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Mathematics Quiz - Class 9 Mathematics Exploring Algebrai...

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

यदि किसी श्रेणी का (n)वाँ पद \(a_n=6n-5\) है तो (18)वाँ पद क्या होगा?

If the (n)th term of a sequence is \(a_n=6n-5\), what will be the (18)th term?

Explanation opens after your attempt

Correct Answer

B. (103)

Step 1

Concept

Putting (n=18) gives \(a_{18}=108-5=103\). In exams, substitute the term number directly in the formula.

Step 2

Why this answer is correct

The correct answer is B. (103). Putting (n=18) gives \(a_{18}=108-5=103\). In exams, substitute the term number directly in the formula.

Step 3

Exam Tip

(n=18) रखने पर \(a_{18}=108-5=103\) मिलता है। परीक्षा में पद संख्या को सीधे सूत्र में रखें।

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

श्रेणी \(8,15,24,35,48,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(8,15,24,35,48,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(n^2+4n+3\)

Step 1

Concept

The given terms are formed by \(n^2+4n+3\). Testing options on the first three terms is a fast method.

Step 2

Why this answer is correct

The correct answer is A. \(n^2+4n+3\). The given terms are formed by \(n^2+4n+3\). Testing options on the first three terms is a fast method.

Step 3

Exam Tip

दिए पद \(n^2+4n+3\) से सही बनते हैं। पहले तीन पदों पर विकल्प जांचना तेज तरीका है।

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

यदि \(a_n=4n^2-3n+2\) है तो \(a_7-a_4\) का मान क्या है?

If \(a_n=4n^2-3n+2\), what is the value of \(a_7-a_4\)?

Explanation opens after your attempt

Correct Answer

D. (123)

Step 1

Concept

\(a_7=177\) and \(a_4=54\), so the difference is (123). Find both terms separately first.

Step 2

Why this answer is correct

The correct answer is D. (123). \(a_7=177\) and \(a_4=54\), so the difference is (123). Find both terms separately first.

Step 3

Exam Tip

\(a_7=177\) और \(a_4=54\) है इसलिए अंतर (123) है। पहले दोनों पद अलग निकालें।

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

श्रेणी \(3,9,18,30,45,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(3,9,18,30,45,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (\frac{3n(n+1)}{2})

Step 1

Concept

The terms are (3) times triangular numbers. Recognize patterns involving (n(n+1)).

Step 2

Why this answer is correct

The correct answer is C. (\frac{3n(n+1)}{2}). The terms are (3) times triangular numbers. Recognize patterns involving (n(n+1)).

Step 3

Exam Tip

पद (3) गुणा त्रिभुज संख्याओं जैसे हैं। (n(n+1)) वाले पैटर्न को पहचानें।

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

एक रैखिक श्रेणी में \(a_5=23\) और \(a_{12}=58\) है तो \(a_{20}\) क्या होगा?

In a linear sequence, \(a_5=23\) and \(a_{12}=58\). What will be \(a_{20}\)?

Explanation opens after your attempt

Correct Answer

A. (98)

Step 1

Concept

The increase over (7) positions is (35), so the difference is (5). The formula \(a_n=5n-2\) gives \(a_{20}=98\).

Step 2

Why this answer is correct

The correct answer is A. (98). The increase over (7) positions is (35), so the difference is (5). The formula \(a_n=5n-2\) gives \(a_{20}=98\).

Step 3

Exam Tip

(7) स्थानों में वृद्धि (35) है इसलिए अंतर (5) है। सूत्र \(a_n=5n-2\) से \(a_{20}=98\) मिलता है।

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

श्रेणी \(\frac{4}{7},\frac{7}{10},\frac{10}{13},\frac{13}{16},\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(\frac{4}{7},\frac{7}{10},\frac{10}{13},\frac{13}{16},\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(\frac{3n+1}{3n+4}\)

Step 1

Concept

The numerator \(4,7,10,\ldots\) gives (3n+1), and the denominator \(7,10,13,\ldots\) gives (3n+4). Observe numerator and denominator separately.

Step 2

Why this answer is correct

The correct answer is D. \(\frac{3n+1}{3n+4}\). The numerator \(4,7,10,\ldots\) gives (3n+1), and the denominator \(7,10,13,\ldots\) gives (3n+4). Observe numerator and denominator separately.

Step 3

Exam Tip

अंश \(4,7,10,\ldots\) से (3n+1) और हर \(7,10,13,\ldots\) से (3n+4) है। भिन्नों में अंश और हर अलग देखें।

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

यदि \(a_n=3n^2+2\) है तो (149) कौन सा पद है?

If \(a_n=3n^2+2\), which term is (149)?

