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Mathematics Quiz - Class 9 Mathematics Sequences and Prog...

Question 1/50 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)

Step 1

Concept

The first term is (8) and the common difference is (6). The (16)th term is \(8+15\times6=98\).

Step 2

Why this answer is correct

The correct answer is C. (98). The first term is (8) and the common difference is (6). The (16)th term is \(8+15\times6=98\).

Step 3

Exam Tip

पहला पद (8) और समान अंतर (6) है। (16)वाँ पद \(8+15\times6=98\) है।

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Question 2/50 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)

Step 1

Concept

Each term decreases by (12). The (11)th term is \(160-10\times12=40\).

Step 2

Why this answer is correct

The correct answer is C. (40). Each term decreases by (12). The (11)th term is \(160-10\times12=40\).

Step 3

Exam Tip

हर बार (12) घट रहा है। (11)वाँ पद \(160-10\times12=40\) है।

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Question 3/50 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)

Step 1

Concept

Putting (n=7), (a_7=4\(7^2\)-3(7)=175). Square first, then multiply and subtract.

Step 2

Why this answer is correct

The correct answer is B. (175). Putting (n=7), (a_7=4\(7^2\)-3(7)=175). Square first, then multiply and subtract.

Step 3

Exam Tip

(n=7) रखने पर (a_7=4\(7^2\)-3(7)=175) है। पहले वर्ग निकालें फिर गुणा और घटाव करें।

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Question 4/50 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)

Step 1

Concept

Putting (n=5), (a_5=5³-2(5)=115). Handle the cube and multiplication carefully.

Step 2

Why this answer is correct

The correct answer is C. (115). Putting (n=5), (a_5=5³-2(5)=115). Handle the cube and multiplication carefully.

Step 3

Exam Tip

(n=5) रखने पर (a_5=5³-2(5)=115) है। घन और गुणा दोनों सावधानी से करें।

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Question 5/50 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)

Step 1

Concept

Each term increases by (9). Since (27+9=36), the missing value is (36).

Step 2

Why this answer is correct

The correct answer is C. (36). Each term increases by (9). Since (27+9=36), the missing value is (36).

Step 3

Exam Tip

हर बार (9) जोड़ा जा रहा है। (27+9=36) इसलिए खाली स्थान (36) है।

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Question 6/50 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)

Step 1

Concept

The sequence decreases by (14) each time. (180-14=166).

Step 2

Why this answer is correct

The correct answer is C. (166). The sequence decreases by (14) each time. (180-14=166).

Step 3

Exam Tip

क्रम में हर बार (14) घट रहा है। (180-14=166) होगा।

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Question 7/50 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)

Step 1

Concept

The differences are (7,10,13,16), increasing by (3). The next difference is (19), so (51+19=70).

Step 2

Why this answer is correct

The correct answer is B. (70). The differences are (7,10,13,16), increasing by (3). The next difference is (19), so (51+19=70).

Step 3

Exam Tip

अंतर (7,10,13,16) हैं और वे (3) से बढ़ रहे हैं। अगला अंतर (19) होगा इसलिए (51+19=70)।

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Question 8/50 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)

Step 1

Concept

The subtractions are (5,10,15,20). The next subtraction is (25), so (200-25=175).

Step 2

Why this answer is correct

The correct answer is A. (175). The subtractions are (5,10,15,20). The next subtraction is (25), so (200-25=175).

Step 3

Exam Tip

घटाव (5,10,15,20) हैं। अगला घटाव (25) होगा इसलिए (200-25=175)।

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Question 9/50 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)

Step 1

Concept

Each term is (4) times the previous term. The (5)th term is (1536) and the (6)th term is (6144).

Step 2

Why this answer is correct

The correct answer is D. (6144). Each term is (4) times the previous term. The (5)th term is (1536) and the (6)th term is (6144).

Step 3

Exam Tip

हर पद पिछले पद का (4) गुना है। (5)वाँ पद (1536) और (6)ठा पद (6144) है।

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Question 10/50 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)

Step 1

Concept

Each term is obtained by dividing the previous term by (3). \(27\div3=9\) is the next term.

Step 2

Why this answer is correct

The correct answer is C. (9). Each term is obtained by dividing the previous term by (3). \(27\div3=9\) is the next term.

Step 3

Exam Tip

हर पद पिछले पद को (3) से भाग देकर मिलता है। \(27\div3=9\) अगला पद है।

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Question 11/50 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)

Step 1

Concept

This is the sequence \(4^2,5^2,6^2,\ldots\). The (8)th term will be \(11^2=121\).

