Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Hard Quiz

Mathematics Exploring Algebraic Identities Factorisation Hard Class 9 Level 57

Level 57 • 50/50 questions • 30 seconds per question.

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Question 1/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी समान्तर श्रेणी के पहले चार पद (7,11,15,19) हैं। इसका (n)वां पद क्या होगा?

The first four terms of an arithmetic sequence are (7,11,15,19). What is its (n)th term?

Explanation opens after your attempt
Correct Answer

A. (4n+3)

Step 1

Concept

The difference is (4), so (a_n=7+(n-1)4=4n+3). In exams, write the first term and common difference first.

Step 2

Why this answer is correct

The correct answer is A. (4n+3). The difference is (4), so (a_n=7+(n-1)4=4n+3). In exams, write the first term and common difference first.

Step 3

Exam Tip

अंतर (4) है इसलिए (a_n=7+(n-1)4=4n+3)। परीक्षा में पहले पद और अंतर को अलग लिखें।

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Question 2/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी श्रेणी का (n)वां पद \(a_n=3n^2-2n+5\) है। \(a_8\) का मान ज्ञात कीजिए।

The (n)th term of a sequence is \(a_n=3n^2-2n+5\). Find \(a_8\).

Explanation opens after your attempt
Correct Answer

A. (181)

Step 1

Concept

Putting (n=8), (3(8)2-2(8)+5=181). For such questions, substitute directly.

Step 2

Why this answer is correct

The correct answer is A. (181). Putting (n=8), (3(8)2-2(8)+5=181). For such questions, substitute directly.

Step 3

Exam Tip

(n=8) रखने पर (3(8)2-2(8)+5=181)। ऐसे प्रश्नों में सीधे प्रतिस्थापन करें।

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Question 3/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(2,7,14,23,34,\ldots\) का (n)वां पद कौन सा है?

Which is the (n)th term of the sequence \(2,7,14,23,34,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(n^2+1\)

Step 1

Concept

The terms match \(n^2+1\). Always test a rule with the first few terms.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+1\). The terms match \(n^2+1\). Always test a rule with the first few terms.

Step 3

Exam Tip

दिए गए पद \(1^2+1,2^2+3\) नहीं बल्कि \(n^2+1\) से मिलते हैं। पहले कुछ पदों से नियम जांचें।

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Question 4/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=5n-3\) और \(a_k=47\), तो (k) का मान क्या है?

If \(a_n=5n-3\) and \(a_k=47\), what is the value of (k)?

Explanation opens after your attempt
Correct Answer

A. (10)

Step 1

Concept

From (5k-3=47), (5k=50), so (k=10). Form an equation when finding the term number.

Step 2

Why this answer is correct

The correct answer is A. (10). From (5k-3=47), (5k=50), so (k=10). Form an equation when finding the term number.

Step 3

Exam Tip

(5k-3=47) से (5k=50), अतः (k=10)। पद संख्या निकालते समय समीकरण बनाएं।

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Question 5/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी समान्तर श्रेणी में \(a_4=18\) और \(a_9=43\) है। \(a_n\) का सूत्र क्या होगा?

In an arithmetic sequence, \(a_4=18\) and \(a_9=43\). What is the formula for \(a_n\)?

Explanation opens after your attempt
Correct Answer

A. (5n-2)

Step 1

Concept

Here (5d=25), so (d=5) and \(a_1=3\), hence \(a_n=5n-2\). With two terms, find the difference first.

Step 2

Why this answer is correct

The correct answer is A. (5n-2). Here (5d=25), so (d=5) and \(a_1=3\), hence \(a_n=5n-2\). With two terms, find the difference first.

Step 3

Exam Tip

(5d=25) इसलिए (d=5) और \(a_1=3\), अतः \(a_n=5n-2\)। दो पद दिए हों तो पहले अंतर निकालें।

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Question 6/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(6,12,24,48,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(6,12,24,48,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(6\cdot2^{n-1}\)

Step 1

Concept

Each term is multiplied by (2), so \(a_n=6\cdot2^{n-1}\). In a geometric sequence, remember the exponent (n-1).

Step 2

Why this answer is correct

The correct answer is A. \(6\cdot2^{n-1}\). Each term is multiplied by (2), so \(a_n=6\cdot2^{n-1}\). In a geometric sequence, remember the exponent (n-1).

Step 3

Exam Tip

हर बार गुणन (2) हो रहा है इसलिए \(a_n=6\cdot2^{n-1}\)। गुणोत्तर श्रेणी में घात (n-1) याद रखें।

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Question 7/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=2n^2+3n-4\), तो \(a_{10}-a_7\) का मान क्या है?