Explanation opens after your attempt

Correct Answer

C. (7)वाँ(7)th

Step 1

Concept

From \(3n^2+2=149\), \(n^2=49\) and (n=7). Take the positive value for the term number.

Step 2

Why this answer is correct

The correct answer is C. (7)वाँ / (7)th. From \(3n^2+2=149\), \(n^2=49\) and (n=7). Take the positive value for the term number.

Step 3

Exam Tip

\(3n^2+2=149\) से \(n^2=49\) और (n=7) मिलता है। पद संख्या के लिए धनात्मक मान लें।

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

यदि \(a_n=40-5n\) है तो पहला ऋणात्मक पद कौन सा होगा?

If \(a_n=40-5n\), which will be the first negative term?

Explanation opens after your attempt

Correct Answer

A. (9)वाँ पद(9)th term

Step 1

Concept

From (40-5n<0), we get (n>8). So the first natural value is (9).

Step 2

Why this answer is correct

The correct answer is A. (9)वाँ पद / (9)th term. From (40-5n<0), we get (n>8). So the first natural value is (9).

Step 3

Exam Tip

(40-5n<0) से (n>8) मिलता है। इसलिए पहला प्राकृतिक मान (9) है।

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

यदि \(a_n=kn^2-n\) और \(a_6=210\) है तो \(a_4\) का मान क्या होगा?

If \(a_n=kn^2-n\) and \(a_6=210\), what will be the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

D. (92)

Step 1

Concept

From (36k-6=210), (k=6). Then \(a_4=6\cdot16-4=92\).

Step 2

Why this answer is correct

The correct answer is D. (92). From (36k-6=210), (k=6). Then \(a_4=6\cdot16-4=92\).

Step 3

Exam Tip

(36k-6=210) से (k=6) मिलता है। फिर \(a_4=6\cdot16-4=92\) है।

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

श्रेणी \(2,11,28,53,86,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(2,11,28,53,86,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(4n^2-3n+1\)

Step 1

Concept

The second difference is (8), so the coefficient of \(n^2\) is (4). Substitution gives \(4n^2-3n+1\).

Step 2

Why this answer is correct

The correct answer is C. \(4n^2-3n+1\). The second difference is (8), so the coefficient of \(n^2\) is (4). Substitution gives \(4n^2-3n+1\).

Step 3

Exam Tip

दूसरा अंतर (8) है इसलिए \(n^2\) का गुणांक (4) होगा। मान रखने पर \(4n^2-3n+1\) सही है।

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

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

If \(a_n=2^n+n\), what is the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (37)

Step 1

Concept

\(2^5=32\) and (32+5=37). Do the exponent and addition separately.

Step 2

Why this answer is correct

The correct answer is B. (37). \(2^5=32\) and (32+5=37). Do the exponent and addition separately.

Step 3

Exam Tip

\(2^5=32\) और (32+5=37) है। घात और जोड़ को अलग-अलग करें।

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

यदि \(a_n=pn+q\), \(a_4+a_7=64\) और \(a_5+a_8=76\) है तो \(a_{10}\) क्या होगा?

If \(a_n=pn+q\), \(a_4+a_7=64\), and \(a_5+a_8=76\), what will be \(a_{10}\)?

Explanation opens after your attempt

Correct Answer

A. (59)

Step 1

Concept

Subtracting the two sums gives (2p=12), so (p=6). Then (q=-1) and \(a_{10}=59\).

Step 2

Why this answer is correct

The correct answer is A. (59). Subtracting the two sums gives (2p=12), so (p=6). Then (q=-1) and \(a_{10}=59\).

Step 3

Exam Tip

दोनों योग घटाने पर (2p=12) इसलिए (p=6) है। फिर (q=-1) और \(a_{10}=59\) मिलता है।

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

श्रेणी \(7,17,31,49,71,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(7,17,31,49,71,\ldots\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The given terms are formed by \(2n^2+4n+1\). Start eliminating wrong options from the first term itself.

Step 2

Why this answer is correct

The correct answer is D. \(2n^2+4n+1\). The given terms are formed by \(2n^2+4n+1\). Start eliminating wrong options from the first term itself.

Step 3

Exam Tip

दिए पद \(2n^2+4n+1\) से बनते हैं। पहले पद से ही गलत विकल्प हटाने शुरू करें।

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

यदि (a_n=\frac{n(n+5)}{3}) है तो \(a_6\) का मान क्या है?

If (a_n=\frac{n(n+5)}{3}), what is the value of \(a_6\)?

Explanation opens after your attempt

Correct Answer

C. (22)

Step 1

Concept

\(a_6=\frac{6\cdot11}{3}=22\). Checking cancellation before multiplying saves time.

