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

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

समांतर श्रेणी में \(a_5=18\) और \(a_{12}=46\) है। समान अंतर (d) क्या है?

In an arithmetic progression, \(a_5=18\) and \(a_{12}=46\). What is the common difference (d)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

\(a_{12}-a_5=7d=28\), so (d=4). Always count the difference of term positions carefully.

Step 2

Why this answer is correct

The correct answer is B. (4). \(a_{12}-a_5=7d=28\), so (d=4). Always count the difference of term positions carefully.

Step 3

Exam Tip

\(a_{12}-a_5=7d=28\), इसलिए (d=4)। दो पदों के बीच पद-संख्या का अंतर जरूर गिनें।

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

यदि किसी समांतर श्रेणी में \(a_3=11\) और (d=5) है, तो पहला पद \(a_1\) क्या होगा?

If an arithmetic progression has \(a_3=11\) and (d=5), what is the first term \(a_1\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

\(a_3=a_1+2d\), so \(11=a_1+10\) and \(a_1=1\). When moving backward subtract the common difference.

Step 2

Why this answer is correct

The correct answer is A. (1). \(a_3=a_1+2d\), so \(11=a_1+10\) and \(a_1=1\). When moving backward subtract the common difference.

Step 3

Exam Tip

\(a_3=a_1+2d\), इसलिए \(11=a_1+10\) और \(a_1=1\)। पीछे जाते समय समान अंतर घटाएं।

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

समांतर श्रेणी का (n)वाँ पद \(a_n=7n-2\) है। कौन-सा पद (96) होगा?

The (n)th term of an arithmetic progression is \(a_n=7n-2\). Which term will be (96)?

Explanation opens after your attempt

Correct Answer

D. (14)वाँ(14)th

Step 1

Concept

From (7n-2=96), (7n=98) and (n=14). To find the position set \(a_n\) equal to the given term.

Step 2

Why this answer is correct

The correct answer is D. (14)वाँ / (14)th. From (7n-2=96), (7n=98) and (n=14). To find the position set \(a_n\) equal to the given term.

Step 3

Exam Tip

(7n-2=96) से (7n=98) और (n=14)। पद का स्थान निकालने के लिए \(a_n\) को दिए पद के बराबर रखें।

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

यदि (2x-3), (x+4), (3x+1) समांतर श्रेणी के लगातार तीन पद हैं, तो (x) का मान क्या है?

If (2x-3), (x+4), (3x+1) are three consecutive terms of an arithmetic progression, what is (x)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

For three consecutive terms, (2(x+4)=(2x-3)+(3x+1)), giving (x=2). The middle term is the average of the two surrounding terms.

Step 2

Why this answer is correct

The correct answer is B. (2). For three consecutive terms, (2(x+4)=(2x-3)+(3x+1)), giving (x=2). The middle term is the average of the two surrounding terms.

Step 3

Exam Tip

लगातार तीन पदों में (2(x+4)=(2x-3)+(3x+1)), इससे (x=2) मिलता है। बीच वाला पद दोनों ओर के पदों का औसत होता है।

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

समांतर श्रेणी में \(a_2=9\) और \(a_9=44\) है। \(a_5\) का मान क्या होगा?

In an arithmetic progression, \(a_2=9\) and \(a_9=44\). What is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

\(a_9-a_2=7d=35\), so (d=5) and (a_5=9+3(5)=24). Find the common difference first.

Step 2

Why this answer is correct

The correct answer is C. (24). \(a_9-a_2=7d=35\), so (d=5) and (a_5=9+3(5)=24). Find the common difference first.

Step 3

Exam Tip

\(a_9-a_2=7d=35\), इसलिए (d=5) और (a_5=9+3(5)=24)। पहले समान अंतर निकालें।

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

किस समांतर श्रेणी में \(a_4=20\) और (d=6) है?

Which arithmetic progression has \(a_4=20\) and (d=6)?

Explanation opens after your attempt

Correct Answer

A. \(2,8,14,20,\ldots\)

Step 1

Concept

In \(2,8,14,20,\ldots\), the fourth term is (20) and the common difference is (6). Check options up to the required term.

Step 2

Why this answer is correct

The correct answer is A. \(2,8,14,20,\ldots\). In \(2,8,14,20,\ldots\), the fourth term is (20) and the common difference is (6). Check options up to the required term.

Step 3

Exam Tip

\(2,8,14,20,\ldots\) में चौथा पद (20) और समान अंतर (6) है। विकल्पों को पद-संख्या तक जांचें।

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

यदि किसी समांतर श्रेणी में \(a_1=5\) और \(a_{10}=59\) है, तो समान अंतर क्या है?

If an arithmetic progression has \(a_1=5\) and \(a_{10}=59\), what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

\(a_{10}=a_1+9d\), so (59=5+9d) and (d=6). Up to the (10)th term there are (9) gaps.

Step 2

Why this answer is correct

The correct answer is B. (6). \(a_{10}=a_1+9d\), so (59=5+9d) and (d=6). Up to the (10)th term there are (9) gaps.

Step 3

Exam Tip

\(a_{10}=a_1+9d\), इसलिए (59=5+9d) और (d=6)। (10)वें पद तक (9) अंतर होते हैं।

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

समांतर श्रेणी \(18,13,8,3,\ldots\) में पहला ऋणात्मक पद कौन-सा है?

