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Mathematics Quiz - Class 9 Mathematics Medium Level 52 Quiz

Question 1/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

अनुक्रम \(6,13,20,27,\ldots\) में समान अंतर क्या है?

What is the common difference in the sequence \(6,13,20,27,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

The difference between consecutive terms is (13-6=7). To find the common difference, subtract the first term from the second term.

Step 2

Why this answer is correct

The correct answer is C. (7). The difference between consecutive terms is (13-6=7). To find the common difference, subtract the first term from the second term.

Step 3

Exam Tip

लगातार पदों का अंतर (13-6=7) है। समान अंतर के लिए दूसरे पद से पहला पद घटाएं।

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Question 2/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि किसी समानांतर श्रेढ़ी में पहला पद (8) और समान अंतर (5) है, तो (7)वाँ पद क्या होगा?

If an arithmetic progression has first term (8) and common difference (5), what is the (7)th term?

Explanation opens after your attempt

Correct Answer

C. (38)

Step 1

Concept

(a_7=8+(7-1)5=38). Use (a_n=a+(n-1)d) for the (n)th term.

Step 2

Why this answer is correct

The correct answer is C. (38). (a_7=8+(7-1)5=38). Use (a_n=a+(n-1)d) for the (n)th term.

Step 3

Exam Tip

(a_7=8+(7-1)5=38)। (n)वें पद के लिए (a_n=a+(n-1)d) लगाएं।

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Question 3/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(42,36,30,24,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the arithmetic progression \(42,36,30,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=48-6n\)

Step 1

Concept

The first term is (42) and the difference is (-6), so (a_n=42+(n-1)(-6)=48-6n). In a decreasing progression, the common difference is negative.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=48-6n\). The first term is (42) and the difference is (-6), so (a_n=42+(n-1)(-6)=48-6n). In a decreasing progression, the common difference is negative.

Step 3

Exam Tip

पहला पद (42) और अंतर (-6) है इसलिए (a_n=42+(n-1)(-6)=48-6n)। घटती श्रेढ़ी में समान अंतर ऋणात्मक होता है।

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Question 4/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=15) और (d=4) है, तो समानांतर श्रेढ़ी का (9)वाँ पद क्या होगा?

If (a=15) and (d=4), what will be the (9)th term of the arithmetic progression?

Explanation opens after your attempt

Correct Answer

B. (47)

Step 1

Concept

(a_9=15+8(4)=47). Up to the (9)th term, (8) common differences are added.

Step 2

Why this answer is correct

The correct answer is B. (47). (a_9=15+8(4)=47). Up to the (9)th term, (8) common differences are added.

Step 3

Exam Tip

(a_9=15+8(4)=47)। (9)वें पद तक (8) समान अंतर जुड़ते हैं।

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Question 5/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(3,11,19,27,\ldots\) में (67) कौन-सा पद है?

In the arithmetic progression \(3,11,19,27,\ldots\), which term is (67)?

Explanation opens after your attempt

Correct Answer

C. (9)वाँ(9)th

Step 1

Concept

From (3+(n-1)8=67), (8(n-1)=64) and (n=9). To find the position, set the given term equal to \(a_n\).

Step 2

Why this answer is correct

The correct answer is C. (9)वाँ / (9)th. From (3+(n-1)8=67), (8(n-1)=64) and (n=9). To find the position, set the given term equal to \(a_n\).

Step 3

Exam Tip

(3+(n-1)8=67) से (8(n-1)=64) और (n=9)। पद का स्थान निकालने के लिए दिए पद को \(a_n\) के बराबर रखें।

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Question 6/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=4n+3\) है, तो पहले चार पद कौन-से होंगे?

If \(a_n=4n+3\), what will be the first four terms?

Explanation opens after your attempt

Correct Answer

A. (7,11,15,19)

Step 1

Concept

Putting (n=1,2,3,4) gives (7,11,15,19). When forming terms from a rule, start (n) from (1).

Step 2

Why this answer is correct

The correct answer is A. (7,11,15,19). Putting (n=1,2,3,4) gives (7,11,15,19). When forming terms from a rule, start (n) from (1).

Step 3

Exam Tip

(n=1,2,3,4) रखने पर (7,11,15,19) मिलते हैं। नियम से पद बनाते समय (n) को (1) से शुरू करें।

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Question 7/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी में \(a_1=17\) और \(a_6=47\) है। समान अंतर क्या है?

In an arithmetic progression, \(a_1=17\) and \(a_6=47\). What is the common difference?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

\(a_6=a_1+5d\), so (47=17+5d) and (d=6). Count the number of gaps between the two terms.

Step 2

Why this answer is correct

The correct answer is B. (6). \(a_6=a_1+5d\), so (47=17+5d) and (d=6). Count the number of gaps between the two terms.

