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

Question 1/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(4,11,22,37,56,\ldots\) का (n)वाँ पद \(a_n=n^2+3n+1\) है। (12)वाँ पद क्या होगा?

The sequence \(4,11,22,37,56,\ldots\) has (n)th term \(a_n=n^2+3n+1\). What will be the (12)th term?

Explanation opens after your attempt

Correct Answer

B. (181)

Step 1

Concept

\(a_{12}=12^2+3\times12+1=181\). Exam tip: substitute the term position for (n).

Step 2

Why this answer is correct

The correct answer is B. (181). \(a_{12}=12^2+3\times12+1=181\). Exam tip: substitute the term position for (n).

Step 3

Exam Tip

\(a_{12}=12^2+3\times12+1=181\) है। सूत्र में (n) की जगह पद संख्या रखें।

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Question 2/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(6,14,26,42,\ldots\) के लिए \(a_n=2n^2+2n+2\) है। \(a_{15}-a_{13}\) का मान क्या है?

For the sequence \(6,14,26,42,\ldots\), \(a_n=2n^2+2n+2\). What is the value of \(a_{15}-a_{13}\)?

Explanation opens after your attempt

Correct Answer

D. (116)

Step 1

Concept

\(a_{15}=482\) and \(a_{13}=366\), so the difference is (116). Exam tip: find both terms separately first.

Step 2

Why this answer is correct

The correct answer is D. (116). \(a_{15}=482\) and \(a_{13}=366\), so the difference is (116). Exam tip: find both terms separately first.

Step 3

Exam Tip

\(a_{15}=482\) और \(a_{13}=366\) इसलिए अंतर (116) है। पहले दोनों पद अलग-अलग निकालें।

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Question 3/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(2,5,10,17,26,\ldots\) में अगला पद क्या होगा?

What will be the next term in the sequence \(2,5,10,17,26,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (37)

Step 1

Concept

The terms are of the form \(n^2+1\), so the next term is \(6^2+1=37\). Exam tip: recognize patterns built around squares.

Step 2

Why this answer is correct

The correct answer is C. (37). The terms are of the form \(n^2+1\), so the next term is \(6^2+1=37\). Exam tip: recognize patterns built around squares.

Step 3

Exam Tip

यहाँ पद \(n^2+1\) के रूप में हैं इसलिए अगला पद \(6^2+1=37\) है। वर्ग के आसपास बने पैटर्न को जल्दी पहचानें।

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Question 4/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(2,6,12,20,\ldots\) में (a_n=n(n+1)) है। कौन सा पद (210) है?

In the sequence \(2,6,12,20,\ldots\), (a_n=n(n+1)). Which term is (210)?

Explanation opens after your attempt

Correct Answer

A. (14)वाँ(14)th

Step 1

Concept

Since \(14\times15=210\), it is the (14)th term. Exam tip: look for products of consecutive numbers.

Step 2

Why this answer is correct

The correct answer is A. (14)वाँ / (14)th. Since \(14\times15=210\), it is the (14)th term. Exam tip: look for products of consecutive numbers.

Step 3

Exam Tip

\(14\times15=210\) इसलिए यह (14)वाँ पद है। लगातार संख्याओं के गुणनफल को ध्यान से देखें।

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Question 5/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(3,6,10,15,21,\ldots\) में (20)वाँ पद क्या होगा?

What will be the (20)th term in the sequence \(3,6,10,15,21,\ldots\)?

Explanation opens after your attempt

Correct Answer

C. (231)

Step 1

Concept

This sequence gives (\frac{(n+1)(n+2)}{2}). For the (20)th term, \(\frac{21\times22}{2}=231\).

Step 2

Why this answer is correct

The correct answer is C. (231). This sequence gives (\frac{(n+1)(n+2)}{2}). For the (20)th term, \(\frac{21\times22}{2}=231\).

Step 3

Exam Tip

यह अनुक्रम (\frac{(n+1)(n+2)}{2}) देता है। (20)वें पद के लिए \(\frac{21\times22}{2}=231\) होगा।

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Question 6/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(1,5,14,30,55,\ldots\) में क्रमागत अंतर \(4,9,16,25,\ldots\) हैं। अगला पद क्या होगा?

In the sequence \(1,5,14,30,55,\ldots\), the successive differences are \(4,9,16,25,\ldots\). What will be the next term?

Explanation opens after your attempt

Correct Answer

B. (91)

Step 1

Concept

The next difference is (36), so (55+36=91). Exam tip: differences can also form a sequence.

Step 2

Why this answer is correct

The correct answer is B. (91). The next difference is (36), so (55+36=91). Exam tip: differences can also form a sequence.

Step 3

Exam Tip

अगला अंतर (36) होगा इसलिए (55+36=91) है। अंतर भी कभी-कभी अलग अनुक्रम बनाते हैं।

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Question 7/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(2,11,26,47,74,\ldots\) में अगला पद क्या होगा?

What will be the next term in the sequence \(2,11,26,47,74,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. (107)

Step 1

Concept

The differences are (9,15,21,27), so the next difference is (33). Hence (74+33=107).

Step 2

Why this answer is correct

The correct answer is D. (107). The differences are (9,15,21,27), so the next difference is (33). Hence (74+33=107).