Step 2

Why this answer is correct

The correct answer is C. (22). \(a_6=\frac{6\cdot11}{3}=22\). Checking cancellation before multiplying saves time.

Step 3

Exam Tip

\(a_6=\frac{6\cdot11}{3}=22\) है। गुणा करने से पहले कटौती देखना समय बचाता है।

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

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

If \(a_n=3n^2+5n\), what is \(a_{n+1}-a_n\)?

Explanation opens after your attempt

Correct Answer

B. (6n+8)

Step 1

Concept

Putting (n+1) in \(a_{n+1}\) and subtracting gives (6n+8). Do not forget brackets while expanding.

Step 2

Why this answer is correct

The correct answer is B. (6n+8). Putting (n+1) in \(a_{n+1}\) and subtracting gives (6n+8). Do not forget brackets while expanding.

Step 3

Exam Tip

\(a_{n+1}\) में (n+1) रखकर घटाने पर (6n+8) मिलता है। विस्तार में कोष्ठक न भूलें।

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

श्रेणी \(0,5,16,33,56,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(0,5,16,33,56,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(3n^2-4n+1\)

Step 1

Concept

The second difference is (6), so the coefficient of \(n^2\) is (3). Checking gives \(3n^2-4n+1\).

Step 2

Why this answer is correct

The correct answer is A. \(3n^2-4n+1\). The second difference is (6), so the coefficient of \(n^2\) is (3). Checking gives \(3n^2-4n+1\).

Step 3

Exam Tip

दूसरा अंतर (6) है इसलिए \(n^2\) का गुणांक (3) होगा। जांचने पर \(3n^2-4n+1\) मिलता है।

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

यदि \(a_n=7n-9\) है तो (131) कौन सा पद है?

If \(a_n=7n-9\), which term is (131)?

Explanation opens after your attempt

Correct Answer

D. (20)वाँ(20)th

Step 1

Concept

From (7n-9=131), (7n=140) and (n=20). Form an equation to find the term number.

Step 2

Why this answer is correct

The correct answer is D. (20)वाँ / (20)th. From (7n-9=131), (7n=140) and (n=20). Form an equation to find the term number.

Step 3

Exam Tip

(7n-9=131) से (7n=140) और (n=20) है। समीकरण बनाकर पद संख्या निकालें।

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

यदि \(a_n=n^2-6n+13\) है तो सबसे छोटा पद मान क्या है?

If \(a_n=n^2-6n+13\), what is the smallest term value?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

At (n=3), \(a_3=4\) is the smallest. In a quadratic formula, check values near the vertex.

Step 2

Why this answer is correct

The correct answer is B. (4). At (n=3), \(a_3=4\) is the smallest. In a quadratic formula, check values near the vertex.

Step 3

Exam Tip

(n=3) पर \(a_3=4\) सबसे छोटा आता है। वर्गीय सूत्र में शीर्ष के आसपास के मान जांचें।

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

श्रेणी \(\frac{1}{3},\frac{4}{8},\frac{9}{15},\frac{16}{24},\ldots\) का सरल (n)वाँ पद क्या है?

What is the simplified (n)th term of the sequence \(\frac{1}{3},\frac{4}{8},\frac{9}{15},\frac{16}{24},\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(\frac{n}{n+2}\)

Step 1

Concept

The numerator is \(n^2\) and the denominator is (n(n+2)). Simplifying gives \(\frac{n}{n+2}\).

Step 2

Why this answer is correct

The correct answer is C. \(\frac{n}{n+2}\). The numerator is \(n^2\) and the denominator is (n(n+2)). Simplifying gives \(\frac{n}{n+2}\).

Step 3

Exam Tip

अंश \(n^2\) और हर (n(n+2)) है। सरल करने पर \(\frac{n}{n+2}\) मिलता है।

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

यदि \(a_n=5\cdot3^{n-1}-2\) है तो \(a_4\) क्या होगा?

If \(a_n=5\cdot3^{n-1}-2\), what will be \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (133)

Step 1

Concept

\(a_4=5\cdot3^3-2=133\). Write the exponent (n-1) carefully.

Step 2

Why this answer is correct

The correct answer is B. (133). \(a_4=5\cdot3^3-2=133\). Write the exponent (n-1) carefully.

Step 3

Exam Tip

\(a_4=5\cdot3^3-2=133\) है। (n-1) वाली घात को सावधानी से लिखें।

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

श्रेणी \(4,7,14,25,40,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(4,7,14,25,40,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(2n^2-3n+5\)

Step 1

Concept

The given terms match \(2n^2-3n+5\). Use second differences to identify a quadratic form.

