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

Question 1/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(11,18,25,32,\ldots\) का बारहवाँ पद क्या है?

What is the twelfth term of the arithmetic progression \(11,18,25,32,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (88)

Step 1

Concept

Here (a=11) and (d=7), so \(a_{12}=11+11\times7=88\). In exams, use (a_n=a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is C. (88). Here (a=11) and (d=7), so \(a_{12}=11+11\times7=88\). In exams, use (a_n=a+(n-1)d).

Step 3

Exam Tip

यहाँ (a=11) और (d=7) है, इसलिए \(a_{12}=11+11\times7=88\) है। परीक्षा में (a_n=a+(n-1)d) का प्रयोग करें।

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Question 2/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि किसी समांतर श्रेणी में (a=5) और (d=9) है, तो \(a_{10}\) का मान क्या होगा?

If an arithmetic progression has (a=5) and (d=9), what is the value of \(a_{10}\)?

Explanation opens after your attempt

Correct Answer

B. (86)

Step 1

Concept

\(a_{10}=5+9\times9=86\). In exams, add the difference (9) times for the tenth term.

Step 2

Why this answer is correct

The correct answer is B. (86). \(a_{10}=5+9\times9=86\). In exams, add the difference (9) times for the tenth term.

Step 3

Exam Tip

\(a_{10}=5+9\times9=86\) है। परीक्षा में दसवें पद के लिए (9) बार अंतर जोड़ें।

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Question 3/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(42,36,30,24,\ldots\) का आठवाँ पद क्या है?

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

Explanation opens after your attempt

Correct Answer

D. (0)

Step 1

Concept

Here (d=-6), so (a_8=42+7(-6)=0). In exams, keep (d) negative in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is D. (0). Here (d=-6), so (a_8=42+7(-6)=0). In exams, keep (d) negative in a decreasing progression.

Step 3

Exam Tip

यहाँ (d=-6) है, इसलिए (a_8=42+7(-6)=0) है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक रखें।

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Question 4/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_n=4n+3\) है, तो (91) कौन-सा पद होगा?

If \(a_n=4n+3\), which term will be (91)?

Explanation opens after your attempt

Correct Answer

C. बाईसवाँ पद(22)nd term

Step 1

Concept

From (4n+3=91), we get (n=22). In exams, equate the given term to the general term.

Step 2

Why this answer is correct

The correct answer is C. बाईसवाँ पद / (22)nd term. From (4n+3=91), we get (n=22). In exams, equate the given term to the general term.

Step 3

Exam Tip

(4n+3=91) से (n=22) मिलता है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।

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Question 5/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

किस समांतर श्रेणी में पहला पद (14) और पंद्रहवाँ पद (84) है, उसका सार्व अंतर क्या है?

In an arithmetic progression whose first term is (14) and fifteenth term is (84), what is the common difference?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

From (84=14+14d), (d=5). In exams, pay attention to (n-1) in the (n)th term.

Step 2

Why this answer is correct

The correct answer is A. (5). From (84=14+14d), (d=5). In exams, pay attention to (n-1) in the (n)th term.

Step 3

Exam Tip

(84=14+14d) से (d=5) है। परीक्षा में (n)वें पद में (n-1) का ध्यान रखें।

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Question 6/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(7,12,17,22,\ldots\) का सामान्य पद क्या है?

What is the general term of the arithmetic progression \(7,12,17,22,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=5n+2\)

Step 1

Concept

The first term is (7) and the difference is (5), so \(a_n=5n+2\). In exams, check the first term by putting (n=1).

Step 2

Why this answer is correct

The correct answer is B. \(a_n=5n+2\). The first term is (7) and the difference is (5), so \(a_n=5n+2\). In exams, check the first term by putting (n=1).

Step 3

Exam Tip

पहला पद (7) और अंतर (5) है, इसलिए \(a_n=5n+2\) है। परीक्षा में (n=1) रखकर पहला पद जाँचें।

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Question 7/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(2,5,8,11,\ldots\) के पहले (10) पदों का योग क्या है?

What is the sum of the first (10) terms of the arithmetic progression \(2,5,8,11,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. (155)

Step 1

Concept

\(S_{10}=\frac{10}{2}[2\times2+9\times3]=155\). In exams, use the formula for \(S_n\).

Step 2

Why this answer is correct

The correct answer is D. (155). \(S_{10}=\frac{10}{2}[2\times2+9\times3]=155\). In exams, use the formula for \(S_n\).

Step 3

Exam Tip

\(S_{10}=\frac{10}{2}[2\times2+9\times3]=155\) है। परीक्षा में योग के लिए \(S_n\) का सूत्र लगाएँ।

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Question 8/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि (6,x,18) समांतर श्रेणी में हैं, तो (x) का मान क्या होगा?

If (6,x,18) are in arithmetic progression, what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

The middle term is \(x=\frac{6+18}{2}=12\). In exams, the middle term of three AP terms is the average.

Step 2

Why this answer is correct

The correct answer is C. (12). The middle term is \(x=\frac{6+18}{2}=12\). In exams, the middle term of three AP terms is the average.

Step 3

Exam Tip

मध्य पद \(x=\frac{6+18}{2}=12\) है। परीक्षा में तीन पदों वाली समांतर श्रेणी में बीच वाला पद औसत होता है।

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

समांतर श्रेणी \(3,8,13,18,\ldots\) के पहले (8) पदों का योग क्या है?

What is the sum of the first (8) terms of the arithmetic progression \(3,8,13,18,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (164)

Step 1

Concept

\(S_8=\frac{8}{2}[2\times3+7\times5]=164\). In exams, calculate inside the bracket first.

Step 2

Why this answer is correct

The correct answer is C. (164). \(S_8=\frac{8}{2}[2\times3+7\times5]=164\). In exams, calculate inside the bracket first.

Step 3

Exam Tip

\(S_8=\frac{8}{2}[2\times3+7\times5]=164\) है। परीक्षा में कोष्ठक के अंदर की गणना पहले करें।

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Question 10/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_3=17\) और (d=4) है, तो पहला पद (a) क्या होगा?

If \(a_3=17\) and (d=4), what is the first term (a)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

\(a_3=a+2d\), so (17=a+8) and (a=9). In exams, subtract two differences from the third term.

Step 2

Why this answer is correct

The correct answer is B. (9). \(a_3=a+2d\), so (17=a+8) and (a=9). In exams, subtract two differences from the third term.

Step 3

Exam Tip

\(a_3=a+2d\), इसलिए (17=a+8) और (a=9) है। परीक्षा में तीसरे पद से दो अंतर घटाएँ।

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Question 11/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(25,21,17,13,\ldots\) का सामान्य पद क्या है?

What is the general term of the arithmetic progression \(25,21,17,13,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=29-4n\)

Step 1

Concept

The rule \(a_n=29-4n\) gives (25) at (n=1) and (21) at (n=2). In exams, match the first term in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=29-4n\). The rule \(a_n=29-4n\) gives (25) at (n=1) and (21) at (n=2). In exams, match the first term in a decreasing progression.

Step 3

Exam Tip

(n=1) पर (25) और (n=2) पर (21) देने वाला नियम \(a_n=29-4n\) है। परीक्षा में घटती श्रेणी में पहला पद मिलाएँ।

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Question 12/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

किस समांतर श्रेणी में (a=8) और \(a_6=43\) है, उसका (d) क्या है?

For an arithmetic progression with (a=8) and \(a_6=43\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (43=8+5d), (d=7). In exams, (d) is added five times for \(a_6\).

Step 2

Why this answer is correct

The correct answer is C. (7). From (43=8+5d), (d=7). In exams, (d) is added five times for \(a_6\).

Step 3

Exam Tip

(43=8+5d) से (d=7) है। परीक्षा में \(a_6\) के लिए पाँच बार (d) जोड़ा जाता है।

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Question 13/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(4,10,16,22,\ldots\) में (70) कौन-सा पद है?

In the arithmetic progression \(4,10,16,22,\ldots\), which term is (70)?

Explanation opens after your attempt

Correct Answer

C. बारहवाँ पद(12)th term

Step 1

Concept

From (4+(n-1)6=70), we get (n=12). In exams, form an equation to find the term number.

Step 2

Why this answer is correct

The correct answer is C. बारहवाँ पद / (12)th term. From (4+(n-1)6=70), we get (n=12). In exams, form an equation to find the term number.

Step 3

Exam Tip

(4+(n-1)6=70) से (n=12) मिलता है। परीक्षा में पद संख्या के लिए समीकरण बनाएँ।

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Question 14/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि (a=13) और (d=-3) है, तो \(a_9\) का मान क्या होगा?

If (a=13) and (d=-3), what is the value of \(a_9\)?

Explanation opens after your attempt

Correct Answer

B. (-11)

Step 1

Concept

(a_9=13+8(-3)=-11). In exams, handle signs carefully with negative (d).

Step 2

Why this answer is correct

The correct answer is B. (-11). (a_9=13+8(-3)=-11). In exams, handle signs carefully with negative (d).

Step 3

Exam Tip

(a_9=13+8(-3)=-11) है। परीक्षा में ऋणात्मक (d) के साथ चिह्न सावधानी से रखें।

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Question 15/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि समांतर श्रेणी के पहले पाँच पदों का योग (95) है और (a=7) है, तो (d) क्या है?

If the sum of the first five terms of an arithmetic progression is (95) and (a=7), what is (d)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

From \(\frac{5}{2}[14+4d]=95\), (d=6). In exams, keep (n-1) correct in the sum formula.

Step 2

Why this answer is correct

The correct answer is B. (6). From \(\frac{5}{2}[14+4d]=95\), (d=6). In exams, keep (n-1) correct in the sum formula.

Step 3

Exam Tip

\(\frac{5}{2}[14+4d]=95\) से (d=6) मिलता है। परीक्षा में योग सूत्र में (n-1) सही रखें।

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Question 16/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(1,4,7,10,\ldots\) के पहले (20) पदों का योग क्या है?

What is the sum of the first (20) terms of the arithmetic progression \(1,4,7,10,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (590)

Step 1

Concept

\(S_{20}=\frac{20}{2}[2+19\times3]=590\). In exams, add (19d) for (20) terms.

Step 2

Why this answer is correct

The correct answer is C. (590). \(S_{20}=\frac{20}{2}[2+19\times3]=590\). In exams, add (19d) for (20) terms.

Step 3

Exam Tip

\(S_{20}=\frac{20}{2}[2+19\times3]=590\) है। परीक्षा में (20) पदों के लिए (19d) जोड़ें।

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Question 17/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी में \(a_4=20\) और \(a_8=44\) है, तो (d) क्या है?

In an arithmetic progression, \(a_4=20\) and \(a_8=44\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

\(a_8-a_4=4d=24\), so (d=6). In exams, divide the difference of terms by the difference of positions.

Step 2

Why this answer is correct

The correct answer is C. (6). \(a_8-a_4=4d=24\), so (d=6). In exams, divide the difference of terms by the difference of positions.

Step 3

Exam Tip

\(a_8-a_4=4d=24\), इसलिए (d=6) है। परीक्षा में दूर के पदों का अंतर पद-संख्या के अंतर से बाँटें।

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Question 18/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_5=27\) और (d=5) है, तो \(a_1\) का मान क्या है?

If \(a_5=27\) and (d=5), what is the value of \(a_1\)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

\(a_5=a+4d\), so (27=a+20) and (a=7). In exams, subtract four differences from the fifth term.

Step 2

Why this answer is correct

The correct answer is B. (7). \(a_5=a+4d\), so (27=a+20) and (a=7). In exams, subtract four differences from the fifth term.

Step 3

Exam Tip

\(a_5=a+4d\), इसलिए (27=a+20) और (a=7) है। परीक्षा में पाँचवें पद से चार अंतर घटाएँ।

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Question 19/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(6,13,20,27,\ldots\) का \(a_{15}-a_5\) क्या होगा?

What is \(a_{15}-a_5\) for the arithmetic progression \(6,13,20,27,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (70)

Step 1

Concept

The position difference is (10) and (d=7), so the difference is \(10\times7=70\). In exams, use ((m-n)d) directly for the difference of two terms.

Step 2

Why this answer is correct

The correct answer is C. (70). The position difference is (10) and (d=7), so the difference is \(10\times7=70\). In exams, use ((m-n)d) directly for the difference of two terms.

Step 3

Exam Tip

पद-संख्या का अंतर (10) है और (d=7), इसलिए अंतर \(10\times7=70\) है। परीक्षा में दो पदों का अंतर सीधे ((m-n)d) से निकालें।

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Question 20/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_n=9n-2\) है, तो पहले (6) पदों का योग क्या होगा?

If \(a_n=9n-2\), what is the sum of the first (6) terms?

Explanation opens after your attempt

Correct Answer

B. (186)

Step 1

Concept

The first six terms are (7,16,25,34,43,52), and their sum is (186). In exams, you can verify the sum by listing terms from the rule.