Step 3

Exam Tip

अंतर (9,15,21,27) हैं इसलिए अगला अंतर (33) होगा। (74+33=107) सही है।

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Question 8/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(3,4,6,8,12,16,\ldots\) में दो छिपे हुए अनुक्रम हैं। अगला पद क्या होगा?

In the sequence \(3,4,6,8,12,16,\ldots\), two hidden sequences are present. What will be the next term?

Explanation opens after your attempt

Correct Answer

A. (24)

Step 1

Concept

Odd positions are \(3,6,12,\ldots\), so the next odd-position term is (24). Exam tip: split alternating sequences by positions.

Step 2

Why this answer is correct

The correct answer is A. (24). Odd positions are \(3,6,12,\ldots\), so the next odd-position term is (24). Exam tip: split alternating sequences by positions.

Step 3

Exam Tip

विषम स्थानों पर \(3,6,12,\ldots\) हैं इसलिए अगला विषम पद (24) है। वैकल्पिक अनुक्रमों में स्थान अलग करके देखें।

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

अनुक्रम \(5,7,14,16,32,34,\ldots\) में क्रम है (2) जोड़ना फिर (2) से गुणा करना। अगला पद क्या होगा?

In the sequence \(5,7,14,16,32,34,\ldots\), the pattern is add (2) and then multiply by (2). What will be the next term?

Explanation opens after your attempt

Correct Answer

C. (68)

Step 1

Concept

After (34), multiplication by (2) is applied, so the next term is (68). Exam tip: identify the next operation in alternating-operation sequences.

Step 2

Why this answer is correct

The correct answer is C. (68). After (34), multiplication by (2) is applied, so the next term is (68). Exam tip: identify the next operation in alternating-operation sequences.

Step 3

Exam Tip

(34) के बाद (2) से गुणा होगा इसलिए अगला पद (68) है। वैकल्पिक क्रिया में अगली क्रिया पहचानना जरूरी है।

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Question 10/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_1=1\) और \(a_{n+1}=2a_n+n\) है तो \(a_5\) क्या होगा?

If \(a_1=1\) and \(a_{n+1}=2a_n+n\), what will be \(a_5\)?

Explanation opens after your attempt

Correct Answer

B. (42)

Step 1

Concept

The terms are (1,3,8,19,42), so \(a_5=42\). Exam tip: apply each recursive step carefully.

Step 2

Why this answer is correct

The correct answer is B. (42). The terms are (1,3,8,19,42), so \(a_5=42\). Exam tip: apply each recursive step carefully.

Step 3

Exam Tip

पद (1,3,8,19,42) मिलते हैं इसलिए \(a_5=42\) है। पुनरावर्ती नियम में हर चरण सावधानी से करें।

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Question 11/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_1=4\) और \(a_{n+1}=a_n+2n+1\) है तो \(a_7\) का मान क्या है?

If \(a_1=4\) and \(a_{n+1}=a_n+2n+1\), what is the value of \(a_7\)?

Explanation opens after your attempt

Correct Answer

D. (52)

Step 1

Concept

The terms are (4,7,12,19,28,39,52). Exam tip: write term positions to reduce recursive mistakes.

Step 2

Why this answer is correct

The correct answer is D. (52). The terms are (4,7,12,19,28,39,52). Exam tip: write term positions to reduce recursive mistakes.

Step 3

Exam Tip

पद (4,7,12,19,28,39,52) हैं। क्रमांक साथ लिखने से पुनरावर्ती गलती कम होती है।

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Question 12/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि (a_n=(-1)^{n+1}n^-2) है तो \(a_9+a_{10}\) का मान क्या होगा?

If (a_n=(-1)^{n+1}n^-2), what will be the value of \(a_9+a_{10}\)?

Explanation opens after your attempt

Correct Answer

A. (-19)

Step 1

Concept

\(a_9=81\) and \(a_{10}=-100\), so the sum is (-19). Exam tip: track both power and sign.

Step 2

Why this answer is correct

The correct answer is A. (-19). \(a_9=81\) and \(a_{10}=-100\), so the sum is (-19). Exam tip: track both power and sign.

Step 3

Exam Tip

\(a_9=81\) और \(a_{10}=-100\) इसलिए योग (-19) है। घात और संकेत दोनों पर ध्यान दें।

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Question 13/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(1,4,13,40,121,\ldots\) में हर अगला पद पिछले पद का (3) गुना करके (1) जोड़ने से मिलता है। छठा पद क्या है?

In the sequence \(1,4,13,40,121,\ldots\), each next term is obtained by multiplying the previous term by (3) and adding (1). What is the sixth term?

Explanation opens after your attempt

Correct Answer

C. (364)

Step 1

Concept

\(3\times121+1=364\). Exam tip: apply the given rule directly to the last term.

Step 2

Why this answer is correct

The correct answer is C. (364). \(3\times121+1=364\). Exam tip: apply the given rule directly to the last term.

Step 3

Exam Tip

\(3\times121+1=364\) है। दिए गए नियम को अंतिम पद पर सीधे लगाएँ।

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Question 14/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

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

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

Explanation opens after your attempt

Correct Answer

B. (70)

Step 1

Concept

\(a_6=2^6+6=70\). Exam tip: calculate the power first and then add.