Step 2

Why this answer is correct

The correct answer is D. \(2n^2-3n+5\). The given terms match \(2n^2-3n+5\). Use second differences to identify a quadratic form.

Step 3

Exam Tip

दिए पद \(2n^2-3n+5\) से सही मिलते हैं। दूसरे अंतर से वर्गीय रूप पहचानें।

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

यदि \(a_n=rn+s\), \(a_3=14\) और \(a_{10}=49\) है तो \(a_{15}\) क्या होगा?

If \(a_n=rn+s\), \(a_3=14\), and \(a_{10}=49\), what will be \(a_{15}\)?

Explanation opens after your attempt

Correct Answer

B. (74)

Step 1

Concept

The increase over (7) positions is (35), so (r=5). The formula \(a_n=5n-1\) gives \(a_{15}=74\).

Step 2

Why this answer is correct

The correct answer is B. (74). The increase over (7) positions is (35), so (r=5). The formula \(a_n=5n-1\) gives \(a_{15}=74\).

Step 3

Exam Tip

(7) स्थानों में वृद्धि (35) है इसलिए (r=5) है। सूत्र \(a_n=5n-1\) से \(a_{15}=74\) मिलता है।

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

यदि \(a_n=4n^2-1\) है तो (100) से बड़ा पहला पद कौन सा होगा?

If \(a_n=4n^2-1\), which is the first term greater than (100)?

Explanation opens after your attempt

Correct Answer

C. (6)वाँ पद(6)th term

Step 1

Concept

From \(4n^2-1>100\), we get \(n^2>25.25\). The first natural value is (6).

Step 2

Why this answer is correct

The correct answer is C. (6)वाँ पद / (6)th term. From \(4n^2-1>100\), we get \(n^2>25.25\). The first natural value is (6).

Step 3

Exam Tip

\(4n^2-1>100\) से \(n^2>25.25\) मिलता है। पहला प्राकृतिक मान (6) है।

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

यदि (a_n=(-1)^n(n+2)) है तो \(a_6+a_7\) का मान क्या होगा?

If (a_n=(-1)^n(n+2)), what will be the value of \(a_6+a_7\)?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

\(a_6=8\) and \(a_7=-9\), so the sum is (-1). In sign-changing formulas, check even and odd values.

Step 2

Why this answer is correct

The correct answer is A. (-1). \(a_6=8\) and \(a_7=-9\), so the sum is (-1). In sign-changing formulas, check even and odd values.

Step 3

Exam Tip

\(a_6=8\) और \(a_7=-9\) है इसलिए योग (-1) है। चिह्न बदलने वाले सूत्रों में सम-विषम जांचें।

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

यदि \(a_n=n^3\) है तो \(a_n-a_{n-1}\) का सूत्र क्या होगा?

If \(a_n=n^3\), what is the formula for \(a_n-a_{n-1}\)?

Explanation opens after your attempt

Correct Answer

D. \(3n^2-3n+1\)

Step 1

Concept

(n^-3-(n-1)³=3n^-2-3n+1). Always put (n-1) in the previous term.

Step 2

Why this answer is correct

The correct answer is D. \(3n^2-3n+1\). (n^-3-(n-1)³=3n^-2-3n+1). Always put (n-1) in the previous term.

Step 3

Exam Tip

(n^-3-(n-1)³=3n^-2-3n+1) होता है। पिछले पद में (n-1) अवश्य रखें।

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

यदि \(a_n=2n^2+kn+3\) और \(a_3=30\) है तो \(a_5\) का मान क्या होगा?

If \(a_n=2n^2+kn+3\) and \(a_3=30\), what will be the value of \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (68)

Step 1

Concept

From (18+3k+3=30), (k=3). Then \(a_5=50+15+3=68\).

Step 2

Why this answer is correct

The correct answer is B. (68). From (18+3k+3=30), (k=3). Then \(a_5=50+15+3=68\).

Step 3

Exam Tip

(18+3k+3=30) से (k=3) मिलता है। फिर \(a_5=50+15+3=68\) है।

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

श्रेणी \(6,20,42,72,110,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(6,20,42,72,110,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(4n^2+2n\)

Step 1

Concept

The given terms are formed by \(4n^2+2n\). The second difference (8) indicates coefficient (4).

Step 2

Why this answer is correct

The correct answer is C. \(4n^2+2n\). The given terms are formed by \(4n^2+2n\). The second difference (8) indicates coefficient (4).

Step 3

Exam Tip

दिए पद \(4n^2+2n\) से बनते हैं। दूसरे अंतर (8) से गुणांक (4) का संकेत मिलता है।

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

यदि (a_n=(n+1)(n+3)) है तो (80) कौन सा पद है?