Step 3

Exam Tip

\(a_6=a_1+5d\), इसलिए (47=17+5d) और (d=6)। दो पदों के बीच अंतरालों की संख्या गिनें।

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Question 8/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(7,15,23,31,\ldots\) के पहले (5) पदों का योग क्या है?

What is the sum of the first (5) terms of the arithmetic progression \(7,15,23,31,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (115)

Step 1

Concept

The first (5) terms are (7,15,23,31,39), and their sum is (115). For a small number of terms, listing and adding is simple.

Step 2

Why this answer is correct

The correct answer is C. (115). The first (5) terms are (7,15,23,31,39), and their sum is (115). For a small number of terms, listing and adding is simple.

Step 3

Exam Tip

पहले (5) पद (7,15,23,31,39) हैं और योग (115) है। कम पद हों तो पद लिखकर जोड़ना सरल है।

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Question 9/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=55-5n\) है, तो इस समानांतर श्रेढ़ी का समान अंतर क्या है?

If \(a_n=55-5n\), what is the common difference of this arithmetic progression?

Explanation opens after your attempt

Correct Answer

A. (-5)

Step 1

Concept

In the linear form, the coefficient of (n) is (-5), so the common difference is (-5). Always check the sign of the coefficient.

Step 2

Why this answer is correct

The correct answer is A. (-5). In the linear form, the coefficient of (n) is (-5), so the common difference is (-5). Always check the sign of the coefficient.

Step 3

Exam Tip

रैखिक रूप में (n) का गुणांक (-5) है, इसलिए समान अंतर (-5) है। गुणांक का चिह्न जरूर देखें।

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Question 10/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि समानांतर श्रेढ़ी का पहला पद (21) और चौथा पद (36) है, तो समान अंतर क्या है?

If the first term of an arithmetic progression is (21) and the fourth term is (36), what is the common difference?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

From \(a_4=21+3d=36\), (3d=15) and (d=5). Up to the fourth term, there are three gaps.

Step 2

Why this answer is correct

The correct answer is C. (5). From \(a_4=21+3d=36\), (3d=15) and (d=5). Up to the fourth term, there are three gaps.

Step 3

Exam Tip

\(a_4=21+3d=36\) से (3d=15) और (d=5)। चौथे पद तक तीन अंतर होते हैं।

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Question 11/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(4,13,22,31,\ldots\) का (10)वाँ पद क्या है?

What is the (10)th term of the arithmetic progression \(4,13,22,31,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (85)

Step 1

Concept

Here (a=4) and (d=9), so (a_{10}=4+9(9)=85). Up to the (10)th term, (9) gaps are added.

Step 2

Why this answer is correct

The correct answer is C. (85). Here (a=4) and (d=9), so (a_{10}=4+9(9)=85). Up to the (10)th term, (9) gaps are added.

Step 3

Exam Tip

यहाँ (a=4) और (d=9), इसलिए (a_{10}=4+9(9)=85)। (10)वें पद तक (9) अंतर जुड़ते हैं।

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Question 12/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_2=18\) और (d=6) है, तो \(a_1\) क्या होगा?

If \(a_2=18\) and (d=6), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

B. (12)

Step 1

Concept

\(a_2=a_1+d\), so \(a_1=18-6=12\). If the second term is given, move one common difference backward.

Step 2

Why this answer is correct

The correct answer is B. (12). \(a_2=a_1+d\), so \(a_1=18-6=12\). If the second term is given, move one common difference backward.

Step 3

Exam Tip

\(a_2=a_1+d\), इसलिए \(a_1=18-6=12\)। दूसरा पद दिया हो तो एक समान अंतर पीछे जाएं।

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Question 13/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(60,54,48,42,\ldots\) का (12)वाँ पद क्या होगा?

What will be the (12)th term of the arithmetic progression \(60,54,48,42,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (-6)

Step 1

Concept

Here (a=60) and (d=-6), so (a_{12}=60+11(-6)=-6). In a decreasing progression, terms can become negative.

Step 2

Why this answer is correct

The correct answer is A. (-6). Here (a=60) and (d=-6), so (a_{12}=60+11(-6)=-6). In a decreasing progression, terms can become negative.

Step 3

Exam Tip

यहाँ (a=60) और (d=-6), इसलिए (a_{12}=60+11(-6)=-6)। घटती श्रेढ़ी में पद ऋणात्मक भी हो सकते हैं।

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Question 14/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

किस समानांतर श्रेढ़ी का पहला पद (12) और समान अंतर (-4) है?

Which arithmetic progression has first term (12) and common difference (-4)?

Explanation opens after your attempt

Correct Answer

C. \(12,8,4,0,\ldots\)

Step 1

Concept

The first term is (12), and (4) is subtracted each time. Therefore the common difference is (-4).