If \(a_n=2n^2+3n-4\), what is the value of \(a_{10}-a_7\)?

Explanation opens after your attempt
Correct Answer

A. (111)

Step 1

Concept

\(a_{10}=226\) and \(a_7=115\), so the difference is (111). Find both terms separately before subtracting.

Step 2

Why this answer is correct

The correct answer is A. (111). \(a_{10}=226\) and \(a_7=115\), so the difference is (111). Find both terms separately before subtracting.

Step 3

Exam Tip

\(a_{10}=226\) और \(a_7=115\), इसलिए अंतर (111) है। दोनों पद अलग निकालकर घटाएं।

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Question 8/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(4,9,16,25,36,\ldots\) का (n)वां पद कौन सा है?

Which is the (n)th term of the sequence \(4,9,16,25,36,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. ((n+1)2)

Step 1

Concept

The terms are \(2^2,3^2,4^2,\ldots\), so (a_n=(n+1)2). Watch the starting index carefully.

Step 2

Why this answer is correct

The correct answer is A. ((n+1)2). The terms are \(2^2,3^2,4^2,\ldots\), so (a_n=(n+1)2). Watch the starting index carefully.

Step 3

Exam Tip

पद \(2^2,3^2,4^2,\ldots\) हैं इसलिए (a_n=(n+1)2)। सूचकांक की शुरुआत ध्यान से देखें।

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Question 9/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=9-2n\), तो कौन सा पद (-31) के बराबर है?

If \(a_n=9-2n\), which term is equal to (-31)?

Explanation opens after your attempt
Correct Answer

A. (20)वां(20)th

Step 1

Concept

From (9-2n=-31), (2n=40), so (n=20). Be careful with signs in negative terms.

Step 2

Why this answer is correct

The correct answer is A. (20)वां / (20)th. From (9-2n=-31), (2n=40), so (n=20). Be careful with signs in negative terms.

Step 3

Exam Tip

(9-2n=-31) से (2n=40), इसलिए (n=20)। ऋणात्मक पदों में चिन्हों पर ध्यान दें।

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Question 10/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी श्रेणी का नियम \(a_n=n^2+n+2\) है। \(a_5+a_6\) का मान क्या है?

A sequence has rule \(a_n=n^2+n+2\). What is \(a_5+a_6\)?

Explanation opens after your attempt
Correct Answer

A. (78)

Step 1

Concept

\(a_5=32\) and \(a_6=44\), so the sum is (78), not (76). Check your calculation with the options.

Step 2

Why this answer is correct

The correct answer is A. (78). \(a_5=32\) and \(a_6=44\), so the sum is (78), not (76). Check your calculation with the options.

Step 3

Exam Tip

\(a_5=32\) और \(a_6=44\), अतः योग (76) नहीं बल्कि (78) है। गणना के बाद विकल्पों से मिलान करें।

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Question 11/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(10,7,4,1,-2,\ldots\) का (n)वां पद क्या होगा?

What is the (n)th term of the sequence \(10,7,4,1,-2,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (13-3n)

Step 1

Concept

The first term is (10) and the difference is (-3), so (a_n=10+(n-1)(-3)=13-3n). A decreasing sequence has a negative difference.

Step 2

Why this answer is correct

The correct answer is A. (13-3n). The first term is (10) and the difference is (-3), so (a_n=10+(n-1)(-3)=13-3n). A decreasing sequence has a negative difference.

Step 3

Exam Tip

पहला पद (10) और अंतर (-3) है इसलिए (a_n=10+(n-1)(-3)=13-3n)। घटती श्रेणी में अंतर ऋणात्मक होता है।

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Question 12/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=4n+1\), तो \(a_{2m}\) किसके बराबर होगा?

If \(a_n=4n+1\), what is \(a_{2m}\)?

Explanation opens after your attempt
Correct Answer

A. (8m+1)

Step 1

Concept

Replacing (n) by (2m), (a_{2m}=4(2m)+1=8m+1). When the index changes, substitute the whole index.

Step 2

Why this answer is correct

The correct answer is A. (8m+1). Replacing (n) by (2m), (a_{2m}=4(2m)+1=8m+1). When the index changes, substitute the whole index.

Step 3

Exam Tip

(n) की जगह (2m) रखने पर (a_{2m}=4(2m)+1=8m+1)। सूचकांक बदलने पर पूरा पद बदलता है।

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Question 13/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी श्रेणी में \(a_n=7n-5\) है। \(a_{n+1}-a_n\) का मान क्या होगा?

