,\ldots\) में पहला धनात्मक पदों की संख्या कितनी है?

In the sequence \(100,93,86,79,\ldots\), how many positive terms are there?

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Correct Answer

C. (15)

Explanation

Simple Explanation

(a_n=100-7(n-1)>0) से (n<15.28) मिलता है। अतः धनात्मक पदों की संख्या (15) है। / (a_n=100-7(n-1)>0) gives (n<15.28). Therefore the number of positive terms is (15).

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Question 119/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(5,10,20,40,\ldots\) में कौन सा पद (320) है?

In the sequence \(5,10,20,40,\ldots\), which term is (320)?

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Correct Answer

C. (7)वाँ(7)th

Explanation

Simple Explanation

पद \(5\times2^{n-1}\) हैं और \(5\times2^6=320\) है। इसलिए यह (7)वाँ पद है। / The terms are \(5\times2^{n-1}\), and \(5\times2^6=320\). Hence it is the (7)th term.

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Question 120/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,3,5,8,13,\ldots\) में हर पद पिछले दो पदों का योग है। आठवाँ पद क्या होगा?

In the sequence \(2,3,5,8,13,\ldots\), each term is the sum of the previous two terms. What is the eighth term?

Explanation opens after your attempt
Correct Answer

B. (34)

Explanation

Simple Explanation

आगे के पद (21,34) हैं इसलिए आठवाँ पद (34) है। पुनरावर्ती अनुक्रम में पद छोड़ना नहीं चाहिए। / The next terms are (21,34), so the eighth term is (34). Exam tip: do not skip steps in recursive sequences.

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Question 121/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(4,6,10,16,26,\ldots\) में हर पद पिछले दो पदों का योग है। सातवाँ पद क्या होगा?

In the sequence \(4,6,10,16,26,\ldots\), each term is the sum of the previous two terms. What is the seventh term?

Explanation opens after your attempt
Correct Answer

C. (42)

Explanation

Simple Explanation

छठा पद (16+26=42) और सातवाँ पद (26+42=68) नहीं है क्योंकि पाँचवाँ (26) है। ध्यान से गिनने पर छठा (42) और सातवाँ (68) होगा। / The sixth term is (16+26=42) and the seventh is (26+42=68). Exam tip: count positions carefully in recursive sequences.

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Question 122/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(1,4,10,19,31,\ldots\) में क्रमागत अंतरों में \(3,6,9,12,\ldots\) मिलते हैं। छठा पद क्या है?

In the sequence \(1,4,10,19,31,\ldots\), the successive differences are \(3,6,9,12,\ldots\). What is the sixth term?

Explanation opens after your attempt
Correct Answer

C. (46)

Explanation

Simple Explanation

अगला अंतर (15) है इसलिए छठा पद (31+15=46) होगा। अंतरों के अनुक्रम को पहचानना मुख्य कदम है। / The next difference is (15), so the sixth term is (31+15=46). Exam tip: identifying the sequence of differences is the key step.

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Question 123/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(50,45,37,26,12,\ldots\) में अंतरों का क्रम \(-5,-8,-11,-14,\ldots\) है। अगला पद क्या होगा?

In the sequence \(50,45,37,26,12,\ldots\), the differences are \(-5,-8,-11,-14,\ldots\). What is the next term?

Explanation opens after your attempt
Correct Answer

C. (-5)

Explanation

Simple Explanation

अगला अंतर (-17) होगा इसलिए (12-17=-5) है। ऋणात्मक अंतरों में संकेत का विशेष ध्यान रखें। / The next difference is (-17), so (12-17=-5). Exam tip: be careful with signs in negative differences.

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Question 124/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,7,14,23,34,\ldots\) में \(a_n=n^2+n\) नहीं है। सही सामान्य पद कौन सा है?

In the sequence \(2,7,14,23,34,\ldots\), \(a_n=n^2+n\) is not correct. Which general term is correct?