If (a_n=(n+1)(n+3)), which term is (80)?

Explanation opens after your attempt

Correct Answer

A. (7)वाँ(7)th

Step 1

Concept

Putting (n=7) in ((n+1)(n+3)=80) gives \(8\cdot10=80\). Test the options quickly.

Step 2

Why this answer is correct

The correct answer is A. (7)वाँ / (7)th. Putting (n=7) in ((n+1)(n+3)=80) gives \(8\cdot10=80\). Test the options quickly.

Step 3

Exam Tip

((n+1)(n+3)=80) में (n=7) रखने पर \(8\cdot10=80\) मिलता है। विकल्पों को जल्दी जांचें।

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

श्रेणी \(\frac{5}{6},\frac{9}{11},\frac{13}{16},\frac{17}{21},\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(\frac{5}{6},\frac{9}{11},\frac{13}{16},\frac{17}{21},\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(\frac{4n+1}{5n+1}\)

Step 1

Concept

The numerator \(5,9,13,\ldots\) gives (4n+1), and the denominator \(6,11,16,\ldots\) gives (5n+1). Make separate rules for both sequences.

Step 2

Why this answer is correct

The correct answer is D. \(\frac{4n+1}{5n+1}\). The numerator \(5,9,13,\ldots\) gives (4n+1), and the denominator \(6,11,16,\ldots\) gives (5n+1). Make separate rules for both sequences.

Step 3

Exam Tip

अंश \(5,9,13,\ldots\) से (4n+1) और हर \(6,11,16,\ldots\) से (5n+1) है। दोनों श्रेणियों का अलग नियम बनाएं।

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

यदि \(a_n=n^2+2n+5\) है तो \(a_9-a_1\) का मान क्या है?

If \(a_n=n^2+2n+5\), what is the value of \(a_9-a_1\)?

Explanation opens after your attempt

Correct Answer

B. (96)

Step 1

Concept

\(a_9=104\) and \(a_1=8\), so the difference is (96). Find the smaller term correctly first.

Step 2

Why this answer is correct

The correct answer is B. (96). \(a_9=104\) and \(a_1=8\), so the difference is (96). Find the smaller term correctly first.

Step 3

Exam Tip

\(a_9=104\) और \(a_1=8\) है इसलिए अंतर (96) है। पहले छोटे पद को सही निकालें।

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

यदि \(a_n=an+b\), \(a_2+a_9=54\) और \(a_4+a_{11}=78\) है तो \(a_{12}\) क्या होगा?

If \(a_n=an+b\), \(a_2+a_9=54\), and \(a_4+a_{11}=78\), what will be \(a_{12}\)?

Explanation opens after your attempt

Correct Answer

C. (66)

Step 1

Concept

Subtracting the two sums gives (4a=24), so (a=6). Then (b=-6) and \(a_{12}=66\).

Step 2

Why this answer is correct

The correct answer is C. (66). Subtracting the two sums gives (4a=24), so (a=6). Then (b=-6) and \(a_{12}=66\).

Step 3

Exam Tip

दोनों योग घटाने पर (4a=24) इसलिए (a=6) है। फिर (b=-6) और \(a_{12}=66\) मिलता है।

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

श्रेणी \(10,21,36,55,78,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(10,21,36,55,78,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(2n^2+5n+3\)

Step 1

Concept

The second difference is (4), so the coefficient of \(n^2\) is (2). Substitution gives \(2n^2+5n+3\).

Step 2

Why this answer is correct

The correct answer is A. \(2n^2+5n+3\). The second difference is (4), so the coefficient of \(n^2\) is (2). Substitution gives \(2n^2+5n+3\).

Step 3

Exam Tip

दूसरा अंतर (4) है इसलिए \(n^2\) का गुणांक (2) होगा। मान रखने पर \(2n^2+5n+3\) सही है।

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

यदि \(a_n=100-7n\) है तो (30) से छोटा पहला पद कौन सा है?

If \(a_n=100-7n\), which is the first term less than (30)?

Explanation opens after your attempt

Correct Answer

D. (11)वाँ पद(11)th term

Step 1

Concept

From (100-7n<30), we get (n>10). The first natural value is (11).

Step 2

Why this answer is correct

The correct answer is D. (11)वाँ पद / (11)th term. From (100-7n<30), we get (n>10). The first natural value is (11).

Step 3

Exam Tip

(100-7n<30) से (n>10) मिलता है। पहला प्राकृतिक मान (11) है।

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

यदि \(a_n=\frac{2n^2+1}{n+1}\) है तो \(a_4\) का मान क्या है?