Step 2

Why this answer is correct

The correct answer is C. \(12,8,4,0,\ldots\). The first term is (12), and (4) is subtracted each time. Therefore the common difference is (-4).

Step 3

Exam Tip

पहला पद (12) है और हर बार (4) घट रहा है। इसलिए समान अंतर (-4) है।

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Question 15/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=6n-1\) है, तो पहला पद क्या है?

If \(a_n=6n-1\), what is the first term?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

For the first term (n=1), so \(a_1=6-1=5\). Put (n=1) to find the first term.

Step 2

Why this answer is correct

The correct answer is A. (5). For the first term (n=1), so \(a_1=6-1=5\). Put (n=1) to find the first term.

Step 3

Exam Tip

पहले पद के लिए (n=1), इसलिए \(a_1=6-1=5\)। पहला पद निकालने में (n=1) रखें।

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Question 16/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(18,25,32,39,\ldots\) में (74) कौन-सा पद है?

In the arithmetic progression \(18,25,32,39,\ldots\), which term is (74)?

Explanation opens after your attempt

Correct Answer

C. (9)वाँ(9)th

Step 1

Concept

From (18+(n-1)7=74), (7(n-1)=56) and (n=9). Solve the linear equation to find the position of a term.

Step 2

Why this answer is correct

The correct answer is C. (9)वाँ / (9)th. From (18+(n-1)7=74), (7(n-1)=56) and (n=9). Solve the linear equation to find the position of a term.

Step 3

Exam Tip

(18+(n-1)7=74) से (7(n-1)=56) और (n=9)। पद की स्थिति के लिए रैखिक समीकरण हल करें।

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Question 17/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(12,20,28,36,\ldots\) के पहले (4) पदों का योग क्या है?

What is the sum of the first (4) terms of the arithmetic progression \(12,20,28,36,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (96)

Step 1

Concept

The sum of the first (4) terms is (12+20+28+36=96). If there are few terms, direct addition is easy.

Step 2

Why this answer is correct

The correct answer is C. (96). The sum of the first (4) terms is (12+20+28+36=96). If there are few terms, direct addition is easy.

Step 3

Exam Tip

पहले (4) पदों का योग (12+20+28+36=96) है। कम पद हों तो सीधे जोड़ना आसान है।

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Question 18/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=34) और (d=-7) है, तो \(a_6\) क्या होगा?

If (a=34) and (d=-7), what will \(a_6\) be?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

(a_6=34+5(-7)=-1). Keep the negative common difference with the correct sign.

Step 2

Why this answer is correct

The correct answer is A. (-1). (a_6=34+5(-7)=-1). Keep the negative common difference with the correct sign.

Step 3

Exam Tip

(a_6=34+5(-7)=-1)। ऋणात्मक समान अंतर को सही चिह्न के साथ रखें।

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Question 19/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(9,17,25,33,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the arithmetic progression \(9,17,25,33,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=8n+1\)

Step 1

Concept

The first term is (9) and (d=8), so (a_n=9+(n-1)8=8n+1). You can also check an option by putting (n=1).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=8n+1\). The first term is (9) and (d=8), so (a_n=9+(n-1)8=8n+1). You can also check an option by putting (n=1).

Step 3

Exam Tip

पहला पद (9) और (d=8) है इसलिए (a_n=9+(n-1)8=8n+1)। विकल्प को (n=1) रखकर भी जांच सकते हैं।

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Question 20/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि समानांतर श्रेढ़ी में \(a_4=25\) और \(a_8=49\) है, तो समान अंतर क्या है?

If an arithmetic progression has \(a_4=25\) and \(a_8=49\), what is the common difference?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

From the fourth to the eighth term there are (4) gaps and the increase is (24), so (d=6). Count the number of gaps correctly.

Step 2

Why this answer is correct

The correct answer is C. (6). From the fourth to the eighth term there are (4) gaps and the increase is (24), so (d=6). Count the number of gaps correctly.

Step 3

Exam Tip

चौथे से आठवें पद तक (4) अंतर हैं और वृद्धि (24) है, इसलिए (d=6)। अंतरालों की संख्या सही गिनें।

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Question 21/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=8n+5\) है, तो \(a_2+a_5\) कितना होगा?

If \(a_n=8n+5\), what is \(a_2+a_5\)?

Explanation opens after your attempt

Correct Answer

B. (62)

Step 1

Concept

\(a_2=21\) and \(a_5=45\), so the sum is (66). Find both terms separately and then add.

Step 2

Why this answer is correct

The correct answer is B. (62). \(a_2=21\) and \(a_5=45\), so the sum is (66). Find both terms separately and then add.

Step 3

Exam Tip

\(a_2=21\) और \(a_5=45\), इसलिए योग (66) है। दोनों पद अलग निकालकर जोड़ें।

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Question 22/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(90,82,74,66,\ldots\) में (18) कौन-सा पद है?