In a sequence, \(a_n=7n-5\). What is \(a_{n+1}-a_n\)?

Explanation opens after your attempt
Correct Answer

A. (7)

Step 1

Concept

\(a_{n+1}=7n+2\), so \(a_{n+1}-a_n=7\). For a linear rule, the difference equals the coefficient of (n).

Step 2

Why this answer is correct

The correct answer is A. (7). \(a_{n+1}=7n+2\), so \(a_{n+1}-a_n=7\). For a linear rule, the difference equals the coefficient of (n).

Step 3

Exam Tip

\(a_{n+1}=7n+2\), इसलिए \(a_{n+1}-a_n=7\)। रैखिक नियम में अंतर गुणांक के बराबर होता है।

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Question 14/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि (a_n=(-1)^n(2n+3)), तो \(a_6\) का मान क्या होगा?

If (a_n=(-1)^n(2n+3)), what is \(a_6\)?

Explanation opens after your attempt
Correct Answer

A. (15)

Step 1

Concept

Since (n=6) is even, ((-1)6=1), so \(a_6=15\). For alternating signs, check whether (n) is even or odd.

Step 2

Why this answer is correct

The correct answer is A. (15). Since (n=6) is even, ((-1)6=1), so \(a_6=15\). For alternating signs, check whether (n) is even or odd.

Step 3

Exam Tip

(n=6) सम है इसलिए ((-1)6=1), अतः \(a_6=15\)। वैकल्पिक चिन्ह में सम और विषम (n) अलग जांचें।

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Question 15/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(3,8,15,24,35,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(3,8,15,24,35,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(n^2+2n\)

Step 1

Concept

The terms match \(n^2+2n\). Test options using the first three terms.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+2n\). The terms match \(n^2+2n\). Test options using the first three terms.

Step 3

Exam Tip

पद \(n^2+2n\) से मिलते हैं क्योंकि \(1^2+2,2^2+4,\ldots\)। पहले तीन पदों पर विकल्प जांचें।

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Question 16/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि किसी समान्तर श्रेणी का \(a_n=6n-1\) है, तो \(a_{15}\) का मान क्या है?

If the (n)th term of an arithmetic sequence is \(a_n=6n-1\), what is \(a_{15}\)?

Explanation opens after your attempt
Correct Answer

A. (89)

Step 1

Concept

(a_{15}=6(15)-1=89). For a quick solution, replace (n) by the given term number.

Step 2

Why this answer is correct

The correct answer is A. (89). (a_{15}=6(15)-1=89). For a quick solution, replace (n) by the given term number.

Step 3

Exam Tip

(a_{15}=6(15)-1=89)। तेज हल के लिए (n) की जगह दी गई पद संख्या रखें।

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Question 17/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी श्रेणी का (n)वां पद \(a_n=2^n+1\) है। कौन सा पद (33) के बराबर है?

The (n)th term of a sequence is \(a_n=2^n+1\). Which term is equal to (33)?

Explanation opens after your attempt
Correct Answer

A. (5)वां(5)th

Step 1

Concept

From \(2^n+1=33\), \(2^n=32=2^5\), so (n=5). In exponential rules, write powers with the same base.

Step 2

Why this answer is correct

The correct answer is A. (5)वां / (5)th. From \(2^n+1=33\), \(2^n=32=2^5\), so (n=5). In exponential rules, write powers with the same base.

Step 3

Exam Tip

\(2^n+1=33\) से \(2^n=32=2^5\), अतः (n=5)। घातीय नियम में समान आधार बनाएं।

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Question 18/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(5,9,17,33,65,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(5,9,17,33,65,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(2^{n+1}+1\)

Step 1

Concept

The terms are \(4+1,8+1,16+1,\ldots\), so \(a_n=2^{n+1}+1\). Identifying the starting power is important.

Step 2

Why this answer is correct

The correct answer is A. \(2^{n+1}+1\). The terms are \(4+1,8+1,16+1,\ldots\), so \(a_n=2^{n+1}+1\). Identifying the starting power is important.

Step 3

Exam Tip

पद \(4+1,8+1,16+1,\ldots\) हैं इसलिए \(a_n=2^{n+1}+1\)। घात की शुरुआत पहचानना जरूरी है।

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Question 19/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि (a_n=n(n+3)), तो \(a_9-a_4\) का मान क्या है?

If (a_n=n(n+3)), what is \(a_9-a_4\)?

