Class 9 Mathematics - Exploring Algebraic Identities - Visual models of identities Expert Quiz

Mathematics Exploring Algebraic Identities Visual models of identities Expert Class 9 Level 43

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Question 1/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=4n^2+2n-3\) है तो \(a_{11}\) का मान क्या होगा?

If \(a_n=4n^2+2n-3\), what will be the value of \(a_{11}\)?

Explanation opens after your attempt
Correct Answer

B. (503)

Step 1

Concept

\(a_{11}=4\times11^2+2\times11-3=503\). Exam tip: square first and then complete the remaining operations.

Step 2

Why this answer is correct

The correct answer is B. (503). \(a_{11}=4\times11^2+2\times11-3=503\). Exam tip: square first and then complete the remaining operations.

Step 3

Exam Tip

\(a_{11}=4\times11^2+2\times11-3=503\) है। पहले वर्ग निकालकर फिर बाकी क्रियाएँ करें।

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Question 2/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(9,21,39,63,93,\ldots\) में अगला पद क्या होगा?

What will be the next term in the sequence \(9,21,39,63,93,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (129)

Step 1

Concept

The differences are (12,18,24,30), so the next difference is (36). Thus (93+36=129).

Step 2

Why this answer is correct

The correct answer is C. (129). The differences are (12,18,24,30), so the next difference is (36). Thus (93+36=129).

Step 3

Exam Tip

अंतर (12,18,24,30) हैं इसलिए अगला अंतर (36) होगा। (93+36=129) सही है।

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Question 3/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_1=5\) और \(a_{n+1}=2a_n+3n\) है तो \(a_5\) क्या होगा?

If \(a_1=5\) and \(a_{n+1}=2a_n+3n\), what will \(a_5\) be?

Explanation opens after your attempt
Correct Answer

C. (139)

Step 1

Concept

The terms are (5,13,32,73,158), so \(a_5=158\). Therefore none of the given options is correct.

Step 2

Why this answer is correct

The correct answer is C. (139). The terms are (5,13,32,73,158), so \(a_5=158\). Therefore none of the given options is correct.

Step 3

Exam Tip

पद (5,13,32,73,158) नहीं बल्कि \(a_5=158\) होता है। इसलिए दिए गए विकल्पों में सही उत्तर नहीं है।

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Question 4/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(4,13,28,49,76,\ldots\) में अगला पद क्या होगा?

What will be the next term in the sequence \(4,13,28,49,76,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (109)

Step 1

Concept

The differences are (9,15,21,27), so the next difference is (33). Hence (76+33=109).

Step 2

Why this answer is correct

The correct answer is B. (109). The differences are (9,15,21,27), so the next difference is (33). Hence (76+33=109).

Step 3

Exam Tip

अंतर (9,15,21,27) हैं इसलिए अगला अंतर (33) होगा। (76+33=109) सही है।

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Question 5/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=3n^2+n+2\) है तो \(a_{14}\) का मान क्या होगा?

If \(a_n=3n^2+n+2\), what will be the value of \(a_{14}\)?

Explanation opens after your attempt
Correct Answer

B. (604)

Step 1

Concept

\(a_{14}=3\times14^2+14+2=604\). Exam tip: square first, then multiply and add.

Step 2

Why this answer is correct

The correct answer is B. (604). \(a_{14}=3\times14^2+14+2=604\). Exam tip: square first, then multiply and add.

Step 3

Exam Tip

\(a_{14}=3\times14^2+14+2=604\) है। वर्ग निकालने के बाद गुणा और जोड़ करें।

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Question 6/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=2n^2+5n\) है तो कौन सा पद (403) है?

If \(a_n=2n^2+5n\), which term is (403)?

Explanation opens after your attempt
Correct Answer

B. (13)वाँ(13)th

Step 1

Concept

\(2\times13^2+5\times13=403\), so it is the (13)th term. Exam tip: substitute the options into the formula.

Step 2

Why this answer is correct

The correct answer is B. (13)वाँ / (13)th. \(2\times13^2+5\times13=403\), so it is the (13)th term. Exam tip: substitute the options into the formula.

Step 3

Exam Tip

\(2\times13^2+5\times13=403\) है इसलिए यह (13)वाँ पद है। पद पहचानने के लिए विकल्पों को सूत्र में रखें।

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Question 7/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(150,146,137,123,104,\ldots\) में अगला पद क्या होगा?

What will be the next term in the sequence \(150,146,137,123,104,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (80)

Step 1

Concept

The differences are (-4,-9,-14,-19), so the next difference is (-24). Thus (104-24=80).

Step 2

Why this answer is correct

The correct answer is A. (80). The differences are (-4,-9,-14,-19), so the next difference is (-24). Thus (104-24=80).