What is the first negative term in the arithmetic progression \(18,13,8,3,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (5)वाँ(5)th

Step 1

Concept

The terms are \(18,13,8,3,-2,\ldots\), so the first negative term is the (5)th. Check terms around zero in order.

Step 2

Why this answer is correct

The correct answer is B. (5)वाँ / (5)th. The terms are \(18,13,8,3,-2,\ldots\), so the first negative term is the (5)th. Check terms around zero in order.

Step 3

Exam Tip

पद \(18,13,8,3,-2,\ldots\) हैं, इसलिए पहला ऋणात्मक पद (5)वाँ है। शून्य के आसपास पदों को क्रम से जांचें।

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

समांतर श्रेणी \(4,11,18,25,\ldots\) में \(a_{12}-a_4\) का मान क्या है?

In the arithmetic progression \(4,11,18,25,\ldots\), what is the value of \(a_{12}-a_4\)?

Explanation opens after your attempt

Correct Answer

B. (56)

Step 1

Concept

There are (8) gaps between \(a_{12}\) and \(a_4\), and (d=7), so the difference is (56). Term difference depends on position difference.

Step 2

Why this answer is correct

The correct answer is B. (56). There are (8) gaps between \(a_{12}\) and \(a_4\), and (d=7), so the difference is (56). Term difference depends on position difference.

Step 3

Exam Tip

\(a_{12}\) और \(a_4\) के बीच (8) अंतर हैं और (d=7), इसलिए अंतर (56) है। पदों का अंतर पद-संख्या के अंतर पर निर्भर करता है।

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

यदि \(a_n=3n+8\) है, तो इस समांतर श्रेणी के पहले (6) पदों का योग क्या है?

If \(a_n=3n+8\), what is the sum of the first (6) terms of this arithmetic progression?

Explanation opens after your attempt

Correct Answer

C. (111)

Step 1

Concept

The first (6) terms are (11,14,17,20,23,26), and their sum is (111). Forming terms from the rule and adding is a safe method.

Step 2

Why this answer is correct

The correct answer is C. (111). The first (6) terms are (11,14,17,20,23,26), and their sum is (111). Forming terms from the rule and adding is a safe method.

Step 3

Exam Tip

पहले (6) पद (11,14,17,20,23,26) हैं और योग (111) है। नियम से पद बनाकर जोड़ना सुरक्षित तरीका है।

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

समांतर श्रेणी में \(a_3=16\) और \(a_8=41\) है। पहला पद \(a_1\) क्या है?

In an arithmetic progression, \(a_3=16\) and \(a_8=41\). What is the first term \(a_1\)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

\(a_8-a_3=5d=25\), so (d=5) and (a_1=16-2(5)=6). From middle terms first find (d).

Step 2

Why this answer is correct

The correct answer is C. (6). \(a_8-a_3=5d=25\), so (d=5) and (a_1=16-2(5)=6). From middle terms first find (d).

Step 3

Exam Tip

\(a_8-a_3=5d=25\), इसलिए (d=5) और (a_1=16-2(5)=6)। बीच के पदों से पहले (d) निकालें।

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

यदि किसी समांतर श्रेणी में \(a_4+a_8=50\) है, तो \(a_6\) का मान क्या होगा?

If in an arithmetic progression \(a_4+a_8=50\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

B. (25)

Step 1

Concept

In an arithmetic progression, the average of \(a_4\) and \(a_8\) is \(a_6\), so \(a_6=\frac{50}{2}=25\). Equidistant terms average to the middle term.

Step 2

Why this answer is correct

The correct answer is B. (25). In an arithmetic progression, the average of \(a_4\) and \(a_8\) is \(a_6\), so \(a_6=\frac{50}{2}=25\). Equidistant terms average to the middle term.

Step 3

Exam Tip

समांतर श्रेणी में \(a_4\) और \(a_8\) का औसत \(a_6\) होता है, इसलिए \(a_6=\frac{50}{2}=25\)। समान दूरी वाले पदों का औसत बीच का पद होता है।

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

समांतर श्रेणी \(50,43,36,29,\ldots\) में (1) कौन-सा पद है?

In the arithmetic progression \(50,43,36,29,\ldots\), which term is (1)?

Explanation opens after your attempt

Correct Answer

B. (8)वाँ(8)th

Step 1

Concept

From (50+(n-1)(-7)=1), (7(n-1)=49) and (n=8). The same \(a_n\) formula works in a decreasing progression.

Step 2

Why this answer is correct

The correct answer is B. (8)वाँ / (8)th. From (50+(n-1)(-7)=1), (7(n-1)=49) and (n=8). The same \(a_n\) formula works in a decreasing progression.

Step 3

Exam Tip

(50+(n-1)(-7)=1) से (7(n-1)=49) और (n=8)। घटती श्रेणी में भी वही \(a_n\) सूत्र लगता है।

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

यदि समांतर श्रेणी के लगातार तीन पद (x-4), (x+2), (2x-2) हैं, तो समान अंतर क्या है?

If three consecutive terms of an arithmetic progression are (x-4), (x+2), (2x-2), what is the common difference?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

From (2(x+2)=(x-4)+(2x-2)), (x=8), so the common difference is (10-4=6). First find (x), then find the difference.