If \(a_n=\frac{2n^2+1}{n+1}\), what is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{33}{5}\)

Step 1

Concept

Putting (n=4) gives \(\frac{33}{5}\). Simplify numerator and denominator separately in a fraction.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{33}{5}\). Putting (n=4) gives \(\frac{33}{5}\). Simplify numerator and denominator separately in a fraction.

Step 3

Exam Tip

(n=4) रखने पर \(\frac{33}{5}\) मिलता है। भिन्न में अंश और हर अलग सरल करें।

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

श्रेणी \(2,6,14,30,62,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(2,6,14,30,62,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(2^{n+1}-2\)

Step 1

Concept

The terms are \(4-2,8-2,16-2,\ldots\). In exponential patterns, look for fixed subtraction.

Step 2

Why this answer is correct

The correct answer is C. \(2^{n+1}-2\). The terms are \(4-2,8-2,16-2,\ldots\). In exponential patterns, look for fixed subtraction.

Step 3

Exam Tip

पद \(4-2,8-2,16-2,\ldots\) हैं। घातीय पैटर्न में स्थिर घटाव देखें।

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

यदि \(a_n=n^2+mn+4\) और \(a_2+a_4=46\) है तो (m) का मान क्या है?

If \(a_n=n^2+mn+4\) and \(a_2+a_4=46\), what is the value of (m)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

\(a_2=8+2m\) and \(a_4=20+4m\). From (28+6m=46), (m=3).

Step 2

Why this answer is correct

The correct answer is A. (3). \(a_2=8+2m\) and \(a_4=20+4m\). From (28+6m=46), (m=3).

Step 3

Exam Tip

\(a_2=8+2m\) और \(a_4=20+4m\) है। (28+6m=46) से (m=3) मिलता है।

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

श्रेणी \(3,13,33,63,103,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(3,13,33,63,103,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(5n^2-5n+3\)

Step 1

Concept

The second difference is (10), so the coefficient of \(n^2\) is (5). The correct formula is \(5n^2-5n+3\).

Step 2

Why this answer is correct

The correct answer is D. \(5n^2-5n+3\). The second difference is (10), so the coefficient of \(n^2\) is (5). The correct formula is \(5n^2-5n+3\).

Step 3

Exam Tip

दूसरा अंतर (10) है इसलिए \(n^2\) का गुणांक (5) होगा। सही सूत्र \(5n^2-5n+3\) है।

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

यदि (a_n=n(n+4)) है तो (117) कौन सा पद है?

If (a_n=n(n+4)), which term is (117)?

Explanation opens after your attempt

Correct Answer

B. (9)वाँ(9)th

Step 1

Concept

Putting (n=9) in (n(n+4)=117) gives \(9\cdot13=117\). Checking options is simple here.

Step 2

Why this answer is correct

The correct answer is B. (9)वाँ / (9)th. Putting (n=9) in (n(n+4)=117) gives \(9\cdot13=117\). Checking options is simple here.

Step 3

Exam Tip

(n(n+4)=117) में (n=9) रखने पर \(9\cdot13=117\) मिलता है। विकल्पों से जांचना यहां सरल है।

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

यदि (a_n=4n+(-1)^{n+1}) है तो \(a_8\) का मान क्या होगा?

If (a_n=4n+(-1)^{n+1}), what will be the value of \(a_8\)?

Explanation opens after your attempt

Correct Answer

C. (31)

Step 1

Concept

(a_8=32+(-1)⁹=31). Check the parity of the exponent in ((-1)^{n+1}).

Step 2

Why this answer is correct

The correct answer is C. (31). (a_8=32+(-1)⁹=31). Check the parity of the exponent in ((-1)^{n+1}).

Step 3

Exam Tip

(a_8=32+(-1)⁹=31) है। ((-1)^{n+1}) में घात की विषमता देखें।

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

श्रेणी \(\frac{2}{9},\frac{5}{16},\frac{8}{23},\frac{11}{30},\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(\frac{2}{9},\frac{5}{16},\frac{8}{23},\frac{11}{30},\ldots\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{3n-1}{7n+2}\)

Step 1

Concept

The numerator is (3n-1), and the denominator is (7n+2). Make separate arithmetic rules.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{3n-1}{7n+2}\). The numerator is (3n-1), and the denominator is (7n+2). Make separate arithmetic rules.

Step 3

Exam Tip

अंश (3n-1) और हर (7n+2) के रूप में है। अलग-अलग समांतर नियम बनाएं।

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

यदि \(a_n=2n^3-n\) है तो \(a_4-a_2\) का मान क्या है?