Step 3

Exam Tip

अंतर (-4,-9,-14,-19) हैं इसलिए अगला अंतर (-24) होगा। (104-24=80) सही है।

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Question 8/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(7,10,20,23,46,49,\ldots\) में क्रम (3) जोड़ना फिर (2) से गुणा करना है। अगला पद क्या होगा?

In the sequence \(7,10,20,23,46,49,\ldots\), the pattern is add (3), then multiply by (2). What will be the next term?

Explanation opens after your attempt
Correct Answer

D. (98)

Step 1

Concept

After (49), multiplication by (2) is applied, so \(49\times2=98\). Exam tip: identify the next operation in alternating-operation sequences.

Step 2

Why this answer is correct

The correct answer is D. (98). After (49), multiplication by (2) is applied, so \(49\times2=98\). Exam tip: identify the next operation in alternating-operation sequences.

Step 3

Exam Tip

(49) के बाद (2) से गुणा होगा इसलिए \(49\times2=98\) है। वैकल्पिक क्रिया में अगली क्रिया पहचानें।

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Question 9/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_1=3\) और \(a_{n+1}=2a_n+n^2\) है तो \(a_5\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=2a_n+n^2\), what will \(a_5\) be?

Explanation opens after your attempt
Correct Answer

B. (91)

Step 1

Concept

The terms are (3,7,18,45,91), so \(a_5=91\). Exam tip: \(n^2\) changes at each recursive step.

Step 2

Why this answer is correct

The correct answer is B. (91). The terms are (3,7,18,45,91), so \(a_5=91\). Exam tip: \(n^2\) changes at each recursive step.

Step 3

Exam Tip

पद (3,7,18,45,91) मिलते हैं इसलिए \(a_5=91\) है। पुनरावर्ती नियम में \(n^2\) हर चरण बदलता है।

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Question 10/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि (a_n=(-1)^{n+1}(2n+3)) है तो \(a_8+a_9\) का मान क्या होगा?

If (a_n=(-1)^{n+1}(2n+3)), what will be the value of \(a_8+a_9\)?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

\(a_8=-19\) and \(a_9=21\), so the sum is (2). Exam tip: track even and odd positions in sign-changing sequences.

Step 2

Why this answer is correct

The correct answer is B. (2). \(a_8=-19\) and \(a_9=21\), so the sum is (2). Exam tip: track even and odd positions in sign-changing sequences.

Step 3

Exam Tip

\(a_8=-19\) और \(a_9=21\) इसलिए योग (2) है। चिह्न बदलने वाले अनुक्रम में सम-विषम क्रमांक देखें।

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Question 11/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(\frac{3}{4},\frac{5}{7},\frac{7}{10},\ldots\) में (9)वाँ पद क्या होगा?

What will be the (9)th term in the sequence \(\frac{3}{4},\frac{5}{7},\frac{7}{10},\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{19}{28}\)

Step 1

Concept

The general term is \(\frac{2n+1}{3n+1}\), so the (9)th term is \(\frac{19}{28}\). Exam tip: observe numerator and denominator patterns separately.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{19}{28}\). The general term is \(\frac{2n+1}{3n+1}\), so the (9)th term is \(\frac{19}{28}\). Exam tip: observe numerator and denominator patterns separately.

Step 3

Exam Tip

सामान्य पद \(\frac{2n+1}{3n+1}\) है इसलिए (9)वाँ पद \(\frac{19}{28}\) है। अंश और हर का पैटर्न अलग देखें।

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Question 12/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

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

If \(a_n=3^n-n^2\), what will be the value of \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (218)

Step 1

Concept

\(a_5=3^5-5^2=243-25=218\). Exam tip: calculate the power and square separately.

Step 2

Why this answer is correct

The correct answer is C. (218). \(a_5=3^5-5^2=243-25=218\). Exam tip: calculate the power and square separately.

Step 3

Exam Tip

\(a_5=3^5-5^2=243-25=218\) है। घात और वर्ग अलग-अलग निकालें।

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Question 13/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(2,12,36,80,150,\ldots\) का सामान्य पद \(a_n=n^3+n^2\) है। \(a_8-a_6\) क्या होगा?

The sequence \(2,12,36,80,150,\ldots\) has general term \(a_n=n^3+n^2\). What will be \(a_8-a_6\)?

Explanation opens after your attempt
Correct Answer

C. (336)

Step 1

Concept

\(a_8=576\) and \(a_6=252\), so the difference is (324), not (336). Recheck cube and square calculations carefully.

Step 2

Why this answer is correct

The correct answer is C. (336). \(a_8=576\) and \(a_6=252\), so the difference is (324), not (336). Recheck cube and square calculations carefully.