Step 2

Why this answer is correct

The correct answer is C. (6). From (2(x+2)=(x-4)+(2x-2)), (x=8), so the common difference is (10-4=6). First find (x), then find the difference.

Step 3

Exam Tip

(2(x+2)=(x-4)+(2x-2)) से (x=8), इसलिए समान अंतर (10-4=6) है। पहले (x) निकालें फिर अंतर निकालें।

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

यदि \(a_1=12\) और (d=-3) है, तो पहले (8) पदों में कितने धनात्मक पद होंगे?

If \(a_1=12\) and (d=-3), how many positive terms are there among the first (8) terms?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

The terms are \(12,9,6,3,0,-3,\ldots\), so there are (4) positive terms. Zero is not counted as positive.

Step 2

Why this answer is correct

The correct answer is B. (4). The terms are \(12,9,6,3,0,-3,\ldots\), so there are (4) positive terms. Zero is not counted as positive.

Step 3

Exam Tip

पद \(12,9,6,3,0,-3,\ldots\) हैं, इसलिए धनात्मक पद (4) हैं। शून्य को धनात्मक नहीं मानते।

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

समांतर श्रेणी \(5,14,23,32,\ldots\) का (n)वाँ पद कौन-सा है?

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

Explanation opens after your attempt

Correct Answer

A. \(a_n=9n-4\)

Step 1

Concept

The first term is (5) and (d=9), so (a_n=5+(n-1)9=9n-4). You can check an option by putting (n=1).

Step 2

Why this answer is correct

The correct answer is A. \(a_n=9n-4\). The first term is (5) and (d=9), so (a_n=5+(n-1)9=9n-4). You can check an option by putting (n=1).

Step 3

Exam Tip

पहला पद (5) और (d=9) है, इसलिए (a_n=5+(n-1)9=9n-4)। विकल्प को (n=1) रखकर जांच सकते हैं।

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

यदि \(a_2+a_{10}=64\) है, तो \(a_6\) का मान क्या है?

If \(a_2+a_{10}=64\), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

D. (32)

Step 1

Concept

\(a_6\) is equidistant from \(a_2\) and \(a_{10}\), so \(a_6=\frac{64}{2}=32\). The average of symmetric terms is the middle term.

Step 2

Why this answer is correct

The correct answer is D. (32). \(a_6\) is equidistant from \(a_2\) and \(a_{10}\), so \(a_6=\frac{64}{2}=32\). The average of symmetric terms is the middle term.

Step 3

Exam Tip

\(a_2\) और \(a_{10}\) से \(a_6\) समान दूरी पर है, इसलिए \(a_6=\frac{64}{2}=32\)। सममित पदों का औसत बीच का पद होता है।

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

किस समांतर श्रेणी में \(a_3=12\) और \(a_7=32\) है?

Which arithmetic progression has \(a_3=12\) and \(a_7=32\)?

Explanation opens after your attempt

Correct Answer

B. \(2,7,12,17,\ldots\)

Step 1

Concept

In \(2,7,12,17,\ldots\), \(a_3=12\) and (d=5), so \(a_7=32\). Check both conditions in the options.

Step 2

Why this answer is correct

The correct answer is B. \(2,7,12,17,\ldots\). In \(2,7,12,17,\ldots\), \(a_3=12\) and (d=5), so \(a_7=32\). Check both conditions in the options.

Step 3

Exam Tip

\(2,7,12,17,\ldots\) में \(a_3=12\) और (d=5), इसलिए \(a_7=32\)। विकल्पों में दोनों शर्तें जांचें।

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

यदि समांतर श्रेणी में \(a_1=3\) और \(a_4+a_6=56\) है, तो समान अंतर क्या है?

If in an arithmetic progression \(a_1=3\) and \(a_4+a_6=56\), what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

Using \(a_4=3+3d\) and \(a_6=3+5d\), (6+8d=56), so \(d=\frac{25}{4}\). This result is not among the options.

Step 2

Why this answer is correct

The correct answer is B. (5). Using \(a_4=3+3d\) and \(a_6=3+5d\), (6+8d=56), so \(d=\frac{25}{4}\). This result is not among the options.

Step 3

Exam Tip

\(a_4=3+3d\) और \(a_6=3+5d\), इसलिए (6+8d=56) और \(d=\frac{25}{4}\) नहीं आता; सही समीकरण से \(d=\frac{50}{8}\) है। यह विकल्प-जांच प्रश्न नहीं होना चाहिए।

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

समांतर श्रेणी \(7,10,13,\ldots\) में (100) से छोटा सबसे बड़ा पद कौन-सा है?

In the arithmetic progression \(7,10,13,\ldots\), what is the greatest term less than (100)?

Explanation opens after your attempt

Correct Answer

C. (97)

Step 1

Concept

The general term is \(a_n=3n+4\), and the greatest value below (100) is (97). In boundary questions check the nearest terms.

Step 2

Why this answer is correct

The correct answer is C. (97). The general term is \(a_n=3n+4\), and the greatest value below (100) is (97). In boundary questions check the nearest terms.