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Correct Answer

C. \(a_n=n^2+2n-1\)

Explanation

Simple Explanation

(n=1,2,3) रखने पर \(n^2+2n-1\) से (2,7,14) मिलते हैं। विकल्प जाँचते समय शुरुआती तीन पदों परखें। / Substituting (n=1,2,3) in \(n^2+2n-1\) gives (2,7,14). Exam tip: test options using the first three terms.

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Question 125/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(0,3,8,15,24,\ldots\) का सामान्य पद कौन सा है?

What is the general term of the sequence \(0,3,8,15,24,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(a_n=n^2-1\)

Explanation

Simple Explanation

यह पद \(1^2-1,2^2-1,3^2-1,\ldots\) के रूप में हैं। वर्गों के पास वाले अनुक्रम को तुरंत पहचानें। / The terms are \(1^2-1,2^2-1,3^2-1,\ldots\). Exam tip: quickly recognize sequences near perfect squares.

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Question 126/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(3,7,13,21,31,\ldots\) के लिए कौन सा सूत्र सही है?

Which formula is correct for the sequence \(3,7,13,21,31,\ldots\)?

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Correct Answer

B. \(a_n=n^2+n+1\)

Explanation

Simple Explanation

\(n^2+n+1\) से (3,7,13,21) मिलते हैं। सूत्र चुनते समय पहले चार पदों से मिलान करें। / \(n^2+n+1\) gives (3,7,13,21). Exam tip: match the first four terms before choosing a formula.

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Question 127/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(11,18,27,38,51,\ldots\) में अगला पद क्या है?

What is the next term in the sequence \(11,18,27,38,51,\ldots\)?

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Correct Answer

C. (66)

Explanation

Simple Explanation

अंतर (7,9,11,13) हैं इसलिए अगला अंतर (15) होगा। (51+15=66) सही है। / The differences are (7,9,11,13), so the next difference is (15). Therefore (51+15=66).

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Question 128/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,12,30,56,90,\ldots\) का (n)वाँ पद (a_n=n(n+1)(?)) जैसा नहीं है। सही \(a_n\) कौन सा है?

The sequence \(2,12,30,56,90,\ldots\) does not simply fit (a_n=n(n+1)(?)). Which \(a_n\) is correct?

Explanation opens after your attempt
Correct Answer

B. \(a_n=n^3+n\)

Explanation

Simple Explanation

\(n^3+n\) से (2,10) नहीं बल्कि (n=2) पर (10) आता है इसलिए यह गलत है। सही मिलान \(a_n=2n^2+?\) जैसा चाहिए था। / This question has inconsistent options because \(n^3+n\) gives (10) at (n=2), not (12). Exam tip: verify every option before accepting a pattern.

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Question 129/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,12,30,56,90,\ldots\) का सही सामान्य पद कौन सा है?

What is the correct general term for the sequence \(2,12,30,56,90,\ldots\)?

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Correct Answer

D. (a_n=n(n+1)2)

Explanation

Simple Explanation

(n(n+1)2) से (2,12,36) नहीं मिलता इसलिए सावधानी जरूरी है। दिए गए विकल्पों में कोई भी पूरा मेल नहीं खाता। / (n(n+1)2) does not give the full sequence, so care is needed. None of the given options matches all terms.

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Question 130/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(9,16,25,36,\ldots\) में (20)वाँ पद क्या है?

What is the (20)th term of the sequence \(9,16,25,36,\ldots\)?

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Correct Answer

D. (484)

Explanation

Simple Explanation

यह \(3^2,4^2,5^2,\ldots\) है इसलिए (20)वाँ पद \(22^2=484\) होगा। शुरुआती संख्या से सूचकांक का संबंध ध्यान रखें। / This is \(3^2,4^2,5^2,\ldots\), so the (20)th term is \(22^2=484\). Exam tip: track how the index shifts.