If \(a_n=2n^3-n\), what is the value of \(a_4-a_2\)?

Explanation opens after your attempt

Correct Answer

D. (110)

Step 1

Concept

\(a_4=124\) and \(a_2=14\), so the difference is (110). Recheck calculations in cubic terms.

Step 2

Why this answer is correct

The correct answer is D. (110). \(a_4=124\) and \(a_2=14\), so the difference is (110). Recheck calculations in cubic terms.

Step 3

Exam Tip

\(a_4=124\) और \(a_2=14\) है इसलिए अंतर (110) है। घन वाले पदों में गणना दोबारा जांचें।

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

श्रेणी \(5,18,43,80,129,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(5,18,43,80,129,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(6n^2-5n+4\)

Step 1

Concept

The second difference is (12), so the coefficient of \(n^2\) is (6). Checking gives \(6n^2-5n+4\).

Step 2

Why this answer is correct

The correct answer is B. \(6n^2-5n+4\). The second difference is (12), so the coefficient of \(n^2\) is (6). Checking gives \(6n^2-5n+4\).

Step 3

Exam Tip

दूसरा अंतर (12) है इसलिए \(n^2\) का गुणांक (6) होगा। जांचने पर \(6n^2-5n+4\) सही है।

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

यदि \(a_n=3n^2-5n+7\) है तो \(a_{n+1}-a_n\) क्या होगा?

If \(a_n=3n^2-5n+7\), what is \(a_{n+1}-a_n\)?

Explanation opens after your attempt

Correct Answer

C. (6n-2)

Step 1

Concept

Expanding \(a_{n+1}\) and subtracting gives (6n-2). Pay attention to the sign of the negative term.

Step 2

Why this answer is correct

The correct answer is C. (6n-2). Expanding \(a_{n+1}\) and subtracting gives (6n-2). Pay attention to the sign of the negative term.

Step 3

Exam Tip

\(a_{n+1}\) का विस्तार करके घटाने पर (6n-2) मिलता है। ऋणात्मक पद का चिह्न ध्यान रखें।

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

यदि (a_n=\frac{n(n+1)}{2}+3) है तो \(a_{10}\) क्या होगा?

If (a_n=\frac{n(n+1)}{2}+3), what will be \(a_{10}\)?

Explanation opens after your attempt

Correct Answer

A. (58)

Step 1

Concept

\(\frac{10\cdot11}{2}=55\) and (55+3=58). Do not forget the constant addition after the triangular number.

Step 2

Why this answer is correct

The correct answer is A. (58). \(\frac{10\cdot11}{2}=55\) and (55+3=58). Do not forget the constant addition after the triangular number.

Step 3

Exam Tip

\(\frac{10\cdot11}{2}=55\) और (55+3=58) है। त्रिभुज संख्या के बाद स्थिर जोड़ न भूलें।

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

श्रेणी \(12,20,30,42,56,\ldots\) का (n)वाँ पद कौन सा है?

Which is the (n)th term of the sequence \(12,20,30,42,56,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(n^2+5n+6\)

Step 1

Concept

The terms are like ((n+2)(n+3)). Therefore the formula is \(n^2+5n+6\).

Step 2

Why this answer is correct

The correct answer is D. \(n^2+5n+6\). The terms are like ((n+2)(n+3)). Therefore the formula is \(n^2+5n+6\).

Step 3

Exam Tip

पद ((n+2)(n+3)) जैसे हैं। इसलिए सूत्र \(n^2+5n+6\) बनता है।

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

यदि \(a_n=8n-17\) है तो पहला धनात्मक पद कौन सा होगा?

If \(a_n=8n-17\), which will be the first positive term?

Explanation opens after your attempt

Correct Answer

B. (3)वाँ पद(3)rd term

Step 1

Concept

From (8n-17>0), we get \(n>\frac{17}{8}\). The first natural value is (3).

Step 2

Why this answer is correct

The correct answer is B. (3)वाँ पद / (3)rd term. From (8n-17>0), we get \(n>\frac{17}{8}\). The first natural value is (3).

Step 3

Exam Tip

(8n-17>0) से \(n>\frac{17}{8}\) मिलता है। पहला प्राकृतिक मान (3) है।

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

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

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

Explanation opens after your attempt

Correct Answer

C. \(\frac{19}{15}\)

Step 1

Concept

Putting (n=7) gives \(\frac{21-2}{15}=\frac{19}{15}\). Simplify numerator and denominator separately.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{19}{15}\). Putting (n=7) gives \(\frac{21-2}{15}=\frac{19}{15}\). Simplify numerator and denominator separately.