Step 2

Why this answer is correct

The correct answer is B. (121). This is the sequence \(4^2,5^2,6^2,\ldots\). The (8)th term will be \(11^2=121\).

Step 3

Exam Tip

यह \(4^2,5^2,6^2,\ldots\) का क्रम है। (8)वाँ पद \(11^2=121\) होगा।

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Question 12/50 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)

Step 1

Concept

This is the sequence \(4^3,5^3,6^3,7^3,\ldots\). The (6)th term is \(9^3=729\).

Step 2

Why this answer is correct

The correct answer is B. (729). This is the sequence \(4^3,5^3,6^3,7^3,\ldots\). The (6)th term is \(9^3=729\).

Step 3

Exam Tip

यह \(4^3,5^3,6^3,7^3,\ldots\) का क्रम है। (6)ठा पद \(9^3=729\) है।

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Question 13/50 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)

Step 1

Concept

The differences are \(4,5,6,7,\ldots\). Extending to the (10)th term gives (64).

Step 2

Why this answer is correct

The correct answer is C. (64). The differences are \(4,5,6,7,\ldots\). Extending to the (10)th term gives (64).

Step 3

Exam Tip

अंतर \(4,5,6,7,\ldots\) हैं। (10)वें पद तक बढ़ने पर मान (64) मिलता है।

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Question 14/50 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)

Step 1

Concept

Here (14=4+10), (24=10+14), and (38=14+24). The next term will be (24+38=62).

Step 2

Why this answer is correct

The correct answer is C. (62). Here (14=4+10), (24=10+14), and (38=14+24). The next term will be (24+38=62).

Step 3

Exam Tip

यहाँ (14=4+10), (24=10+14) और (38=14+24) है। अगला पद (24+38=62) होगा।

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Question 15/50 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

Step 1

Concept

The sequence is (9,27,81,243,729). So (729) is the (5)th term.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The sequence is (9,27,81,243,729). So (729) is the (5)th term.

Step 3

Exam Tip

क्रम (9,27,81,243,729) है। इसलिए (729) (5)वाँ पद है।

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Question 16/50 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

Step 1

Concept

The first term is (15) and the difference is (9). From (15+(n-1)9=105), (n=11).

Step 2

Why this answer is correct

The correct answer is C. (11)वाँ / (11)th. The first term is (15) and the difference is (9). From (15+(n-1)9=105), (n=11).

Step 3

Exam Tip

पहला पद (15) और अंतर (9) है। (15+(n-1)9=105) से (n=11) मिलता है।

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Question 17/50 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

Step 1

Concept

Each term decreases by (12). From (170-(n-1)12=74), (n=9).

Step 2

Why this answer is correct

The correct answer is C. (9)वाँ / (9)th. Each term decreases by (12). From (170-(n-1)12=74), (n=9).

Step 3

Exam Tip

हर बार (12) घट रहा है। (170-(n-1)12=74) से (n=9) है।

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Question 18/50 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. \(a_n=11n-2\)

Step 1

Concept

The first term is (9) and the difference is (11). \(a_n=11n-2\) gives the same sequence.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=11n-2\). The first term is (9) and the difference is (11). \(a_n=11n-2\) gives the same sequence.

Step 3

Exam Tip

पहला पद (9) और अंतर (11) है। \(a_n=11n-2\) से वही क्रम मिलता है।

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Question 19/50 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. \(a_n=9n+7\)

Step 1

Concept

The first term is (16) and the difference is (9). \(a_n=9n+7\) gives \(16,25,34,\ldots\).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=9n+7\). The first term is (16) and the difference is (9). \(a_n=9n+7\) gives \(16,25,34,\ldots\).

Step 3

Exam Tip

पहला पद (16) और अंतर (9) है। \(a_n=9n+7\) से \(16,25,34,\ldots\) मिलते हैं।

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Question 20/50 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)

Step 1

Concept

Putting (n=1,2,3,4) gives (3,11,19,27). Start with (n=1) for the first term.

Step 2

Why this answer is correct

The correct answer is A. (3,11,19,27). Putting (n=1,2,3,4) gives (3,11,19,27). Start with (n=1) for the first term.