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Question 131/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(8,27,64,125,\ldots\) में (10)वाँ पद क्या है?

What is the (10)th term of the sequence \(8,27,64,125,\ldots\)?

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Correct Answer

B. (1331)

Explanation

Simple Explanation

यह \(2^3,3^3,4^3,\ldots\) है इसलिए (10)वाँ पद \(11^3=1331\) है। शिफ्ट वाले घन अनुक्रमों में क्रमांक ध्यान से बदलें। / This is \(2^3,3^3,4^3,\ldots\), so the (10)th term is \(11^3=1331\). Exam tip: handle shifted cube sequences carefully.

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Question 132/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(1,2,4,7,11,\ldots\) में प्रत्येक बार जोड़ी जाने वाली संख्या \(1,2,3,4,\ldots\) है। आठवाँ पद क्या होगा?

In the sequence \(1,2,4,7,11,\ldots\), the added numbers are \(1,2,3,4,\ldots\). What is the eighth term?

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Correct Answer

D. (29)

Explanation

Simple Explanation

आगे (16,22,29) मिलते हैं इसलिए आठवाँ पद (29) है। क्रमागत जोड़ को पूरा लिखना गलती घटाता है। / Continuing gives (16,22,29), so the eighth term is (29). Exam tip: write each successive addition to avoid mistakes.

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Question 133/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(3,5,9,17,33,\ldots\) में हर अगला पद पिछले पद का दोगुना घटाकर (1) है। अगला पद क्या होगा?

In the sequence \(3,5,9,17,33,\ldots\), each next term is double the previous term minus (1). What is the next term?

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Correct Answer

C. (65)

Explanation

Simple Explanation

\(2\times33-1=65\) है। पुनरावर्ती नियम में पहले दिए गए नियम को ठीक से लागू करें। / \(2\times33-1=65\). Exam tip: apply the given recurrence rule exactly.

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Question 134/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,5,11,23,47,\ldots\) में हर अगला पद पिछले पद का दोगुना जोड़कर (1) है। अगला पद क्या होगा?

In the sequence \(2,5,11,23,47,\ldots\), each next term is double the previous term plus (1). What is the next term?

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Correct Answer

C. (95)

Explanation

Simple Explanation

\(2\times47+1=95\) है। ऐसे प्रश्नों में गुणा और जोड़ का क्रम न बदलें। / \(2\times47+1=95\). Exam tip: do not change the order of multiplication and addition.

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Question 135/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(30,15,17,8.5,10.5,\ldots\) में क्रम है आधा करना फिर (2) जोड़ना। अगला पद क्या होगा?

In the sequence \(30,15,17,8.5,10.5,\ldots\), the pattern is divide by (2), then add (2). What is the next term?

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Correct Answer

B. (5.25)

Explanation

Simple Explanation

(10.5) के बाद आधा करने पर (5.25) मिलता है। वैकल्पिक क्रिया वाले अनुक्रम में अगली क्रिया पहचानें। / After (10.5), dividing by (2) gives (5.25). Exam tip: identify the next operation in alternating-operation sequences.

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Question 136/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(1,4,13,40,121,\ldots\) में हर अगला पद पिछले पद का (3) गुना जोड़कर (1) है। अगला पद क्या होगा?

In the sequence \(1,4,13,40,121,\ldots\), each next term is (3) times the previous term plus (1). What is the next term?

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Correct Answer

C. (364)

Explanation

Simple Explanation

\(3\times121+1=364\) है। दिए गए नियम को अंतिम पद पर लगाना सबसे सुरक्षित तरीका है। / \(3\times121+1=364\). Exam tip: apply the given rule to the last term directly.

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Question 137/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,6,18,54,\ldots\) में \(a_1=2\) और \(a_{n+1}=3a_n\) है। \(a_6\) क्या है?

In the sequence \(2,6,18,54,\ldots\), \(a_1=2\) and \(a_{n+1}=3a_n\). What is \(a_6\)?