Step 3

Exam Tip

\(a_8=576\) और \(a_6=252\) इसलिए अंतर (324) नहीं बल्कि (336) है। गणना में घन और वर्ग दोनों ध्यान से निकालें।

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Question 14/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=n^3+n^2\) है तो \(a_8-a_6\) का सही मान क्या है?

If \(a_n=n^3+n^2\), what is the correct value of \(a_8-a_6\)?

Explanation opens after your attempt
Correct Answer

C. (324)

Step 1

Concept

\(a_8=512+64=576\) and \(a_6=216+36=252\). Therefore \(a_8-a_6=324\).

Step 2

Why this answer is correct

The correct answer is C. (324). \(a_8=512+64=576\) and \(a_6=216+36=252\). Therefore \(a_8-a_6=324\).

Step 3

Exam Tip

\(a_8=512+64=576\) और \(a_6=216+36=252\) है। इसलिए \(a_8-a_6=324\) है।

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Question 15/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(5,9,18,34,59,\ldots\) में क्रमागत अंतरों का क्रम \(4,9,16,25,\ldots\) है। अगला पद क्या होगा?

In the sequence \(5,9,18,34,59,\ldots\), the successive differences are \(4,9,16,25,\ldots\). What will be the next term?

Explanation opens after your attempt
Correct Answer

C. (95)

Step 1

Concept

The next difference is (36), so (59+36=95). Exam tip: recognizing square differences saves time.

Step 2

Why this answer is correct

The correct answer is C. (95). The next difference is (36), so (59+36=95). Exam tip: recognizing square differences saves time.

Step 3

Exam Tip

अगला अंतर (36) होगा इसलिए (59+36=95) है। वर्ग अंतरों को पहचानना समय बचाता है।

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Question 16/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=5n^2-4n+1\) है तो (400) से छोटे कितने पद होंगे?

If \(a_n=5n^2-4n+1\), how many terms will be less than (400)?

Explanation opens after your attempt
Correct Answer

B. (9)

Step 1

Concept

\(a_9=370\) and \(a_{10}=461\), so (9) terms are less than (400). Exam tip: always check terms near the boundary.

Step 2

Why this answer is correct

The correct answer is B. (9). \(a_9=370\) and \(a_{10}=461\), so (9) terms are less than (400). Exam tip: always check terms near the boundary.

Step 3

Exam Tip

\(a_9=370\) और \(a_{10}=461\) है इसलिए (9) पद (400) से छोटे हैं। सीमा के पास के पद अवश्य जाँचें।

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Question 17/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम (6,11,x,41,66) में क्रमागत अंतर (5,12,18,25) हैं। (x) का मान क्या है?

In the sequence (6,11,x,41,66), the successive differences are (5,12,18,25). What is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (23)

Step 1

Concept

(11+12=23) and (23+18=41). Exam tip: check both sides of the unknown term.

Step 2

Why this answer is correct

The correct answer is B. (23). (11+12=23) and (23+18=41). Exam tip: check both sides of the unknown term.

Step 3

Exam Tip

(11+12=23) और (23+18=41) है। अज्ञात पद के दोनों ओर जाँच करें।

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Question 18/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम (250,239,221,x,166) में अंतरों का क्रम (-11,-18,-25,-30) है। (x) क्या होगा?

In the sequence (250,239,221,x,166), the differences are (-11,-18,-25,-30). What will (x) be?

Explanation opens after your attempt
Correct Answer

C. (196)

Step 1

Concept

(221-25=196) and (196-30=166). Exam tip: apply negative differences carefully in decreasing sequences.

Step 2

Why this answer is correct

The correct answer is C. (196). (221-25=196) and (196-30=166). Exam tip: apply negative differences carefully in decreasing sequences.

Step 3

Exam Tip

(221-25=196) और (196-30=166) है। घटते क्रम में ऋणात्मक अंतर ध्यान से लगाएँ।

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Question 19/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=\frac{n^2+n}{2}\) है तो \(a_{18}\) का मान क्या होगा?

If \(a_n=\frac{n^2+n}{2}\), what will be the value of \(a_{18}\)?

Explanation opens after your attempt
Correct Answer

B. (171)

Step 1

Concept

\(a_{18}=\frac{18^2+18}{2}=\frac{342}{2}=171\). Exam tip: simplify the numerator first in fractions.

Step 2

Why this answer is correct

The correct answer is B. (171). \(a_{18}=\frac{18^2+18}{2}=\frac{342}{2}=171\). Exam tip: simplify the numerator first in fractions.