Step 3

Exam Tip

(n=1,2,3,4) रखने पर (3,11,19,27) मिलते हैं। पहले पद के लिए (n=1) से शुरू करें।

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Question 21/50 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)

Step 1

Concept

Putting (n=6), (a_6=3\(6^2\)+4(6)=132). Handle both the square and multiplication carefully.

Step 2

Why this answer is correct

The correct answer is C. (132). Putting (n=6), (a_6=3\(6^2\)+4(6)=132). Handle both the square and multiplication carefully.

Step 3

Exam Tip

(n=6) रखने पर (a_6=3\(6^2\)+4(6)=132) है। वर्ग और गुणा दोनों सावधानी से करें।

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Question 22/50 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)

Step 1

Concept

Putting (n=8), \(a_8=140-72=68\). Pay attention to the sign in subtraction rules.

Step 2

Why this answer is correct

The correct answer is C. (68). Putting (n=8), \(a_8=140-72=68\). Pay attention to the sign in subtraction rules.

Step 3

Exam Tip

(n=8) रखने पर \(a_8=140-72=68\) है। घटाव वाले नियम में चिन्ह पर ध्यान दें।

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Question 23/50 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)

Step 1

Concept

Putting (n=1,2,3,4) gives (7,28,63,112). Multiply \(n^2\) by (7).

Step 2

Why this answer is correct

The correct answer is B. (7,28,63,112). Putting (n=1,2,3,4) gives (7,28,63,112). Multiply \(n^2\) by (7).

Step 3

Exam Tip

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

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Question 24/50 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)

Step 1

Concept

\(3^1+1=4\), \(3^2+2=11\), \(3^3+3=30\), and \(3^4+4=85\). Add (n) after evaluating the power.

Step 2

Why this answer is correct

The correct answer is A. (4,11,30,85). \(3^1+1=4\), \(3^2+2=11\), \(3^3+3=30\), and \(3^4+4=85\). Add (n) after evaluating the power.

Step 3

Exam Tip

\(3^1+1=4\), \(3^2+2=11\), \(3^3+3=30\), \(3^4+4=85\)। घात के बाद (n) जोड़ें।

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Question 25/50 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)

Step 1

Concept

Both sequences have common difference (7), so the term difference always remains (4). The (12)th terms also differ by (4).

Step 2

Why this answer is correct

The correct answer is B. (4). Both sequences have common difference (7), so the term difference always remains (4). The (12)th terms also differ by (4).

Step 3

Exam Tip

दोनों क्रमों का समान अंतर (7) है इसलिए पदों का अंतर हमेशा (4) रहेगा। (12)वें पदों में भी यही अंतर है।

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Question 26/50 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)

Step 1

Concept

Both sequences have difference (8), and their first terms differ by (9). So their (9)th terms also differ by (9).

Step 2

Why this answer is correct

The correct answer is B. पहला (9) अधिक है / The first is greater by (9). Both sequences have difference (8), and their first terms differ by (9). So their (9)th terms also differ by (9).

Step 3

Exam Tip

दोनों क्रमों का अंतर (8) है और पहले पदों का अंतर (9) है। इसलिए (9)वें पदों का अंतर भी (9) होगा।

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Question 27/50 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)

Step 1

Concept

The first (9) terms run from (8) to (72). Their sum is (360).

Step 2

Why this answer is correct

The correct answer is C. (360). The first (9) terms run from (8) to (72). Their sum is (360).

Step 3

Exam Tip

पहले (9) पद (8) से (72) तक हैं। उनका योग (360) है।

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Question 28/50 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)

Step 1

Concept

The first (6) terms are (132,121,110,99,88,77). Their sum is (627).

Step 2

Why this answer is correct

The correct answer is B. (627). The first (6) terms are (132,121,110,99,88,77). Their sum is (627).

Step 3

Exam Tip

पहले (6) पद (132,121,110,99,88,77) हैं। इनका योग (627) है।

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Question 29/50 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

Step 1

Concept

The first term is (10) and the difference is (8). From (10+(n-1)8=90), (n=11).

Step 2

Why this answer is correct

The correct answer is C. (11)वाँ / (11)th. The first term is (10) and the difference is (8). From (10+(n-1)8=90), (n=11).

Step 3

Exam Tip

पहला पद (10) और अंतर (8) है। (10+(n-1)8=90) से (n=11) मिलता है।

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Question 30/50 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)

Step 1

Concept

\(a_8=53\) and \(a_9=59\). Therefore \(a_8+a_9=112\), so the correct value is not in the options.