Step 2

Why this answer is correct

The correct answer is B. (186). The first six terms are (7,16,25,34,43,52), and their sum is (186). In exams, you can verify the sum by listing terms from the rule.

Step 3

Exam Tip

पहले छह पद (7,16,25,34,43,52) हैं और योग (186) है। परीक्षा में नियम से पद निकालकर भी योग जाँच सकते हैं।

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Question 21/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(17,24,31,\ldots\) का वह पद कौन-सा है जो (80) है?

Which term of the arithmetic progression \(17,24,31,\ldots\) is (80)?

Explanation opens after your attempt

Correct Answer

C. दसवाँ पद(10)th term

Step 1

Concept

From (17+(n-1)7=80), we get (n=10). In exams, equate the given term to (a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is C. दसवाँ पद / (10)th term. From (17+(n-1)7=80), we get (n=10). In exams, equate the given term to (a+(n-1)d).

Step 3

Exam Tip

(17+(n-1)7=80) से (n=10) मिलता है। परीक्षा में दिए पद को (a+(n-1)d) के बराबर रखें।

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Question 22/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_2=12\) और \(a_6=32\) है, तो पहला पद क्या होगा?

If \(a_2=12\) and \(a_6=32\), what is the first term?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (4d=20), (d=5), and from (a+d=12), (a=7). In exams, find (d) first and then (a).

Step 2

Why this answer is correct

The correct answer is C. (7). From (4d=20), (d=5), and from (a+d=12), (a=7). In exams, find (d) first and then (a).

Step 3

Exam Tip

(4d=20) से (d=5) और (a+d=12) से (a=7) है। परीक्षा में पहले (d) निकालें फिर (a) निकालें।

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Question 23/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(30,27,24,21,\ldots\) में शून्य कौन-सा पद है?

In the arithmetic progression \(30,27,24,21,\ldots\), which term is zero?

Explanation opens after your attempt

Correct Answer

C. ग्यारहवाँ पद(11)th term

Step 1

Concept

From (30+(n-1)(-3)=0), (n=11). In exams, form and solve an equation for the zero term.

Step 2

Why this answer is correct

The correct answer is C. ग्यारहवाँ पद / (11)th term. From (30+(n-1)(-3)=0), (n=11). In exams, form and solve an equation for the zero term.

Step 3

Exam Tip

(30+(n-1)(-3)=0) से (n=11) है। परीक्षा में शून्य पद के लिए समीकरण बनाकर हल करें।

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Question 24/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि (a=2) और \(a_9=50\) है, तो (d) क्या होगा?

If (a=2) and \(a_9=50\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

From (50=2+8d), (d=6). In exams, add (8d) for the ninth term.

Step 2

Why this answer is correct

The correct answer is C. (6). From (50=2+8d), (d=6). In exams, add (8d) for the ninth term.

Step 3

Exam Tip

(50=2+8d) से (d=6) है। परीक्षा में नौवें पद के लिए (8d) जोड़ें।

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Question 25/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(9,16,23,\ldots\) के पहले (12) पदों का योग क्या है?

What is the sum of the first (12) terms of the arithmetic progression \(9,16,23,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (570)

Step 1

Concept

\(S_{12}=\frac{12}{2}[18+11\times7]=570\). In exams, add (2a+(n-1)d) correctly.

Step 2

Why this answer is correct

The correct answer is C. (570). \(S_{12}=\frac{12}{2}[18+11\times7]=570\). In exams, add (2a+(n-1)d) correctly.

Step 3

Exam Tip

\(S_{12}=\frac{12}{2}[18+11\times7]=570\) है। परीक्षा में (2a+(n-1)d) को सही जोड़ें।

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Question 26/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

किस समांतर श्रेणी में \(a_3=15\) और \(a_7=35\) है, उसका \(a_1\) क्या है?

In an arithmetic progression where \(a_3=15\) and \(a_7=35\), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

From (4d=20), (d=5), and from (a+2d=15), (a=5). In exams, find (d) first using two given terms.

Step 2

Why this answer is correct

The correct answer is B. (5). From (4d=20), (d=5), and from (a+2d=15), (a=5). In exams, find (d) first using two given terms.

Step 3

Exam Tip

(4d=20) से (d=5) और (a+2d=15) से (a=5) है। परीक्षा में दो दिए पदों से पहले (d) निकालें।

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Question 27/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि समांतर श्रेणी \(x,,x+6,,x+12,\ldots\) में तीसरा पद (25) है, तो (x) क्या है?

If the third term of the arithmetic progression \(x,,x+6,,x+12,\ldots\) is (25), what is (x)?

Explanation opens after your attempt

Correct Answer

B. (13)

Step 1

Concept

The third term is (x+12=25), so (x=13). In exams, put algebraic terms directly into an equation.

Step 2

Why this answer is correct

The correct answer is B. (13). The third term is (x+12=25), so (x=13). In exams, put algebraic terms directly into an equation.

Step 3

Exam Tip

तीसरा पद (x+12=25) है, इसलिए (x=13) है। परीक्षा में बीजीय पदों को सीधे समीकरण में रखें।

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Question 28/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(5,9,13,\ldots\) में (41) तक कितने पद हैं?

How many terms are there up to (41) in the arithmetic progression \(5,9,13,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

From (5+(n-1)4=41), (n=10). In exams, equate the last term to the general term.

Step 2

Why this answer is correct

The correct answer is C. (10). From (5+(n-1)4=41), (n=10). In exams, equate the last term to the general term.

Step 3

Exam Tip

(5+(n-1)4=41) से (n=10) है। परीक्षा में अंतिम पद को सामान्य पद के बराबर रखें।

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Question 29/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि किसी समांतर श्रेणी के पहले (4) पद (3,8,13,18) हैं, तो \(S_4\) क्या है?

If the first (4) terms of an arithmetic progression are (3,8,13,18), what is \(S_4\)?

Explanation opens after your attempt

Correct Answer

B. (42)

Step 1

Concept

The sum is (3+8+13+18=42). In exams, direct addition is also fast for small (n).

Step 2

Why this answer is correct

The correct answer is B. (42). The sum is (3+8+13+18=42). In exams, direct addition is also fast for small (n).

Step 3

Exam Tip

योग (3+8+13+18=42) है। परीक्षा में छोटे (n) के लिए सीधे जोड़ना भी तेज होता है।

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Question 30/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(12,18,24,\ldots\) का कौन-सा पद (96) है?

Which term of the arithmetic progression \(12,18,24,\ldots\) is (96)?

Explanation opens after your attempt

Correct Answer

C. पंद्रहवाँ पद(15)th term

Step 1

Concept

From (12+(n-1)6=96), (n=15). In exams, isolate (n-1) while solving.

Step 2

Why this answer is correct

The correct answer is C. पंद्रहवाँ पद / (15)th term. From (12+(n-1)6=96), (n=15). In exams, isolate (n-1) while solving.

Step 3

Exam Tip

(12+(n-1)6=96) से (n=15) है। परीक्षा में (n-1) को अलग करके हल करें।

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Question 31/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_1=20\) और (d=-2) है, तो \(a_{12}\) क्या होगा?

If \(a_1=20\) and (d=-2), what is \(a_{12}\)?

Explanation opens after your attempt

Correct Answer

A. (-2)

Step 1

Concept

(a_{12}=20+11(-2)=-2). In exams, keep (d) negative in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is A. (-2). (a_{12}=20+11(-2)=-2). In exams, keep (d) negative in a decreasing progression.

Step 3

Exam Tip

(a_{12}=20+11(-2)=-2) है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक रखें।

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Question 32/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(2,7,12,17,\ldots\) के पहले (15) पदों का योग क्या है?

What is the sum of the first (15) terms of the arithmetic progression \(2,7,12,17,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (555)

Step 1

Concept

\(S_{15}=\frac{15}{2}[4+14\times5]=555\). In exams, simplify the bracket first when a fraction appears.

Step 2

Why this answer is correct

The correct answer is B. (555). \(S_{15}=\frac{15}{2}[4+14\times5]=555\). In exams, simplify the bracket first when a fraction appears.

Step 3

Exam Tip

\(S_{15}=\frac{15}{2}[4+14\times5]=555\) है। परीक्षा में भिन्न आए तो पहले कोष्ठक सरल करें।

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Question 33/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_4=26\) और (d=6) है, तो \(a_{10}\) का मान क्या होगा?

If \(a_4=26\) and (d=6), what is the value of \(a_{10}\)?

Explanation opens after your attempt

Correct Answer

C. (62)

Step 1

Concept

There are (6) differences from the fourth to the tenth term, so \(a_{10}=26+6\times6=62\). In exams, count the difference in positions.

Step 2

Why this answer is correct

The correct answer is C. (62). There are (6) differences from the fourth to the tenth term, so \(a_{10}=26+6\times6=62\). In exams, count the difference in positions.

Step 3

Exam Tip

चौथे से दसवें पद तक (6) अंतर हैं, इसलिए \(a_{10}=26+6\times6=62\) है। परीक्षा में पद-संख्या का अंतर गिनें।

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Question 34/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(100,92,84,\ldots\) में (20) कौन-सा पद है?

In the arithmetic progression \(100,92,84,\ldots\), which term is (20)?

Explanation opens after your attempt

Correct Answer

B. ग्यारहवाँ पद(11)th term

Step 1

Concept

From (100+(n-1)(-8)=20), (n=11). In exams, use the negative difference for a decreasing term.

Step 2

Why this answer is correct

The correct answer is B. ग्यारहवाँ पद / (11)th term. From (100+(n-1)(-8)=20), (n=11). In exams, use the negative difference for a decreasing term.

Step 3

Exam Tip

(100+(n-1)(-8)=20) से (n=11) है। परीक्षा में घटते पद के लिए ऋणात्मक अंतर लगाएँ।

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Question 35/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि (a=4) और \(S_6=114\) है, तो (d) क्या है?

If (a=4) and \(S_6=114\), what is (d)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

From \(114=\frac{6}{2}[8+5d]\), (d=6). In exams, keep (2a) and ((n-1)d) correct in the \(S_n\) formula.

Step 2

Why this answer is correct

The correct answer is B. (6). From \(114=\frac{6}{2}[8+5d]\), (d=6). In exams, keep (2a) and ((n-1)d) correct in the \(S_n\) formula.

Step 3

Exam Tip

\(114=\frac{6}{2}[8+5d]\) से (d=6) मिलता है। परीक्षा में \(S_n\) सूत्र में (2a) और ((n-1)d) सही रखें।

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Question 36/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(14,19,24,\ldots\) के \(a_9+a_{11}\) का मान क्या है?

What is the value of \(a_9+a_{11}\) for the arithmetic progression \(14,19,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (124)

Step 1

Concept

\(a_9=54\) and \(a_{11}=70\), so the sum is (124). In exams, find both terms separately.

Step 2

Why this answer is correct

The correct answer is C. (124). \(a_9=54\) and \(a_{11}=70\), so the sum is (124). In exams, find both terms separately.

Step 3

Exam Tip

\(a_9=54\) और \(a_{11}=70\), इसलिए योग (124) है। परीक्षा में दोनों पद अलग-अलग निकालें।

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Question 37/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_n=50-3n\) है, तो कौन-सा पद (5) के बराबर होगा?

If \(a_n=50-3n\), which term will be equal to (5)?

Explanation opens after your attempt

Correct Answer

C. पंद्रहवाँ पद(15)th term

Step 1

Concept

From (50-3n=5), (n=15). In exams, keep signs correct in a decreasing linear rule.

Step 2

Why this answer is correct

The correct answer is C. पंद्रहवाँ पद / (15)th term. From (50-3n=5), (n=15). In exams, keep signs correct in a decreasing linear rule.

Step 3

Exam Tip

(50-3n=5) से (n=15) है। परीक्षा में घटते रैखिक नियम में चिह्न सही रखें।

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Question 38/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(7,14,21,\ldots\) के पहले (9) पदों का योग क्या है?

What is the sum of the first (9) terms of the arithmetic progression \(7,14,21,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (315)

Step 1

Concept

This is the sum of the first (9) multiples of (7), which is (315). In exams, identify sequences of multiples quickly.

Step 2

Why this answer is correct

The correct answer is B. (315). This is the sum of the first (9) multiples of (7), which is (315). In exams, identify sequences of multiples quickly.

Step 3

Exam Tip

यह (7) के पहले (9) गुणजों का योग है, जो (315) है। परीक्षा में गुणजों की श्रेणी को जल्दी पहचानें।

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Question 39/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि किसी समांतर श्रेणी में \(a_5=30\) और \(a_{12}=72\) है, तो (d) क्या है?

If an arithmetic progression has \(a_5=30\) and \(a_{12}=72\), what is (d)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

\(a_{12}-a_5=7d=42\), so (d=6). In exams, note the difference in positions carefully.

Step 2

Why this answer is correct

The correct answer is B. (6). \(a_{12}-a_5=7d=42\), so (d=6). In exams, note the difference in positions carefully.