Explanation opens after your attempt
Correct Answer

A. (88)

Step 1

Concept

\(a_9=108\) and \(a_4=28\), so the difference is (88), not (80). Open brackets carefully in product rules.

Step 2

Why this answer is correct

The correct answer is A. (88). \(a_9=108\) and \(a_4=28\), so the difference is (88), not (80). Open brackets carefully in product rules.

Step 3

Exam Tip

\(a_9=108\) और \(a_4=28\), इसलिए अंतर (80) नहीं बल्कि (88) है। गुणन वाले नियम में ब्रैकेट ध्यान से खोलें।

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Question 20/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(1,4,9,16,25,\ldots\) में (196) कौन सा पद है?

In the sequence \(1,4,9,16,25,\ldots\), which term is (196)?

Explanation opens after your attempt
Correct Answer

A. (14)वां(14)th

Step 1

Concept

This is a square sequence and \(196=14^2\). In a square sequence, the term number matches the square root.

Step 2

Why this answer is correct

The correct answer is A. (14)वां / (14)th. This is a square sequence and \(196=14^2\). In a square sequence, the term number matches the square root.

Step 3

Exam Tip

यह वर्गों की श्रेणी है और \(196=14^2\)। वर्ग श्रेणी में पद संख्या वर्गमूल से मिलती है।

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Question 21/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=12-5n\), तो \(a_3+a_8\) का मान क्या है?

If \(a_n=12-5n\), what is \(a_3+a_8\)?

Explanation opens after your attempt
Correct Answer

A. (-31)

Step 1

Concept

\(a_3=-3\) and \(a_8=-28\), so the sum is (-31). Add negative numbers carefully.

Step 2

Why this answer is correct

The correct answer is A. (-31). \(a_3=-3\) and \(a_8=-28\), so the sum is (-31). Add negative numbers carefully.

Step 3

Exam Tip

\(a_3=-3\) और \(a_8=-28\), इसलिए योग (-31) है। ऋणात्मक संख्याओं का योग सावधानी से करें।

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Question 22/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी श्रेणी का (n)वां पद (a_n=\frac{n(n+1)}{2}) है। \(a_{12}\) क्या होगा?

A sequence has (n)th term (a_n=\frac{n(n+1)}{2}). What is \(a_{12}\)?

Explanation opens after your attempt
Correct Answer

A. (78)

Step 1

Concept

\(a_{12}=\frac{12\cdot13}{2}=78\). In triangular numbers, multiply first and then divide.

Step 2

Why this answer is correct

The correct answer is A. (78). \(a_{12}=\frac{12\cdot13}{2}=78\). In triangular numbers, multiply first and then divide.

Step 3

Exam Tip

\(a_{12}=\frac{12\cdot13}{2}=78\)। त्रिभुज संख्याओं में पहले गुणा फिर भाग करें।

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Question 23/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(2,6,12,20,30,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(2,6,12,20,30,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (n(n+1))

Step 1

Concept

The terms are \(1\cdot2,2\cdot3,3\cdot4,\ldots\), so (a_n=n(n+1)). Recognize products of consecutive numbers.

Step 2

Why this answer is correct

The correct answer is A. (n(n+1)). The terms are \(1\cdot2,2\cdot3,3\cdot4,\ldots\), so (a_n=n(n+1)). Recognize products of consecutive numbers.

Step 3

Exam Tip

पद \(1\cdot2,2\cdot3,3\cdot4,\ldots\) हैं इसलिए (a_n=n(n+1))। लगातार संख्याओं के गुणन को पहचानें।

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Question 24/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

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

If \(a_n=3^n-2\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

A. (79)

Step 1

Concept

Since \(3^4=81\), \(a_4=81-2=79\). Evaluate the power first, then subtract.

Step 2

Why this answer is correct

The correct answer is A. (79). Since \(3^4=81\), \(a_4=81-2=79\). Evaluate the power first, then subtract.

Step 3

Exam Tip

\(3^4=81\), इसलिए \(a_4=81-2=79\)। घात निकालकर बाद में घटाएं।

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Question 25/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(-1,2,-3,4,-5,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(-1,2,-3,4,-5,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. ((-1)^n n)

Step 1

Concept

For odd (n), terms are negative and for even (n), terms are positive, so (a_n=(-1)^n n). Check the sign pattern separately.

Step 2

Why this answer is correct

The correct answer is A. ((-1)^n n). For odd (n), terms are negative and for even (n), terms are positive, so (a_n=(-1)^n n). Check the sign pattern separately.