In the arithmetic progression \(90,82,74,66,\ldots\), which term is (18)?

Explanation opens after your attempt

Correct Answer

B. (10)वाँ(10)th

Step 1

Concept

From (90+(n-1)(-8)=18), (8(n-1)=72) and (n=10). The same \(a_n\) formula works in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is B. (10)वाँ / (10)th. From (90+(n-1)(-8)=18), (8(n-1)=72) and (n=10). The same \(a_n\) formula works in a decreasing progression.

Step 3

Exam Tip

(90+(n-1)(-8)=18) से (8(n-1)=72) और (n=10)। घटती श्रेढ़ी में भी वही \(a_n\) सूत्र लगता है।

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Question 23/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि समानांतर श्रेढ़ी का (6)वाँ पद (41) और समान अंतर (5) है, तो पहला पद क्या है?

If the (6)th term of an arithmetic progression is (41) and the common difference is (5), what is the first term?

Explanation opens after your attempt

Correct Answer

B. (16)

Step 1

Concept

\(a_6=a+5d\), so (41=a+25) and (a=16). To move backward from a given term, subtract common differences.

Step 2

Why this answer is correct

The correct answer is B. (16). \(a_6=a+5d\), so (41=a+25) and (a=16). To move backward from a given term, subtract common differences.

Step 3

Exam Tip

\(a_6=a+5d\), इसलिए (41=a+25) और (a=16)। दिए पद से पीछे जाने के लिए समान अंतर घटाएं।

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Question 24/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(12,12,12,12,\ldots\) का समान अंतर क्या है?

What is the common difference of the arithmetic progression \(12,12,12,12,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

Every consecutive difference is (12-12=0). A constant sequence is also an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is A. (0). Every consecutive difference is (12-12=0). A constant sequence is also an arithmetic progression.

Step 3

Exam Tip

हर लगातार अंतर (12-12=0) है। स्थिर अनुक्रम भी समानांतर श्रेढ़ी होता है।

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Question 25/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=7) और (d=3) है, तो पहले (6) पदों का योग क्या होगा?

If (a=7) and (d=3), what will be the sum of the first (6) terms?

Explanation opens after your attempt

Correct Answer

C. (87)

Step 1

Concept

The first (6) terms are (7,10,13,16,19,22), and their sum is (87). For small (n), writing and adding terms is easy.

Step 2

Why this answer is correct

The correct answer is C. (87). The first (6) terms are (7,10,13,16,19,22), and their sum is (87). For small (n), writing and adding terms is easy.

Step 3

Exam Tip

पहले (6) पद (7,10,13,16,19,22) हैं और योग (87) है। छोटे (n) में पद लिखकर जोड़ना आसान है।

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Question 26/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(22,29,36,43,\ldots\) का (n)वाँ पद कौन-सा है?

What is the (n)th term of the arithmetic progression \(22,29,36,43,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=7n+15\)

Step 1

Concept

The first term is (22) and (d=7), so (a_n=22+(n-1)7=7n+15). Remember (n-1) while forming the general term.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=7n+15\). The first term is (22) and (d=7), so (a_n=22+(n-1)7=7n+15). Remember (n-1) while forming the general term.

Step 3

Exam Tip

पहला पद (22) और (d=7) है इसलिए (a_n=22+(n-1)7=7n+15)। सामान्य पद बनाते समय (n-1) का ध्यान रखें।

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Question 27/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि किसी समानांतर श्रेढ़ी में \(a_5=33\) और (d=4) है, तो \(a_{10}\) क्या होगा?

If an arithmetic progression has \(a_5=33\) and (d=4), what will be \(a_{10}\)?

Explanation opens after your attempt

Correct Answer

C. (53)

Step 1

Concept

From \(a_5\) to \(a_{10}\), there are (5) gaps, so (a_{10}=33+5(4)=53). Moving forward from a nearby term is a quick method.

Step 2

Why this answer is correct

The correct answer is C. (53). From \(a_5\) to \(a_{10}\), there are (5) gaps, so (a_{10}=33+5(4)=53). Moving forward from a nearby term is a quick method.

Step 3

Exam Tip

\(a_5\) से \(a_{10}\) तक (5) अंतर हैं, इसलिए (a_{10}=33+5(4)=53)। पास के पद से आगे बढ़ना तेज तरीका है।

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Question 28/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

किस विकल्प में (a=20) और (d=-5) वाली समानांतर श्रेढ़ी के पहले चार पद हैं?

Which option has the first four terms of the arithmetic progression with (a=20) and (d=-5)?

Explanation opens after your attempt

Correct Answer

C. (20,15,10,5)

Step 1

Concept

The first term is (20), and subtracting (5) each time gives (20,15,10,5). Form terms directly from the given (a) and (d).