Step 2

Why this answer is correct

The correct answer is C. (106). \(a_8=53\) and \(a_9=59\). Therefore \(a_8+a_9=112\), so the correct value is not in the options.

Step 3

Exam Tip

\(a_8=53\) और \(a_9=59\) है। इसलिए \(a_8+a_9=112\), अतः विकल्पों में सही मान नहीं है।

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Question 31/50 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)

Step 1

Concept

The common difference is (10), and the gap in positions is (5). Therefore \(a_9-a_4=5\times10=50\).

Step 2

Why this answer is correct

The correct answer is C. (50). The common difference is (10), and the gap in positions is (5). Therefore \(a_9-a_4=5\times10=50\).

Step 3

Exam Tip

समान अंतर (10) है और स्थानों का अंतर (5) है। इसलिए \(a_9-a_4=5\times10=50\) है।

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Question 32/50 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)

Step 1

Concept

The common difference is (7), and the position gap is (5). So the difference is \(5\times7=35\).

Step 2

Why this answer is correct

The correct answer is B. (35). The common difference is (7), and the position gap is (5). So the difference is \(5\times7=35\).

Step 3

Exam Tip

समान अंतर (7) है और स्थानों का अंतर (5) है। इसलिए अंतर \(5\times7=35\) है।

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Question 33/50 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)

Step 1

Concept

\(a_{12}=18+11\times9=117\). To reach the (12)th term, the difference is added (11) times.

Step 2

Why this answer is correct

The correct answer is B. (117). \(a_{12}=18+11\times9=117\). To reach the (12)th term, the difference is added (11) times.

Step 3

Exam Tip

\(a_{12}=18+11\times9=117\) है। (12)वें पद तक पहुँचने के लिए (11) बार अंतर जोड़ा जाता है।

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Question 34/50 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)

Step 1

Concept

\(a_{10}=180-9\times13=63\). There are (9) subtractions before the (10)th term.

Step 2

Why this answer is correct

The correct answer is A. (63). \(a_{10}=180-9\times13=63\). There are (9) subtractions before the (10)th term.

Step 3

Exam Tip

\(a_{10}=180-9\times13=63\) है। (10)वें पद तक (9) बार घटाव होगा।

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Question 35/50 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)

Step 1

Concept

By the rule, \(161\times3+2=485\). Apply the given rule to the last term.

Step 2

Why this answer is correct

The correct answer is B. (485). By the rule, \(161\times3+2=485\). Apply the given rule to the last term.

Step 3

Exam Tip

नियम के अनुसार \(161\times3+2=485\) है। अंतिम पद पर दिया गया नियम लगाएँ।

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Question 36/50 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)

Step 1

Concept

\(18.25\div2-1=8.125\). Divide first and then subtract (1).

Step 2

Why this answer is correct

The correct answer is A. (8.125). \(18.25\div2-1=8.125\). Divide first and then subtract (1).

Step 3

Exam Tip

\(18.25\div2-1=8.125\) है। पहले भाग दें और फिर (1) घटाएँ।

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Question 37/50 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)

Step 1

Concept

The differences are (8,16,24,32). The next difference is (40), so (90+40=130).

Step 2

Why this answer is correct

The correct answer is C. (130). The differences are (8,16,24,32). The next difference is (40), so (90+40=130).

Step 3

Exam Tip

अंतर (8,16,24,32) हैं। अगला अंतर (40) होगा इसलिए (90+40=130)।

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Question 38/50 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)

Step 1

Concept

The subtractions are (15,30,45,60). The next subtraction is (75), so (210-75=135).

Step 2

Why this answer is correct

The correct answer is C. (135). The subtractions are (15,30,45,60). The next subtraction is (75), so (210-75=135).

Step 3

Exam Tip

घटाव (15,30,45,60) है। अगला घटाव (75) होगा इसलिए (210-75=135)।

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Question 39/50 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)

Step 1

Concept

The terms are multiplied by (2,3,4) successively. The next multiplier is (5), so \(120\times5=600\).

Step 2

Why this answer is correct

The correct answer is C. (600). The terms are multiplied by (2,3,4) successively. The next multiplier is (5), so \(120\times5=600\).

Step 3

Exam Tip

यहाँ क्रमशः (2,3,4) से गुणा किया गया है। अगला गुणक (5) होगा इसलिए \(120\times5=600\)।

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Question 40/50 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)

Step 1

Concept

The third terms are (252) and (180). Their ratio is (252:180=7:5).