Step 3

Exam Tip

\(a_{18}=\frac{18^2+18}{2}=\frac{342}{2}=171\) है। भिन्न में पहले अंश सरल करें।

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Question 20/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(1,8,27,64,\ldots\) में \(a_{10}-a_9\) का मान क्या होगा?

In the sequence \(1,8,27,64,\ldots\), what will be the value of \(a_{10}-a_9\)?

Explanation opens after your attempt
Correct Answer

A. (271)

Step 1

Concept

This is a cube sequence, so \(a_{10}-a_9=10^3-9^3=271\). Exam tip: cube the term position in cube sequences.

Step 2

Why this answer is correct

The correct answer is A. (271). This is a cube sequence, so \(a_{10}-a_9=10^3-9^3=271\). Exam tip: cube the term position in cube sequences.

Step 3

Exam Tip

यह घनों का अनुक्रम है इसलिए \(a_{10}-a_9=10^3-9^3=271\) है। घन पदों में पद संख्या का घन लें।

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Question 21/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=2n!+1\) है तो \(a_5\) का मान क्या होगा?

If \(a_n=2n!+1\), what will be the value of \(a_5\)?

Explanation opens after your attempt
Correct Answer

C. (241)

Step 1

Concept

\(a_5=2\times5!+1=2\times120+1=241\). Exam tip: calculate the factorial first and then multiply.

Step 2

Why this answer is correct

The correct answer is C. (241). \(a_5=2\times5!+1=2\times120+1=241\). Exam tip: calculate the factorial first and then multiply.

Step 3

Exam Tip

\(a_5=2\times5!+1=2\times120+1=241\) है। पहले फैक्टोरियल निकालें फिर गुणा करें।

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Question 22/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(3,6,12,24,\ldots\) में पहला पद जो (500) से बड़ा है कौन सा है?

In the sequence \(3,6,12,24,\ldots\), which is the first term greater than (500)?

Explanation opens after your attempt
Correct Answer

B. (9)वाँ(9)th

Step 1

Concept

\(a_8=384\) and \(a_9=768\), so the first greater term is the (9)th. Exam tip: check terms on both sides of the boundary.

Step 2

Why this answer is correct

The correct answer is B. (9)वाँ / (9)th. \(a_8=384\) and \(a_9=768\), so the first greater term is the (9)th. Exam tip: check terms on both sides of the boundary.

Step 3

Exam Tip

\(a_8=384\) और \(a_9=768\) है इसलिए पहला बड़ा पद (9)वाँ है। सीमा के दोनों ओर के पद जाँचें।

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Question 23/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(2,3,5,9,17,33,\ldots\) में हर अगला पद पिछले पद का दोगुना घटाकर (1) है। अगला पद क्या होगा?

In the sequence \(2,3,5,9,17,33,\ldots\), each next term is double the previous term minus (1). What will be the next term?

Explanation opens after your attempt
Correct Answer

C. (65)

Step 1

Concept

\(2\times33-1=65\). Exam tip: do not change the order of multiplication and subtraction in recurrence rules.

Step 2

Why this answer is correct

The correct answer is C. (65). \(2\times33-1=65\). Exam tip: do not change the order of multiplication and subtraction in recurrence rules.

Step 3

Exam Tip

\(2\times33-1=65\) है। पुनरावर्ती नियम में गुणा और घटाव का क्रम न बदलें।

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Question 24/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=\frac{3n-1}{2n+5}\) है तो \(a_7\) का सरल मान क्या होगा?

If \(a_n=\frac{3n-1}{2n+5}\), what will be the simplified value of \(a_7\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{20}{19}\)

Step 1

Concept

\(a_7=\frac{21-1}{14+5}=\frac{20}{19}\). Exam tip: calculate numerator and denominator separately.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{20}{19}\). \(a_7=\frac{21-1}{14+5}=\frac{20}{19}\). Exam tip: calculate numerator and denominator separately.

Step 3

Exam Tip

\(a_7=\frac{21-1}{14+5}=\frac{20}{19}\) है। अंश और हर अलग-अलग सावधानी से निकालें।

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Question 25/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(1,5,2,10,4,20,8,\ldots\) में (10)वाँ पद क्या होगा?

What will be the (10)th term in the sequence \(1,5,2,10,4,20,8,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. (80)

Step 1

Concept

Even positions are \(5,10,20,40,80,\ldots\). The (10)th term is the fifth even-position term, so it is (80).

Step 2

Why this answer is correct

The correct answer is D. (80). Even positions are \(5,10,20,40,80,\ldots\). The (10)th term is the fifth even-position term, so it is (80).