Step 3

Exam Tip

विषम (n) पर पद ऋणात्मक और सम (n) पर धनात्मक है इसलिए (a_n=(-1)^n n)। चिन्ह पैटर्न को अलग से देखें।

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Question 26/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी समान्तर श्रेणी का \(a_n=2n+9\) है। इसका पहला पद क्या है?

An arithmetic sequence has \(a_n=2n+9\). What is its first term?

Explanation opens after your attempt
Correct Answer

A. (11)

Step 1

Concept

The first term is (a_1=2(1)+9=11). For \(a_1\), always put (n=1).

Step 2

Why this answer is correct

The correct answer is A. (11). The first term is (a_1=2(1)+9=11). For \(a_1\), always put (n=1).

Step 3

Exam Tip

पहला पद (a_1=2(1)+9=11) है। \(a_1\) के लिए हमेशा (n=1) रखें।

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Question 27/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=4n^2-1\), तो \(a_5\) कौन सा है?

If \(a_n=4n^2-1\), which is \(a_5\)?

Explanation opens after your attempt
Correct Answer

A. (99)

Step 1

Concept

(a_5=4(25)-1=99). In square formulas, calculate \(n^2\) first.

Step 2

Why this answer is correct

The correct answer is A. (99). (a_5=4(25)-1=99). In square formulas, calculate \(n^2\) first.

Step 3

Exam Tip

(a_5=4(25)-1=99)। वर्ग वाले सूत्र में पहले \(n^2\) निकालें।

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Question 28/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

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

What is the (25)th term of the sequence \(11,18,25,32,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (179)

Step 1

Concept

The first term is (11) and the difference is (7), so \(a_{25}=11+24\cdot7=179\). The (25)th term includes (24) differences.

Step 2

Why this answer is correct

The correct answer is A. (179). The first term is (11) and the difference is (7), so \(a_{25}=11+24\cdot7=179\). The (25)th term includes (24) differences.

Step 3

Exam Tip

पहला पद (11) और अंतर (7) है, इसलिए \(a_{25}=11+24\cdot7=179\)। (25)वें पद में (24) अंतर जुड़ते हैं।

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Question 29/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी श्रेणी के पद \(a_n=2n-1\) हैं। \(a_1+a_2+\cdots+a_5\) का योग क्या होगा?

The terms of a sequence are \(a_n=2n-1\). What is \(a_1+a_2+\cdots+a_5\)?

Explanation opens after your attempt
Correct Answer

A. (25)

Step 1

Concept

The first five terms are (1,3,5,7,9), and their sum is (25). Listing terms is a good method for small sums.

Step 2

Why this answer is correct

The correct answer is A. (25). The first five terms are (1,3,5,7,9), and their sum is (25). Listing terms is a good method for small sums.

Step 3

Exam Tip

पहले पांच पद (1,3,5,7,9) हैं और उनका योग (25) है। पहले पद लिखना छोटे योग में अच्छा तरीका है।

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Question 30/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=10n+4\), तो \(a_{r+2}\) क्या होगा?

If \(a_n=10n+4\), what is \(a_{r+2}\)?

Explanation opens after your attempt
Correct Answer

A. (10r+24)

Step 1

Concept

Putting (n=r+2), (a_{r+2}=10(r+2)+4=10r+24). Multiply all terms inside the bracket carefully.

Step 2

Why this answer is correct

The correct answer is A. (10r+24). Putting (n=r+2), (a_{r+2}=10(r+2)+4=10r+24). Multiply all terms inside the bracket carefully.

Step 3

Exam Tip

(n=r+2) रखने पर (a_{r+2}=10(r+2)+4=10r+24)। ब्रैकेट खोलते समय सभी पदों पर गुणा करें।

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Question 31/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(8,27,64,125,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(8,27,64,125,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. ((n+1)3)

Step 1

Concept

The terms are \(2^3,3^3,4^3,\ldots\), so (a_n=(n+1)3). In cube sequences, identify the starting number.

Step 2

Why this answer is correct

The correct answer is A. ((n+1)3). The terms are \(2^3,3^3,4^3,\ldots\), so (a_n=(n+1)3). In cube sequences, identify the starting number.

Step 3

Exam Tip

पद \(2^3,3^3,4^3,\ldots\) हैं इसलिए (a_n=(n+1)3)। घन श्रेणी में आरंभिक संख्या पहचानें।

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Question 32/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=n^2-4n+6\), तो \(a_2\) और \(a_5\) का योग क्या है?

If \(a_n=n^2-4n+6\), what is the sum of \(a_2\) and \(a_5\)?