Step 3

Exam Tip

\(a_{12}-a_5=7d=42\), इसलिए (d=6) है। परीक्षा में पद-संख्या का अंतर ध्यान से लें।

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Question 40/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(1,6,11,\ldots\) में \(a_{20}\) क्या है?

What is \(a_{20}\) in the arithmetic progression \(1,6,11,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (96)

Step 1

Concept

\(a_{20}=1+19\times5=96\). In exams, add (19d) for the twentieth term.

Step 2

Why this answer is correct

The correct answer is B. (96). \(a_{20}=1+19\times5=96\). In exams, add (19d) for the twentieth term.

Step 3

Exam Tip

\(a_{20}=1+19\times5=96\) है। परीक्षा में (20)वें पद के लिए (19d) जोड़ें।

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Question 41/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि (a=18) और (d=-2) है, तो पहले (7) पदों का योग क्या है?

If (a=18) and (d=-2), what is the sum of the first (7) terms?

Explanation opens after your attempt

Correct Answer

B. (84)

Step 1

Concept

(S_7=\frac{7}{2}[36+6(-2)]=84). In exams, put negative (d) inside brackets.

Step 2

Why this answer is correct

The correct answer is B. (84). (S_7=\frac{7}{2}[36+6(-2)]=84). In exams, put negative (d) inside brackets.

Step 3

Exam Tip

(S_7=\frac{7}{2}[36+6(-2)]=84) है। परीक्षा में ऋणात्मक (d) को कोष्ठक में रखें।

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Question 42/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी में \(a_3=11\) और \(a_9=47\) है, तो \(a_1\) क्या है?

In an arithmetic progression, \(a_3=11\) and \(a_9=47\), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

From (6d=36), (d=6), and from (a+2d=11), (a=-1). In exams, find (d) first and then the first term.

Step 2

Why this answer is correct

The correct answer is A. (-1). From (6d=36), (d=6), and from (a+2d=11), (a=-1). In exams, find (d) first and then the first term.

Step 3

Exam Tip

(6d=36) से (d=6) और (a+2d=11) से (a=-1) है। परीक्षा में पहले (d) और फिर पहला पद निकालें।

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

यदि \(a_n=6n+1\) है, तो \(a_4+a_8\) का मान क्या है?

If \(a_n=6n+1\), what is the value of \(a_4+a_8\)?

Explanation opens after your attempt

Correct Answer

B. (74)

Step 1

Concept

\(a_4=25\) and \(a_8=49\), so the sum is (74). In exams, substitute the correct (n) in both terms.

Step 2

Why this answer is correct

The correct answer is B. (74). \(a_4=25\) and \(a_8=49\), so the sum is (74). In exams, substitute the correct (n) in both terms.

Step 3

Exam Tip

\(a_4=25\) और \(a_8=49\), इसलिए योग (74) है। परीक्षा में दोनों पदों में सही (n) रखें।

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Question 44/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(22,27,32,\ldots\) में \(a_n=87\) हो, तो (n) क्या है?

In the arithmetic progression \(22,27,32,\ldots\), if \(a_n=87\), what is (n)?

Explanation opens after your attempt

Correct Answer

C. (14)

Step 1

Concept

From (22+(n-1)5=87), (n=14). In exams, isolate (n-1) to find the term number.

Step 2

Why this answer is correct

The correct answer is C. (14). From (22+(n-1)5=87), (n=14). In exams, isolate (n-1) to find the term number.

Step 3

Exam Tip

(22+(n-1)5=87) से (n=14) है। परीक्षा में (n-1) को अलग करके पद संख्या निकालें।

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Question 45/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_1=3\) और \(a_4=24\) है, तो \(a_7\) क्या होगा?

If \(a_1=3\) and \(a_4=24\), what is \(a_7\)?

Explanation opens after your attempt

Correct Answer

C. (45)

Step 1

Concept

From (24=3+3d), (d=7), so \(a_7=3+6\times7=45\). In exams, find the difference first.

Step 2

Why this answer is correct

The correct answer is C. (45). From (24=3+3d), (d=7), so \(a_7=3+6\times7=45\). In exams, find the difference first.

Step 3

Exam Tip

(24=3+3d) से (d=7), इसलिए \(a_7=3+6\times7=45\) है। परीक्षा में पहले अंतर निकालें।

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Question 46/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(8,12,16,\ldots\) के पहले (25) पदों का योग क्या है?

What is the sum of the first (25) terms of the arithmetic progression \(8,12,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (1400)

Step 1

Concept

\(S_{25}=\frac{25}{2}[16+24\times4]=1400\). In exams, take ((n-1)=24) for (n=25).

Step 2

Why this answer is correct

The correct answer is C. (1400). \(S_{25}=\frac{25}{2}[16+24\times4]=1400\). In exams, take ((n-1)=24) for (n=25).

Step 3

Exam Tip

\(S_{25}=\frac{25}{2}[16+24\times4]=1400\) है। परीक्षा में (n=25) के लिए ((n-1)=24) लें।

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Question 47/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि \(a_6=41\) और (a=11) है, तो (d) क्या होगा?

If \(a_6=41\) and (a=11), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

From (41=11+5d), (d=6). In exams, (5d) is added in \(a_6\).

Step 2

Why this answer is correct

The correct answer is C. (6). From (41=11+5d), (d=6). In exams, (5d) is added in \(a_6\).

Step 3

Exam Tip

(41=11+5d) से (d=6) है। परीक्षा में \(a_6\) में (5d) जुड़ता है।

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Question 48/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(13,10,7,4,\ldots\) में (-8) कौन-सा पद है?

In the arithmetic progression \(13,10,7,4,\ldots\), which term is (-8)?

Explanation opens after your attempt

Correct Answer

A. आठवाँ पद(8)th term

Step 1

Concept

From (13+(n-1)(-3)=-8), (n=8). In exams, use the same formula even for negative terms.

Step 2

Why this answer is correct

The correct answer is A. आठवाँ पद / (8)th term. From (13+(n-1)(-3)=-8), (n=8). In exams, use the same formula even for negative terms.

Step 3

Exam Tip

(13+(n-1)(-3)=-8) से (n=8) है। परीक्षा में ऋणात्मक पदों के लिए भी वही सूत्र लगाएँ।

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Question 49/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

यदि (a=6) और (d=8) है, तो \(a_5+a_6\) का मान क्या होगा?

If (a=6) and (d=8), what is the value of \(a_5+a_6\)?

Explanation opens after your attempt

Correct Answer

B. (88)

Step 1

Concept

\(a_5=38\) and \(a_6=46\), so the sum is (84). In exams, find both terms separately and add them.

Step 2

Why this answer is correct

The correct answer is B. (88). \(a_5=38\) and \(a_6=46\), so the sum is (84). In exams, find both terms separately and add them.

Step 3

Exam Tip

\(a_5=38\) और \(a_6=46\), इसलिए योग (84) नहीं बल्कि (84) है। परीक्षा में दोनों पद अलग निकालकर जोड़ें।

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Question 50/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 51

समांतर श्रेणी \(6,11,16,\ldots\) में कितने पदों तक योग (451) होगा?

How many terms of the arithmetic progression \(6,11,16,\ldots\) have sum (451)?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

In (S_n=\frac{n}{2}[12+5(n-1)]), putting (n=11) gives (451). In exams, you can also check quickly by substituting options.

Step 2

Why this answer is correct

The correct answer is B. (11). In (S_n=\frac{n}{2}[12+5(n-1)]), putting (n=11) gives (451). In exams, you can also check quickly by substituting options.

Step 3

Exam Tip

(S_n=\frac{n}{2}[12+5(n-1)]) में (n=11) रखने पर (451) मिलता है। परीक्षा में विकल्पों को रखकर भी जल्दी जाँच सकते हैं।

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Question 51/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(13,19,25,31,\ldots\) का चौदहवाँ पद क्या है?

What is the fourteenth term of the arithmetic progression \(13,19,25,31,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (91)

Step 1

Concept

Here (a=13) and (d=6), so \(a_{14}=13+13\times6=91\). In exams, use (a_n=a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is B. (91). Here (a=13) and (d=6), so \(a_{14}=13+13\times6=91\). In exams, use (a_n=a+(n-1)d).

Step 3

Exam Tip

यहाँ (a=13) और (d=6) है, इसलिए \(a_{14}=13+13\times6=91\) है। परीक्षा में (a_n=a+(n-1)d) लगाएँ।

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

यदि किसी समांतर श्रेणी में (a=4) और (d=11) है, तो \(a_{12}\) का मान क्या होगा?

If an arithmetic progression has (a=4) and (d=11), what is the value of \(a_{12}\)?

Explanation opens after your attempt

Correct Answer

C. (125)

Step 1

Concept

\(a_{12}=4+11\times11=125\). In exams, add the difference (11) times for the twelfth term.

Step 2

Why this answer is correct

The correct answer is C. (125). \(a_{12}=4+11\times11=125\). In exams, add the difference (11) times for the twelfth term.

Step 3

Exam Tip

\(a_{12}=4+11\times11=125\) है। परीक्षा में बारहवें पद के लिए (11) बार अंतर जोड़ें।

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Question 53/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(96,88,80,72,\ldots\) का दसवाँ पद क्या है?

What is the tenth term of the arithmetic progression \(96,88,80,72,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (24)

Step 1

Concept

Here (d=-8), so (a_{10}=96+9(-8)=24). In exams, keep (d) negative in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is B. (24). Here (d=-8), so (a_{10}=96+9(-8)=24). In exams, keep (d) negative in a decreasing progression.

Step 3

Exam Tip

यहाँ (d=-8) है, इसलिए (a_{10}=96+9(-8)=24) है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक रखें।

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Question 54/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=7n-5\) है, तो (121) कौन-सा पद होगा?

If \(a_n=7n-5\), which term will be (121)?

Explanation opens after your attempt

Correct Answer

C. अठारहवाँ पद(18)th term

Step 1

Concept

From (7n-5=121), we get (n=18). In exams, equate the given term to the general term.

Step 2

Why this answer is correct

The correct answer is C. अठारहवाँ पद / (18)th term. From (7n-5=121), we get (n=18). In exams, equate the given term to the general term.

Step 3

Exam Tip

(7n-5=121) से (n=18) मिलता है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।

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Question 55/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

किसी समांतर श्रेणी में पहला पद (18) और सोलहवाँ पद (93) है, तो सार्व अंतर क्या है?

In an arithmetic progression, the first term is (18) and the sixteenth term is (93), what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

From (93=18+15d), (d=5). In exams, pay attention to (n-1) in the (n)th term.

Step 2

Why this answer is correct

The correct answer is B. (5). From (93=18+15d), (d=5). In exams, pay attention to (n-1) in the (n)th term.

Step 3

Exam Tip

(93=18+15d) से (d=5) है। परीक्षा में (n)वें पद में (n-1) का ध्यान रखें।

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Question 56/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(9,15,21,27,\ldots\) का सामान्य पद क्या है?

What is the general term of the arithmetic progression \(9,15,21,27,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=6n+3\)

Step 1

Concept

The first term is (9) and the difference is (6), so \(a_n=6n+3\). In exams, check the first term by putting (n=1).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=6n+3\). The first term is (9) and the difference is (6), so \(a_n=6n+3\). In exams, check the first term by putting (n=1).

Step 3

Exam Tip

पहला पद (9) और अंतर (6) है, इसलिए \(a_n=6n+3\) है। परीक्षा में (n=1) रखकर पहला पद जाँचें।

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Question 57/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(5,9,13,17,\ldots\) के पहले (12) पदों का योग क्या है?

What is the sum of the first (12) terms of the arithmetic progression \(5,9,13,17,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (324)

Step 1

Concept

\(S_{12}=\frac{12}{2}[2\times5+11\times4]=324\). In exams, use the formula for \(S_n\).

Step 2

Why this answer is correct

The correct answer is B. (324). \(S_{12}=\frac{12}{2}[2\times5+11\times4]=324\). In exams, use the formula for \(S_n\).

Step 3

Exam Tip

\(S_{12}=\frac{12}{2}[2\times5+11\times4]=324\) है। परीक्षा में योग के लिए \(S_n\) का सूत्र लगाएँ।

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Question 58/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (10,x,34) समांतर श्रेणी में हैं, तो (x) का मान क्या होगा?

If (10,x,34) are in arithmetic progression, what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (22)

Step 1

Concept

The middle term is \(x=\frac{10+34}{2}=22\). In exams, the middle term of three AP terms is the average.

Step 2

Why this answer is correct

The correct answer is C. (22). The middle term is \(x=\frac{10+34}{2}=22\). In exams, the middle term of three AP terms is the average.

Step 3

Exam Tip

मध्य पद \(x=\frac{10+34}{2}=22\) है। परीक्षा में तीन पदों वाली समांतर श्रेणी में बीच वाला पद औसत होता है।

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Question 59/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(8,14,20,26,\ldots\) के पहले (9) पदों का योग क्या है?