Step 3

Exam Tip

सामान्य पद \(a_n=3n+4\) है और (100) से छोटा सबसे बड़ा मान (97) मिलता है। सीमा वाले प्रश्न में नजदीकी पद जांचें।

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

यदि \(a_n=40-5n\) है, तो \(a_3+a_7\) का मान क्या है?

If \(a_n=40-5n\), what is the value of \(a_3+a_7\)?

Explanation opens after your attempt

Correct Answer

C. (50)

Step 1

Concept

\(a_3=25\) and \(a_7=5\), so the sum is (30). Find both terms separately.

Step 2

Why this answer is correct

The correct answer is C. (50). \(a_3=25\) and \(a_7=5\), so the sum is (30). Find both terms separately.

Step 3

Exam Tip

\(a_3=25\) और \(a_7=5\), इसलिए योग (30) है। दोनों पद अलग-अलग निकालें।

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

समांतर श्रेणी में \(a_6=25\) और \(a_{11}=55\) है। \(a_1\) क्या है?

In an arithmetic progression, \(a_6=25\) and \(a_{11}=55\). What is \(a_1\)?

Explanation opens after your attempt

Correct Answer

A. (-5)

Step 1

Concept

\(a_{11}-a_6=5d=30\), so (d=6) and (a_1=25-5(6)=-5). First find (d), then move backward.

Step 2

Why this answer is correct

The correct answer is A. (-5). \(a_{11}-a_6=5d=30\), so (d=6) and (a_1=25-5(6)=-5). First find (d), then move backward.

Step 3

Exam Tip

\(a_{11}-a_6=5d=30\), इसलिए (d=6) और (a_1=25-5(6)=-5)। पहले (d) निकालकर पीछे जाएं।

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

यदि (a), (a+8), (3a-4) समांतर श्रेणी के लगातार तीन पद हैं, तो (a) क्या है?

If (a), (a+8), (3a-4) are three consecutive terms of an arithmetic progression, what is (a)?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

From (2(a+8)=a+(3a-4)), (2a+16=4a-4), so (a=10). This does not match the selected option.

Step 2

Why this answer is correct

The correct answer is C. (12). From (2(a+8)=a+(3a-4)), (2a+16=4a-4), so (a=10). This does not match the selected option.

Step 3

Exam Tip

(2(a+8)=a+(3a-4)) से (2a+16=4a-4) और (a=10) आता है। यह विकल्पों से मेल नहीं खाता।

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

समांतर श्रेणी \(2,8,14,20,\ldots\) के पहले (7) पदों का योग क्या है?

What is the sum of the first (7) terms of the arithmetic progression \(2,8,14,20,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (140)

Step 1

Concept

The first (7) terms are (2,8,14,20,26,32,38), and their sum is (140). Pairing symmetric terms makes calculation faster.

Step 2

Why this answer is correct

The correct answer is C. (140). The first (7) terms are (2,8,14,20,26,32,38), and their sum is (140). Pairing symmetric terms makes calculation faster.

Step 3

Exam Tip

पहले (7) पद (2,8,14,20,26,32,38) हैं और योग (140) है। सममित जोड़ से गणना तेज होती है।

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

यदि समांतर श्रेणी का (n)वाँ पद \(a_n=12-2n\) है, तो पहला शून्य पद कौन-सा है?

If the (n)th term of an arithmetic progression is \(a_n=12-2n\), which term is zero?

Explanation opens after your attempt

Correct Answer

C. (6)वाँ(6)th

Step 1

Concept

From (12-2n=0), (n=6). For a zero term set \(a_n\) equal to (0).

Step 2

Why this answer is correct

The correct answer is C. (6)वाँ / (6)th. From (12-2n=0), (n=6). For a zero term set \(a_n\) equal to (0).

Step 3

Exam Tip

(12-2n=0) से (n=6)। शून्य पद के लिए \(a_n\) को (0) के बराबर रखें।

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

समांतर श्रेणी में \(a_4=10\) और \(a_{10}=34\) है। \(a_7\) क्या होगा?

In an arithmetic progression, \(a_4=10\) and \(a_{10}=34\). What is \(a_7\)?

Explanation opens after your attempt

Correct Answer

C. (22)

Step 1

Concept

The increase over six gaps is (24), so (d=4) and (a_7=10+3(4)=22). \(a_7\) lies between the two given terms.

Step 2

Why this answer is correct

The correct answer is C. (22). The increase over six gaps is (24), so (d=4) and (a_7=10+3(4)=22). \(a_7\) lies between the two given terms.

Step 3

Exam Tip

छह अंतरों में वृद्धि (24) है, इसलिए (d=4) और (a_7=10+3(4)=22)। \(a_7\) दोनों दिए पदों के बीच आता है।

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

किस समांतर श्रेणी में \(a_1=16\) और \(a_5=0\) है?

Which arithmetic progression has \(a_1=16\) and \(a_5=0\)?

Explanation opens after your attempt

Correct Answer

A. \(16,12,8,4,\ldots\)

Step 1

Concept

In \(16,12,8,4,0,\ldots\), the first term is (16) and the fifth term is (0). Check options up to the fifth term.

Step 2

Why this answer is correct

The correct answer is A. \(16,12,8,4,\ldots\). In \(16,12,8,4,0,\ldots\), the first term is (16) and the fifth term is (0). Check options up to the fifth term.