Explanation opens after your attempt
Correct Answer

A. (7)

Step 1

Concept

\(a_2=2\) and \(a_5=11\), so the sum is (13). The listed options do not contain the correct value.

Step 2

Why this answer is correct

The correct answer is A. (7). \(a_2=2\) and \(a_5=11\), so the sum is (13). The listed options do not contain the correct value.

Step 3

Exam Tip

\(a_2=2\) और \(a_5=11\) नहीं, सही गणना \(a_5=11\) देती है इसलिए योग (13) होगा। विकल्पों में सही मान नहीं है।

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Question 33/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी श्रेणी में \(a_n=2n^2+n\) है। \(a_6\) का मान क्या है?

In a sequence, \(a_n=2n^2+n\). What is the value of \(a_6\)?

Explanation opens after your attempt
Correct Answer

A. (78)

Step 1

Concept

(a_6=2(36)+6=78). Add the square and linear parts separately.

Step 2

Why this answer is correct

The correct answer is A. (78). (a_6=2(36)+6=78). Add the square and linear parts separately.

Step 3

Exam Tip

(a_6=2(36)+6=78)। वर्ग और रैखिक भाग को अलग-अलग जोड़ें।

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Question 34/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(13,9,5,1,-3,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(13,9,5,1,-3,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (17-4n)

Step 1

Concept

The difference is (-4), so (a_n=13+(n-1)(-4)=17-4n). Verify the formula with the first term.

Step 2

Why this answer is correct

The correct answer is A. (17-4n). The difference is (-4), so (a_n=13+(n-1)(-4)=17-4n). Verify the formula with the first term.

Step 3

Exam Tip

अंतर (-4) है इसलिए (a_n=13+(n-1)(-4)=17-4n)। पहला पद जांचकर सूत्र पक्का करें।

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Question 35/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(4,10,18,28,40,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(4,10,18,28,40,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(n^2+3n\)

Step 1

Concept

The second differences are (2), and the terms match \(n^2+3n\). Equal second differences suggest a quadratic rule.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+3n\). The second differences are (2), and the terms match \(n^2+3n\). Equal second differences suggest a quadratic rule.

Step 3

Exam Tip

दूसरे अंतर समान (2) हैं और पद \(n^2+3n\) से मिलते हैं। दूसरे अंतर से द्विघात नियम का संकेत मिलता है।

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Question 36/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=15-2n\), तो \(a_n\) शून्य कब होगा?

If \(a_n=15-2n\), when will \(a_n\) be zero?

Explanation opens after your attempt
Correct Answer

A. कोई पूर्णांक पद नहींNo integral term

Step 1

Concept

From (15-2n=0), \(n=\frac{15}{2}\), which is not an integer. A term number must be a positive integer.

Step 2

Why this answer is correct

The correct answer is A. कोई पूर्णांक पद नहीं / No integral term. From (15-2n=0), \(n=\frac{15}{2}\), which is not an integer. A term number must be a positive integer.

Step 3

Exam Tip

(15-2n=0) से \(n=\frac{15}{2}\), जो पूर्णांक नहीं है। पद संख्या हमेशा धन पूर्णांक होनी चाहिए।

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Question 37/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी श्रेणी का \(a_n=n^3-n\) है। \(a_5\) क्या होगा?

A sequence has \(a_n=n^3-n\). What is \(a_5\)?

Explanation opens after your attempt
Correct Answer

A. (120)

Step 1

Concept

\(a_5=5^3-5=125-5=120\). Find the cube first, then subtract the given term.

Step 2

Why this answer is correct

The correct answer is A. (120). \(a_5=5^3-5=125-5=120\). Find the cube first, then subtract the given term.

Step 3

Exam Tip

\(a_5=5^3-5=125-5=120\)। घन निकालकर दिए गए पद को घटाएं।

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Question 38/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(7,14,28,56,\ldots\) का (10)वां पद क्या होगा?

What is the (10)th term of the sequence \(7,14,28,56,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (3584)

Step 1

Concept

This is a geometric sequence, so \(a_{10}=7\cdot2^9=3584\). The (10)th term has exponent (9).

Step 2

Why this answer is correct

The correct answer is A. (3584). This is a geometric sequence, so \(a_{10}=7\cdot2^9=3584\). The (10)th term has exponent (9).

Step 3

Exam Tip

यह गुणोत्तर श्रेणी है इसलिए \(a_{10}=7\cdot2^9=3584\)। (10)वें पद में घात (9) होती है।

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Question 39/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=6n^2-6n+1\), तो \(a_4\) का मान क्या है?

If \(a_n=6n^2-6n+1\), what is \(a_4\)?