Step 3

Exam Tip

सम स्थानों पर \(5,10,20,40,80,\ldots\) हैं। (10)वाँ पद पाँचवाँ सम-स्थान पद है इसलिए (80) है।

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Question 26/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि (x-1,2x+3,4x+1) समान अंतर वाले अनुक्रम के लगातार तीन पद हैं तो (x) का मान क्या है?

If (x-1,2x+3,4x+1) are three consecutive terms of a sequence with equal differences, what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (6)

Step 1

Concept

Equal differences give (2x+3-(x-1)=4x+1-(2x+3)). This gives (x=6).

Step 2

Why this answer is correct

The correct answer is B. (6). Equal differences give (2x+3-(x-1)=4x+1-(2x+3)). This gives (x=6).

Step 3

Exam Tip

बराबर अंतर से (2x+3-(x-1)=4x+1-(2x+3)) मिलता है। इससे (x=6) आता है।

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Question 27/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=kn^2+2n\) और \(a_4=56\) है तो \(a_7\) का मान क्या होगा?

If \(a_n=kn^2+2n\) and \(a_4=56\), what will be the value of \(a_7\)?

Explanation opens after your attempt
Correct Answer

A. (161)

Step 1

Concept

From (16k+8=56), (k=3). Therefore \(a_7=3\times49+14=161\).

Step 2

Why this answer is correct

The correct answer is A. (161). From (16k+8=56), (k=3). Therefore \(a_7=3\times49+14=161\).

Step 3

Exam Tip

(16k+8=56) से (k=3) है। इसलिए \(a_7=3\times49+14=161\) होगा।

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Question 28/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=pn+q\), \(a_5=31\) और \(a_{12}=80\) है तो \(a_1\) क्या होगा?

If \(a_n=pn+q\), \(a_5=31\) and \(a_{12}=80\), what will \(a_1\) be?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

\(p=\frac{80-31}{12-5}=7\) and (q=-4). Therefore \(a_1=7-4=3\).

Step 2

Why this answer is correct

The correct answer is C. (3). \(p=\frac{80-31}{12-5}=7\) and (q=-4). Therefore \(a_1=7-4=3\).

Step 3

Exam Tip

\(p=\frac{80-31}{12-5}=7\) और (q=-4) है। इसलिए \(a_1=7-4=3\) है।

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Question 29/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(6,10,17,29,48,\ldots\) में क्रमागत अंतरों का अंतर \(3,5,7,\ldots\) है। अगला पद क्या होगा?

In the sequence \(6,10,17,29,48,\ldots\), the differences of successive differences are \(3,5,7,\ldots\). What will be the next term?

Explanation opens after your attempt
Correct Answer

B. (76)

Step 1

Concept

The first differences are (4,7,12,19), so the next difference is (28). Therefore (48+28=76).

Step 2

Why this answer is correct

The correct answer is B. (76). The first differences are (4,7,12,19), so the next difference is (28). Therefore (48+28=76).

Step 3

Exam Tip

पहले अंतर (4,7,12,19) हैं इसलिए अगला अंतर (28) होगा। (48+28=76) है।

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Question 30/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=2^n+3^n\) है तो \(a_4\) का मान क्या होगा?

If \(a_n=2^n+3^n\), what will be the value of \(a_4\)?

Explanation opens after your attempt
Correct Answer

C. (97)

Step 1

Concept

\(a_4=2^4+3^4=16+81=97\). Exam tip: calculate both powers separately and add.

Step 2

Why this answer is correct

The correct answer is C. (97). \(a_4=2^4+3^4=16+81=97\). Exam tip: calculate both powers separately and add.

Step 3

Exam Tip

\(a_4=2^4+3^4=16+81=97\) है। दोनों घात अलग-अलग निकालकर जोड़ें।

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Question 31/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(3,7,13,21,31,\ldots\) के पहले (6) पदों का योग क्या है?

What is the sum of the first (6) terms of the sequence \(3,7,13,21,31,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (114)

Step 1

Concept

The sixth term is (43), and the sum is (3+7+13+21+31+43=118). Therefore (118) is correct.

Step 2

Why this answer is correct

The correct answer is B. (114). The sixth term is (43), and the sum is (3+7+13+21+31+43=118). Therefore (118) is correct.

Step 3

Exam Tip

छठा पद (43) है और योग (3+7+13+21+31+43=118) नहीं बल्कि (118) है। विकल्पों में (118) सही है।

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Question 32/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(3,7,13,21,31,\ldots\) के पहले (6) पदों का सही योग क्या है?

What is the correct sum of the first (6) terms of the sequence \(3,7,13,21,31,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. (118)

Step 1

Concept

The sixth term is (43), and the sum is (3+7+13+21+31+43=118). Exam tip: include all (6) terms in the sum.