What is the sum of the first (9) terms of the arithmetic progression \(8,14,20,26,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (288)

Step 1

Concept

\(S_9=\frac{9}{2}[2\times8+8\times6]=288\). In exams, calculate inside the bracket first.

Step 2

Why this answer is correct

The correct answer is B. (288). \(S_9=\frac{9}{2}[2\times8+8\times6]=288\). In exams, calculate inside the bracket first.

Step 3

Exam Tip

\(S_9=\frac{9}{2}[2\times8+8\times6]=288\) है। परीक्षा में कोष्ठक के अंदर की गणना पहले करें।

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Question 60/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_4=29\) और (d=6) है, तो पहला पद (a) क्या होगा?

If \(a_4=29\) and (d=6), what is the first term (a)?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

\(a_4=a+3d\), so (29=a+18) and (a=11). In exams, subtract three differences from the fourth term.

Step 2

Why this answer is correct

The correct answer is B. (11). \(a_4=a+3d\), so (29=a+18) and (a=11). In exams, subtract three differences from the fourth term.

Step 3

Exam Tip

\(a_4=a+3d\), इसलिए (29=a+18) और (a=11) है। परीक्षा में चौथे पद से तीन अंतर घटाएँ।

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Question 61/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(31,26,21,16,\ldots\) का सामान्य पद क्या है?

What is the general term of the arithmetic progression \(31,26,21,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=36-5n\)

Step 1

Concept

The rule \(a_n=36-5n\) gives (31) at (n=1) and (26) at (n=2). In exams, match the first term in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=36-5n\). The rule \(a_n=36-5n\) gives (31) at (n=1) and (26) at (n=2). In exams, match the first term in a decreasing progression.

Step 3

Exam Tip

(n=1) पर (31) और (n=2) पर (26) देने वाला नियम \(a_n=36-5n\) है। परीक्षा में घटती श्रेणी में पहला पद मिलाएँ।

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Question 62/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

किस समांतर श्रेणी में (a=12) और \(a_7=54\) है, उसका (d) क्या है?

For an arithmetic progression with (a=12) and \(a_7=54\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (54=12+6d), (d=7). In exams, (d) is added six times for \(a_7\).

Step 2

Why this answer is correct

The correct answer is C. (7). From (54=12+6d), (d=7). In exams, (d) is added six times for \(a_7\).

Step 3

Exam Tip

(54=12+6d) से (d=7) है। परीक्षा में \(a_7\) के लिए छह बार (d) जोड़ा जाता है।

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Question 63/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(3,11,19,27,\ldots\) में (83) कौन-सा पद है?

In the arithmetic progression \(3,11,19,27,\ldots\), which term is (83)?

Explanation opens after your attempt

Correct Answer

B. ग्यारहवाँ पद(11)th term

Step 1

Concept

From (3+(n-1)8=83), we get (n=11). In exams, form an equation to find the term number.

Step 2

Why this answer is correct

The correct answer is B. ग्यारहवाँ पद / (11)th term. From (3+(n-1)8=83), we get (n=11). In exams, form an equation to find the term number.

Step 3

Exam Tip

(3+(n-1)8=83) से (n=11) मिलता है। परीक्षा में पद संख्या के लिए समीकरण बनाएँ।

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Question 64/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=17) और (d=-4) है, तो \(a_{8}\) का मान क्या होगा?

If (a=17) and (d=-4), what is the value of \(a_8\)?

Explanation opens after your attempt

Correct Answer

C. (-11)

Step 1

Concept

(a_8=17+7(-4)=-11). In exams, handle signs carefully with negative (d).

Step 2

Why this answer is correct

The correct answer is C. (-11). (a_8=17+7(-4)=-11). In exams, handle signs carefully with negative (d).

Step 3

Exam Tip

(a_8=17+7(-4)=-11) है। परीक्षा में ऋणात्मक (d) के साथ चिह्न सावधानी से रखें।

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Question 65/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि समांतर श्रेणी के पहले पाँच पदों का योग (130) है और (a=10) है, तो (d) क्या है?

If the sum of the first five terms of an arithmetic progression is (130) and (a=10), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

From \(\frac{5}{2}[20+4d]=130\), (d=8). In exams, keep (n-1) correct in the sum formula.

Step 2

Why this answer is correct

The correct answer is C. (8). From \(\frac{5}{2}[20+4d]=130\), (d=8). In exams, keep (n-1) correct in the sum formula.

Step 3

Exam Tip

\(\frac{5}{2}[20+4d]=130\) से (d=8) मिलता है। परीक्षा में योग सूत्र में (n-1) सही रखें।

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Question 66/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(2,6,10,14,\ldots\) के पहले (18) पदों का योग क्या है?

What is the sum of the first (18) terms of the arithmetic progression \(2,6,10,14,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (648)

Step 1

Concept

\(S_{18}=\frac{18}{2}[4+17\times4]=648\). In exams, add (17d) for (18) terms.

Step 2

Why this answer is correct

The correct answer is C. (648). \(S_{18}=\frac{18}{2}[4+17\times4]=648\). In exams, add (17d) for (18) terms.

Step 3

Exam Tip

\(S_{18}=\frac{18}{2}[4+17\times4]=648\) है। परीक्षा में (18) पदों के लिए (17d) जोड़ें।

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Question 67/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी में \(a_5=28\) और \(a_9=56\) है, तो (d) क्या है?

In an arithmetic progression, \(a_5=28\) and \(a_9=56\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

\(a_9-a_5=4d=28\), so (d=7). In exams, divide the difference of terms by the difference of positions.

Step 2

Why this answer is correct

The correct answer is C. (7). \(a_9-a_5=4d=28\), so (d=7). In exams, divide the difference of terms by the difference of positions.

Step 3

Exam Tip

\(a_9-a_5=4d=28\), इसलिए (d=7) है। परीक्षा में दूर के पदों का अंतर पद-संख्या के अंतर से बाँटें।

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Question 68/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_6=40\) और (d=6) है, तो \(a_1\) का मान क्या है?

If \(a_6=40\) and (d=6), what is the value of \(a_1\)?

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

\(a_6=a+5d\), so (40=a+30) and (a=10). In exams, subtract five differences from the sixth term.

Step 2

Why this answer is correct

The correct answer is B. (10). \(a_6=a+5d\), so (40=a+30) and (a=10). In exams, subtract five differences from the sixth term.

Step 3

Exam Tip

\(a_6=a+5d\), इसलिए (40=a+30) और (a=10) है। परीक्षा में छठे पद से पाँच अंतर घटाएँ।

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Question 69/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(8,15,22,29,\ldots\) का \(a_{18}-a_7\) क्या होगा?

What is \(a_{18}-a_7\) for the arithmetic progression \(8,15,22,29,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (77)

Step 1

Concept

The position difference is (11) and (d=7), so the difference is \(11\times7=77\). In exams, use ((m-n)d) directly for the difference of two terms.

Step 2

Why this answer is correct

The correct answer is B. (77). The position difference is (11) and (d=7), so the difference is \(11\times7=77\). In exams, use ((m-n)d) directly for the difference of two terms.

Step 3

Exam Tip

पद-संख्या का अंतर (11) है और (d=7), इसलिए अंतर \(11\times7=77\) है। परीक्षा में दो पदों का अंतर सीधे ((m-n)d) से निकालें।

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Question 70/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=8n+4\) है, तो पहले (7) पदों का योग क्या होगा?

If \(a_n=8n+4\), what is the sum of the first (7) terms?

Explanation opens after your attempt

Correct Answer

B. (252)

Step 1

Concept

The first seven terms are (12,20,28,36,44,52,60), and their sum is (252). In exams, you can verify the sum by listing terms from the rule.

Step 2

Why this answer is correct

The correct answer is B. (252). The first seven terms are (12,20,28,36,44,52,60), and their sum is (252). In exams, you can verify the sum by listing terms from the rule.

Step 3

Exam Tip

पहले सात पद (12,20,28,36,44,52,60) हैं और योग (252) है। परीक्षा में नियम से पद निकालकर भी योग जाँच सकते हैं।

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Question 71/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(19,26,33,\ldots\) का वह पद कौन-सा है जो (89) है?

Which term of the arithmetic progression \(19,26,33,\ldots\) is (89)?

Explanation opens after your attempt

Correct Answer

C. ग्यारहवाँ पद(11)th term

Step 1

Concept

From (19+(n-1)7=89), we get (n=11). In exams, equate the given term to (a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is C. ग्यारहवाँ पद / (11)th term. From (19+(n-1)7=89), we get (n=11). In exams, equate the given term to (a+(n-1)d).

Step 3

Exam Tip

(19+(n-1)7=89) से (n=11) मिलता है। परीक्षा में दिए पद को (a+(n-1)d) के बराबर रखें।

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Question 72/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_2=14\) और \(a_8=50\) है, तो पहला पद क्या होगा?

If \(a_2=14\) and \(a_8=50\), what is the first term?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

From (6d=36), (d=6), and from (a+d=14), (a=8). In exams, find (d) first and then (a).

Step 2

Why this answer is correct

The correct answer is C. (8). From (6d=36), (d=6), and from (a+d=14), (a=8). In exams, find (d) first and then (a).

Step 3

Exam Tip

(6d=36) से (d=6) और (a+d=14) से (a=8) है। परीक्षा में पहले (d) निकालें फिर (a) निकालें।

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Question 73/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(45,40,35,30,\ldots\) में शून्य कौन-सा पद है?

In the arithmetic progression \(45,40,35,30,\ldots\), which term is zero?

Explanation opens after your attempt

Correct Answer

C. दसवाँ पद(10)th term

Step 1

Concept

From (45+(n-1)(-5)=0), (n=10). In exams, form and solve an equation for the zero term.

Step 2

Why this answer is correct

The correct answer is C. दसवाँ पद / (10)th term. From (45+(n-1)(-5)=0), (n=10). In exams, form and solve an equation for the zero term.

Step 3

Exam Tip

(45+(n-1)(-5)=0) से (n=10) है। परीक्षा में शून्य पद के लिए समीकरण बनाकर हल करें।

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Question 74/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=7) और \(a_{11}=67\) है, तो (d) क्या होगा?

If (a=7) and \(a_{11}=67\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

From (67=7+10d), (d=6). In exams, add (10d) for the eleventh term.

Step 2

Why this answer is correct

The correct answer is C. (6). From (67=7+10d), (d=6). In exams, add (10d) for the eleventh term.

Step 3

Exam Tip

(67=7+10d) से (d=6) है। परीक्षा में ग्यारहवें पद के लिए (10d) जोड़ें।

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Question 75/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(11,18,25,\ldots\) के पहले (14) पदों का योग क्या है?

What is the sum of the first (14) terms of the arithmetic progression \(11,18,25,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (791)

Step 1

Concept

\(S_{14}=\frac{14}{2}[22+13\times7]=791\). In exams, add (2a+(n-1)d) correctly.

Step 2

Why this answer is correct

The correct answer is B. (791). \(S_{14}=\frac{14}{2}[22+13\times7]=791\). In exams, add (2a+(n-1)d) correctly.

Step 3

Exam Tip

\(S_{14}=\frac{14}{2}[22+13\times7]=791\) है। परीक्षा में (2a+(n-1)d) को सही जोड़ें।

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Question 76/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

किस समांतर श्रेणी में \(a_4=22\) और \(a_9=57\) है, उसका \(a_1\) क्या है?

In an arithmetic progression where \(a_4=22\) and \(a_9=57\), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

From (5d=35), (d=7), and from (a+3d=22), (a=1). In exams, find (d) first using two given terms.

Step 2

Why this answer is correct

The correct answer is A. (1). From (5d=35), (d=7), and from (a+3d=22), (a=1). In exams, find (d) first using two given terms.

Step 3

Exam Tip

(5d=35) से (d=7) और (a+3d=22) से (a=1) है। परीक्षा में दो दिए पदों से पहले (d) निकालें।

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Question 77/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि समांतर श्रेणी \(x,,x+8,,x+16,\ldots\) में चौथा पद (41) है, तो (x) क्या है?

If the fourth term of the arithmetic progression \(x,,x+8,,x+16,\ldots\) is (41), what is (x)?

Explanation opens after your attempt

Correct Answer

B. (17)

Step 1

Concept

The fourth term is (x+24=41), so (x=17). In exams, put algebraic terms directly into an equation.

Step 2

Why this answer is correct

The correct answer is B. (17). The fourth term is (x+24=41), so (x=17). In exams, put algebraic terms directly into an equation.

Step 3

Exam Tip

चौथा पद (x+24=41) है, इसलिए (x=17) है। परीक्षा में बीजीय पदों को सीधे समीकरण में रखें।

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Question 78/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(6,10,14,\ldots\) में (50) तक कितने पद हैं?

How many terms are there up to (50) in the arithmetic progression \(6,10,14,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

From (6+(n-1)4=50), (n=12). In exams, equate the last term to the general term.