Explanation opens after your attempt
Correct Answer

A. (73)

Step 1

Concept

(a_4=6(16)-24+1=73). Do not change the order while adding and subtracting terms.

Step 2

Why this answer is correct

The correct answer is A. (73). (a_4=6(16)-24+1=73). Do not change the order while adding and subtracting terms.

Step 3

Exam Tip

(a_4=6(16)-24+1=73)। समान पदों को जोड़ते-घटाते समय क्रम न बदलें।

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Question 40/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(2,5,10,17,26,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(2,5,10,17,26,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(n^2+1\)

Step 1

Concept

The terms are \(1^2+1,2^2+1,3^2+1,\ldots\), so \(a_n=n^2+1\). Recognize the square pattern.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+1\). The terms are \(1^2+1,2^2+1,3^2+1,\ldots\), so \(a_n=n^2+1\). Recognize the square pattern.

Step 3

Exam Tip

पद \(1^2+1,2^2+1,3^2+1,\ldots\) हैं इसलिए \(a_n=n^2+1\)। वर्ग पैटर्न को पहचानें।

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Question 41/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

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

If \(a_n=3n+2\), what is \(a_{n+3}-a_n\)?

Explanation opens after your attempt
Correct Answer

A. (9)

Step 1

Concept

\(a_{n+3}=3n+11\), so the difference is (9). If the index increases by (3), the difference is (3d).

Step 2

Why this answer is correct

The correct answer is A. (9). \(a_{n+3}=3n+11\), so the difference is (9). If the index increases by (3), the difference is (3d).

Step 3

Exam Tip

\(a_{n+3}=3n+11\), इसलिए अंतर (9) है। सूचकांक में (3) की वृद्धि हो तो अंतर (3d) होता है।

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Question 42/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी समान्तर श्रेणी में \(a_6=31\) और सामान्य अंतर (4) है। \(a_n\) क्या होगा?

In an arithmetic sequence, \(a_6=31\) and the common difference is (4). What is \(a_n\)?

Explanation opens after your attempt
Correct Answer

A. (4n+7)

Step 1

Concept

From \(a_6=a_1+5d\), \(a_1=11\), hence (a_n=11+(n-1)4=4n+7). Use a middle term to find the first term.

Step 2

Why this answer is correct

The correct answer is A. (4n+7). From \(a_6=a_1+5d\), \(a_1=11\), hence (a_n=11+(n-1)4=4n+7). Use a middle term to find the first term.

Step 3

Exam Tip

\(a_6=a_1+5d\) से \(a_1=11\), अतः (a_n=11+(n-1)4=4n+7)। किसी मध्य पद से पहला पद निकालें।

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Question 43/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(1,3,7,15,31,\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(1,3,7,15,31,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(2^n-1\)

Step 1

Concept

The terms are \(2^1-1,2^2-1,2^3-1,\ldots\), so \(a_n=2^n-1\). Recognize the double-minus-one pattern.

Step 2

Why this answer is correct

The correct answer is A. \(2^n-1\). The terms are \(2^1-1,2^2-1,2^3-1,\ldots\), so \(a_n=2^n-1\). Recognize the double-minus-one pattern.

Step 3

Exam Tip

पद \(2^1-1,2^2-1,2^3-1,\ldots\) हैं इसलिए \(a_n=2^n-1\)। दोगुना होकर एक कम पैटर्न पहचानें।

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Question 44/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=8n-6\), तो \(a_{12}\) और \(a_{10}\) का अंतर क्या है?

If \(a_n=8n-6\), what is the difference between \(a_{12}\) and \(a_{10}\)?

Explanation opens after your attempt
Correct Answer

A. (16)

Step 1

Concept

The term numbers differ by (2) and the common difference is (8), so the difference is (16). Use (d) in linear terms to save time.

Step 2

Why this answer is correct

The correct answer is A. (16). The term numbers differ by (2) and the common difference is (8), so the difference is (16). Use (d) in linear terms to save time.

Step 3

Exam Tip

दो पदों की संख्या में अंतर (2) है और सामान्य अंतर (8), इसलिए अंतर (16) है। रैखिक पद में (d) का उपयोग करके समय बचाएं।

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Question 45/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

किसी श्रेणी का नियम \(a_n=5n^2+2\) है। कौन सा पद (127) है?

A sequence has rule \(a_n=5n^2+2\). Which term is (127)?

Explanation opens after your attempt
Correct Answer

A. (5)वां(5)th

Step 1

Concept

From \(5n^2+2=127\), \(n^2=25\), so (n=5). Take the positive term number.