Step 2

Why this answer is correct

The correct answer is C. (20,15,10,5). The first term is (20), and subtracting (5) each time gives (20,15,10,5). Form terms directly from the given (a) and (d).

Step 3

Exam Tip

पहला पद (20) है और हर बार (5) घटाने पर (20,15,10,5) मिलते हैं। दिए (a) और (d) से सीधे पद बनाएं।

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Question 29/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि समानांतर श्रेढ़ी के लगातार तीन पद (x+1), (2x), (3x-5) हैं, तो (x) का मान क्या है?

If three consecutive terms of an arithmetic progression are (x+1), (2x), (3x-5), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

In an arithmetic progression, (2(2x)=(x+1)+(3x-5)), which gives (x=6). The middle term is the average of the two surrounding terms.

Step 2

Why this answer is correct

The correct answer is C. (6). In an arithmetic progression, (2(2x)=(x+1)+(3x-5)), which gives (x=6). The middle term is the average of the two surrounding terms.

Step 3

Exam Tip

समानांतर श्रेढ़ी में (2(2x)=(x+1)+(3x-5)), इससे (x=6) मिलता है। बीच का पद दोनों ओर के पदों का औसत होता है।

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Question 30/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(38,33,28,23,\ldots\) का पहला ऋणात्मक पद कौन-सा है?

What is the first negative term of the arithmetic progression \(38,33,28,23,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (9)वाँ(9)th

Step 1

Concept

\(a_8=3\) and \(a_9=-2\), so the first negative term is the (9)th. Check the first term that goes below zero.

Step 2

Why this answer is correct

The correct answer is B. (9)वाँ / (9)th. \(a_8=3\) and \(a_9=-2\), so the first negative term is the (9)th. Check the first term that goes below zero.

Step 3

Exam Tip

\(a_8=3\) और \(a_9=-2\), इसलिए पहला ऋणात्मक पद (9)वाँ है। शून्य से नीचे जाने वाला पहला पद जांचें।

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Question 31/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=17-3n\) है, तो इस समानांतर श्रेढ़ी का चौथा पद क्या है?

If \(a_n=17-3n\), what is the fourth term of this arithmetic progression?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

(a_4=17-3(4)=5). Substitute (n=4) directly in the given rule.

Step 2

Why this answer is correct

The correct answer is B. (5). (a_4=17-3(4)=5). Substitute (n=4) directly in the given rule.

Step 3

Exam Tip

(a_4=17-3(4)=5)। दिए नियम में सीधे (n=4) रखें।

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Question 32/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(10,18,26,34,\ldots\) के पहले (3) पदों का औसत क्या है?

What is the average of the first (3) terms of the arithmetic progression \(10,18,26,34,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (18)

Step 1

Concept

The average of the first three terms is \(\frac{10+18+26}{3}=18\). In an arithmetic progression, the average of three consecutive terms is the middle term.

Step 2

Why this answer is correct

The correct answer is B. (18). The average of the first three terms is \(\frac{10+18+26}{3}=18\). In an arithmetic progression, the average of three consecutive terms is the middle term.

Step 3

Exam Tip

पहले तीन पदों का औसत \(\frac{10+18+26}{3}=18\) है। समानांतर श्रेढ़ी में तीन क्रमिक पदों का औसत बीच वाला पद होता है।

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Question 33/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_1=11\) और \(a_{10}=65\) है, तो समान अंतर क्या होगा?

If \(a_1=11\) and \(a_{10}=65\), what will be the common difference?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

From \(a_{10}=11+9d=65\), (9d=54) and (d=6). Up to the (10)th term, there are (9) gaps.

Step 2

Why this answer is correct

The correct answer is C. (6). From \(a_{10}=11+9d=65\), (9d=54) and (d=6). Up to the (10)th term, there are (9) gaps.

Step 3

Exam Tip

\(a_{10}=11+9d=65\) से (9d=54) और (d=6)। (10)वें पद तक (9) अंतर होते हैं।

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Question 34/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(5,14,23,32,\ldots\) का (14)वाँ पद क्या है?

What is the (14)th term of the arithmetic progression \(5,14,23,32,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. (122)

Step 1

Concept

Here (a=5) and (d=9), so (a_{14}=5+13(9)=122). Use the same formula even for a larger term.

Step 2

Why this answer is correct

The correct answer is D. (122). Here (a=5) and (d=9), so (a_{14}=5+13(9)=122). Use the same formula even for a larger term.

Step 3

Exam Tip

यहाँ (a=5) और (d=9), इसलिए (a_{14}=5+13(9)=122)। बड़े पद के लिए भी वही सूत्र लगाएं।

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Question 35/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

किस समानांतर श्रेढ़ी का समान अंतर (8) है?

Which arithmetic progression has common difference (8)?