Step 2

Why this answer is correct

The correct answer is B. (70). \(a_6=2^6+6=70\). Exam tip: calculate the power first and then add.

Step 3

Exam Tip

\(a_6=2^6+6=70\) है। घात निकालने के बाद ही जोड़ करें।

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Question 15/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(1,3,7,15,31,\ldots\) में कौन सा पद (127) है?

In the sequence \(1,3,7,15,31,\ldots\), which term is (127)?

Explanation opens after your attempt

Correct Answer

D. (7)वाँ(7)th

Step 1

Concept

This sequence is \(2^n-1\), and \(2^7-1=127\). Exam tip: recognizing powers of (2) is useful.

Step 2

Why this answer is correct

The correct answer is D. (7)वाँ / (7)th. This sequence is \(2^n-1\), and \(2^7-1=127\). Exam tip: recognizing powers of (2) is useful.

Step 3

Exam Tip

यह अनुक्रम \(2^n-1\) है और \(2^7-1=127\) है। (2) की घातों को पहचानना उपयोगी है।

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Question 16/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(4,9,16,25,\ldots\) में (169) कौन सा पद है?

In the sequence \(4,9,16,25,\ldots\), which term is (169)?

Explanation opens after your attempt

Correct Answer

A. (12)वाँ(12)th

Step 1

Concept

This is \(2^2,3^2,4^2,\ldots\), so \(169=13^2\) is the (12)th term. Exam tip: count positions carefully in shifted square sequences.

Step 2

Why this answer is correct

The correct answer is A. (12)वाँ / (12)th. This is \(2^2,3^2,4^2,\ldots\), so \(169=13^2\) is the (12)th term. Exam tip: count positions carefully in shifted square sequences.

Step 3

Exam Tip

यह \(2^2,3^2,4^2,\ldots\) है इसलिए \(169=13^2\) (12)वाँ पद है। शिफ्ट हुए वर्ग अनुक्रम में क्रमांक ध्यान से गिनें।

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Question 17/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम (7,12,x,34,51) में अंतर (5,9,13,17) के क्रम में बढ़ते हैं। (x) का मान क्या है?

In the sequence (7,12,x,34,51), the differences increase as (5,9,13,17). What is the value of (x)?

Explanation opens after your attempt

Correct Answer

C. (21)

Step 1

Concept

(12+9=21) and (21+13=34). Exam tip: check both sides of a missing term.

Step 2

Why this answer is correct

The correct answer is C. (21). (12+9=21) and (21+13=34). Exam tip: check both sides of a missing term.

Step 3

Exam Tip

(12+9=21) और (21+13=34) है। missing पद के दोनों तरफ जाँच करें।

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Question 18/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम (100,96,89,x,66) में अंतर (-4,-7,-10,-13) हैं। (x) क्या होगा?

In the sequence (100,96,89,x,66), the differences are (-4,-7,-10,-13). What will (x) be?

Explanation opens after your attempt

Correct Answer

B. (79)

Step 1

Concept

(89-10=79) and (79-13=66). Exam tip: handle negative signs carefully in decreasing sequences.

Step 2

Why this answer is correct

The correct answer is B. (79). (89-10=79) and (79-13=66). Exam tip: handle negative signs carefully in decreasing sequences.

Step 3

Exam Tip

(89-10=79) और (79-13=66) है। घटते अनुक्रम में ऋण चिह्न सावधानी से रखें।

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Question 19/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(2,6,18,54,\ldots\) में प्रत्येक पद पिछले पद का (3) गुना है। आठवाँ पद क्या होगा?

In the sequence \(2,6,18,54,\ldots\), each term is (3) times the previous term. What will be the eighth term?

Explanation opens after your attempt

Correct Answer

D. (4374)

Step 1

Concept

The eighth term is \(2\times3^7=4374\). Exam tip: from the first term, the exponent is (n-1).

Step 2

Why this answer is correct

The correct answer is D. (4374). The eighth term is \(2\times3^7=4374\). Exam tip: from the first term, the exponent is (n-1).

Step 3

Exam Tip

आठवाँ पद \(2\times3^7=4374\) है। पहले पद से गिनते समय घात (n-1) होती है।

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Question 20/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(512,256,128,64,\ldots\) में पहला पद जो (10) से छोटा है कौन सा है?

In the sequence \(512,256,128,64,\ldots\), which is the first term less than (10)?

Explanation opens after your attempt

Correct Answer

A. (7)वाँ(7)th

Step 1

Concept

The terms are (512,256,128,64,32,16,8), so the (7)th term is the first smaller term. Exam tip: move stepwise until the condition is met.

Step 2

Why this answer is correct

The correct answer is A. (7)वाँ / (7)th. The terms are (512,256,128,64,32,16,8), so the (7)th term is the first smaller term. Exam tip: move stepwise until the condition is met.

Step 3

Exam Tip

पद (512,256,128,64,32,16,8) हैं इसलिए (7)वाँ पद पहला छोटा पद है। शर्त वाले प्रश्न में क्रम से सीमा तक जाएँ।

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Question 21/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_n=3n^2-2n\) है तो कौन सा पद (408) के बराबर है?