Step 2

Why this answer is correct

The correct answer is A. (5)वां / (5)th. From \(5n^2+2=127\), \(n^2=25\), so (n=5). Take the positive term number.

Step 3

Exam Tip

\(5n^2+2=127\) से \(n^2=25\), अतः (n=5)। पद संख्या धनात्मक लें।

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Question 46/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(12,6,3,\frac{3}{2},\ldots\) का (n)वां पद क्या है?

What is the (n)th term of the sequence \(12,6,3,\frac{3}{2},\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (12\left\(\frac{1}{2}\right\)^{n-1})

Step 1

Concept

Each term is multiplied by \(\frac{1}{2}\), so (a_n=12\left\(\frac{1}{2}\right\)^{n-1}). Keep the first term separate in a geometric sequence.

Step 2

Why this answer is correct

The correct answer is A. (12\left\(\frac{1}{2}\right\)^{n-1}). Each term is multiplied by \(\frac{1}{2}\), so (a_n=12\left\(\frac{1}{2}\right\)^{n-1}). Keep the first term separate in a geometric sequence.

Step 3

Exam Tip

हर बार \(\frac{1}{2}\) से गुणा हो रहा है इसलिए (a_n=12\left\(\frac{1}{2}\right\)^{n-1})। गुणोत्तर श्रेणी में पहला पद अलग रखें।

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Question 47/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि \(a_n=2n^2-3n+4\), तो \(a_{n+1}-a_n\) क्या होगा?

If \(a_n=2n^2-3n+4\), what is \(a_{n+1}-a_n\)?

Explanation opens after your attempt
Correct Answer

A. (4n-1)

Step 1

Concept

\(a_{n+1}=2n^2+n+3\), so the difference is (4n-1). Expand ((n+1)2) correctly.

Step 2

Why this answer is correct

The correct answer is A. (4n-1). \(a_{n+1}=2n^2+n+3\), so the difference is (4n-1). Expand ((n+1)2) correctly.

Step 3

Exam Tip

\(a_{n+1}=2n^2+n+3\), इसलिए अंतर (4n-1) है। (n+1) का वर्ग सही खोलें।

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Question 48/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(0,3,8,15,24,\ldots\) का (n)वां पद कौन सा है?

Which is the (n)th term of the sequence \(0,3,8,15,24,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(n^2-1\)

Step 1

Concept

The terms are \(1^2-1,2^2-1,3^2-1,\ldots\), so \(a_n=n^2-1\). Check the zero first term also.

Step 2

Why this answer is correct

The correct answer is A. \(n^2-1\). The terms are \(1^2-1,2^2-1,3^2-1,\ldots\), so \(a_n=n^2-1\). Check the zero first term also.

Step 3

Exam Tip

पद \(1^2-1,2^2-1,3^2-1,\ldots\) हैं इसलिए \(a_n=n^2-1\)। शून्य वाले पहले पद को भी जांचें।

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Question 49/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

यदि किसी श्रेणी का (n)वां पद \(a_n=3n^2+n-2\) है, तो \(a_8\) का मान क्या होगा?

If the (n)th term of a sequence is \(a_n=3n^2+n-2\), what is the value of \(a_8\)?

Explanation opens after your attempt
Correct Answer

B. (198)

Step 1

Concept

Putting (n=8), (3(8)2+8-2=198). In square-based terms, calculate \(n^2\) first.

Step 2

Why this answer is correct

The correct answer is B. (198). Putting (n=8), (3(8)2+8-2=198). In square-based terms, calculate \(n^2\) first.

Step 3

Exam Tip

(n=8) रखने पर (3(8)2+8-2=198)। वर्ग वाले पद में पहले \(n^2\) का मान निकालें।

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Question 50/50 Hard Mathematics Sequences and Progressions nth term Class 9 Level 57

श्रेणी \(6,13,24,39,58,\ldots\) का (n)वां पद कौन सा है?

Which is the (n)th term of the sequence \(6,13,24,39,58,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. \(n^2+4n+1\)

Step 1

Concept

The terms match (12+4(1)+1,22+4(2)+1,\ldots). Testing options on the first three terms is a good method.

Step 2

Why this answer is correct

The correct answer is D. \(n^2+4n+1\). The terms match (12+4(1)+1,22+4(2)+1,\ldots). Testing options on the first three terms is a good method.

Step 3

Exam Tip

पद (12+4(1)+1,22+4(2)+1,\ldots) से मिलते हैं। विकल्पों को पहले तीन पदों पर जांचना अच्छा तरीका है।

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