Explanation opens after your attempt

Correct Answer

A. \(8,16,24,32,\ldots\)

Step 1

Concept

In \(8,16,24,32,\ldots\), (8) is added each time. To find the common difference, check the difference of two consecutive terms.

Step 2

Why this answer is correct

The correct answer is A. \(8,16,24,32,\ldots\). In \(8,16,24,32,\ldots\), (8) is added each time. To find the common difference, check the difference of two consecutive terms.

Step 3

Exam Tip

\(8,16,24,32,\ldots\) में हर बार (8) जुड़ता है। समान अंतर निकालने में लगातार दो पदों का अंतर देखें।

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Question 36/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=9n+4\) है, तो \(a_n=85\) किस पद पर होगा?

If \(a_n=9n+4\), at which term will \(a_n=85\)?

Explanation opens after your attempt

Correct Answer

C. (9)वाँ(9)th

Step 1

Concept

From (9n+4=85), (9n=81) and (n=9). To find the position, set \(a_n\) equal to the given value.

Step 2

Why this answer is correct

The correct answer is C. (9)वाँ / (9)th. From (9n+4=85), (9n=81) and (n=9). To find the position, set \(a_n\) equal to the given value.

Step 3

Exam Tip

(9n+4=85) से (9n=81) और (n=9)। पद का स्थान निकालने के लिए \(a_n\) को दिए मान के बराबर रखें।

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Question 37/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(44,38,32,26,\ldots\) के पहले (5) पदों का योग क्या है?

What is the sum of the first (5) terms of the arithmetic progression \(44,38,32,26,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (160)

Step 1

Concept

The first (5) terms are (44,38,32,26,20), and their sum is (160). In a decreasing progression, also list the terms in order and add.

Step 2

Why this answer is correct

The correct answer is B. (160). The first (5) terms are (44,38,32,26,20), and their sum is (160). In a decreasing progression, also list the terms in order and add.

Step 3

Exam Tip

पहले (5) पद (44,38,32,26,20) हैं और योग (160) है। घटती श्रेढ़ी में भी पद क्रम से लिखकर जोड़ें।

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Question 38/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि समानांतर श्रेढ़ी में \(a_7=58\) और (d=8) है, तो \(a_4\) क्या होगा?

If an arithmetic progression has \(a_7=58\) and (d=8), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (34)

Step 1

Concept

From \(a_7\) to \(a_4\), move back (3) gaps, so (a_4=58-3(8)=34). When moving backward, subtract the common difference.

Step 2

Why this answer is correct

The correct answer is B. (34). From \(a_7\) to \(a_4\), move back (3) gaps, so (a_4=58-3(8)=34). When moving backward, subtract the common difference.

Step 3

Exam Tip

\(a_7\) से \(a_4\) तक (3) अंतर पीछे जाना है, इसलिए (a_4=58-3(8)=34)। पीछे जाते समय समान अंतर घटाएं।

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Question 39/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(35,28,21,14,\ldots\) में (0) कौन-सा पद है?

In the arithmetic progression \(35,28,21,14,\ldots\), which term is (0)?

Explanation opens after your attempt

Correct Answer

C. (6)वाँ(6)th

Step 1

Concept

From (35+(n-1)(-7)=0), (n=6). Zero can also be a term of a progression.

Step 2

Why this answer is correct

The correct answer is C. (6)वाँ / (6)th. From (35+(n-1)(-7)=0), (n=6). Zero can also be a term of a progression.

Step 3

Exam Tip

(35+(n-1)(-7)=0) से (n=6) मिलता है। शून्य भी श्रेढ़ी का पद हो सकता है।

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Question 40/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=23) और (d=0) है, तो (15)वाँ पद क्या होगा?

If (a=23) and (d=0), what will be the (15)th term?

Explanation opens after your attempt

Correct Answer

C. (23)

Step 1

Concept

When (d=0), every term remains (23). In a constant arithmetic progression, all terms are equal.

Step 2

Why this answer is correct

The correct answer is C. (23). When (d=0), every term remains (23). In a constant arithmetic progression, all terms are equal.

Step 3

Exam Tip

(d=0) होने पर हर पद (23) ही रहेगा। स्थिर समानांतर श्रेढ़ी में सभी पद बराबर होते हैं।

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Question 41/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(4,12,20,28,\ldots\) में \(a_{12}-a_6\) का मान क्या है?

In the arithmetic progression \(4,12,20,28,\ldots\), what is the value of \(a_{12}-a_6\)?

Explanation opens after your attempt

Correct Answer

B. (48)

Step 1

Concept

There are (6) gaps between \(a_{12}\) and \(a_6\), and (d=8), so the difference is (48). Term difference depends on the difference of positions.

Step 2

Why this answer is correct

The correct answer is B. (48). There are (6) gaps between \(a_{12}\) and \(a_6\), and (d=8), so the difference is (48). Term difference depends on the difference of positions.