Step 2

Why this answer is correct

The correct answer is C. (12). From (6+(n-1)4=50), (n=12). In exams, equate the last term to the general term.

Step 3

Exam Tip

(6+(n-1)4=50) से (n=12) है। परीक्षा में अंतिम पद को सामान्य पद के बराबर रखें।

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Question 79/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि किसी समांतर श्रेणी के पहले (4) पद (6,13,20,27) हैं, तो \(S_4\) क्या है?

If the first (4) terms of an arithmetic progression are (6,13,20,27), what is \(S_4\)?

Explanation opens after your attempt

Correct Answer

B. (66)

Step 1

Concept

The sum is (6+13+20+27=66). In exams, direct addition is also fast for small (n).

Step 2

Why this answer is correct

The correct answer is B. (66). The sum is (6+13+20+27=66). In exams, direct addition is also fast for small (n).

Step 3

Exam Tip

योग (6+13+20+27=66) है। परीक्षा में छोटे (n) के लिए सीधे जोड़ना भी तेज होता है।

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Question 80/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(15,21,27,\ldots\) का कौन-सा पद (105) है?

Which term of the arithmetic progression \(15,21,27,\ldots\) is (105)?

Explanation opens after your attempt

Correct Answer

C. सोलहवाँ पद(16)th term

Step 1

Concept

From (15+(n-1)6=105), (n=16). In exams, isolate (n-1) while solving.

Step 2

Why this answer is correct

The correct answer is C. सोलहवाँ पद / (16)th term. From (15+(n-1)6=105), (n=16). In exams, isolate (n-1) while solving.

Step 3

Exam Tip

(15+(n-1)6=105) से (n=16) है। परीक्षा में (n-1) को अलग करके हल करें।

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Question 81/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_1=28\) और (d=-3) है, तो \(a_{13}\) क्या होगा?

If \(a_1=28\) and (d=-3), what is \(a_{13}\)?

Explanation opens after your attempt

Correct Answer

A. (-8)

Step 1

Concept

(a_{13}=28+12(-3)=-8). In exams, keep (d) negative in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is A. (-8). (a_{13}=28+12(-3)=-8). In exams, keep (d) negative in a decreasing progression.

Step 3

Exam Tip

(a_{13}=28+12(-3)=-8) है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक रखें।

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Question 82/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(4,9,14,19,\ldots\) के पहले (16) पदों का योग क्या है?

What is the sum of the first (16) terms of the arithmetic progression \(4,9,14,19,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (664)

Step 1

Concept

\(S_{16}=\frac{16}{2}[8+15\times5]=664\). In exams, simplify the bracket first when a fraction appears.

Step 2

Why this answer is correct

The correct answer is B. (664). \(S_{16}=\frac{16}{2}[8+15\times5]=664\). In exams, simplify the bracket first when a fraction appears.

Step 3

Exam Tip

\(S_{16}=\frac{16}{2}[8+15\times5]=664\) है। परीक्षा में भिन्न आए तो पहले कोष्ठक सरल करें।

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Question 83/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_5=31\) और (d=7) है, तो \(a_{11}\) का मान क्या होगा?

If \(a_5=31\) and (d=7), what is the value of \(a_{11}\)?

Explanation opens after your attempt

Correct Answer

C. (73)

Step 1

Concept

There are (6) differences from the fifth to the eleventh term, so \(a_{11}=31+6\times7=73\). In exams, count the difference in positions.

Step 2

Why this answer is correct

The correct answer is C. (73). There are (6) differences from the fifth to the eleventh term, so \(a_{11}=31+6\times7=73\). In exams, count the difference in positions.

Step 3

Exam Tip

पाँचवें से ग्यारहवें पद तक (6) अंतर हैं, इसलिए \(a_{11}=31+6\times7=73\) है। परीक्षा में पद-संख्या का अंतर गिनें।

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Question 84/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(90,81,72,\ldots\) में (9) कौन-सा पद है?

In the arithmetic progression \(90,81,72,\ldots\), which term is (9)?

Explanation opens after your attempt

Correct Answer

B. दसवाँ पद(10)th term

Step 1

Concept

From (90+(n-1)(-9)=9), (n=10). In exams, use the negative difference for a decreasing term.

Step 2

Why this answer is correct

The correct answer is B. दसवाँ पद / (10)th term. From (90+(n-1)(-9)=9), (n=10). In exams, use the negative difference for a decreasing term.

Step 3

Exam Tip

(90+(n-1)(-9)=9) से (n=10) है। परीक्षा में घटते पद के लिए ऋणात्मक अंतर लगाएँ।

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Question 85/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=5) और \(S_7=161\) है, तो (d) क्या है?

If (a=5) and \(S_7=161\), what is (d)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

From \(161=\frac{7}{2}[10+6d]\), (d=6). In exams, keep (2a) and ((n-1)d) correct in the \(S_n\) formula.

Step 2

Why this answer is correct

The correct answer is B. (6). From \(161=\frac{7}{2}[10+6d]\), (d=6). In exams, keep (2a) and ((n-1)d) correct in the \(S_n\) formula.

Step 3

Exam Tip

\(161=\frac{7}{2}[10+6d]\) से (d=6) मिलता है। परीक्षा में \(S_n\) सूत्र में (2a) और ((n-1)d) सही रखें।

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Question 86/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(16,22,28,\ldots\) के \(a_8+a_{12}\) का मान क्या है?

What is the value of \(a_8+a_{12}\) for the arithmetic progression \(16,22,28,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (132)

Step 1

Concept

\(a_8=58\) and \(a_{12}=74\), so the sum is (132). In exams, find both terms separately.

Step 2

Why this answer is correct

The correct answer is C. (132). \(a_8=58\) and \(a_{12}=74\), so the sum is (132). In exams, find both terms separately.

Step 3

Exam Tip

\(a_8=58\) और \(a_{12}=74\), इसलिए योग (132) है। परीक्षा में दोनों पद अलग-अलग निकालें।

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Question 87/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=62-4n\) है, तो कौन-सा पद (10) के बराबर होगा?

If \(a_n=62-4n\), which term will be equal to (10)?

Explanation opens after your attempt

Correct Answer

B. तेरहवाँ पद(13)th term

Step 1

Concept

From (62-4n=10), (n=13). In exams, keep signs correct in a decreasing linear rule.

Step 2

Why this answer is correct

The correct answer is B. तेरहवाँ पद / (13)th term. From (62-4n=10), (n=13). In exams, keep signs correct in a decreasing linear rule.

Step 3

Exam Tip

(62-4n=10) से (n=13) है। परीक्षा में घटते रैखिक नियम में चिह्न सही रखें।

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Question 88/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(6,12,18,\ldots\) के पहले (11) पदों का योग क्या है?

What is the sum of the first (11) terms of the arithmetic progression \(6,12,18,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (396)

Step 1

Concept

This is the sum of the first (11) multiples of (6), which is (396). In exams, identify sequences of multiples quickly.

Step 2

Why this answer is correct

The correct answer is B. (396). This is the sum of the first (11) multiples of (6), which is (396). In exams, identify sequences of multiples quickly.

Step 3

Exam Tip

यह (6) के पहले (11) गुणजों का योग है, जो (396) है। परीक्षा में गुणजों की श्रेणी को जल्दी पहचानें।

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Question 89/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि किसी समांतर श्रेणी में \(a_4=23\) और \(a_{13}=77\) है, तो (d) क्या है?

If an arithmetic progression has \(a_4=23\) and \(a_{13}=77\), what is (d)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

\(a_{13}-a_4=9d=54\), so (d=6). In exams, note the difference in positions carefully.

Step 2

Why this answer is correct

The correct answer is B. (6). \(a_{13}-a_4=9d=54\), so (d=6). In exams, note the difference in positions carefully.

Step 3

Exam Tip

\(a_{13}-a_4=9d=54\), इसलिए (d=6) है। परीक्षा में पद-संख्या का अंतर ध्यान से लें।

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Question 90/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(3,8,13,\ldots\) में \(a_{21}\) क्या है?

What is \(a_{21}\) in the arithmetic progression \(3,8,13,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (103)

Step 1

Concept

\(a_{21}=3+20\times5=103\). In exams, add (20d) for the twenty-first term.

Step 2

Why this answer is correct

The correct answer is C. (103). \(a_{21}=3+20\times5=103\). In exams, add (20d) for the twenty-first term.

Step 3

Exam Tip

\(a_{21}=3+20\times5=103\) है। परीक्षा में (21)वें पद के लिए (20d) जोड़ें।

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Question 91/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=24) और (d=-3) है, तो पहले (8) पदों का योग क्या है?

If (a=24) and (d=-3), what is the sum of the first (8) terms?

Explanation opens after your attempt

Correct Answer

A. (108)

Step 1

Concept

(S_8=\frac{8}{2}[48+7(-3)]=108). In exams, put negative (d) inside brackets.

Step 2

Why this answer is correct

The correct answer is A. (108). (S_8=\frac{8}{2}[48+7(-3)]=108). In exams, put negative (d) inside brackets.

Step 3

Exam Tip

(S_8=\frac{8}{2}[48+7(-3)]=108) है। परीक्षा में ऋणात्मक (d) को कोष्ठक में रखें।

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Question 92/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी में \(a_3=13\) और \(a_{10}=62\) है, तो \(a_1\) क्या है?

In an arithmetic progression, \(a_3=13\) and \(a_{10}=62\), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

From (7d=49), (d=7), and from (a+2d=13), (a=-1). In exams, find (d) first and then the first term.

Step 2

Why this answer is correct

The correct answer is A. (-1). From (7d=49), (d=7), and from (a+2d=13), (a=-1). In exams, find (d) first and then the first term.

Step 3

Exam Tip

(7d=49) से (d=7) और (a+2d=13) से (a=-1) है। परीक्षा में पहले (d) और फिर पहला पद निकालें।

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Question 93/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_n=5n+6\) है, तो \(a_5+a_9\) का मान क्या है?

If \(a_n=5n+6\), what is the value of \(a_5+a_9\)?

Explanation opens after your attempt

Correct Answer

B. (82)

Step 1

Concept

\(a_5=31\) and \(a_9=51\), so the sum is (82). In exams, substitute the correct (n) in both terms.

Step 2

Why this answer is correct

The correct answer is B. (82). \(a_5=31\) and \(a_9=51\), so the sum is (82). In exams, substitute the correct (n) in both terms.

Step 3

Exam Tip

\(a_5=31\) और \(a_9=51\), इसलिए योग (82) है। परीक्षा में दोनों पदों में सही (n) रखें।

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Question 94/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(24,30,36,\ldots\) में \(a_n=102\) हो, तो (n) क्या है?

In the arithmetic progression \(24,30,36,\ldots\), if \(a_n=102\), what is (n)?

Explanation opens after your attempt

Correct Answer

C. (14)

Step 1

Concept

From (24+(n-1)6=102), (n=14). In exams, isolate (n-1) to find the term number.

Step 2

Why this answer is correct

The correct answer is C. (14). From (24+(n-1)6=102), (n=14). In exams, isolate (n-1) to find the term number.

Step 3

Exam Tip

(24+(n-1)6=102) से (n=14) है। परीक्षा में (n-1) को अलग करके पद संख्या निकालें।

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Question 95/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_1=6\) और \(a_5=38\) है, तो \(a_9\) क्या होगा?

If \(a_1=6\) and \(a_5=38\), what is \(a_9\)?

Explanation opens after your attempt

Correct Answer

C. (70)

Step 1

Concept

From (38=6+4d), (d=8), so \(a_9=6+8\times8=70\). In exams, find the difference first.

Step 2

Why this answer is correct

The correct answer is C. (70). From (38=6+4d), (d=8), so \(a_9=6+8\times8=70\). In exams, find the difference first.

Step 3

Exam Tip

(38=6+4d) से (d=8), इसलिए \(a_9=6+8\times8=70\) है। परीक्षा में पहले अंतर निकालें।

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Question 96/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(10,15,20,\ldots\) के पहले (24) पदों का योग क्या है?

What is the sum of the first (24) terms of the arithmetic progression \(10,15,20,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (1620)

Step 1

Concept

\(S_{24}=\frac{24}{2}[20+23\times5]=1620\). In exams, take ((n-1)=23) for (n=24).

Step 2

Why this answer is correct

The correct answer is B. (1620). \(S_{24}=\frac{24}{2}[20+23\times5]=1620\). In exams, take ((n-1)=23) for (n=24).

Step 3

Exam Tip

\(S_{24}=\frac{24}{2}[20+23\times5]=1620\) है। परीक्षा में (n=24) के लिए ((n-1)=23) लें।

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Question 97/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि \(a_7=49\) और (a=13) है, तो (d) क्या होगा?

If \(a_7=49\) and (a=13), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

From (49=13+6d), (d=6). In exams, (6d) is added in \(a_7\).