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Correct Answer

D. (486)

Explanation

Simple Explanation

\(a_6=2\times3^5=486\) है। पहले पद से गिनते समय घात (n-1) होती है। / \(a_6=2\times3^5=486\). Exam tip: when starting from the first term, the exponent is (n-1).

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Question 138/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(7,10,16,28,52,\ldots\) में हर बार जोड़ा गया पद दोगुना हो रहा है। अगला पद क्या होगा?

In the sequence \(7,10,16,28,52,\ldots\), the added amount doubles each time. What is the next term?

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Correct Answer

D. (100)

Explanation

Simple Explanation

अंतर (3,6,12,24) हैं इसलिए अगला अंतर (48) होगा। (52+48=100) मिलता है। / The differences are (3,6,12,24), so the next difference is (48). Thus (52+48=100).

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Question 139/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(2,4,7,11,16,\ldots\) में (20)वाँ पद क्या होगा?

What is the (20)th term of the sequence \(2,4,7,11,16,\ldots\)?

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Correct Answer

C. (211)

Explanation

Simple Explanation

यह (1) से शुरू होकर क्रमागत संख्याएँ जोड़ता है और (a_n=1+\frac{n(n+1)}{2}) है। \(a_{20}=1+\frac{20\times21}{2}=211\) है। / It adds consecutive numbers starting from (1), so (a_n=1+\frac{n(n+1)}{2}). Thus \(a_{20}=1+\frac{20\times21}{2}=211\).

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Question 140/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(13,18,23,28,\ldots\) में कौन सा पद (98) है?

In the sequence \(13,18,23,28,\ldots\), which term is (98)?

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Correct Answer

C. (18)वाँ(18)th

Explanation

Simple Explanation

(a_n=13+5(n-1)) और (13+5(n-1)=98) से (n=18) मिलता है। पद संख्या निकालते समय (n-1) न भूलें। / (a_n=13+5(n-1)), and (13+5(n-1)=98) gives (n=18). Exam tip: do not forget (n-1) when finding position.

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Question 141/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(6,13,20,27,\ldots\) का कौन सा पद (83) है?

Which term of the sequence \(6,13,20,27,\ldots\) is (83)?

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Correct Answer

C. (12)वाँ(12)th

Explanation

Simple Explanation

(6+7(n-1)=83) से (7(n-1)=77) और (n=12) मिलता है। समान अंतर वाले अनुक्रम में सूत्र सीधे लगाएँ। / (6+7(n-1)=83) gives (7(n-1)=77) and (n=12). Exam tip: use the arithmetic sequence formula directly.

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Question 142/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(-5,-1,3,7,\ldots\) में (25)वाँ पद क्या है?

What is the (25)th term of the sequence \(-5,-1,3,7,\ldots\)?

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Correct Answer

B. (91)

Explanation

Simple Explanation

(a_n=-5+4(n-1)) है इसलिए \(a_{25}=-5+96=91\) है। ऋणात्मक पहले पद में संकेत सावधानी से रखें। / (a_n=-5+4(n-1)), so \(a_{25}=-5+96=91\). Exam tip: handle the sign of a negative first term carefully.

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Question 143/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(1,-2,4,-8,16,\ldots\) में आठवाँ पद क्या होगा?

What will be the eighth term in the sequence \(1,-2,4,-8,16,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. (-128)

Explanation

Simple Explanation

हर बार (-2) से गुणा हो रहा है इसलिए आठवाँ पद ((-2)7=-128) है। संकेत और घात दोनों साथ देखें। / Each term is multiplied by (-2), so the eighth term is ((-2)7=-128). Exam tip: track both sign and power.

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Question 144/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(5,-10,20,-40,\ldots\) में सातवाँ पद क्या है?

What is the seventh term in the sequence \(5,-10,20,-40,\ldots\)?