Step 3

Exam Tip

(n=7) रखने पर \(\frac{21-2}{15}=\frac{19}{15}\) मिलता है। अंश और हर को अलग-अलग सरल करें।

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

श्रेणी \(4,-7,10,-13,16,\ldots\) का (n)वाँ पद क्या है?

What is the (n)th term of the sequence \(4,-7,10,-13,16,\ldots\)?

Explanation opens after your attempt

Correct Answer

A. ((-1)^{n+1}(3n+1))

Step 1

Concept

The magnitudes are (3n+1), and signs alternate. For a positive first term, ((-1)^{n+1}) is correct.

Step 2

Why this answer is correct

The correct answer is A. ((-1)^{n+1}(3n+1)). The magnitudes are (3n+1), and signs alternate. For a positive first term, ((-1)^{n+1}) is correct.

Step 3

Exam Tip

मान (3n+1) हैं और चिह्न बारी-बारी से बदलता है। धनात्मक पहले पद के लिए ((-1)^{n+1}) सही है।

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

यदि \(a_n=an^2+bn+1\), \(a_1=6\) और \(a_2=17\) है तो \(a_5\) क्या होगा?

If \(a_n=an^2+bn+1\), \(a_1=6\), and \(a_2=17\), what will be \(a_5\)?

Explanation opens after your attempt

Correct Answer

D. (86)

Step 1

Concept

From (a+b=5) and (2a+b=8), we get (a=3), (b=2). Therefore \(a_5=86\).

Step 2

Why this answer is correct

The correct answer is D. (86). From (a+b=5) and (2a+b=8), we get (a=3), (b=2). Therefore \(a_5=86\).

Step 3

Exam Tip

(a+b=5) और (2a+b=8) से (a=3), (b=2) मिलता है। इसलिए \(a_5=86\) है।

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

यदि \(a_n=2n^2+7n-4\) है तो \(a_8-a_3\) का मान क्या होगा?

If \(a_n=2n^2+7n-4\), what will be the value of \(a_8-a_3\)?

Explanation opens after your attempt

Correct Answer

C. (155)

Step 1

Concept

\(a_8=180\) and \(a_3=25\), so the difference is (155). In such questions, find both terms separately and subtract.

Step 2

Why this answer is correct

The correct answer is C. (155). \(a_8=180\) and \(a_3=25\), so the difference is (155). In such questions, find both terms separately and subtract.

Step 3

Exam Tip

\(a_8=180\) और \(a_3=25\) है इसलिए अंतर (155) है। ऐसे प्रश्नों में दोनों पद अलग-अलग निकालकर घटाएं।

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Class 9 Mathematics - Exploring Algebraic Identities - Factorisation Expert Quiz

यदि किसी श्रेणी का (n)वाँ पद \(a_n=6n-5\) है तो (18)वाँ पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

श्रेणी \(8,15,24,35,48,\ldots\) का (n)वाँ पद कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=4n^2-3n+2\) है तो \(a_7-a_4\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

श्रेणी \(3,9,18,30,45,\ldots\) का (n)वाँ पद क्या है?

Concept

Why this answer is correct

Exam Tip

एक रैखिक श्रेणी में \(a_5=23\) और \(a_{12}=58\) है तो \(a_{20}\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

श्रेणी \(\frac{4}{7},\frac{7}{10},\frac{10}{13},\frac{13}{16},\ldots\) का (n)वाँ पद कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=3n^2+2\) है तो (149) कौन सा पद है?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=40-5n\) है तो पहला ऋणात्मक पद कौन सा होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=kn^2-n\) और \(a_6=210\) है तो \(a_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

श्रेणी \(2,11,28,53,86,\ldots\) का (n)वाँ पद कौन सा है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(a_n=pn+q\), \(a_4+a_7=64\) और \(a_5+a_8=76\) है तो \(a_{10}\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

श्रेणी \(7,17,31,49,71,\ldots\) का (n)वाँ पद क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (a_n=\frac{n(n+5)}{3}) है तो \(a_6\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

श्रेणी \(0,5,16,33,56,\ldots\) का (n)वाँ पद कौन सा है?

Concept

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Exam Tip

यदि \(a_n=7n-9\) है तो (131) कौन सा पद है?

Concept

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Exam Tip

यदि \(a_n=n^2-6n+13\) है तो सबसे छोटा पद मान क्या है?

Concept

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Exam Tip

श्रेणी \(\frac{1}{3},\frac{4}{8},\frac{9}{15},\frac{16}{24},\ldots\) का सरल (n)वाँ पद क्या है?

Concept

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यदि \(a_n=5\cdot3^{n-1}-2\) है तो \(a_4\) क्या होगा?

Concept

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