If \(a_n=3n^2-2n\), which term is equal to (408)?

Explanation opens after your attempt

Correct Answer

C. (12)वाँ(12)th

Step 1

Concept

\(3\times12^2-2\times12=408\). Exam tip: test the given positions quickly in the formula.

Step 2

Why this answer is correct

The correct answer is C. (12)वाँ / (12)th. \(3\times12^2-2\times12=408\). Exam tip: test the given positions quickly in the formula.

Step 3

Exam Tip

\(3\times12^2-2\times12=408\) है। विकल्पों को जल्दी जाँचने के लिए दिए गए क्रमांक रखें।

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Question 22/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_n=n^3-n\) है तो \(a_7-a_5\) का मान क्या होगा?

If \(a_n=n^3-n\), what will be the value of \(a_7-a_5\)?

Explanation opens after your attempt

Correct Answer

B. (216)

Step 1

Concept

\(a_7=336\) and \(a_5=120\), so the difference is (216). Exam tip: calculate cube-based terms separately first.

Step 2

Why this answer is correct

The correct answer is B. (216). \(a_7=336\) and \(a_5=120\), so the difference is (216). Exam tip: calculate cube-based terms separately first.

Step 3

Exam Tip

\(a_7=336\) और \(a_5=120\) इसलिए अंतर (216) है। घन वाले पदों में पहले मान अलग निकालें।

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Question 23/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(5,12,23,38,57,\ldots\) के लिए सही सामान्य पद कौन सा है?

Which is the correct general term for the sequence \(5,12,23,38,57,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. \(a_n=2n^2+n+2\)

Step 1

Concept

\(2n^2+n+2\) gives the starting terms (5,12,23). Exam tip: check at least three terms before choosing a formula.

Step 2

Why this answer is correct

The correct answer is D. \(a_n=2n^2+n+2\). \(2n^2+n+2\) gives the starting terms (5,12,23). Exam tip: check at least three terms before choosing a formula.

Step 3

Exam Tip

\(2n^2+n+2\) से शुरुआती पद (5,12,23) मिलते हैं। सूत्र चुनते समय कम से कम तीन पद जाँचें।

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Question 24/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(3,10,21,36,55,\ldots\) का सामान्य पद \(a_n=2n^2+n\) है। (11)वाँ पद क्या होगा?

The sequence \(3,10,21,36,55,\ldots\) has general term \(a_n=2n^2+n\). What will be the (11)th term?

Explanation opens after your attempt

Correct Answer

A. (253)

Step 1

Concept

\(a_{11}=2\times11^2+11=253\). Exam tip: square and multiply first, then add.

Step 2

Why this answer is correct

The correct answer is A. (253). \(a_{11}=2\times11^2+11=253\). Exam tip: square and multiply first, then add.

Step 3

Exam Tip

\(a_{11}=2\times11^2+11=253\) है। वर्ग और गुणा पहले करके अंत में जोड़ें।

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Question 25/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_n=n^2+4n\) है तो (200) से छोटे कितने पद होंगे?

If \(a_n=n^2+4n\), how many terms will be less than (200)?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

\(a_{12}=192\) and \(a_{13}=221\), so (12) terms are less than (200). Exam tip: check the two terms near the boundary.

Step 2

Why this answer is correct

The correct answer is C. (12). \(a_{12}=192\) and \(a_{13}=221\), so (12) terms are less than (200). Exam tip: check the two terms near the boundary.

Step 3

Exam Tip

\(a_{12}=192\) और \(a_{13}=221\) है इसलिए (12) पद (200) से छोटे हैं। सीमा के पास वाले दो पद जरूर जाँचें।

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Question 26/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(5,12,19,26,\ldots\) में (50) से बड़े और (150) से छोटे कितने पद हैं?

In the sequence \(5,12,19,26,\ldots\), how many terms are greater than (50) and less than (150)?

Explanation opens after your attempt

Correct Answer

B. (14)

Step 1

Concept

The first valid term is (54) and the last valid term is (145). From the (8)th to the (21)st term, there are (14) terms.

Step 2

Why this answer is correct

The correct answer is B. (14). The first valid term is (54) and the last valid term is (145). From the (8)th to the (21)st term, there are (14) terms.

Step 3

Exam Tip

पहला योग्य पद (54) है और अंतिम योग्य पद (145) है। (8)वें से (21)वें पद तक कुल (14) पद हैं।

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Question 27/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(2,5,10,17,26,\ldots\) के पहले (5) पदों का योग क्या है?

What is the sum of the first (5) terms of the sequence \(2,5,10,17,26,\ldots\)?

Explanation opens after your attempt

Correct Answer

D. (60)

Step 1

Concept

The sum of the first (5) terms is (2+5+10+17+26=60). Exam tip: include all required terms in sum questions.

Step 2

Why this answer is correct

The correct answer is D. (60). The sum of the first (5) terms is (2+5+10+17+26=60). Exam tip: include all required terms in sum questions.

Step 3

Exam Tip

पहले (5) पदों का योग (2+5+10+17+26=60) है। योग प्रश्न में सभी मांगे गए पद शामिल करें।

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Question 28/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

एक अनुक्रम में \(a_1=2\) है और क्रमागत अंतर \(3,7,11,15,\ldots\) हैं। \(a_5\) क्या होगा?