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Correct Answer

C. (320)

Explanation

Simple Explanation

सामान्य पद (a_n=5(-2)^{n-1}) है इसलिए (a_7=5(-2)6=320) है। सम घात पर चिह्न धनात्मक होता है। / The general term is (a_n=5(-2)^{n-1}), so (a_7=5(-2)6=320). Exam tip: an even power gives a positive sign.

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Question 145/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(1,1,2,3,5,8,\ldots\) में (10)वाँ पद क्या है?

What is the (10)th term in the sequence \(1,1,2,3,5,8,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (55)

Explanation

Simple Explanation

पद आगे (13,21,34,55) हैं इसलिए (10)वाँ पद (55) है। फिबोनाची जैसे अनुक्रम में क्रमांक लिखकर बढ़ें। / The next terms are (13,21,34,55), so the (10)th term is (55). Exam tip: write positions when extending Fibonacci-type sequences.

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Question 146/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(0,2,6,12,20,\ldots\) में (a_n=n(n-1)) है। \(a_{15}\) क्या है?

In the sequence \(0,2,6,12,20,\ldots\), (a_n=n(n-1)). What is \(a_{15}\)?

Explanation opens after your attempt
Correct Answer

D. (210)

Explanation

Simple Explanation

\(a_{15}=15\times14=210\) है। सूत्र में (n) की जगह पद संख्या रखें। / \(a_{15}=15\times14=210\). Exam tip: substitute the term number for (n) in the formula.

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Question 147/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(3,12,27,48,75,\ldots\) का सामान्य पद \(a_n=3n^2\) है। \(a_8-a_6\) क्या है?

The sequence \(3,12,27,48,75,\ldots\) has general term \(a_n=3n^2\). What is \(a_8-a_6\)?

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Correct Answer

C. (84)

Explanation

Simple Explanation

\(a_8=192\) और \(a_6=108\) इसलिए अंतर (84) है। दोनों पद निकालकर घटाएँ। / \(a_8=192\) and \(a_6=108\), so the difference is (84). Exam tip: find both terms and then subtract.

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Question 148/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(4,10,18,28,40,\ldots\) में अगला पद क्या होगा?

What will be the next term in the sequence \(4,10,18,28,40,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (54)

Explanation

Simple Explanation

अंतर (6,8,10,12) हैं इसलिए अगला अंतर (14) होगा। (40+14=54) सही है। / The differences are (6,8,10,12), so the next difference is (14). Therefore (40+14=54).

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Question 149/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(15,12,7,0,-9,\ldots\) में अंतरों का क्रम \(-3,-5,-7,-9,\ldots\) है। अगला पद क्या होगा?

In the sequence \(15,12,7,0,-9,\ldots\), the differences are \(-3,-5,-7,-9,\ldots\). What will be the next term?

Explanation opens after your attempt
Correct Answer

D. (-20)

Explanation

Simple Explanation

अगला अंतर (-11) होगा इसलिए (-9-11=-20) है। घटते अनुक्रम में ऋण चिह्न की जाँच जरूर करें। / The next difference is (-11), so (-9-11=-20). Exam tip: always check the negative sign in decreasing sequences.

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Question 150/150 Hard Mathematics Sequences and Progressions Sequences Class 9 Level 44

अनुक्रम \(4,11,22,37,56,\ldots\) में क्रमागत अंतरों का क्रम \(7,11,15,19,\ldots\) है। अगला पद क्या होगा?

In the sequence \(4,11,22,37,56,\ldots\), the successive differences are \(7,11,15,19,\ldots\). What will be the next term?

Explanation opens after your attempt
Correct Answer

C. (79)

Explanation

Simple Explanation

अगला अंतर (23) होगा इसलिए (56+23=79) है। अंतर के अंतर को पहचानना ऐसे प्रश्नों में सबसे तेज तरीका है। / The next difference is (23), so (56+23=79). Exam tip: identifying the difference of differences is the fastest method here.

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