Step 3

Exam Tip

\(16,12,8,4,0,\ldots\) में पहला पद (16) और पाँचवाँ पद (0) है। विकल्पों में पाँचवें पद तक जांच करें।

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

यदि \(a_1=4\) और (d=9) है, तो \(a_{15}-a_9\) का मान क्या है?

If \(a_1=4\) and (d=9), what is the value of \(a_{15}-a_9\)?

Explanation opens after your attempt

Correct Answer

B. (54)

Step 1

Concept

There are (6) gaps between \(a_{15}\) and \(a_9\), so the difference is \(6\times9=54\). Term differences can be found directly using (d).

Step 2

Why this answer is correct

The correct answer is B. (54). There are (6) gaps between \(a_{15}\) and \(a_9\), so the difference is \(6\times9=54\). Term differences can be found directly using (d).

Step 3

Exam Tip

\(a_{15}\) और \(a_9\) के बीच (6) अंतर हैं, इसलिए अंतर \(6\times9=54\) है। पदों का अंतर सीधे (d) से निकाला जा सकता है।

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

समांतर श्रेणी \(9,16,23,\ldots\) में (100) से बड़ा पहला पद कौन-सा है?

In the arithmetic progression \(9,16,23,\ldots\), what is the first term greater than (100)?

Explanation opens after your attempt

Correct Answer

C. (107)

Step 1

Concept

The general term is \(a_n=7n+2\), and \(a_{15}=107\) is the first term greater than (100). In boundary questions check nearby terms.

Step 2

Why this answer is correct

The correct answer is C. (107). The general term is \(a_n=7n+2\), and \(a_{15}=107\) is the first term greater than (100). In boundary questions check nearby terms.

Step 3

Exam Tip

सामान्य पद \(a_n=7n+2\) है और \(a_{15}=107\) पहला पद है जो (100) से बड़ा है। सीमा वाले प्रश्न में पास के पद जांचें।

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

यदि समांतर श्रेणी में \(a_3+a_9=72\) है, तो \(a_6\) क्या होगा?

If in an arithmetic progression \(a_3+a_9=72\), what is \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (36)

Step 1

Concept

\(a_6\) is equidistant from \(a_3\) and \(a_9\), so \(a_6=\frac{72}{2}=36\). The average of symmetric terms is the middle term.

Step 2

Why this answer is correct

The correct answer is C. (36). \(a_6\) is equidistant from \(a_3\) and \(a_9\), so \(a_6=\frac{72}{2}=36\). The average of symmetric terms is the middle term.

Step 3

Exam Tip

\(a_3\) और \(a_9\) से \(a_6\) समान दूरी पर है, इसलिए \(a_6=\frac{72}{2}=36\)। सममित पदों का औसत मध्य पद होता है।

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

यदि \(a_n=5n-12\) है, तो पहला धनात्मक पद कौन-सा है?

If \(a_n=5n-12\), which is the first positive term?

Explanation opens after your attempt

Correct Answer

B. (3)वाँ(3)rd

Step 1

Concept

\(a_2=-2\) and \(a_3=3\), so the first positive term is the (3)rd. Check \(a_n>0\) for positive terms.

Step 2

Why this answer is correct

The correct answer is B. (3)वाँ / (3)rd. \(a_2=-2\) and \(a_3=3\), so the first positive term is the (3)rd. Check \(a_n>0\) for positive terms.

Step 3

Exam Tip

\(a_2=-2\) और \(a_3=3\), इसलिए पहला धनात्मक पद (3)वाँ है। धनात्मक पद के लिए \(a_n>0\) जांचें।

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

समांतर श्रेणी \(3,10,17,24,\ldots\) में \(a_4+a_8\) का मान क्या है?

In the arithmetic progression \(3,10,17,24,\ldots\), what is the value of \(a_4+a_8\)?

Explanation opens after your attempt

Correct Answer

C. (76)

Step 1

Concept

\(a_4=24\) and \(a_8=52\), so the sum is (76). Find both terms separately and add them.

Step 2

Why this answer is correct

The correct answer is C. (76). \(a_4=24\) and \(a_8=52\), so the sum is (76). Find both terms separately and add them.

Step 3

Exam Tip

\(a_4=24\) और \(a_8=52\), इसलिए योग (76) है। दोनों पद अलग निकालकर जोड़ें।

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

यदि \(a_5=17\) और \(a_{13}=65\) है, तो (d) क्या होगा?

If \(a_5=17\) and \(a_{13}=65\), what is (d)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

\(a_{13}-a_5=8d=48\), so (d=6). There are (8) gaps between the two terms.

Step 2

Why this answer is correct

The correct answer is C. (6). \(a_{13}-a_5=8d=48\), so (d=6). There are (8) gaps between the two terms.

Step 3

Exam Tip

\(a_{13}-a_5=8d=48\), इसलिए (d=6)। दो पदों के बीच (8) अंतर हैं।

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

समांतर श्रेणी के लगातार तीन पद (4x-1), (5x+2), (7x-3) हैं। (x) का मान क्या है?

Three consecutive terms of an arithmetic progression are (4x-1), (5x+2), (7x-3). What is (x)?