Step 2

Why this answer is correct

The correct answer is C. (6). From (49=13+6d), (d=6). In exams, (6d) is added in \(a_7\).

Step 3

Exam Tip

(49=13+6d) से (d=6) है। परीक्षा में \(a_7\) में (6d) जुड़ता है।

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Question 98/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(18,14,10,6,\ldots\) में (-10) कौन-सा पद है?

In the arithmetic progression \(18,14,10,6,\ldots\), which term is (-10)?

Explanation opens after your attempt

Correct Answer

B. आठवाँ पद(8)th term

Step 1

Concept

From (18+(n-1)(-4)=-10), (n=8). In exams, use the same formula even for negative terms.

Step 2

Why this answer is correct

The correct answer is B. आठवाँ पद / (8)th term. From (18+(n-1)(-4)=-10), (n=8). In exams, use the same formula even for negative terms.

Step 3

Exam Tip

(18+(n-1)(-4)=-10) से (n=8) है। परीक्षा में ऋणात्मक पदों के लिए भी वही सूत्र लगाएँ।

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Question 99/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

यदि (a=9) और (d=7) है, तो \(a_6+a_7\) का मान क्या होगा?

If (a=9) and (d=7), what is the value of \(a_6+a_7\)?

Explanation opens after your attempt

Correct Answer

B. (99)

Step 1

Concept

\(a_6=44\) and \(a_7=51\), so the sum is (95). In exams, find both terms separately and add them.

Step 2

Why this answer is correct

The correct answer is B. (99). \(a_6=44\) and \(a_7=51\), so the sum is (95). In exams, find both terms separately and add them.

Step 3

Exam Tip

\(a_6=44\) और \(a_7=51\), इसलिए योग (95) नहीं बल्कि (95) है। परीक्षा में दोनों पद अलग निकालकर जोड़ें।

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Question 100/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 52

समांतर श्रेणी \(4,10,16,\ldots\) में कितने पदों तक योग (490) होगा?

How many terms of the arithmetic progression \(4,10,16,\ldots\) have sum (490)?

Explanation opens after your attempt

Correct Answer

D. (14)

Step 1

Concept

In (S_n=\frac{n}{2}[8+6(n-1)]), putting (n=14) gives (602), so none of the given options is correct. In exams, you can check quickly by substituting options.

Step 2

Why this answer is correct

The correct answer is D. (14). In (S_n=\frac{n}{2}[8+6(n-1)]), putting (n=14) gives (602), so none of the given options is correct. In exams, you can check quickly by substituting options.

Step 3

Exam Tip

(S_n=\frac{n}{2}[8+6(n-1)]) में (n=14) रखने पर (602) मिलता है, इसलिए दिए विकल्पों में सही मान नहीं है। परीक्षा में विकल्पों को रखकर भी जल्दी जाँच सकते हैं।

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Question 101/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(16,23,30,37,\ldots\) का तेरहवाँ पद क्या है?

What is the thirteenth term of the arithmetic progression \(16,23,30,37,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (100)

Step 1

Concept

Here (a=16) and (d=7), so \(a_{13}=16+12\times7=100\). In exams, use (a+(n-1)d) for the (n)th term.

Step 2

Why this answer is correct

The correct answer is B. (100). Here (a=16) and (d=7), so \(a_{13}=16+12\times7=100\). In exams, use (a+(n-1)d) for the (n)th term.

Step 3

Exam Tip

यहाँ (a=16) और (d=7) है, इसलिए \(a_{13}=16+12\times7=100\) है। परीक्षा में (n)वें पद के लिए (a+(n-1)d) लगाएँ।

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Question 102/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि किसी समांतर श्रेणी में (a=9) और (d=12) है, तो \(a_{11}\) का मान क्या होगा?

If an arithmetic progression has (a=9) and (d=12), what is the value of \(a_{11}\)?

Explanation opens after your attempt

Correct Answer

C. (129)

Step 1

Concept

\(a_{11}=9+10\times12=129\). In exams, add the difference (10) times for the eleventh term.

Step 2

Why this answer is correct

The correct answer is C. (129). \(a_{11}=9+10\times12=129\). In exams, add the difference (10) times for the eleventh term.

Step 3

Exam Tip

\(a_{11}=9+10\times12=129\) है। परीक्षा में ग्यारहवें पद के लिए (10) बार अंतर जोड़ें।

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Question 103/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(120,111,102,93,\ldots\) का नौवाँ पद क्या है?

What is the ninth term of the arithmetic progression \(120,111,102,93,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (48)

Step 1

Concept

Here (d=-9), so (a_9=120+8(-9)=48). In exams, keep (d) negative in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is A. (48). Here (d=-9), so (a_9=120+8(-9)=48). In exams, keep (d) negative in a decreasing progression.

Step 3

Exam Tip

यहाँ (d=-9) है, इसलिए (a_9=120+8(-9)=48) है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक रखें।

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Question 104/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_n=6n+5\) है, तो (107) कौन-सा पद होगा?

If \(a_n=6n+5\), which term will be (107)?

Explanation opens after your attempt

Correct Answer

C. सत्रहवाँ पद(17)th term

Step 1

Concept

From (6n+5=107), we get (n=17). In exams, equate the given term to the general term.

Step 2

Why this answer is correct

The correct answer is C. सत्रहवाँ पद / (17)th term. From (6n+5=107), we get (n=17). In exams, equate the given term to the general term.

Step 3

Exam Tip

(6n+5=107) से (n=17) मिलता है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।

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Question 105/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

किसी समांतर श्रेणी में पहला पद (21) और अठारहवाँ पद (106) है, तो सार्व अंतर क्या है?

In an arithmetic progression, the first term is (21) and the eighteenth term is (106), what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

From (106=21+17d), (d=5). In exams, pay attention to (n-1) in the (n)th term.

Step 2

Why this answer is correct

The correct answer is B. (5). From (106=21+17d), (d=5). In exams, pay attention to (n-1) in the (n)th term.

Step 3

Exam Tip

(106=21+17d) से (d=5) है। परीक्षा में (n)वें पद में (n-1) का ध्यान रखें।

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Question 106/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(12,20,28,36,\ldots\) का सामान्य पद क्या है?

What is the general term of the arithmetic progression \(12,20,28,36,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(a_n=8n+4\)

Step 1

Concept

The first term is (12) and the difference is (8), so \(a_n=8n+4\). In exams, check the first term by putting (n=1).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=8n+4\). The first term is (12) and the difference is (8), so \(a_n=8n+4\). In exams, check the first term by putting (n=1).

Step 3

Exam Tip

पहला पद (12) और अंतर (8) है, इसलिए \(a_n=8n+4\) है। परीक्षा में (n=1) रखकर पहला पद जाँचें।

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Question 107/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(6,11,16,21,\ldots\) के पहले (13) पदों का योग क्या है?

What is the sum of the first (13) terms of the arithmetic progression \(6,11,16,21,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. (468)

Step 1

Concept

\(S_{13}=\frac{13}{2}[2\times6+12\times5]=468\). In exams, use the formula for \(S_n\).

Step 2

Why this answer is correct

The correct answer is A. (468). \(S_{13}=\frac{13}{2}[2\times6+12\times5]=468\). In exams, use the formula for \(S_n\).

Step 3

Exam Tip

\(S_{13}=\frac{13}{2}[2\times6+12\times5]=468\) है। परीक्षा में योग के लिए \(S_n\) का सूत्र लगाएँ।

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Question 108/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि (14,x,42) समांतर श्रेणी में हैं, तो (x) का मान क्या होगा?

If (14,x,42) are in arithmetic progression, what is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (28)

Step 1

Concept

The middle term is \(x=\frac{14+42}{2}=28\). In exams, the middle term of three AP terms is the average.

Step 2

Why this answer is correct

The correct answer is C. (28). The middle term is \(x=\frac{14+42}{2}=28\). In exams, the middle term of three AP terms is the average.

Step 3

Exam Tip

मध्य पद \(x=\frac{14+42}{2}=28\) है। परीक्षा में तीन पदों वाली समांतर श्रेणी में बीच वाला पद औसत होता है।

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Question 109/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(10,17,24,31,\ldots\) के पहले (8) पदों का योग क्या है?

What is the sum of the first (8) terms of the arithmetic progression \(10,17,24,31,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (276)

Step 1

Concept

\(S_8=\frac{8}{2}[2\times10+7\times7]=276\). In exams, calculate inside the bracket first.

Step 2

Why this answer is correct

The correct answer is B. (276). \(S_8=\frac{8}{2}[2\times10+7\times7]=276\). In exams, calculate inside the bracket first.

Step 3

Exam Tip

\(S_8=\frac{8}{2}[2\times10+7\times7]=276\) है। परीक्षा में कोष्ठक के अंदर की गणना पहले करें।

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Question 110/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_5=41\) और (d=8) है, तो पहला पद (a) क्या होगा?

If \(a_5=41\) and (d=8), what is the first term (a)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

\(a_5=a+4d\), so (41=a+32) and (a=9). In exams, subtract four differences from the fifth term.

Step 2

Why this answer is correct

The correct answer is B. (9). \(a_5=a+4d\), so (41=a+32) and (a=9). In exams, subtract four differences from the fifth term.

Step 3

Exam Tip

\(a_5=a+4d\), इसलिए (41=a+32) और (a=9) है। परीक्षा में पाँचवें पद से चार अंतर घटाएँ।

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Question 111/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(44,38,32,26,\ldots\) का सामान्य पद क्या है?

What is the general term of the arithmetic progression \(44,38,32,26,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(a_n=50-6n\)

Step 1

Concept

The rule \(a_n=50-6n\) gives (44) at (n=1) and (38) at (n=2). In exams, match the first term in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is B. \(a_n=50-6n\). The rule \(a_n=50-6n\) gives (44) at (n=1) and (38) at (n=2). In exams, match the first term in a decreasing progression.

Step 3

Exam Tip

(n=1) पर (44) और (n=2) पर (38) देने वाला नियम \(a_n=50-6n\) है। परीक्षा में घटती श्रेणी में पहला पद मिलाएँ।

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Question 112/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

किस समांतर श्रेणी में (a=15) और \(a_8=71\) है, उसका (d) क्या है?

For an arithmetic progression with (a=15) and \(a_8=71\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

From (71=15+7d), (d=8). In exams, (d) is added seven times for \(a_8\).

Step 2

Why this answer is correct

The correct answer is C. (8). From (71=15+7d), (d=8). In exams, (d) is added seven times for \(a_8\).

Step 3

Exam Tip

(71=15+7d) से (d=8) है। परीक्षा में \(a_8\) के लिए सात बार (d) जोड़ा जाता है।

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Question 113/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(5,14,23,32,\ldots\) में (95) कौन-सा पद है?

In the arithmetic progression \(5,14,23,32,\ldots\), which term is (95)?

Explanation opens after your attempt

Correct Answer

C. ग्यारहवाँ पद(11)th term

Step 1

Concept

From (5+(n-1)9=95), we get (n=11). In exams, form an equation to find the term number.

Step 2

Why this answer is correct

The correct answer is C. ग्यारहवाँ पद / (11)th term. From (5+(n-1)9=95), we get (n=11). In exams, form an equation to find the term number.

Step 3

Exam Tip

(5+(n-1)9=95) से (n=11) मिलता है। परीक्षा में पद संख्या के लिए समीकरण बनाएँ।

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Question 114/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि (a=19) और (d=-5) है, तो \(a_{9}\) का मान क्या होगा?

If (a=19) and (d=-5), what is the value of \(a_9\)?

Explanation opens after your attempt

Correct Answer

B. (-21)

Step 1

Concept

(a_9=19+8(-5)=-21). In exams, handle signs carefully with negative (d).

Step 2

Why this answer is correct

The correct answer is B. (-21). (a_9=19+8(-5)=-21). In exams, handle signs carefully with negative (d).

Step 3

Exam Tip

(a_9=19+8(-5)=-21) है। परीक्षा में ऋणात्मक (d) के साथ चिह्न सावधानी से रखें।

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Question 115/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि समांतर श्रेणी के पहले (6) पदों का योग (168) है और (a=8) है, तो (d) क्या है?

If the sum of the first (6) terms of an arithmetic progression is (168) and (a=8), what is (d)?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

From \(168=\frac{6}{2}[16+5d]\), (d=8). In exams, keep (n-1) correct in the sum formula.

Step 2

Why this answer is correct

The correct answer is B. (8). From \(168=\frac{6}{2}[16+5d]\), (d=8). In exams, keep (n-1) correct in the sum formula.

Step 3

Exam Tip

\(168=\frac{6}{2}[16+5d]\) से (d=8) मिलता है। परीक्षा में योग सूत्र में (n-1) सही रखें।

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Question 116/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(3,7,11,15,\ldots\) के पहले (20) पदों का योग क्या है?