Step 3

Exam Tip

\(a_{12}\) और \(a_6\) के बीच (6) अंतर हैं और (d=8), इसलिए अंतर (48) है। पदों का अंतर पद-संख्या के अंतर पर निर्भर करता है।

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Question 42/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

किस विकल्प में \(a_n=16-2n\) से बने पहले चार पद हैं?

Which option has the first four terms formed by \(a_n=16-2n\)?

Explanation opens after your attempt

Correct Answer

A. (14,12,10,8)

Step 1

Concept

Putting (n=1,2,3,4) gives (14,12,10,8). When forming terms from a rule, start with (n=1).

Step 2

Why this answer is correct

The correct answer is A. (14,12,10,8). Putting (n=1,2,3,4) gives (14,12,10,8). When forming terms from a rule, start with (n=1).

Step 3

Exam Tip

(n=1,2,3,4) रखने पर (14,12,10,8) मिलते हैं। नियम से पद बनाते समय (n=1) से शुरू करें।

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Question 43/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(15,21,27,33,\ldots\) के पहले (6) पदों का योग क्या है?

What is the sum of the first (6) terms of the arithmetic progression \(15,21,27,33,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (180)

Step 1

Concept

The first (6) terms are (15,21,27,33,39,45), and their sum is (180). Write the terms in correct order and add.

Step 2

Why this answer is correct

The correct answer is C. (180). The first (6) terms are (15,21,27,33,39,45), and their sum is (180). Write the terms in correct order and add.

Step 3

Exam Tip

पहले (6) पद (15,21,27,33,39,45) हैं और योग (180) है। पद सही क्रम में लिखकर जोड़ें।

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Question 44/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि समानांतर श्रेढ़ी में \(a_3=14\) और \(a_9=50\) है, तो \(a_6\) क्या होगा?

If an arithmetic progression has \(a_3=14\) and \(a_9=50\), what is \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (32)

Step 1

Concept

From \(a_3\) to \(a_9\), the increase over (6) gaps is (36), so (d=6), hence (a_6=14+3(6)=32). Find the common difference first.

Step 2

Why this answer is correct

The correct answer is C. (32). From \(a_3\) to \(a_9\), the increase over (6) gaps is (36), so (d=6), hence (a_6=14+3(6)=32). Find the common difference first.

Step 3

Exam Tip

\(a_3\) से \(a_9\) तक (6) अंतर में वृद्धि (36) है इसलिए (d=6), अतः (a_6=14+3(6)=32)। पहले समान अंतर निकालें।

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Question 45/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(9,16,23,\ldots\) में अगले दो पद कौन-से हैं?

In the arithmetic progression \(9,16,23,\ldots\), what are the next two terms?

Explanation opens after your attempt

Correct Answer

B. (30,37)

Step 1

Concept

The common difference is (7), so after (23) the next terms are (30) and (37). Keep adding the common difference for next terms.

Step 2

Why this answer is correct

The correct answer is B. (30,37). The common difference is (7), so after (23) the next terms are (30) and (37). Keep adding the common difference for next terms.

Step 3

Exam Tip

समान अंतर (7) है इसलिए (23) के बाद (30) और (37) आएंगे। अगले पदों के लिए समान अंतर जोड़ते रहें।

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Question 46/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=5) और (d=13) है, तो \(a_7-a_2\) क्या होगा?

If (a=5) and (d=13), what will \(a_7-a_2\) be?

Explanation opens after your attempt

Correct Answer

B. (65)

Step 1

Concept

There are (5) gaps between \(a_7\) and \(a_2\), so the difference is \(5\times13=65\). For term difference, look at the difference of positions.

Step 2

Why this answer is correct

The correct answer is B. (65). There are (5) gaps between \(a_7\) and \(a_2\), so the difference is \(5\times13=65\). For term difference, look at the difference of positions.

Step 3

Exam Tip

\(a_7\) और \(a_2\) के बीच (5) अंतर हैं इसलिए अंतर \(5\times13=65\) है। पदों के अंतर के लिए पद-संख्या का अंतर देखें।

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Question 47/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(31,35,39,43,\ldots\) का सामान्य पद कौन-सा है?

What is the general term of the arithmetic progression \(31,35,39,43,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=4n+27\)

Step 1

Concept

The first term is (31) and (d=4), so (a_n=31+(n-1)4=4n+27). Put (n=1) to check an option.

Step 2

Why this answer is correct

The correct answer is A. \(a_n=4n+27\). The first term is (31) and (d=4), so (a_n=31+(n-1)4=4n+27). Put (n=1) to check an option.

Step 3

Exam Tip

पहला पद (31) और (d=4) है इसलिए (a_n=31+(n-1)4=4n+27)। विकल्प की जांच के लिए (n=1) रखें।

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Question 48/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समानांतर श्रेढ़ी \(2,9,16,23,\ldots\) में \(a_8+a_3\) का मान क्या है?