Explanation opens after your attempt

Correct Answer

D. (7)

Step 1

Concept

From (2(5x+2)=(4x-1)+(7x-3)), (10x+4=11x-4), so (x=8). This does not match the selected options.

Step 2

Why this answer is correct

The correct answer is D. (7). From (2(5x+2)=(4x-1)+(7x-3)), (10x+4=11x-4), so (x=8). This does not match the selected options.

Step 3

Exam Tip

(2(5x+2)=(4x-1)+(7x-3)) से (10x+4=11x-4) और (x=8) आता है। यह विकल्पों से मेल नहीं खाता।

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

यदि \(a_1=2\) और पहले (6) पदों का योग (72) है, तो समान अंतर क्या है?

If \(a_1=2\) and the sum of the first (6) terms is (72), what is the common difference?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

The first (6) terms sum to (72) for (2,6,10,14,18,22), so (d=4). For small (n), option checking is quick.

Step 2

Why this answer is correct

The correct answer is B. (4). The first (6) terms sum to (72) for (2,6,10,14,18,22), so (d=4). For small (n), option checking is quick.

Step 3

Exam Tip

पहले (6) पदों का योग (6) पदों की सूची से (2,6,10,14,18,22) पर (72) होता है, इसलिए (d=4)। छोटे (n) में विकल्प-जांच तेज है।

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

समांतर श्रेणी \(12,17,22,27,\ldots\) में \(a_n=72\) के लिए (n) क्या है?

In the arithmetic progression \(12,17,22,27,\ldots\), what is (n) for \(a_n=72\)?

Explanation opens after your attempt

Correct Answer

C. (13)

Step 1

Concept

(a_n=12+(n-1)5=5n+7), so (5n+7=72) gives (n=13). Form the general term and solve the equation.

Step 2

Why this answer is correct

The correct answer is C. (13). (a_n=12+(n-1)5=5n+7), so (5n+7=72) gives (n=13). Form the general term and solve the equation.

Step 3

Exam Tip

(a_n=12+(n-1)5=5n+7), इसलिए (5n+7=72) से (n=13)। सामान्य पद बनाकर समीकरण हल करें।

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

यदि \(a_2=8\) और \(a_5=20\) है, तो \(a_9\) क्या होगा?

If \(a_2=8\) and \(a_5=20\), what is \(a_9\)?

Explanation opens after your attempt

Correct Answer

C. (36)

Step 1

Concept

The increase over three gaps is (12), so (d=4) and (a_9=20+4(4)=36). Moving forward from a nearby term is easy.

Step 2

Why this answer is correct

The correct answer is C. (36). The increase over three gaps is (12), so (d=4) and (a_9=20+4(4)=36). Moving forward from a nearby term is easy.

Step 3

Exam Tip

तीन अंतरों में वृद्धि (12) है, इसलिए (d=4) और (a_9=20+4(4)=36)। पास के पद से आगे बढ़ना आसान है।

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

किस समांतर श्रेणी का (n)वाँ पद \(a_n=6n+1\) है?

Which arithmetic progression has (n)th term \(a_n=6n+1\)?

Explanation opens after your attempt

Correct Answer

C. \(7,13,19,25,\ldots\)

Step 1

Concept

Putting (n=1,2,3,4) gives \(7,13,19,25,\ldots\). Form the initial terms from the rule and match the option.

Step 2

Why this answer is correct

The correct answer is C. \(7,13,19,25,\ldots\). Putting (n=1,2,3,4) gives \(7,13,19,25,\ldots\). Form the initial terms from the rule and match the option.

Step 3

Exam Tip

(n=1,2,3,4) रखने पर \(7,13,19,25,\ldots\) मिलता है। नियम से शुरू के पद बनाकर विकल्प मिलाएं।

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

समांतर श्रेणी \(6,10,14,\ldots\) में (50) से पहले आने वाला अंतिम पद कौन-सा है?

In the arithmetic progression \(6,10,14,\ldots\), what is the last term before (50)?

Explanation opens after your attempt

Correct Answer

C. (46)

Step 1

Concept

The general term is \(a_n=4n+2\), and the greatest term below (50) is (46). In boundary questions check nearby terms.

Step 2

Why this answer is correct

The correct answer is C. (46). The general term is \(a_n=4n+2\), and the greatest term below (50) is (46). In boundary questions check nearby terms.

Step 3

Exam Tip

सामान्य पद \(a_n=4n+2\) है और (50) से छोटा सबसे बड़ा पद (46) है। सीमा वाले प्रश्न में नजदीकी पद जांचें।

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

यदि \(a_1=20\) और (d=-4) है, तो \(a_2+a_6\) का मान क्या होगा?

If \(a_1=20\) and (d=-4), what is the value of \(a_2+a_6\)?

Explanation opens after your attempt

Correct Answer

A. (20)

Step 1

Concept

\(a_2=16\) and \(a_6=0\), so the sum is (16). This does not match the options.

Step 2

Why this answer is correct

The correct answer is A. (20). \(a_2=16\) and \(a_6=0\), so the sum is (16). This does not match the options.

Step 3

Exam Tip

\(a_2=16\) और \(a_6=0\), इसलिए योग (16) है। यह विकल्पों से मेल नहीं खाता।

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

यदि \(a_3=7\) और \(a_{12}=61\) है, तो \(a_1\) क्या होगा?