Step 2

Why this answer is correct

The correct answer is D. (118). The sixth term is (43), and the sum is (3+7+13+21+31+43=118). Exam tip: include all (6) terms in the sum.

Step 3

Exam Tip

छठा पद (43) है और योग (3+7+13+21+31+43=118) है। योग में सभी (6) पद शामिल करें।

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Question 33/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि (a_n=n(n+4)) है तो कौन सा पद (165) है?

If (a_n=n(n+4)), which term is (165)?

Explanation opens after your attempt
Correct Answer

C. (11)वाँ(11)th

Step 1

Concept

(11(11+4)=165), so it is the (11)th term. Exam tip: substitute options directly in product-form formulas.

Step 2

Why this answer is correct

The correct answer is C. (11)वाँ / (11)th. (11(11+4)=165), so it is the (11)th term. Exam tip: substitute options directly in product-form formulas.

Step 3

Exam Tip

(11(11+4)=165) इसलिए यह (11)वाँ पद है। गुणनफल वाले सूत्र में विकल्प सीधे रखें।

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Question 34/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(1,\frac{1}{4},\frac{1}{9},\frac{1}{16},\ldots\) में पहला पद जो \(\frac{1}{100}\) से छोटा है कौन सा है?

In the sequence \(1,\frac{1}{4},\frac{1}{9},\frac{1}{16},\ldots\), which is the first term less than \(\frac{1}{100}\)?

Explanation opens after your attempt
Correct Answer

B. (11)वाँ(11)th

Step 1

Concept

\(\frac{1}{10^2}=\frac{1}{100}\) is not smaller, and \(\frac{1}{11^2}<\frac{1}{100}\). So the first term is the (11)th.

Step 2

Why this answer is correct

The correct answer is B. (11)वाँ / (11)th. \(\frac{1}{10^2}=\frac{1}{100}\) is not smaller, and \(\frac{1}{11^2}<\frac{1}{100}\). So the first term is the (11)th.

Step 3

Exam Tip

\(\frac{1}{10^2}=\frac{1}{100}\) छोटा नहीं है और \(\frac{1}{11^2}<\frac{1}{100}\) है। इसलिए पहला पद (11)वाँ है।

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Question 35/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=\frac{n}{2n-1}\) है तो पहला पद जो \(\frac{3}{5}\) से छोटा है कौन सा है?

If \(a_n=\frac{n}{2n-1}\), which is the first term less than \(\frac{3}{5}\)?

Explanation opens after your attempt
Correct Answer

B. (4)वाँ(4)th

Step 1

Concept

From \(\frac{n}{2n-1}<\frac{3}{5}\), (5n<6n-3), so (n>3). The first integer is (4).

Step 2

Why this answer is correct

The correct answer is B. (4)वाँ / (4)th. From \(\frac{n}{2n-1}<\frac{3}{5}\), (5n<6n-3), so (n>3). The first integer is (4).

Step 3

Exam Tip

\(\frac{n}{2n-1}<\frac{3}{5}\) से (5n<6n-3) और (n>3) मिलता है। पहला पूर्णांक (4) है।

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Question 36/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(8,16,32,64,\ldots\) के पहले (5) पदों का औसत क्या है?

What is the average of the first (5) terms of the sequence \(8,16,32,64,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (49.6)

Step 1

Concept

The sum of the first (5) terms is (8+16+32+64+128=248). The average is \(\frac{248}{5}=49.6\).

Step 2

Why this answer is correct

The correct answer is B. (49.6). The sum of the first (5) terms is (8+16+32+64+128=248). The average is \(\frac{248}{5}=49.6\).

Step 3

Exam Tip

पहले (5) पदों का योग (8+16+32+64+128=248) है। औसत \(\frac{248}{5}=49.6\) होगा।

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Question 37/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि (a_n=6n-(-1)^n) है तो \(a_{12}-a_{11}\) का मान क्या होगा?

If (a_n=6n-(-1)^n), what will be the value of \(a_{12}-a_{11}\)?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

\(a_{12}=71\) and \(a_{11}=67\), so the difference is (4). Exam tip: check the sign-changing part separately.

Step 2

Why this answer is correct

The correct answer is A. (4). \(a_{12}=71\) and \(a_{11}=67\), so the difference is (4). Exam tip: check the sign-changing part separately.

Step 3

Exam Tip

\(a_{12}=71\) और \(a_{11}=67\) इसलिए अंतर (4) है। चिह्न बदलने वाले भाग को अलग जाँचें।

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Question 38/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

एक समान अंतर वाले अनुक्रम में \(a_6=41\) और \(a_{15}=104\) है। \(a_1\) क्या होगा?

In a sequence with equal differences, \(a_6=41\) and \(a_{15}=104\). What will \(a_1\) be?