In the arithmetic progression \(2,9,16,23,\ldots\), what is the value of \(a_8+a_3\)?

Explanation opens after your attempt

Correct Answer

A. (67)

Step 1

Concept

Here (d=7), so \(a_8=51\) and \(a_3=16\), and the sum is (67). Find both terms separately and then add.

Step 2

Why this answer is correct

The correct answer is A. (67). Here (d=7), so \(a_8=51\) and \(a_3=16\), and the sum is (67). Find both terms separately and then add.

Step 3

Exam Tip

यहाँ (d=7), इसलिए \(a_8=51\) और \(a_3=16\), योग (67) है। दोनों पद अलग निकालकर जोड़ें।

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Question 49/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि समानांतर श्रेढ़ी में \(a_4=19\) और \(a_7=31\) है, तो \(a_1\) क्या होगा?

If an arithmetic progression has \(a_4=19\) and \(a_7=31\), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

The increase over three gaps is (12), so (d=4), then (a_1=19-3(4)=7). From middle terms first find the common difference.

Step 2

Why this answer is correct

The correct answer is B. (7). The increase over three gaps is (12), so (d=4), then (a_1=19-3(4)=7). From middle terms first find the common difference.

Step 3

Exam Tip

तीन अंतरों में वृद्धि (12) है इसलिए (d=4), फिर (a_1=19-3(4)=7)। बीच के पदों से पहले समान अंतर निकालें।

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Question 50/50 Medium Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

किस समानांतर श्रेढ़ी में \(a_5=30\) और समान अंतर (6) है?

Which arithmetic progression has \(a_5=30\) and common difference (6)?

Explanation opens after your attempt

Correct Answer

A. \(6,12,18,24,\ldots\)

Step 1

Concept

In \(6,12,18,24,30,\ldots\), the fifth term is (30) and the common difference is (6). Check each option up to the fifth term.

Step 2

Why this answer is correct

The correct answer is A. \(6,12,18,24,\ldots\). In \(6,12,18,24,30,\ldots\), the fifth term is (30) and the common difference is (6). Check each option up to the fifth term.

Step 3

Exam Tip

\(6,12,18,24,30,\ldots\) में पाँचवाँ पद (30) और समान अंतर (6) है। विकल्प में पहले पाँच पदों तक जांच करें।

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Class 9 Mathematics Medium Quiz

अनुक्रम \(6,13,20,27,\ldots\) में समान अंतर क्या है?

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यदि किसी समानांतर श्रेढ़ी में पहला पद (8) और समान अंतर (5) है, तो (7)वाँ पद क्या होगा?

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समानांतर श्रेढ़ी \(42,36,30,24,\ldots\) का (n)वाँ पद कौन-सा है?

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यदि (a=15) और (d=4) है, तो समानांतर श्रेढ़ी का (9)वाँ पद क्या होगा?

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समानांतर श्रेढ़ी \(3,11,19,27,\ldots\) में (67) कौन-सा पद है?

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यदि \(a_n=4n+3\) है, तो पहले चार पद कौन-से होंगे?

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समानांतर श्रेढ़ी में \(a_1=17\) और \(a_6=47\) है। समान अंतर क्या है?

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समानांतर श्रेढ़ी \(7,15,23,31,\ldots\) के पहले (5) पदों का योग क्या है?

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यदि \(a_n=55-5n\) है, तो इस समानांतर श्रेढ़ी का समान अंतर क्या है?

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यदि समानांतर श्रेढ़ी का पहला पद (21) और चौथा पद (36) है, तो समान अंतर क्या है?

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समानांतर श्रेढ़ी \(4,13,22,31,\ldots\) का (10)वाँ पद क्या है?

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यदि \(a_2=18\) और (d=6) है, तो \(a_1\) क्या होगा?

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समानांतर श्रेढ़ी \(60,54,48,42,\ldots\) का (12)वाँ पद क्या होगा?

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किस समानांतर श्रेढ़ी का पहला पद (12) और समान अंतर (-4) है?

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यदि \(a_n=6n-1\) है, तो पहला पद क्या है?

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समानांतर श्रेढ़ी \(18,25,32,39,\ldots\) में (74) कौन-सा पद है?

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समानांतर श्रेढ़ी \(12,20,28,36,\ldots\) के पहले (4) पदों का योग क्या है?

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यदि (a=34) और (d=-7) है, तो \(a_6\) क्या होगा?

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समानांतर श्रेढ़ी \(9,17,25,33,\ldots\) का सामान्य पद कौन-सा है?

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यदि समानांतर श्रेढ़ी में \(a_4=25\) और \(a_8=49\) है, तो समान अंतर क्या है?

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