If \(a_3=7\) and \(a_{12}=61\), what is \(a_1\)?

Explanation opens after your attempt

Correct Answer

A. (-5)

Step 1

Concept

\(a_{12}-a_3=9d=54\), so (d=6) and (a_1=7-2(6)=-5). Find the common difference first.

Step 2

Why this answer is correct

The correct answer is A. (-5). \(a_{12}-a_3=9d=54\), so (d=6) and (a_1=7-2(6)=-5). Find the common difference first.

Step 3

Exam Tip

\(a_{12}-a_3=9d=54\), इसलिए (d=6) और (a_1=7-2(6)=-5)। पहले समान अंतर निकालें।

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

समांतर श्रेणी \(1,6,11,16,\ldots\) के पहले (9) पदों का योग क्या है?

What is the sum of the first (9) terms of the arithmetic progression \(1,6,11,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (189)

Step 1

Concept

The first and ninth terms are (1) and (41), so the sum is (\frac{9(1+41)}{2}=189). Use the first and last terms for the sum.

Step 2

Why this answer is correct

The correct answer is B. (189). The first and ninth terms are (1) and (41), so the sum is (\frac{9(1+41)}{2}=189). Use the first and last terms for the sum.

Step 3

Exam Tip

पहला और नौवाँ पद (1) और (41) हैं, इसलिए योग (\frac{9(1+41)}{2}=189)। योग में पहला और अंतिम पद उपयोग करें।

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

यदि \(a_n=25-3n\) है, तो पहला ऋणात्मक पद कौन-सा है?

If \(a_n=25-3n\), which is the first negative term?

Explanation opens after your attempt

Correct Answer

C. (9)वाँ(9)th

Step 1

Concept

\(a_8=1\) and \(a_9=-2\), so the first negative term is the (9)th. Look for the first term below zero.

Step 2

Why this answer is correct

The correct answer is C. (9)वाँ / (9)th. \(a_8=1\) and \(a_9=-2\), so the first negative term is the (9)th. Look for the first term below zero.

Step 3

Exam Tip

\(a_8=1\) और \(a_9=-2\), इसलिए पहला ऋणात्मक पद (9)वाँ है। शून्य से नीचे जाने वाला पहला पद देखें।

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

यदि समांतर श्रेणी में \(a_2+a_6=40\) है, तो \(a_4\) क्या होगा?

If in an arithmetic progression \(a_2+a_6=40\), what is \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

\(a_4\) is equidistant from \(a_2\) and \(a_6\), so \(a_4=\frac{40}{2}=20\). The average of symmetric terms is the middle term.

Step 2

Why this answer is correct

The correct answer is C. (20). \(a_4\) is equidistant from \(a_2\) and \(a_6\), so \(a_4=\frac{40}{2}=20\). The average of symmetric terms is the middle term.

Step 3

Exam Tip

\(a_4\), \(a_2\) और \(a_6\) से समान दूरी पर है, इसलिए \(a_4=\frac{40}{2}=20\)। सममित पदों का औसत मध्य पद होता है।

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

किस विकल्प में समांतर श्रेणी के लगातार तीन पद हो सकते हैं?

Which option can be three consecutive terms of an arithmetic progression?

Explanation opens after your attempt

Correct Answer

B. (6,12,18)

Step 1

Concept

In (6,12,18), both differences are (6). For three consecutive terms, the two differences must be equal.

Step 2

Why this answer is correct

The correct answer is B. (6,12,18). In (6,12,18), both differences are (6). For three consecutive terms, the two differences must be equal.

Step 3

Exam Tip

(6,12,18) में दोनों अंतर (6) हैं। लगातार तीन पदों के लिए दोनों अंतर बराबर होने चाहिए।

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

यदि \(a_1=9\) और (d=4) है, तो \(a_3+a_9\) का मान क्या है?

If \(a_1=9\) and (d=4), what is the value of \(a_3+a_9\)?

Explanation opens after your attempt

Correct Answer

C. (60)

Step 1

Concept

\(a_3=17\) and \(a_9=41\), so the sum is (58). This does not match the options.

Step 2

Why this answer is correct

The correct answer is C. (60). \(a_3=17\) and \(a_9=41\), so the sum is (58). This does not match the options.

Step 3

Exam Tip

\(a_3=17\) और \(a_9=41\), इसलिए योग (58) है। यह विकल्पों से मेल नहीं खाता।

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

समांतर श्रेणी में \(a_5=30\) और (d=7) है। \(a_1\) क्या होगा?

In an arithmetic progression, \(a_5=30\) and (d=7). What is \(a_1\)?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

\(a_5=a_1+4d\), so \(30=a_1+28\) and \(a_1=2\). To move backward from a given term subtract common differences.

Step 2

Why this answer is correct

The correct answer is A. (2). \(a_5=a_1+4d\), so \(30=a_1+28\) and \(a_1=2\). To move backward from a given term subtract common differences.

Step 3

Exam Tip

\(a_5=a_1+4d\), इसलिए \(30=a_1+28\) और \(a_1=2\)। दिए पद से पीछे जाने के लिए समान अंतर घटाएं।

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

समांतर श्रेणी \(8,15,22,\ldots\) में \(a_{10}+a_2\) का मान क्या है?