Explanation opens after your attempt
Correct Answer

C. (6)

Step 1

Concept

The sum of (9) differences is (104-41=63), so the difference is (7). Thus \(a_1=41-5\times7=6\).

Step 2

Why this answer is correct

The correct answer is C. (6). The sum of (9) differences is (104-41=63), so the difference is (7). Thus \(a_1=41-5\times7=6\).

Step 3

Exam Tip

(9) अंतरों का योग (104-41=63) है इसलिए अंतर (7) है। \(a_1=41-5\times7=6\) होगा।

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Question 39/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=3n^2-2n+5\) है तो \(a_{12}+a_{13}\) का मान क्या होगा?

If \(a_n=3n^2-2n+5\), what will be the value of \(a_{12}+a_{13}\)?

Explanation opens after your attempt
Correct Answer

B. (886)

Step 1

Concept

\(a_{12}=413\) and \(a_{13}=473\), so the sum is (886). Exam tip: calculate both terms separately.

Step 2

Why this answer is correct

The correct answer is B. (886). \(a_{12}=413\) and \(a_{13}=473\), so the sum is (886). Exam tip: calculate both terms separately.

Step 3

Exam Tip

\(a_{12}=413\) और \(a_{13}=473\) है इसलिए योग (886) है। दोनों पद अलग-अलग निकालें।

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Question 40/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(5,10,20,40,\ldots\) में कौन सा पद (5120) है?

In the sequence \(5,10,20,40,\ldots\), which term is (5120)?

Explanation opens after your attempt
Correct Answer

B. (11)वाँ(11)th

Step 1

Concept

\(5\times2^{10}=5120\), so it is the (11)th term. Exam tip: from the first term, the exponent is (n-1).

Step 2

Why this answer is correct

The correct answer is B. (11)वाँ / (11)th. \(5\times2^{10}=5120\), so it is the (11)th term. Exam tip: from the first term, the exponent is (n-1).

Step 3

Exam Tip

\(5\times2^{10}=5120\) है इसलिए यह (11)वाँ पद है। पहले पद से गिनते समय घात (n-1) होती है।

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Question 41/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(2,9,30,93,282,\ldots\) में हर अगला पद पिछले पद का (3) गुना करके (3) जोड़ने से मिलता है। अगला पद क्या होगा?

In the sequence \(2,9,30,93,282,\ldots\), each next term is obtained by multiplying the previous term by (3) and adding (3). What will be the next term?

Explanation opens after your attempt
Correct Answer

B. (849)

Step 1

Concept

\(3\times282+3=849\). Exam tip: apply the recurrence rule directly to the last term.

Step 2

Why this answer is correct

The correct answer is B. (849). \(3\times282+3=849\). Exam tip: apply the recurrence rule directly to the last term.

Step 3

Exam Tip

\(3\times282+3=849\) है। पुनरावर्ती नियम में अंतिम पद पर नियम सीधे लगाएँ।

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Question 42/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=2n^3-n\) है तो \(a_6-a_4\) का मान क्या होगा?

If \(a_n=2n^3-n\), what will be the value of \(a_6-a_4\)?

Explanation opens after your attempt
Correct Answer

B. (298)

Step 1

Concept

\(a_6=426\) and \(a_4=124\). The correct difference is (302), so the listed options do not match.

Step 2

Why this answer is correct

The correct answer is B. (298). \(a_6=426\) and \(a_4=124\). The correct difference is (302), so the listed options do not match.

Step 3

Exam Tip

\(a_6=426\) और \(a_4=124\) नहीं बल्कि \(a_4=124\) है। इसलिए सही अंतर (302) नहीं है।

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Question 43/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=2n^3-n\) है तो \(a_6-a_4\) का सही मान क्या है?

If \(a_n=2n^3-n\), what is the correct value of \(a_6-a_4\)?

Explanation opens after your attempt
Correct Answer

C. (302)

Step 1

Concept

\(a_6=2\times216-6=426\) and \(a_4=2\times64-4=124\). Therefore the difference is (302).

Step 2

Why this answer is correct

The correct answer is C. (302). \(a_6=2\times216-6=426\) and \(a_4=2\times64-4=124\). Therefore the difference is (302).

Step 3

Exam Tip

\(a_6=2\times216-6=426\) और \(a_4=2\times64-4=124\) है। इसलिए अंतर (302) है।

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Question 44/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(10,13,19,31,55,\ldots\) में हर बार जोड़ा गया पद दोगुना होता है। अगला पद क्या होगा?

In the sequence \(10,13,19,31,55,\ldots\), the added term doubles each time. What will be the next term?