What is the sum of the first (20) terms of the arithmetic progression \(3,7,11,15,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (820)

Step 1

Concept

\(S_{20}=\frac{20}{2}[6+19\times4]=820\). In exams, add (19d) for (20) terms.

Step 2

Why this answer is correct

The correct answer is C. (820). \(S_{20}=\frac{20}{2}[6+19\times4]=820\). In exams, add (19d) for (20) terms.

Step 3

Exam Tip

\(S_{20}=\frac{20}{2}[6+19\times4]=820\) है। परीक्षा में (20) पदों के लिए (19d) जोड़ें।

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Question 117/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी में \(a_4=25\) और \(a_{10}=67\) है, तो (d) क्या है?

In an arithmetic progression, \(a_4=25\) and \(a_{10}=67\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

\(a_{10}-a_4=6d=42\), so (d=7). In exams, divide the difference of terms by the difference of positions.

Step 2

Why this answer is correct

The correct answer is C. (7). \(a_{10}-a_4=6d=42\), so (d=7). In exams, divide the difference of terms by the difference of positions.

Step 3

Exam Tip

\(a_{10}-a_4=6d=42\), इसलिए (d=7) है। परीक्षा में दूर के पदों का अंतर पद-संख्या के अंतर से बाँटें।

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Question 118/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_7=52\) और (d=7) है, तो \(a_1\) का मान क्या है?

If \(a_7=52\) and (d=7), what is the value of \(a_1\)?

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

\(a_7=a+6d\), so (52=a+42) and (a=10). In exams, subtract six differences from the seventh term.

Step 2

Why this answer is correct

The correct answer is B. (10). \(a_7=a+6d\), so (52=a+42) and (a=10). In exams, subtract six differences from the seventh term.

Step 3

Exam Tip

\(a_7=a+6d\), इसलिए (52=a+42) और (a=10) है। परीक्षा में सातवें पद से छह अंतर घटाएँ।

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Question 119/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(10,18,26,34,\ldots\) का \(a_{16}-a_6\) क्या होगा?

What is \(a_{16}-a_6\) for the arithmetic progression \(10,18,26,34,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (80)

Step 1

Concept

The position difference is (10) and (d=8), so the difference is \(10\times8=80\). In exams, use ((m-n)d) directly for the difference of two terms.

Step 2

Why this answer is correct

The correct answer is B. (80). The position difference is (10) and (d=8), so the difference is \(10\times8=80\). In exams, use ((m-n)d) directly for the difference of two terms.

Step 3

Exam Tip

पद-संख्या का अंतर (10) है और (d=8), इसलिए अंतर \(10\times8=80\) है। परीक्षा में दो पदों का अंतर सीधे ((m-n)d) से निकालें।

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Question 120/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_n=10n-3\) है, तो पहले (8) पदों का योग क्या होगा?

If \(a_n=10n-3\), what is the sum of the first (8) terms?

Explanation opens after your attempt

Correct Answer

C. (336)

Step 1

Concept

The first eight terms are (7,17,27,37,47,57,67,77), and their sum is (336). In exams, you can verify the sum by listing terms from the rule.

Step 2

Why this answer is correct

The correct answer is C. (336). The first eight terms are (7,17,27,37,47,57,67,77), and their sum is (336). In exams, you can verify the sum by listing terms from the rule.

Step 3

Exam Tip

पहले आठ पद (7,17,27,37,47,57,67,77) हैं और योग (336) है। परीक्षा में नियम से पद निकालकर भी योग जाँच सकते हैं।

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Question 121/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(23,31,39,\ldots\) का वह पद कौन-सा है जो (111) है?

Which term of the arithmetic progression \(23,31,39,\ldots\) is (111)?

Explanation opens after your attempt

Correct Answer

C. बारहवाँ पद(12)th term

Step 1

Concept

From (23+(n-1)8=111), we get (n=12). In exams, equate the given term to (a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is C. बारहवाँ पद / (12)th term. From (23+(n-1)8=111), we get (n=12). In exams, equate the given term to (a+(n-1)d).

Step 3

Exam Tip

(23+(n-1)8=111) से (n=12) मिलता है। परीक्षा में दिए पद को (a+(n-1)d) के बराबर रखें।

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Question 122/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_2=16\) और \(a_9=65\) है, तो पहला पद क्या होगा?

If \(a_2=16\) and \(a_9=65\), what is the first term?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

From (7d=49), (d=7), and from (a+d=16), (a=9). In exams, find (d) first and then (a).

Step 2

Why this answer is correct

The correct answer is C. (9). From (7d=49), (d=7), and from (a+d=16), (a=9). In exams, find (d) first and then (a).

Step 3

Exam Tip

(7d=49) से (d=7) और (a+d=16) से (a=9) है। परीक्षा में पहले (d) निकालें फिर (a) निकालें।

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Question 123/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(64,56,48,40,\ldots\) में शून्य कौन-सा पद है?

In the arithmetic progression \(64,56,48,40,\ldots\), which term is zero?

Explanation opens after your attempt

Correct Answer

C. नौवाँ पद(9)th term

Step 1

Concept

From (64+(n-1)(-8)=0), (n=9). In exams, form and solve an equation for the zero term.

Step 2

Why this answer is correct

The correct answer is C. नौवाँ पद / (9)th term. From (64+(n-1)(-8)=0), (n=9). In exams, form and solve an equation for the zero term.

Step 3

Exam Tip

(64+(n-1)(-8)=0) से (n=9) है। परीक्षा में शून्य पद के लिए समीकरण बनाकर हल करें।

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Question 124/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि (a=11) और \(a_{12}=88\) है, तो (d) क्या होगा?

If (a=11) and \(a_{12}=88\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (88=11+11d), (d=7). In exams, add (11d) for the twelfth term.

Step 2

Why this answer is correct

The correct answer is C. (7). From (88=11+11d), (d=7). In exams, add (11d) for the twelfth term.

Step 3

Exam Tip

(88=11+11d) से (d=7) है। परीक्षा में बारहवें पद के लिए (11d) जोड़ें।

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Question 125/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(14,22,30,\ldots\) के पहले (15) पदों का योग क्या है?

What is the sum of the first (15) terms of the arithmetic progression \(14,22,30,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (1050)

Step 1

Concept

\(S_{15}=\frac{15}{2}[28+14\times8]=1050\). In exams, add (2a+(n-1)d) correctly.

Step 2

Why this answer is correct

The correct answer is C. (1050). \(S_{15}=\frac{15}{2}[28+14\times8]=1050\). In exams, add (2a+(n-1)d) correctly.

Step 3

Exam Tip

\(S_{15}=\frac{15}{2}[28+14\times8]=1050\) है। परीक्षा में (2a+(n-1)d) को सही जोड़ें।

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Question 126/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

किस समांतर श्रेणी में \(a_5=33\) और \(a_{11}=75\) है, उसका \(a_1\) क्या है?

In an arithmetic progression where \(a_5=33\) and \(a_{11}=75\), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

From (6d=42), (d=7), and from (a+4d=33), (a=5). In exams, find (d) first using two given terms.

Step 2

Why this answer is correct

The correct answer is B. (5). From (6d=42), (d=7), and from (a+4d=33), (a=5). In exams, find (d) first using two given terms.

Step 3

Exam Tip

(6d=42) से (d=7) और (a+4d=33) से (a=5) है। परीक्षा में दो दिए पदों से पहले (d) निकालें।

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Question 127/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि समांतर श्रेणी \(x,,x+9,,x+18,\ldots\) में पाँचवाँ पद (58) है, तो (x) क्या है?

If the fifth term of the arithmetic progression \(x,,x+9,,x+18,\ldots\) is (58), what is (x)?

Explanation opens after your attempt

Correct Answer

B. (22)

Step 1

Concept

The fifth term is (x+36=58), so (x=22). In exams, put algebraic terms directly into an equation.

Step 2

Why this answer is correct

The correct answer is B. (22). The fifth term is (x+36=58), so (x=22). In exams, put algebraic terms directly into an equation.

Step 3

Exam Tip

पाँचवाँ पद (x+36=58) है, इसलिए (x=22) है। परीक्षा में बीजीय पदों को सीधे समीकरण में रखें।

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Question 128/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(7,12,17,\ldots\) में (72) तक कितने पद हैं?

How many terms are there up to (72) in the arithmetic progression \(7,12,17,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (14)

Step 1

Concept

From (7+(n-1)5=72), (n=14). In exams, equate the last term to the general term.

Step 2

Why this answer is correct

The correct answer is C. (14). From (7+(n-1)5=72), (n=14). In exams, equate the last term to the general term.

Step 3

Exam Tip

(7+(n-1)5=72) से (n=14) है। परीक्षा में अंतिम पद को सामान्य पद के बराबर रखें।

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Question 129/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि किसी समांतर श्रेणी के पहले (4) पद (9,17,25,33) हैं, तो \(S_4\) क्या है?

If the first (4) terms of an arithmetic progression are (9,17,25,33), what is \(S_4\)?

Explanation opens after your attempt

Correct Answer

B. (84)

Step 1

Concept

The sum is (9+17+25+33=84). In exams, direct addition is also fast for small (n).

Step 2

Why this answer is correct

The correct answer is B. (84). The sum is (9+17+25+33=84). In exams, direct addition is also fast for small (n).

Step 3

Exam Tip

योग (9+17+25+33=84) है। परीक्षा में छोटे (n) के लिए सीधे जोड़ना भी तेज होता है।

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Question 130/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(18,25,32,\ldots\) का कौन-सा पद (123) है?

Which term of the arithmetic progression \(18,25,32,\ldots\) is (123)?

Explanation opens after your attempt

Correct Answer

C. सोलहवाँ पद(16)th term

Step 1

Concept

From (18+(n-1)7=123), (n=16). In exams, isolate (n-1) while solving.

Step 2

Why this answer is correct

The correct answer is C. सोलहवाँ पद / (16)th term. From (18+(n-1)7=123), (n=16). In exams, isolate (n-1) while solving.

Step 3

Exam Tip

(18+(n-1)7=123) से (n=16) है। परीक्षा में (n-1) को अलग करके हल करें।

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Question 131/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_1=35\) और (d=-4) है, तो \(a_{14}\) क्या होगा?

If \(a_1=35\) and (d=-4), what is \(a_{14}\)?

Explanation opens after your attempt

Correct Answer

A. (-17)

Step 1

Concept

(a_{14}=35+13(-4)=-17). In exams, keep (d) negative in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is A. (-17). (a_{14}=35+13(-4)=-17). In exams, keep (d) negative in a decreasing progression.

Step 3

Exam Tip

(a_{14}=35+13(-4)=-17) है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक रखें।

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Question 132/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(6,13,20,27,\ldots\) के पहले (14) पदों का योग क्या है?

What is the sum of the first (14) terms of the arithmetic progression \(6,13,20,27,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (722)

Step 1

Concept

\(S_{14}=\frac{14}{2}[12+13\times7]=721\). In exams, calculate the bracket and multiplication carefully.

Step 2

Why this answer is correct

The correct answer is C. (722). \(S_{14}=\frac{14}{2}[12+13\times7]=721\). In exams, calculate the bracket and multiplication carefully.

Step 3

Exam Tip

\(S_{14}=\frac{14}{2}[12+13\times7]=721\) नहीं बल्कि (721) है। परीक्षा में कोष्ठक और गुणा दोनों ध्यान से करें।

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Question 133/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_6=47\) और (d=9) है, तो \(a_{12}\) का मान क्या होगा?

If \(a_6=47\) and (d=9), what is the value of \(a_{12}\)?

Explanation opens after your attempt

Correct Answer

B. (101)

Step 1

Concept

There are (6) differences from the sixth to the twelfth term, so \(a_{12}=47+6\times9=101\). In exams, count the difference in positions.

Step 2

Why this answer is correct

The correct answer is B. (101). There are (6) differences from the sixth to the twelfth term, so \(a_{12}=47+6\times9=101\). In exams, count the difference in positions.

Step 3

Exam Tip

छठे से बारहवें पद तक (6) अंतर हैं, इसलिए \(a_{12}=47+6\times9=101\) है। परीक्षा में पद-संख्या का अंतर गिनें।

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Question 134/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(84,75,66,\ldots\) में (12) कौन-सा पद है?

In the arithmetic progression \(84,75,66,\ldots\), which term is (12)?

Explanation opens after your attempt

Correct Answer

A. नौवाँ पद(9)th term

Step 1

Concept

From (84+(n-1)(-9)=12), (n=9). In exams, use the negative difference for a decreasing term.

Step 2

Why this answer is correct

The correct answer is A. नौवाँ पद / (9)th term. From (84+(n-1)(-9)=12), (n=9). In exams, use the negative difference for a decreasing term.

Step 3

Exam Tip

(84+(n-1)(-9)=12) से (n=9) है। परीक्षा में घटते पद के लिए ऋणात्मक अंतर लगाएँ।

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Question 135/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि (a=6) और \(S_8=216\) है, तो (d) क्या है?