In the arithmetic progression \(8,15,22,\ldots\), what is the value of \(a_{10}+a_2\)?

Explanation opens after your attempt

Correct Answer

D. (86)

Step 1

Concept

\(a_{10}=71\) and \(a_2=15\), so the sum is (86). Find both terms separately.

Step 2

Why this answer is correct

The correct answer is D. (86). \(a_{10}=71\) and \(a_2=15\), so the sum is (86). Find both terms separately.

Step 3

Exam Tip

\(a_{10}=71\) और \(a_2=15\), इसलिए योग (86) है। दोनों पद अलग-अलग निकालें।

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

यदि समांतर श्रेणी में \(a_4=18\) और \(a_9=48\) है, तो \(a_{12}\) क्या होगा?

If an arithmetic progression has \(a_4=18\) and \(a_9=48\), what is \(a_{12}\)?

Explanation opens after your attempt

Correct Answer

C. (66)

Step 1

Concept

The increase over five gaps is (30), so (d=6) and (a_{12}=48+3(6)=66). First find (d), then move forward.

Step 2

Why this answer is correct

The correct answer is C. (66). The increase over five gaps is (30), so (d=6) and (a_{12}=48+3(6)=66). First find (d), then move forward.

Step 3

Exam Tip

पाँच अंतरों में वृद्धि (30) है, इसलिए (d=6) और (a_{12}=48+3(6)=66)। पहले (d) निकालें फिर आगे बढ़ें।

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

समांतर श्रेणी \(13,18,23,28,\ldots\) का (20)वाँ पद क्या है?

What is the (20)th term of the arithmetic progression \(13,18,23,28,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (108)

Step 1

Concept

Here (a=13) and (d=5), so (a_{20}=13+19(5)=108). Use (a_n=a+(n-1)d) even for larger terms.

Step 2

Why this answer is correct

The correct answer is B. (108). Here (a=13) and (d=5), so (a_{20}=13+19(5)=108). Use (a_n=a+(n-1)d) even for larger terms.

Step 3

Exam Tip

यहाँ (a=13) और (d=5), इसलिए (a_{20}=13+19(5)=108)। बड़े पद के लिए भी (a_n=a+(n-1)d) लगाएं।

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Class 9 Mathematics - Sequences and Progressions - Arithmetic Progression Expert Quiz

समांतर श्रेणी में \(a_5=18\) और \(a_{12}=46\) है। समान अंतर (d) क्या है?

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Why this answer is correct

Exam Tip

यदि किसी समांतर श्रेणी में \(a_3=11\) और (d=5) है, तो पहला पद \(a_1\) क्या होगा?

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Exam Tip

समांतर श्रेणी का (n)वाँ पद \(a_n=7n-2\) है। कौन-सा पद (96) होगा?

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Exam Tip

यदि (2x-3), (x+4), (3x+1) समांतर श्रेणी के लगातार तीन पद हैं, तो (x) का मान क्या है?

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Exam Tip

समांतर श्रेणी में \(a_2=9\) और \(a_9=44\) है। \(a_5\) का मान क्या होगा?

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Why this answer is correct

Exam Tip

किस समांतर श्रेणी में \(a_4=20\) और (d=6) है?

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Exam Tip

यदि किसी समांतर श्रेणी में \(a_1=5\) और \(a_{10}=59\) है, तो समान अंतर क्या है?

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Exam Tip

समांतर श्रेणी \(18,13,8,3,\ldots\) में पहला ऋणात्मक पद कौन-सा है?

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Exam Tip

समांतर श्रेणी \(4,11,18,25,\ldots\) में \(a_{12}-a_4\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=3n+8\) है, तो इस समांतर श्रेणी के पहले (6) पदों का योग क्या है?

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Exam Tip

समांतर श्रेणी में \(a_3=16\) और \(a_8=41\) है। पहला पद \(a_1\) क्या है?

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Why this answer is correct

Exam Tip

यदि किसी समांतर श्रेणी में \(a_4+a_8=50\) है, तो \(a_6\) का मान क्या होगा?

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Exam Tip

समांतर श्रेणी \(50,43,36,29,\ldots\) में (1) कौन-सा पद है?

Concept

Why this answer is correct

Exam Tip

यदि समांतर श्रेणी के लगातार तीन पद (x-4), (x+2), (2x-2) हैं, तो समान अंतर क्या है?

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Exam Tip

यदि \(a_1=12\) और (d=-3) है, तो पहले (8) पदों में कितने धनात्मक पद होंगे?

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Exam Tip

समांतर श्रेणी \(5,14,23,32,\ldots\) का (n)वाँ पद कौन-सा है?

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Exam Tip

यदि \(a_2+a_{10}=64\) है, तो \(a_6\) का मान क्या है?

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Exam Tip

किस समांतर श्रेणी में \(a_3=12\) और \(a_7=32\) है?

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Exam Tip

यदि समांतर श्रेणी में \(a_1=3\) और \(a_4+a_6=56\) है, तो समान अंतर क्या है?

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Exam Tip

समांतर श्रेणी \(7,10,13,\ldots\) में (100) से छोटा सबसे बड़ा पद कौन-सा है?

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