In a sequence, \(a_1=2\) and the successive differences are \(3,7,11,15,\ldots\). What will be \(a_5\)?

Explanation opens after your attempt

Correct Answer

A. (38)

Step 1

Concept

\(a_5=2+3+7+11+15=38\). Exam tip: include the first term when adding differences.

Step 2

Why this answer is correct

The correct answer is A. (38). \(a_5=2+3+7+11+15=38\). Exam tip: include the first term when adding differences.

Step 3

Exam Tip

\(a_5=2+3+7+11+15=38\) है। अंतर जोड़ते समय पहला पद भी शामिल रखें।

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Question 29/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\ldots\) में (10)वाँ पद क्या होगा?

What will be the (10)th term in the sequence \(\frac{1}{2},\frac{2}{3},\frac{3}{4},\ldots\)?

Explanation opens after your attempt

Correct Answer

C. \(\frac{10}{11}\)

Step 1

Concept

The general term is \(\frac{n}{n+1}\), so the (10)th term is \(\frac{10}{11}\). Exam tip: observe numerator and denominator patterns separately.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{10}{11}\). The general term is \(\frac{n}{n+1}\), so the (10)th term is \(\frac{10}{11}\). Exam tip: observe numerator and denominator patterns separately.

Step 3

Exam Tip

सामान्य पद \(\frac{n}{n+1}\) है इसलिए (10)वाँ पद \(\frac{10}{11}\) है। भिन्नों में अंश और हर का पैटर्न अलग देखें।

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Question 30/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(\frac{1}{3},\frac{2}{5},\frac{3}{7},\ldots\) में (8)वाँ पद क्या होगा?

What will be the (8)th term in the sequence \(\frac{1}{3},\frac{2}{5},\frac{3}{7},\ldots\)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{8}{17}\)

Step 1

Concept

The general term is \(\frac{n}{2n+1}\), so the (8)th term is \(\frac{8}{17}\). Exam tip: identify the denominator pattern separately.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{8}{17}\). The general term is \(\frac{n}{2n+1}\), so the (8)th term is \(\frac{8}{17}\). Exam tip: identify the denominator pattern separately.

Step 3

Exam Tip

सामान्य पद \(\frac{n}{2n+1}\) है इसलिए (8)वाँ पद \(\frac{8}{17}\) है। हर में बढ़ोतरी अलग से पहचानें।

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Question 31/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\ldots\) में पहला पद जो \(\frac{1}{20}\) से छोटा है कौन सा है?

In the sequence \(1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\ldots\), which is the first term less than \(\frac{1}{20}\)?

Explanation opens after your attempt

Correct Answer

D. (21)वाँ(21)th

Step 1

Concept

\(\frac{1}{21}<\frac{1}{20}\), while \(\frac{1}{20}\) is not smaller. Exam tip: strict inequality does not include equality.

Step 2

Why this answer is correct

The correct answer is D. (21)वाँ / (21)th. \(\frac{1}{21}<\frac{1}{20}\), while \(\frac{1}{20}\) is not smaller. Exam tip: strict inequality does not include equality.

Step 3

Exam Tip

\(\frac{1}{21}<\frac{1}{20}\) है और \(\frac{1}{20}\) छोटा नहीं है। सख्त असमानता में बराबरी शामिल नहीं होती।

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Question 32/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_n=\frac{n}{n+2}\) है तो पहला पद जो \(\frac{4}{5}\) से बड़ा है कौन सा होगा?

If \(a_n=\frac{n}{n+2}\), which is the first term greater than \(\frac{4}{5}\)?

Explanation opens after your attempt

Correct Answer

A. (9)वाँ(9)th

Step 1

Concept

From \(\frac{n}{n+2}>\frac{4}{5}\), we get (n>8). The first integer is (n=9).

Step 2

Why this answer is correct

The correct answer is A. (9)वाँ / (9)th. From \(\frac{n}{n+2}>\frac{4}{5}\), we get (n>8). The first integer is (n=9).

Step 3

Exam Tip

\(\frac{n}{n+2}>\frac{4}{5}\) से (n>8) मिलता है। पहला पूर्णांक (n=9) है।

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Question 33/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(1,4,11,26,57,\ldots\) में नियम \(a_{n+1}=2a_n+n+1\) है। अगला पद क्या होगा?

In the sequence \(1,4,11,26,57,\ldots\), the rule is \(a_{n+1}=2a_n+n+1\). What will be the next term?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

After the fifth term, (n=5), so \(2\times57+6=120\). Exam tip: use the correct current value of (n) in recursion.

Step 2

Why this answer is correct

The correct answer is C. (120). After the fifth term, (n=5), so \(2\times57+6=120\). Exam tip: use the correct current value of (n) in recursion.

Step 3

Exam Tip

पाँचवें पद के बाद (n=5) है इसलिए \(2\times57+6=120\) होगा। पुनरावर्ती सूत्र में वर्तमान (n) सही रखें।

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Question 34/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_1=3\) और \(a_{n+1}=a_n+n^2\) है तो \(a_6\) क्या होगा?