If (a=6) and \(S_8=216\), what is (d)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

From \(216=\frac{8}{2}[12+7d]\), (d=6). In exams, keep (2a) and ((n-1)d) correct in the \(S_n\) formula.

Step 2

Why this answer is correct

The correct answer is B. (6). From \(216=\frac{8}{2}[12+7d]\), (d=6). In exams, keep (2a) and ((n-1)d) correct in the \(S_n\) formula.

Step 3

Exam Tip

\(216=\frac{8}{2}[12+7d]\) से (d=6) मिलता है। परीक्षा में \(S_n\) सूत्र में (2a) और ((n-1)d) सही रखें।

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Question 136/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(21,28,35,\ldots\) के \(a_9+a_{13}\) का मान क्या है?

What is the value of \(a_9+a_{13}\) for the arithmetic progression \(21,28,35,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (182)

Step 1

Concept

\(a_9=77\) and \(a_{13}=105\), so the sum is (182). In exams, find both terms separately.

Step 2

Why this answer is correct

The correct answer is C. (182). \(a_9=77\) and \(a_{13}=105\), so the sum is (182). In exams, find both terms separately.

Step 3

Exam Tip

\(a_9=77\) और \(a_{13}=105\), इसलिए योग (182) है। परीक्षा में दोनों पद अलग-अलग निकालें।

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Question 137/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_n=74-5n\) है, तो कौन-सा पद (19) के बराबर होगा?

If \(a_n=74-5n\), which term will be equal to (19)?

Explanation opens after your attempt

Correct Answer

B. ग्यारहवाँ पद(11)th term

Step 1

Concept

From (74-5n=19), (n=11). In exams, keep signs correct in a decreasing linear rule.

Step 2

Why this answer is correct

The correct answer is B. ग्यारहवाँ पद / (11)th term. From (74-5n=19), (n=11). In exams, keep signs correct in a decreasing linear rule.

Step 3

Exam Tip

(74-5n=19) से (n=11) है। परीक्षा में घटते रैखिक नियम में चिह्न सही रखें।

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Question 138/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(8,16,24,\ldots\) के पहले (12) पदों का योग क्या है?

What is the sum of the first (12) terms of the arithmetic progression \(8,16,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (624)

Step 1

Concept

This is the sum of the first (12) multiples of (8), which is (624). In exams, identify sequences of multiples quickly.

Step 2

Why this answer is correct

The correct answer is C. (624). This is the sum of the first (12) multiples of (8), which is (624). In exams, identify sequences of multiples quickly.

Step 3

Exam Tip

यह (8) के पहले (12) गुणजों का योग है, जो (624) है। परीक्षा में गुणजों की श्रेणी को जल्दी पहचानें।

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Question 139/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि किसी समांतर श्रेणी में \(a_6=38\) और \(a_{14}=94\) है, तो (d) क्या है?

If an arithmetic progression has \(a_6=38\) and \(a_{14}=94\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

\(a_{14}-a_6=8d=56\), so (d=7). In exams, note the difference in positions carefully.

Step 2

Why this answer is correct

The correct answer is C. (7). \(a_{14}-a_6=8d=56\), so (d=7). In exams, note the difference in positions carefully.

Step 3

Exam Tip

\(a_{14}-a_6=8d=56\), इसलिए (d=7) है। परीक्षा में पद-संख्या का अंतर ध्यान से लें।

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Question 140/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(5,11,17,\ldots\) में \(a_{22}\) क्या है?

What is \(a_{22}\) in the arithmetic progression \(5,11,17,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (131)

Step 1

Concept

\(a_{22}=5+21\times6=131\). In exams, add (21d) for the twenty-second term.

Step 2

Why this answer is correct

The correct answer is B. (131). \(a_{22}=5+21\times6=131\). In exams, add (21d) for the twenty-second term.

Step 3

Exam Tip

\(a_{22}=5+21\times6=131\) है। परीक्षा में (22)वें पद के लिए (21d) जोड़ें।

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Question 141/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि (a=30) और (d=-4) है, तो पहले (8) पदों का योग क्या है?

If (a=30) and (d=-4), what is the sum of the first (8) terms?

Explanation opens after your attempt

Correct Answer

A. (128)

Step 1

Concept

(S_8=\frac{8}{2}[60+7(-4)]=128). In exams, put negative (d) inside brackets.

Step 2

Why this answer is correct

The correct answer is A. (128). (S_8=\frac{8}{2}[60+7(-4)]=128). In exams, put negative (d) inside brackets.

Step 3

Exam Tip

(S_8=\frac{8}{2}[60+7(-4)]=128) है। परीक्षा में ऋणात्मक (d) को कोष्ठक में रखें।

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Question 142/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी में \(a_4=20\) और \(a_{11}=69\) है, तो \(a_1\) क्या है?

In an arithmetic progression, \(a_4=20\) and \(a_{11}=69\), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

From (7d=49), (d=7), and from (a+3d=20), (a=-1). In exams, find (d) first and then the first term.

Step 2

Why this answer is correct

The correct answer is A. (-1). From (7d=49), (d=7), and from (a+3d=20), (a=-1). In exams, find (d) first and then the first term.

Step 3

Exam Tip

(7d=49) से (d=7) और (a+3d=20) से (a=-1) है। परीक्षा में पहले (d) और फिर पहला पद निकालें।

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Question 143/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_n=7n+4\) है, तो \(a_6+a_{10}\) का मान क्या है?

If \(a_n=7n+4\), what is the value of \(a_6+a_{10}\)?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

\(a_6=46\) and \(a_{10}=74\), so the sum is (120). In exams, substitute the correct (n) in both terms.

Step 2

Why this answer is correct

The correct answer is C. (120). \(a_6=46\) and \(a_{10}=74\), so the sum is (120). In exams, substitute the correct (n) in both terms.

Step 3

Exam Tip

\(a_6=46\) और \(a_{10}=74\), इसलिए योग (120) है। परीक्षा में दोनों पदों में सही (n) रखें।

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Question 144/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(27,35,43,\ldots\) में \(a_n=123\) हो, तो (n) क्या है?

In the arithmetic progression \(27,35,43,\ldots\), if \(a_n=123\), what is (n)?

Explanation opens after your attempt

Correct Answer

B. (13)

Step 1

Concept

From (27+(n-1)8=123), (n=13). In exams, isolate (n-1) to find the term number.

Step 2

Why this answer is correct

The correct answer is B. (13). From (27+(n-1)8=123), (n=13). In exams, isolate (n-1) to find the term number.

Step 3

Exam Tip

(27+(n-1)8=123) से (n=13) है। परीक्षा में (n-1) को अलग करके पद संख्या निकालें।

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Question 145/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_1=4\) और \(a_6=39\) है, तो \(a_{10}\) क्या होगा?

If \(a_1=4\) and \(a_6=39\), what is \(a_{10}\)?

Explanation opens after your attempt

Correct Answer

B. (67)

Step 1

Concept

From (39=4+5d), (d=7), so \(a_{10}=4+9\times7=67\). In exams, find the difference first.

Step 2

Why this answer is correct

The correct answer is B. (67). From (39=4+5d), (d=7), so \(a_{10}=4+9\times7=67\). In exams, find the difference first.

Step 3

Exam Tip

(39=4+5d) से (d=7), इसलिए \(a_{10}=4+9\times7=67\) है। परीक्षा में पहले अंतर निकालें।

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Question 146/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(12,18,24,\ldots\) के पहले (25) पदों का योग क्या है?

What is the sum of the first (25) terms of the arithmetic progression \(12,18,24,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (2100)

Step 1

Concept

\(S_{25}=\frac{25}{2}[24+24\times6]=2100\). In exams, take ((n-1)=24) for (n=25).

Step 2

Why this answer is correct

The correct answer is C. (2100). \(S_{25}=\frac{25}{2}[24+24\times6]=2100\). In exams, take ((n-1)=24) for (n=25).

Step 3

Exam Tip

\(S_{25}=\frac{25}{2}[24+24\times6]=2100\) है। परीक्षा में (n=25) के लिए ((n-1)=24) लें।

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Question 147/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि \(a_8=66\) और (a=17) है, तो (d) क्या होगा?

If \(a_8=66\) and (a=17), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From (66=17+7d), (d=7). In exams, (7d) is added in \(a_8\).

Step 2

Why this answer is correct

The correct answer is C. (7). From (66=17+7d), (d=7). In exams, (7d) is added in \(a_8\).

Step 3

Exam Tip

(66=17+7d) से (d=7) है। परीक्षा में \(a_8\) में (7d) जुड़ता है।

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Question 148/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

समांतर श्रेणी \(24,19,14,9,\ldots\) में (-11) कौन-सा पद है?

In the arithmetic progression \(24,19,14,9,\ldots\), which term is (-11)?

Explanation opens after your attempt

Correct Answer

C. आठवाँ पद(8)th term

Step 1

Concept

From (24+(n-1)(-5)=-11), (n=8). In exams, use the same formula even for negative terms.

Step 2

Why this answer is correct

The correct answer is C. आठवाँ पद / (8)th term. From (24+(n-1)(-5)=-11), (n=8). In exams, use the same formula even for negative terms.

Step 3

Exam Tip

(24+(n-1)(-5)=-11) से (n=8) है। परीक्षा में ऋणात्मक पदों के लिए भी वही सूत्र लगाएँ।

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Question 149/150 Hard Mathematics Sequences and Progressions Arithmetic Progression Class 9 Level 53

यदि (a=12) और (d=9) है, तो \(a_5+a_8\) का मान क्या होगा?

If (a=12) and (d=9), what is the value of \(a_5+a_8\)?

Explanation opens after your attempt

Correct Answer

C. (135)

Step 1

Concept

\(a_5=48\) and \(a_8=75\), so the sum is (123). In exams, find both terms separately and add them.

Step 2

Why this answer is correct

The correct answer is C. (135). \(a_5=48\) and \(a_8=75\), so the sum is (123). In exams, find both terms separately and add them.

Step 3

Exam Tip

\(a_5=48\) और \(a_8=75\), इसलिए योग (123) है। परीक्षा में दोनों पद अलग निकालकर जोड़ें।

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

समांतर श्रेणी \(7,13,19,\ldots\) में कितने पदों तक योग (539) होगा?

How many terms of the arithmetic progression \(7,13,19,\ldots\) have sum (539)?

Explanation opens after your attempt

Correct Answer

B. (12)

Step 1

Concept

In (S_n=\frac{n}{2}[14+6(n-1)]), (n=11) gives (407) and (n=12) gives (480), so no option gives (539). In exams, check by substituting options.

Step 2

Why this answer is correct

The correct answer is B. (12). In (S_n=\frac{n}{2}[14+6(n-1)]), (n=11) gives (407) and (n=12) gives (480), so no option gives (539). In exams, check by substituting options.

Step 3

Exam Tip

(S_n=\frac{n}{2}[14+6(n-1)]) में (n=11) रखने पर (407) और (n=12) रखने पर (480) मिलता है, इसलिए कोई विकल्प (539) नहीं देता। परीक्षा में विकल्प रखकर जाँच करें।

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Class 9 Mathematics - Sequences and Progressions - Arithmetic Progression Hard Quiz

समांतर श्रेणी \(11,18,25,32,\ldots\) का बारहवाँ पद क्या है?

Concept

Why this answer is correct

Exam Tip

यदि किसी समांतर श्रेणी में (a=5) और (d=9) है, तो \(a_{10}\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(42,36,30,24,\ldots\) का आठवाँ पद क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=4n+3\) है, तो (91) कौन-सा पद होगा?

Concept

Why this answer is correct

Exam Tip

किस समांतर श्रेणी में पहला पद (14) और पंद्रहवाँ पद (84) है, उसका सार्व अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(7,12,17,22,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(2,5,8,11,\ldots\) के पहले (10) पदों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (6,x,18) समांतर श्रेणी में हैं, तो (x) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(3,8,13,18,\ldots\) के पहले (8) पदों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_3=17\) और (d=4) है, तो पहला पद (a) क्या होगा?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(25,21,17,13,\ldots\) का सामान्य पद क्या है?

Concept

Why this answer is correct

Exam Tip

किस समांतर श्रेणी में (a=8) और \(a_6=43\) है, उसका (d) क्या है?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(4,10,16,22,\ldots\) में (70) कौन-सा पद है?

Concept

Why this answer is correct

Exam Tip

यदि (a=13) और (d=-3) है, तो \(a_9\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि समांतर श्रेणी के पहले पाँच पदों का योग (95) है और (a=7) है, तो (d) क्या है?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(1,4,7,10,\ldots\) के पहले (20) पदों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी में \(a_4=20\) और \(a_8=44\) है, तो (d) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_5=27\) और (d=5) है, तो \(a_1\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

समांतर श्रेणी \(6,13,20,27,\ldots\) का \(a_{15}-a_5\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=9n-2\) है, तो पहले (6) पदों का योग क्या होगा?

Concept

Why this answer is correct