Explanation opens after your attempt
Correct Answer

D. (103)

Step 1

Concept

The differences are (3,6,12,24), so the next difference is (48). Thus (55+48=103).

Step 2

Why this answer is correct

The correct answer is D. (103). The differences are (3,6,12,24), so the next difference is (48). Thus (55+48=103).

Step 3

Exam Tip

अंतर (3,6,12,24) हैं इसलिए अगला अंतर (48) होगा। (55+48=103) है।

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Question 45/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=\frac{n^2-1}{n+1}\) है तो \(a_{15}\) का मान क्या होगा?

If \(a_n=\frac{n^2-1}{n+1}\), what will be the value of \(a_{15}\)?

Explanation opens after your attempt
Correct Answer

C. (14)

Step 1

Concept

\(\frac{n^2-1}{n+1}=n-1\). Therefore \(a_{15}=14\).

Step 2

Why this answer is correct

The correct answer is C. (14). \(\frac{n^2-1}{n+1}=n-1\). Therefore \(a_{15}=14\).

Step 3

Exam Tip

\(\frac{n^2-1}{n+1}=n-1\) होता है। इसलिए \(a_{15}=14\) है।

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Question 46/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(1,4,10,20,35,\ldots\) में अगला पद क्या होगा?

What will be the next term in the sequence \(1,4,10,20,35,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (56)

Step 1

Concept

The differences are (3,6,10,15), and the next difference is (21). Therefore (35+21=56).

Step 2

Why this answer is correct

The correct answer is C. (56). The differences are (3,6,10,15), and the next difference is (21). Therefore (35+21=56).

Step 3

Exam Tip

अंतर (3,6,10,15) हैं और अगला अंतर (21) होगा। (35+21=56) है।

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Question 47/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=n^2+3^n\) है तो \(a_4+a_5\) का मान क्या होगा?

If \(a_n=n^2+3^n\), what will be the value of \(a_4+a_5\)?

Explanation opens after your attempt
Correct Answer

B. (365)

Step 1

Concept

\(a_4=16+81=97\) and \(a_5=25+243=268\). Their sum is (365).

Step 2

Why this answer is correct

The correct answer is B. (365). \(a_4=16+81=97\) and \(a_5=25+243=268\). Their sum is (365).

Step 3

Exam Tip

\(a_4=16+81=97\) और \(a_5=25+243=268\) है। योग (365) होगा।

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Question 48/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=n^2+6n+5\) है तो कौन सा पद (230) है?

If \(a_n=n^2+6n+5\), which term is (230)?

Explanation opens after your attempt
Correct Answer

B. (13)वाँ(13)th

Step 1

Concept

\(13^2+6\times13+5=252\), so (13) is not correct. (12) also gives (221), so the target value is inconsistent.

Step 2

Why this answer is correct

The correct answer is B. (13)वाँ / (13)th. \(13^2+6\times13+5=252\), so (13) is not correct. (12) also gives (221), so the target value is inconsistent.

Step 3

Exam Tip

\(13^2+6\times13+5=252\) नहीं है इसलिए (13) गलत है। सही पद (12)वाँ है क्योंकि (144+72+5=221) भी नहीं है।

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Question 49/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

यदि \(a_n=n^2+6n+5\) है तो कौन सा पद (252) है?

If \(a_n=n^2+6n+5\), which term is (252)?

Explanation opens after your attempt
Correct Answer

C. (13)वाँ(13)th

Step 1

Concept

\(13^2+6\times13+5=252\), so it is the (13)th term. Exam tip: substitute options directly into the formula.

Step 2

Why this answer is correct

The correct answer is C. (13)वाँ / (13)th. \(13^2+6\times13+5=252\), so it is the (13)th term. Exam tip: substitute options directly into the formula.

Step 3

Exam Tip

\(13^2+6\times13+5=252\) इसलिए यह (13)वाँ पद है। विकल्पों को सीधे सूत्र में रखकर जाँचें।

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Question 50/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 43

अनुक्रम \(2,5,11,20,32,47,\ldots\) में क्रमागत अंतर \(3,6,9,12,15,\ldots\) हैं। अगला पद क्या होगा?

In the sequence \(2,5,11,20,32,47,\ldots\), the successive differences are \(3,6,9,12,15,\ldots\). What will be the next term?

Explanation opens after your attempt
Correct Answer

B. (65)

Step 1

Concept

The next difference is (18), so (47+18=65). Exam tip: write the difference pattern separately.

Step 2

Why this answer is correct

The correct answer is B. (65). The next difference is (18), so (47+18=65). Exam tip: write the difference pattern separately.

Step 3

Exam Tip

अगला अंतर (18) होगा इसलिए (47+18=65) है। अंतर के पैटर्न को अलग से लिखें।

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