If \(a_1=3\) and \(a_{n+1}=a_n+n^2\), what will be \(a_6\)?

Explanation opens after your attempt

Correct Answer

B. (58)

Step 1

Concept

The terms are (3,4,8,17,33,58). Exam tip: start adding squares from \(1^2\).

Step 2

Why this answer is correct

The correct answer is B. (58). The terms are (3,4,8,17,33,58). Exam tip: start adding squares from \(1^2\).

Step 3

Exam Tip

पद (3,4,8,17,33,58) मिलते हैं। वर्ग जोड़ते समय \(1^2\) से शुरुआत करें।

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Question 35/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_n=2n^3+1\) है तो \(a_5+a_6\) का मान क्या होगा?

If \(a_n=2n^3+1\), what will be the value of \(a_5+a_6\)?

Explanation opens after your attempt

Correct Answer

D. (684)

Step 1

Concept

\(a_5=251\) and \(a_6=433\), so the sum is (684). Exam tip: recheck calculations in cubic terms.

Step 2

Why this answer is correct

The correct answer is D. (684). \(a_5=251\) and \(a_6=433\), so the sum is (684). Exam tip: recheck calculations in cubic terms.

Step 3

Exam Tip

\(a_5=251\) और \(a_6=433\) इसलिए योग (684) है। घन पदों में गणना दोबारा जाँचें।

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Question 36/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि (a_n=5n-(-1)^n) है तो \(a_8\) का मान क्या होगा?

If (a_n=5n-(-1)^n), what will be the value of \(a_8\)?

Explanation opens after your attempt

Correct Answer

A. (39)

Step 1

Concept

\(a_8=40-1=39\) because ((-1)⁸=1). Exam tip: remember the sign of even and odd powers.

Step 2

Why this answer is correct

The correct answer is A. (39). \(a_8=40-1=39\) because ((-1)⁸=1). Exam tip: remember the sign of even and odd powers.

Step 3

Exam Tip

\(a_8=40-1=39\) है क्योंकि ((-1)⁸=1) होता है। सम और विषम घात का संकेत याद रखें।

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Question 37/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(2,9,28,65,\ldots\) में पद \(n^3+1\) के रूप में हैं। अगला पद क्या होगा?

In the sequence \(2,9,28,65,\ldots\), the terms are of the form \(n^3+1\). What will be the next term?

Explanation opens after your attempt

Correct Answer

C. (126)

Step 1

Concept

The next term is \(5^3+1=126\). Exam tip: notice the constant added to cubes.

Step 2

Why this answer is correct

The correct answer is C. (126). The next term is \(5^3+1=126\). Exam tip: notice the constant added to cubes.

Step 3

Exam Tip

अगला पद \(5^3+1=126\) है। घन के साथ जोड़ी गई स्थिर संख्या पर ध्यान दें।

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Question 38/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(0,3,10,21,36,\ldots\) का सामान्य पद \(a_n=2n^2-3n+1\) है। (12)वाँ पद क्या होगा?

The sequence \(0,3,10,21,36,\ldots\) has general term \(a_n=2n^2-3n+1\). What will be the (12)th term?

Explanation opens after your attempt

Correct Answer

B. (253)

Step 1

Concept

\(a_{12}=2\times12^2-3\times12+1=253\). Exam tip: write each step clearly in longer calculations.

Step 2

Why this answer is correct

The correct answer is B. (253). \(a_{12}=2\times12^2-3\times12+1=253\). Exam tip: write each step clearly in longer calculations.

Step 3

Exam Tip

\(a_{12}=2\times12^2-3\times12+1=253\) है। लंबी गणना में हर चरण साफ लिखें।

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Question 39/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(2,8,18,32,50,\ldots\) में \(a_n=2n^2\) है। (14)वाँ पद क्या होगा?

In the sequence \(2,8,18,32,50,\ldots\), \(a_n=2n^2\). What will be the (14)th term?

Explanation opens after your attempt

Correct Answer

D. (392)

Step 1

Concept

\(a_{14}=2\times14^2=392\). Exam tip: square first and then multiply.

Step 2

Why this answer is correct

The correct answer is D. (392). \(a_{14}=2\times14^2=392\). Exam tip: square first and then multiply.

Step 3

Exam Tip

\(a_{14}=2\times14^2=392\) है। वर्ग निकालकर फिर गुणा करें।

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Question 40/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि (x,x+3,2x+1) किसी अनुक्रम के लगातार तीन पद हैं और उनके अंतर बराबर हैं तो (x) का मान क्या है?

If (x,x+3,2x+1) are three consecutive terms of a sequence and their differences are equal, what is the value of (x)?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

Equal differences give (x+3-x=2x+1-(x+3)), so (x=5). Exam tip: set the two consecutive differences equal.

Step 2

Why this answer is correct

The correct answer is A. (5). Equal differences give (x+3-x=2x+1-(x+3)), so (x=5). Exam tip: set the two consecutive differences equal.

Step 3

Exam Tip

बराबर अंतर से (x+3-x=2x+1-(x+3)) मिलता है इसलिए (x=5) है। समान अंतर में दोनों अंतर बराबर रखें।

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

यदि \(a_n=kn+2\) और \(a_5=27\) है तो \(a_9\) का मान क्या होगा?

If \(a_n=kn+2\) and \(a_5=27\), what will be the value of \(a_9\)?

Explanation opens after your attempt

Correct Answer

C. (47)

Step 1

Concept

From (5k+2=27), (k=5), and \(a_9=47\). Exam tip: find the unknown constant first.

Step 2

Why this answer is correct

The correct answer is C. (47). From (5k+2=27), (k=5), and \(a_9=47\). Exam tip: find the unknown constant first.

Step 3

Exam Tip

(5k+2=27) से (k=5) और \(a_9=47\) मिलता है। पहले अज्ञात स्थिरांक निकालें।

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Question 42/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_n=pn^2+q\), \(a_1=5\) और \(a_2=14\) है तो \(a_4\) क्या होगा?

If \(a_n=pn^2+q\), \(a_1=5\) and \(a_2=14\), what will be \(a_4\)?

Explanation opens after your attempt

Correct Answer

B. (50)

Step 1

Concept

From (p+q=5) and (4p+q=14), we get (p=3) and (q=2). Then \(a_4=50\).

Step 2

Why this answer is correct

The correct answer is B. (50). From (p+q=5) and (4p+q=14), we get (p=3) and (q=2). Then \(a_4=50\).

Step 3

Exam Tip

(p+q=5) और (4p+q=14) से (p=3) और (q=2) मिलता है। फिर \(a_4=50\) होगा।

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Question 43/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि \(a_n=n^2+cn\) और \(a_4=32\) है तो \(a_9\) का मान क्या होगा?

If \(a_n=n^2+cn\) and \(a_4=32\), what will be the value of \(a_9\)?

Explanation opens after your attempt

Correct Answer

D. (117)

Step 1

Concept

From (16+4c=32), (c=4). Therefore \(a_9=81+36=117\).

Step 2

Why this answer is correct

The correct answer is D. (117). From (16+4c=32), (c=4). Therefore \(a_9=81+36=117\).

Step 3

Exam Tip

(16+4c=32) से (c=4) है। इसलिए \(a_9=81+36=117\) होगा।

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Question 44/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(2,6,12,20,\ldots\) में (100) से छोटे कितने पद हैं?

In the sequence \(2,6,12,20,\ldots\), how many terms are less than (100)?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

Here (a_n=n(n+1)), and \(9\times10=90\) while \(10\times11=110\). So (9) terms are less than (100).

Step 2

Why this answer is correct

The correct answer is A. (9). Here (a_n=n(n+1)), and \(9\times10=90\) while \(10\times11=110\). So (9) terms are less than (100).

Step 3

Exam Tip

यहाँ (a_n=n(n+1)) है और \(9\times10=90\) जबकि \(10\times11=110\) है। इसलिए (9) पद (100) से छोटे हैं।

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Question 45/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

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

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

Explanation opens after your attempt

Correct Answer

C. (57)

Step 1

Concept

\(a_5=2^5+5^2=32+25=57\). Exam tip: calculate the power and square separately.

Step 2

Why this answer is correct

The correct answer is C. (57). \(a_5=2^5+5^2=32+25=57\). Exam tip: calculate the power and square separately.

Step 3

Exam Tip

\(a_5=2^5+5^2=32+25=57\) है। घात और वर्ग दोनों अलग-अलग निकालें।

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Question 46/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(3,5,9,15,23,\ldots\) में (12)वाँ पद क्या होगा?

What will be the (12)th term in the sequence \(3,5,9,15,23,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (135)

Step 1

Concept

Here \(a_n=n^2-n+3\), so \(a_{12}=144-12+3=135\). Exam tip: identify the formula from initial differences.

Step 2

Why this answer is correct

The correct answer is B. (135). Here \(a_n=n^2-n+3\), so \(a_{12}=144-12+3=135\). Exam tip: identify the formula from initial differences.

Step 3

Exam Tip

यहाँ \(a_n=n^2-n+3\) है इसलिए \(a_{12}=144-12+3=135\) है। शुरुआती अंतरों से सूत्र पहचानें।

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Question 47/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि (a_n=\frac{n(n+3)}{2}) है तो कौन सा पद (65) है?

If (a_n=\frac{n(n+3)}{2}), which term is (65)?

Explanation opens after your attempt

Correct Answer

D. (10)वाँ(10)th

Step 1

Concept

Since \(\frac{10\times13}{2}=65\), it is the (10)th term. Exam tip: substitute options directly into the formula.

Step 2

Why this answer is correct

The correct answer is D. (10)वाँ / (10)th. Since \(\frac{10\times13}{2}=65\), it is the (10)th term. Exam tip: substitute options directly into the formula.

Step 3

Exam Tip

\(\frac{10\times13}{2}=65\) इसलिए यह (10)वाँ पद है। विकल्पों को सीधे सूत्र में रखकर जाँच सकते हैं।

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Question 48/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

यदि (a_n=n(n+2)) है तो \(a_{11}-a_8\) का मान क्या होगा?

If (a_n=n(n+2)), what will be the value of \(a_{11}-a_8\)?

Explanation opens after your attempt

Correct Answer

A. (63)

Step 1

Concept

\(a_{11}=143\) and \(a_8=80\), so the difference is (63). Exam tip: find the terms separately and then subtract.

Step 2

Why this answer is correct

The correct answer is A. (63). \(a_{11}=143\) and \(a_8=80\), so the difference is (63). Exam tip: find the terms separately and then subtract.

Step 3

Exam Tip

\(a_{11}=143\) और \(a_8=80\) है इसलिए अंतर (63) है। पदों को अलग निकालकर घटाएँ।

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Question 49/50 Expert Mathematics Sequences and Progressions Sequences Class 9 Level 41

अनुक्रम \(2,5,9,16,28,\ldots\) में अंतरों के अंतर \(1,3,5,\ldots\) हैं। अगला पद क्या होगा?

In the sequence \(2,5,9,16,28,\ldots\), the differences of differences are \(1,3,5,\ldots\). What will be the next term?

Explanation opens after your attempt

Correct Answer

C. (47)

Step 1

Concept

The differences are (3,4,7,12), and the next difference will be (19). Therefore (28+19=47).

Step 2

Why this answer is correct

The correct answer is C. (47). The differences are (3,4,7,12), and the next difference will be (19). Therefore (28+19=47).

Step 3

Exam Tip

अंतर (3,4,7,12) हैं और अगला अंतर (19) होगा। इसलिए (28+19=47) है।

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

अनुक्रम \(1,4,2,8,3,16,4,\ldots\) में (10)वाँ पद क्या होगा?

What will be the (10)th term in the sequence \(1,4,2,8,3,16,4,\ldots\)?

Explanation opens after your attempt

Correct Answer

B. (64)

Step 1

Concept

Even positions are \(4,8,16,32,64,\ldots\). The (10)th term is the fifth even-position term, so it is (64).

Step 2

Why this answer is correct

The correct answer is B. (64). Even positions are \(4,8,16,32,64,\ldots\). The (10)th term is the fifth even-position term, so it is (64).

Step 3

Exam Tip

सम स्थानों पर \(4,8,16,32,64,\ldots\) हैं। (10)वाँ पद पाँचवाँ सम-स्थान पद है इसलिए (64) है।

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

अनुक्रम \(4,11,22,37,56,\ldots\) का (n)वाँ पद \(a_n=n^2+3n+1\) है। (12)वाँ पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(6,14,26,42,\ldots\) के लिए \(a_n=2n^2+2n+2\) है। \(a_{15}-a_{13}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

अनुक्रम \(2,5,10,17,26,\ldots\) में अगला पद क्या होगा?

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Exam Tip

अनुक्रम \(2,6,12,20,\ldots\) में (a_n=n(n+1)) है। कौन सा पद (210) है?

Concept

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Exam Tip

अनुक्रम \(3,6,10,15,21,\ldots\) में (20)वाँ पद क्या होगा?

Concept

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Exam Tip

अनुक्रम \(1,5,14,30,55,\ldots\) में क्रमागत अंतर \(4,9,16,25,\ldots\) हैं। अगला पद क्या होगा?

Concept

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अनुक्रम \(2,11,26,47,74,\ldots\) में अगला पद क्या होगा?

Concept

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Exam Tip

अनुक्रम \(3,4,6,8,12,16,\ldots\) में दो छिपे हुए अनुक्रम हैं। अगला पद क्या होगा?

Concept

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Exam Tip

अनुक्रम \(5,7,14,16,32,34,\ldots\) में क्रम है (2) जोड़ना फिर (2) से गुणा करना। अगला पद क्या होगा?

Concept

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यदि \(a_1=1\) और \(a_{n+1}=2a_n+n\) है तो \(a_5\) क्या होगा?

Concept

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यदि \(a_1=4\) और \(a_{n+1}=a_n+2n+1\) है तो \(a_7\) का मान क्या है?

Concept

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Exam Tip

यदि (a_n=(-1)^{n+1}n-2) है तो \(a_9+a_{10}\) का मान क्या होगा?

Concept

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Exam Tip

अनुक्रम \(1,4,13,40,121,\ldots\) में हर अगला पद पिछले पद का (3) गुना करके (1) जोड़ने से मिलता है। छठा पद क्या है?

Concept

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

Concept

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Exam Tip

अनुक्रम \(1,3,7,15,31,\ldots\) में कौन सा पद (127) है?

Concept

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अनुक्रम \(4,9,16,25,\ldots\) में (169) कौन सा पद है?

Concept

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अनुक्रम (7,12,x,34,51) में अंतर (5,9,13,17) के क्रम में बढ़ते हैं। (x) का मान क्या है?

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अनुक्रम (100,96,89,x,66) में अंतर (-4,-7,-10,-13) हैं। (x) क्या होगा?

Concept

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Exam Tip

अनुक्रम \(2,6,18,54,\ldots\) में प्रत्येक पद पिछले पद का (3) गुना है। आठवाँ पद क्या होगा?

Concept

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Exam Tip

अनुक्रम \(512,256,128,64,\ldots\) में पहला पद जो (10) से छोटा है कौन सा है?

Concept

Why this answer is correct

यदि (a_n=(-1)^{n+1}n^-2) है तो \(a_9+a_{10}\) का मान क्या होगा?