Step 2

Why this answer is correct

The correct answer is B. (7:5). The third terms are (252) and (180). Their ratio is (252:180=7:5).

Step 3

Exam Tip

तीसरे पद (252) और (180) हैं। उनका अनुपात (252:180=7:5) है।

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Question 41/50 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)

Step 1

Concept

The first (5) terms are (12,21,30,39,48). Their sum is (150).

Step 2

Why this answer is correct

The correct answer is B. (5). The first (5) terms are (12,21,30,39,48). Their sum is (150).

Step 3

Exam Tip

पहले (5) पद (12,21,30,39,48) हैं। उनका योग (150) है।

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Question 42/50 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)

Step 1

Concept

The sequence is (14,25,36,47,58,69,80,91). The term just before (91) is (80).

Step 2

Why this answer is correct

The correct answer is C. (80). The sequence is (14,25,36,47,58,69,80,91). The term just before (91) is (80).

Step 3

Exam Tip

क्रम (14,25,36,47,58,69,80,91) है। (91) से ठीक पहले (80) आता है।

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Question 43/50 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)

Step 1

Concept

Each term is halved. The sequence is (768,384,192,96,48,24), so (48) comes before (24).

Step 2

Why this answer is correct

The correct answer is C. (48). Each term is halved. The sequence is (768,384,192,96,48,24), so (48) comes before (24).

Step 3

Exam Tip

हर बार आधा हो रहा है। क्रम (768,384,192,96,48,24) है इसलिए (24) से पहले (48) है।

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Question 44/50 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)

Step 1

Concept

At (n=1), (8(1)+11=19), and the difference is (8). So the correct rule is (8n+11).

Step 2

Why this answer is correct

The correct answer is A. यह (8n+11) है / It is (8n+11). At (n=1), (8(1)+11=19), and the difference is (8). So the correct rule is (8n+11).

Step 3

Exam Tip

(n=1) पर (8(1)+11=19) और अंतर (8) मिलता है। इसलिए सही नियम (8n+11) है।

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Question 45/50 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. \(a_n=168-12n\)

Step 1

Concept

Putting (n=1) gives (168-12=156). This rule decreases by (12) each time.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=168-12n\). Putting (n=1) gives (168-12=156). This rule decreases by (12) each time.

Step 3

Exam Tip

(n=1) रखने पर (168-12=156) मिलता है। यह हर बार (12) घटाने वाला नियम है।

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Question 46/50 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)

Step 1

Concept

The sequence becomes (9,16,25,41,66,107). Therefore \(a_6=107\).

Step 2

Why this answer is correct

The correct answer is D. (107). The sequence becomes (9,16,25,41,66,107). Therefore \(a_6=107\).

Step 3

Exam Tip

क्रम (9,16,25,41,66,107) बनेगा। इसलिए \(a_6=107\) है।

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Question 47/50 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)

Step 1

Concept

The sequence is (8,40,200,1000,5000). (5000) is the fifth term, so (n=5).

Step 2

Why this answer is correct

The correct answer is B. (5). The sequence is (8,40,200,1000,5000). (5000) is the fifth term, so (n=5).

Step 3

Exam Tip

क्रम (8,40,200,1000,5000) है। (5000) पाँचवाँ पद है इसलिए (n=5)।

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Question 48/50 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)

Step 1

Concept

(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.

Step 2

Why this answer is correct

The correct answer is C. (111). (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.

Step 3

Exam Tip

(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।

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Question 49/50 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)

Step 1

Concept

By the rule, \(61\times2+1=123\). Apply the rule to the last term to get the next term.

Step 2

Why this answer is correct

The correct answer is C. (123). By the rule, \(61\times2+1=123\). Apply the rule to the last term to get the next term.

Step 3

Exam Tip

नियम के अनुसार \(61\times2+1=123\) है। अंतिम पद पर नियम लगाकर अगला पद निकालें।

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Question 50/50 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)

Step 1

Concept

The differences are (11,15,19,23), increasing by (4). The next difference is (27), so (88+27=115).

Step 2

Why this answer is correct

The correct answer is C. (115). The differences are (11,15,19,23), increasing by (4). The next difference is (27), so (88+27=115).

Step 3

Exam Tip

अंतर (11,15,19,23) हैं और वे (4) से बढ़ रहे हैं। अगला अंतर (27) होगा इसलिए (88+27=115)।

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Class 9 Mathematics - Sequences and Progressions - Sequences Hard Quiz

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct