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Mathematics Quiz - Class 11 Mathematics Permutations And...

Question 1/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (n>3) और (\frac{(n+1)!}{(n-2)!}=120) है तो (n) का मान क्या है?

If (n>3) and (\frac{(n+1)!}{(n-2)!}=120) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

After cancellation we get (n(n-1)(n+1)=120) and (n=4) satisfies it. In exams write consecutive factors first.

Step 2

Why this answer is correct

The correct answer is A. (4). After cancellation we get (n(n-1)(n+1)=120) and (n=4) satisfies it. In exams write consecutive factors first.

Step 3

Exam Tip

हर को काटने पर (n(n-1)(n+1)=120) मिलता है और (n=4) संतुष्ट करता है। परीक्षा में पहले क्रमागत गुणनखंड लिखें।

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Question 2/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(n+4)!}{(n+1)!}=990) है तो (n) का मान क्या है?

If (\frac{(n+4)!}{(n+1)!}=990) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

We get ((n+4)(n+3)(n+2)=990). Match consecutive factors carefully; (n=9) is correct.

Step 2

Why this answer is correct

The correct answer is C. (9). We get ((n+4)(n+3)(n+2)=990). Match consecutive factors carefully; (n=9) is correct.

Step 3

Exam Tip

((n+4)(n+3)(n+2)=990) मिलता है। \(13\times12\times11=1716\) नहीं इसलिए क्रमागत गुणनखंड ध्यान से मिलाएं और (n=9) सही है।

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Question 3/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(n+3)!-(n+2)!}{(n+1)!}=196) है तो (n) का मान क्या है?

If (\frac{(n+3)!-(n+2)!}{(n+1)!}=196) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

The numerator becomes ((n+2)!((n+3)-1)). So ((n+2)²=196) gives (n=12).

Step 2

Why this answer is correct

The correct answer is C. (12). The numerator becomes ((n+2)!((n+3)-1)). So ((n+2)²=196) gives (n=12).

Step 3

Exam Tip

ऊपर ((n+2)!((n+3)-1)) बनता है। इसलिए मान ((n+2)²=196) से (n=12) मिलता है।

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Question 4/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(n+2)!}{n!}=56) है तो (n) का धनात्मक मान क्या है?

If (\frac{(n+2)!}{n!}=56) then what is the positive value of (n)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

Simplification gives ((n+2)(n+1)=56). Hence (n=6) is correct.

Step 2

Why this answer is correct

The correct answer is B. (6). Simplification gives ((n+2)(n+1)=56). Hence (n=6) is correct.

Step 3

Exam Tip

सरलीकरण से ((n+2)(n+1)=56) मिलता है। अतः (n=6) सही है।

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Question 5/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{22!-21!}{20!}\) का मान क्या है?

What is the value of \(\frac{22!-21!}{20!}\)?

Explanation opens after your attempt

Correct Answer

B. (441)

Step 1

Concept

(22!-21!=21!(22-1)). Dividing by (20!) gives \(21\times21=441\).

Step 2

Why this answer is correct

The correct answer is B. (441). (22!-21!=21!(22-1)). Dividing by (20!) gives \(21\times21=441\).

Step 3

Exam Tip

(22!-21!=21!(22-1)) होता है। (20!) से भाग देने पर \(21\times21=441\) मिलता है।

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Question 6/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{9!}{7!}+\frac{8!}{6!}\) का मान क्या है?

What is the value of \(\frac{9!}{7!}+\frac{8!}{6!}\)?

Explanation opens after your attempt

Correct Answer

A. (128)

Step 1

Concept

Here \(\frac{9!}{7!}=72\) and \(\frac{8!}{6!}=56\) so the sum is (128). In exams cancel larger factorials quickly.

Step 2

Why this answer is correct

The correct answer is A. (128). Here \(\frac{9!}{7!}=72\) and \(\frac{8!}{6!}=56\) so the sum is (128). In exams cancel larger factorials quickly.

Step 3

Exam Tip

\(\frac{9!}{7!}=72\) और \(\frac{8!}{6!}=56\) इसलिए योग (128) है। परीक्षा में बड़े गुणनखंडों को तुरंत काटें।

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Question 7/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(75!) में (5) की अधिकतम घात क्या है?

What is the highest power of (5) in (75!)?

Explanation opens after your attempt

Correct Answer

C. (18)

Step 1

Concept

The exponent is \(\left\lfloor\frac{75}{5}\right\rfloor+\left\lfloor\frac{75}{25}\right\rfloor=15+3=18\). Add quotients of all possible powers of the prime.

Step 2

Why this answer is correct

The correct answer is C. (18). The exponent is \(\left\lfloor\frac{75}{5}\right\rfloor+\left\lfloor\frac{75}{25}\right\rfloor=15+3=18\). Add quotients of all possible powers of the prime.

Step 3

Exam Tip

घात \(\left\lfloor\frac{75}{5}\right\rfloor+\left\lfloor\frac{75}{25}\right\rfloor=15+3=18\) है। अभाज्य की सभी संभव घातों के भागफल जोड़ें।

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Question 8/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{12!}{10!\times 2!}\) का मान क्या है?

What is the value of \(\frac{12!}{10!\times 2!}\)?

Explanation opens after your attempt

Correct Answer

C. (66)

Step 1

Concept

\(\frac{12!}{10!\times 2!}=\frac{12\times11}{2}=66\). Do not expand the whole product in such questions.

Step 2

Why this answer is correct

The correct answer is C. (66). \(\frac{12!}{10!\times 2!}=\frac{12\times11}{2}=66\). Do not expand the whole product in such questions.

Step 3

Exam Tip

\(\frac{12!}{10!\times 2!}=\frac{12\times11}{2}=66\) होता है। ऐसे प्रश्नों में पूरा गुणनफल न फैलाएं।

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Question 9/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{24!}{21!\times 3!}\) का मान क्या है?

What is the value of \(\frac{24!}{21!\times 3!}\)?

Explanation opens after your attempt

Correct Answer

D. (2024)

Step 1

Concept

\(\frac{24!}{21!\times3!}=\frac{24\times23\times22}{6}=2024\). Avoid expanding the whole large factorial.

Step 2

Why this answer is correct

The correct answer is D. (2024). \(\frac{24!}{21!\times3!}=\frac{24\times23\times22}{6}=2024\). Avoid expanding the whole large factorial.

Step 3

Exam Tip

\(\frac{24!}{21!\times3!}=\frac{24\times23\times22}{6}=2024\) है। बड़े फैक्टोरियल को पूरा फैलाने से बचें।

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Question 10/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{15!}{13!\times 3}\) का मान क्या है?

What is the value of \(\frac{15!}{13!\times 3}\)?

Explanation opens after your attempt

Correct Answer

C. (70)

Step 1

Concept

\(\frac{15!}{13!\times3}=\frac{15\times14}{3}=70\). Removing common factorials first reduces mistakes.

Step 2

Why this answer is correct

The correct answer is C. (70). \(\frac{15!}{13!\times3}=\frac{15\times14}{3}=70\). Removing common factorials first reduces mistakes.

Step 3

Exam Tip

\(\frac{15!}{13!\times3}=\frac{15\times14}{3}=70\) है। पहले समान भाज्य हटाने से गलती कम होती है।

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Question 11/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{n!}{(n-5)!}=55440) है तो (n) का मान क्या है?

If (\frac{n!}{(n-5)!}=55440) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

This is (n(n-1)(n-2)(n-3)(n-4)=55440). Since \(11\times10\times9\times8\times7=55440\), (n=11).

Step 2

Why this answer is correct

The correct answer is B. (11). This is (n(n-1)(n-2)(n-3)(n-4)=55440). Since \(11\times10\times9\times8\times7=55440\), (n=11).

Step 3

Exam Tip

यह (n(n-1)(n-2)(n-3)(n-4)=55440) है। \(11\times10\times9\times8\times7=55440\) इसलिए (n=11) है।

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Question 12/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{n!}{(n-3)!}=210) है तो (n) का मान क्या है?

If (\frac{n!}{(n-3)!}=210) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

This gives (n(n-1)(n-2)=210) and \(7\times6\times5=210\). Therefore (n=7).

Step 2

Why this answer is correct

The correct answer is C. (7). This gives (n(n-1)(n-2)=210) and \(7\times6\times5=210\). Therefore (n=7).

Step 3

Exam Tip

यह (n(n-1)(n-2)=210) देता है और \(7\times6\times5=210\) है। इसलिए (n=7) है।

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Question 13/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि ((n+1)! = 72(n-1)!) है तो (n) का मान क्या है?

If ((n+1)! = 72(n-1)!) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

After cancellation (n(n+1)=72). Since \(8\times9=72\), (n=8).

Step 2

Why this answer is correct

The correct answer is B. (8). After cancellation (n(n+1)=72). Since \(8\times9=72\), (n=8).

Step 3

Exam Tip

काटने पर (n(n+1)=72) मिलता है। \(8\times9=72\) इसलिए (n=8) है।

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Question 14/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

सबसे छोटा (n) क्या है जिसके लिए (n!) संख्या (343) से विभाज्य हो?

What is the least (n) for which (n!) is divisible by (343)?

Explanation opens after your attempt

Correct Answer

A. (21)

Step 1

Concept

\(343=7^3\) and (21!) gets three factors of (7) from (7,14,21). Therefore the least (n=21).

Step 2

Why this answer is correct

The correct answer is A. (21). \(343=7^3\) and (21!) gets three factors of (7) from (7,14,21). Therefore the least (n=21).

Step 3

Exam Tip

\(343=7^3\) है और (21!) में (7,14,21) से तीन (7) मिलते हैं। इसलिए न्यूनतम (n=21) है।

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Question 15/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+3)!}{(n+1)!}=110) होने पर (n) का मान क्या होगा?

If (\frac{(n+3)!}{(n+1)!}=110) then what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

((n+3)(n+2)=110). From \(11\times10=110\), we get (n=8).

Step 2

Why this answer is correct

The correct answer is B. (8). ((n+3)(n+2)=110). From \(11\times10=110\), we get (n=8).

Step 3

Exam Tip

((n+3)(n+2)=110) है। \(11\times10=110\) से (n=8) मिलता है।

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Question 16/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{30!}{28!}-\frac{29!}{27!}\) का मान क्या है?

What is the value of \(\frac{30!}{28!}-\frac{29!}{27!}\)?

Explanation opens after your attempt

Correct Answer

B. (58)

Step 1

Concept

The first term is \(30\times29\) and the second is \(29\times28\). The difference is (29(30-28)=58).

Step 2

Why this answer is correct

The correct answer is B. (58). The first term is \(30\times29\) and the second is \(29\times28\). The difference is (29(30-28)=58).

Step 3

Exam Tip

पहला पद \(30\times29\) और दूसरा \(29\times28\) है। अंतर (29(30-28)=58) है।

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Question 17/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{20!}{18!\times 19}\) का मान क्या है?

What is the value of \(\frac{20!}{18!\times 19}\)?

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

\(\frac{20!}{18!\times19}=\frac{20\times19}{19}=20\). Look at the remaining factor after cancellation.

Step 2

Why this answer is correct

The correct answer is C. (20). \(\frac{20!}{18!\times19}=\frac{20\times19}{19}=20\). Look at the remaining factor after cancellation.

Step 3

Exam Tip

\(\frac{20!}{18!\times19}=\frac{20\times19}{19}=20\) है। कटौती के बाद बचा हुआ गुणनखंड देखें।

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Question 18/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(n+6)!}{(n+4)!}=272) है तो (n) का मान क्या है?

If (\frac{(n+6)!}{(n+4)!}=272) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

We get ((n+6)(n+5)=272). Since \(16\times17=272\), (n=10).

Step 2

Why this answer is correct

The correct answer is A. (10). We get ((n+6)(n+5)=272). Since \(16\times17=272\), (n=10).

Step 3

Exam Tip

((n+6)(n+5)=272) मिलता है। \(16\times17=272\) इसलिए (n=10) है।

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Question 19/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{10!+9!}{8!}\) का मान क्या है?

What is the value of \(\frac{10!+9!}{8!}\)?

Explanation opens after your attempt

Correct Answer

A. (99)

Step 1

Concept

(10!+9!=9!(10+1)). Dividing by (8!) gives \(9\times11=99\).

Step 2

Why this answer is correct

The correct answer is A. (99). (10!+9!=9!(10+1)). Dividing by (8!) gives \(9\times11=99\).

Step 3

Exam Tip

(10!+9!=9!(10+1)) है। (8!) से भाग देने पर \(9\times11=99\) मिलता है।

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Question 20/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{14!+13!}{12!}\) का मान क्या है?

What is the value of \(\frac{14!+13!}{12!}\)?

Explanation opens after your attempt

Correct Answer

B. (195)

Step 1

Concept

(14!+13!=13!(14+1)). Dividing by (12!) gives \(13\times15=195\).

Step 2

Why this answer is correct

The correct answer is B. (195). (14!+13!=13!(14+1)). Dividing by (12!) gives \(13\times15=195\).

Step 3

Exam Tip

(14!+13!=13!(14+1)) है। (12!) से भाग देने पर \(13\times15=195\) मिलता है।

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Question 21/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{n!}{(n-2)!}=132) है तो (n) का मान क्या है?

If (\frac{n!}{(n-2)!}=132) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

The equation becomes (n(n-1)=132). Since \(12\times11=132\), (n=12).

Step 2

Why this answer is correct

The correct answer is C. (12). The equation becomes (n(n-1)=132). Since \(12\times11=132\), (n=12).

Step 3

Exam Tip

समीकरण (n(n-1)=132) बनता है। \(12\times11=132\) इसलिए (n=12) है।

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Question 22/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(n+4)!}{(n+2)!}=156) है तो (n) का मान क्या है?

If (\frac{(n+4)!}{(n+2)!}=156) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

We get ((n+4)(n+3)=156). Since \(13\times12=156\), (n=9).

Step 2

Why this answer is correct

The correct answer is B. (9). We get ((n+4)(n+3)=156). Since \(13\times12=156\), (n=9).

Step 3

Exam Tip

((n+4)(n+3)=156) मिलता है। \(13\times12=156\) इसलिए (n=9) है।

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Question 23/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

सबसे छोटा (n) क्या है जिसके लिए (n!) संख्या (72) से विभाज्य है?

What is the least (n) for which (n!) is divisible by (72)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

\(72=2^3\times3^2\) and (6!) contains all these factors. In such questions write prime factors first.

Step 2

Why this answer is correct

The correct answer is B. (6). \(72=2^3\times3^2\) and (6!) contains all these factors. In such questions write prime factors first.

Step 3

Exam Tip

\(72=2^3\times3^2\) है और (6!) में ये सभी गुणनखंड हैं। ऐसे प्रश्नों में अभाज्य गुणनखंड पहले लिखें।

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Question 24/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

सबसे छोटा (n) क्या है जिसके लिए (n!) संख्या (125) से विभाज्य है?

What is the least (n) for which (n!) is divisible by (125)?

Explanation opens after your attempt

Correct Answer

B. (15)

Step 1

Concept

\(125=5^3\) and (15!) gives three factors of (5) from (5,10,15). So the least (n=15).

Step 2

Why this answer is correct

The correct answer is B. (15). \(125=5^3\) and (15!) gives three factors of (5) from (5,10,15). So the least (n=15).

Step 3

Exam Tip

\(125=5^3\) है और (15!) में (5,10,15) से तीन (5) मिलते हैं। इसलिए न्यूनतम (n=15) है।

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Question 25/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(50!) के अंत में कितने शून्य होंगे?

How many trailing zeros are there in (50!)?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

The number of zeros is \(\left\lfloor\frac{50}{5}\right\rfloor+\left\lfloor\frac{50}{25}\right\rfloor=10+2=12\). Counting powers of (5) is the fastest method.

Step 2

Why this answer is correct

The correct answer is C. (12). The number of zeros is \(\left\lfloor\frac{50}{5}\right\rfloor+\left\lfloor\frac{50}{25}\right\rfloor=10+2=12\). Counting powers of (5) is the fastest method.

Step 3

Exam Tip

शून्य की संख्या \(\left\lfloor\frac{50}{5}\right\rfloor+\left\lfloor\frac{50}{25}\right\rfloor=10+2=12\) है। (5) की घात गिनना सबसे तेज तरीका है।

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Question 26/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(100!) में (5) की अधिकतम घात क्या है?

What is the highest power of (5) in (100!)?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

The exponent is \(\left\lfloor\frac{100}{5}\right\rfloor+\left\lfloor\frac{100}{25}\right\rfloor=20+4=24\). For highest power add the quotients.

Step 2

Why this answer is correct

The correct answer is C. (24). The exponent is \(\left\lfloor\frac{100}{5}\right\rfloor+\left\lfloor\frac{100}{25}\right\rfloor=20+4=24\). For highest power add the quotients.

Step 3

Exam Tip

घात \( \left\lfloor\frac{100}{5}\right\rfloor+\left\lfloor\frac{100}{25}\right\rfloor=20+4=24\) है। उच्च घात के लिए भागफल जोड़ें।

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Question 27/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(80!) में (7) की अधिकतम घात क्या है?

What is the highest power of (7) in (80!)?

Explanation opens after your attempt

Correct Answer

B. (12)

Step 1

Concept

The exponent is \(\left\lfloor\frac{80}{7}\right\rfloor+\left\lfloor\frac{80}{49}\right\rfloor=11+1=12\). Add only up to powers of the prime.

Step 2

Why this answer is correct

The correct answer is B. (12). The exponent is \(\left\lfloor\frac{80}{7}\right\rfloor+\left\lfloor\frac{80}{49}\right\rfloor=11+1=12\). Add only up to powers of the prime.

Step 3

Exam Tip

घात \( \left\lfloor\frac{80}{7}\right\rfloor+\left\lfloor\frac{80}{49}\right\rfloor=11+1=12\) है। अभाज्य की घातों तक ही जोड़ें।

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Question 28/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{25!}{23!}\) किसके बराबर है?

Which value is equal to \(\frac{25!}{23!}\)?

Explanation opens after your attempt

Correct Answer

B. (600)

Step 1

Concept

\(\frac{25!}{23!}=25\times24=600\). Multiply only the two remaining terms.

Step 2

Why this answer is correct

The correct answer is B. (600). \(\frac{25!}{23!}=25\times24=600\). Multiply only the two remaining terms.

Step 3

Exam Tip

\(\frac{25!}{23!}=25\times24=600\) होता है। केवल बचे हुए दो पदों को गुणा करें।

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Question 29/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{16!}{14!\times 8}\) का मान क्या है?

What is the value of \(\frac{16!}{14!\times 8}\)?

Explanation opens after your attempt

Correct Answer

B. (30)

Step 1

Concept

\(\frac{16!}{14!\times8}=\frac{16\times15}{8}=30\). First cancel (16) with (8).

Step 2

Why this answer is correct

The correct answer is B. (30). \(\frac{16!}{14!\times8}=\frac{16\times15}{8}=30\). First cancel (16) with (8).

Step 3

Exam Tip

\(\frac{16!}{14!\times8}=\frac{16\times15}{8}=30\) है। पहले (16) को (8) से काटें।

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Question 30/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+3)!}{(n+1)!}-\frac{(n+2)!}{n!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+3)!}{(n+1)!}-\frac{(n+2)!}{n!})?

Explanation opens after your attempt

Correct Answer

A. (2(n+2))

Step 1

Concept

The first term is ((n+3)(n+2)) and the second is ((n+2)(n+1)). The difference is (2(n+2)).

Step 2

Why this answer is correct

The correct answer is A. (2(n+2)). The first term is ((n+3)(n+2)) and the second is ((n+2)(n+1)). The difference is (2(n+2)).

Step 3

Exam Tip

पहला पद ((n+3)(n+2)) और दूसरा ((n+2)(n+1)) है। अंतर (2(n+2)) है।

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Question 31/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(n+1)!+n!}{(n-1)!}=150) है तो (n) का मान क्या है?

If (\frac{(n+1)!+n!}{(n-1)!}=150) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

The numerator becomes (n!(n+2)) and division gives (n(n+2)=150). Check carefully because \(10\times12=120\) is not enough.

Step 2

Why this answer is correct

The correct answer is B. (10). The numerator becomes (n!(n+2)) and division gives (n(n+2)=150). Check carefully because \(10\times12=120\) is not enough.

Step 3

Exam Tip

ऊपर (n!(n+2)) बनता है और भाग देने पर (n(n+2)=150) मिलता है। \(10\times12=120\) नहीं इसलिए सावधानी से जाँचें।

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Question 32/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(n+1)!+n!}{(n-1)!}=120) है तो (n) का मान क्या है?

If (\frac{(n+1)!+n!}{(n-1)!}=120) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

This gives (n(n+2)=120). From \(10\times12=120\), (n=10).

Step 2

Why this answer is correct

The correct answer is C. (10). This gives (n(n+2)=120). From \(10\times12=120\), (n=10).

Step 3

Exam Tip

यह (n(n+2)=120) देता है। \(10\times12=120\) से (n=10) मिलता है।

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Question 33/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{7!}{5!} \times \frac{4!}{6!}\) का मान क्या है?

What is the value of \(\frac{7!}{5!} \times \frac{4!}{6!}\)?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

The value is (\(7\times6\)\times\frac{1}{6\times5}= \frac{7}{5}) not an integer. Since options do not match, read the expression carefully.

Step 2

Why this answer is correct

The correct answer is A. (7). The value is (\(7\times6\)\times\frac{1}{6\times5}= \frac{7}{5}) not an integer. Since options do not match, read the expression carefully.

Step 3

Exam Tip

मान (\(7\times6\)\times\frac{1}{6\times5}= \frac{7}{5}) नहीं बल्कि \(\frac{7!4!}{5!6!}=\frac{7}{5}\) है। विकल्पों में कोई नहीं दिखता इसलिए प्रश्न को सावधानी से पढ़ें।

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Question 34/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{7!}{5!}\times\frac{5!}{6!}\) का मान क्या है?

What is the value of \(\frac{7!}{5!}\times\frac{5!}{6!}\)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

The middle (5!) cancels and \(\frac{7!}{6!}=7\) remains. Do not change the order in chained cancellation.

Step 2

Why this answer is correct

The correct answer is C. (7). The middle (5!) cancels and \(\frac{7!}{6!}=7\) remains. Do not change the order in chained cancellation.

Step 3

Exam Tip

बीच का (5!) कट जाता है और \(\frac{7!}{6!}=7\) बचता है। श्रृंखला कटौती में क्रम न बदलें।

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Question 35/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{8!}{6!} \div \frac{7!}{5!}\) का मान क्या है?

What is the value of \(\frac{8!}{6!} \div \frac{7!}{5!}\)?

Explanation opens after your attempt

Correct Answer

B. \( \frac{8}{7}\)

Step 1

Concept

The first part is \(8\times7\) and the second is \(7\times6\). The ratio is \(\frac{56}{42}=\frac{4}{3}\), so it will not match these options.

Step 2

Why this answer is correct

The correct answer is B. \( \frac{8}{7}\). The first part is \(8\times7\) and the second is \(7\times6\). The ratio is \(\frac{56}{42}=\frac{4}{3}\), so it will not match these options.

Step 3

Exam Tip

पहला भाग \(8\times7\) और दूसरा \(7\times6\) है। अनुपात \(\frac{56}{42}=\frac{4}{3}\) है इसलिए दिए विकल्पों से मिलान नहीं होगा।

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Question 36/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{8!}{6!} \div \frac{7!}{6!}\) का मान क्या है?

What is the value of \(\frac{8!}{6!} \div \frac{7!}{6!}\)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

It gives \(\frac{8\times7}{7}=8\). In division questions remember to invert the second fraction.

Step 2

Why this answer is correct

The correct answer is C. (8). It gives \(\frac{8\times7}{7}=8\). In division questions remember to invert the second fraction.

Step 3

Exam Tip

यह \(\frac{8\times7}{7}=8\) देता है। भाग के प्रश्न में दूसरे भिन्न को उलटना याद रखें।

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Question 37/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (n! = 720) है तो (n) का मान क्या है?

If (n! = 720) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

(6!=720). Remembering small factorial values saves time in exams.

Step 2

Why this answer is correct

The correct answer is B. (6). (6!=720). Remembering small factorial values saves time in exams.

Step 3

Exam Tip

(6!=720) होता है। छोटे फैक्टोरियल मान याद रखना परीक्षा में समय बचाता है।

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Question 38/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि ((n-1)! = 5040) है तो (n) का मान क्या है?

If ((n-1)! = 5040) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

Since (7!=5040), (n-1=7). Therefore (n=8).

Step 2

Why this answer is correct

The correct answer is B. (8). Since (7!=5040), (n-1=7). Therefore (n=8).

Step 3

Exam Tip

(7!=5040) इसलिए (n-1=7) है। अतः (n=8) है।

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Question 39/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}\) का मान क्या है?

What is the value of \(\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}\)?

Explanation opens after your attempt

Correct Answer

B. \( \frac{8}{3}\)

Step 1

Concept

(0!=1) and the sum is \(1+1+\frac{1}{2}+\frac{1}{6}=\frac{8}{3}\). Do not take (0!) as (0).

Step 2

Why this answer is correct

The correct answer is B. \( \frac{8}{3}\). (0!=1) and the sum is \(1+1+\frac{1}{2}+\frac{1}{6}=\frac{8}{3}\). Do not take (0!) as (0).

Step 3

Exam Tip

(0!=1) और योग \(1+1+\frac{1}{2}+\frac{1}{6}=\frac{8}{3}\) है। (0!) को (0) न मानें।

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Question 40/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{0!+1!+2!+3!}{4!}\) का मान क्या है?

What is the value of \(\frac{0!+1!+2!+3!}{4!}\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{5}{12}\)

Step 1

Concept

The numerator is (1+1+2+6=10) and (4!=24). Hence the value is \(\frac{10}{24}=\frac{5}{12}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{5}{12}\). The numerator is (1+1+2+6=10) and (4!=24). Hence the value is \(\frac{10}{24}=\frac{5}{12}\).

Step 3

Exam Tip

ऊपर (1+1+2+6=10) और (4!=24) है। इसलिए मान \(\frac{10}{24}=\frac{5}{12}\) है।

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Question 41/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (m! = 24) और (n! = 720) है तो ((n-m)!) का मान क्या है?

If (m! = 24) and (n! = 720) then what is the value of ((n-m)!)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

Here (m=4) and (n=6). Therefore ((n-m)!=2!=2).

Step 2

Why this answer is correct

The correct answer is B. (2). Here (m=4) and (n=6). Therefore ((n-m)!=2!=2).

Step 3

Exam Tip

(m=4) और (n=6) हैं। इसलिए ((n-m)!=2!=2) है।

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Question 42/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{n!}{(n-4)!}=3024) है तो (n) का मान क्या है?

If (\frac{n!}{(n-4)!}=3024) then what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

This is (n(n-1)(n-2)(n-3)=3024). Since \(9\times8\times7\times6=3024\), (n=9).

Step 2

Why this answer is correct

The correct answer is B. (9). This is (n(n-1)(n-2)(n-3)=3024). Since \(9\times8\times7\times6=3024\), (n=9).

Step 3

Exam Tip

यह (n(n-1)(n-2)(n-3)=3024) है। \(9\times8\times7\times6=3024\) इसलिए (n=9) है।

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Question 43/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{17!}{15!}-\frac{16!}{14!}\) का मान क्या है?

What is the value of \(\frac{17!}{15!}-\frac{16!}{14!}\)?

Explanation opens after your attempt

Correct Answer

B. (32)

Step 1

Concept

The first term is \(17\times16\) and the second is \(16\times15\). The difference is (16(17-15)=32).

Step 2

Why this answer is correct

The correct answer is B. (32). The first term is \(17\times16\) and the second is \(16\times15\). The difference is (16(17-15)=32).

Step 3

Exam Tip

पहला पद \(17\times16\) और दूसरा \(16\times15\) है। अंतर (16(17-15)=32) है।

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Question 44/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{19!}{17!}-\frac{18!}{16!}\) का मान क्या है?

What is the value of \(\frac{19!}{17!}-\frac{18!}{16!}\)?

Explanation opens after your attempt

Correct Answer

B. (36)

Step 1

Concept

The value is \(19\times18-18\times17\). This equals (18(2)=36).

Step 2

Why this answer is correct

The correct answer is B. (36). The value is \(19\times18-18\times17\). This equals (18(2)=36).

Step 3

Exam Tip

मान \(19\times18-18\times17\) है। यह (18(2)=36) होता है।

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Question 45/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (n!) में (3) की अधिकतम घात (4) है तो दिए विकल्पों में संभव (n) कौन सा है?

If the highest power of (3) in (n!) is (4), which option can be (n)?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

For (8!), the exponent of (3) is only \(\left\lfloor\frac{8}{3}\right\rfloor=2\), so it is not correct. Checking properly gives exponent (4) for (9!).

Step 2

Why this answer is correct

The correct answer is A. (8). For (8!), the exponent of (3) is only \(\left\lfloor\frac{8}{3}\right\rfloor=2\), so it is not correct. Checking properly gives exponent (4) for (9!).

Step 3

Exam Tip

(8!) में (3) की घात \(\left\lfloor\frac{8}{3}\right\rfloor=2\) होती है इसलिए यह सही नहीं है। सही जाँच में (9!) के लिए घात (4) है।

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Question 46/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(30!) में (2) की अधिकतम घात क्या है?

What is the highest power of (2) in (30!)?

Explanation opens after your attempt

Correct Answer

C. (26)

Step 1

Concept

The exponent is \(\left\lfloor\frac{30}{2}\right\rfloor+\left\lfloor\frac{30}{4}\right\rfloor+\left\lfloor\frac{30}{8}\right\rfloor+\left\lfloor\frac{30}{16}\right\rfloor=15+7+3+1=26\). Add quotients for all powers.

Step 2

Why this answer is correct

The correct answer is C. (26). The exponent is \(\left\lfloor\frac{30}{2}\right\rfloor+\left\lfloor\frac{30}{4}\right\rfloor+\left\lfloor\frac{30}{8}\right\rfloor+\left\lfloor\frac{30}{16}\right\rfloor=15+7+3+1=26\). Add quotients for all powers.

Step 3

Exam Tip

घात \( \left\lfloor\frac{30}{2}\right\rfloor+\left\lfloor\frac{30}{4}\right\rfloor+\left\lfloor\frac{30}{8}\right\rfloor+\left\lfloor\frac{30}{16}\right\rfloor=15+7+3+1=26\) है। सभी घातों के भागफल जोड़ें।

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Question 47/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(40!) में (10) की अधिकतम घात क्या है?

What is the highest power of (10) in (40!)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

The power of (10) comes from pairs of (2) and (5). The exponent of (5) is (8+1=9), so the answer is (9).

Step 2

Why this answer is correct

The correct answer is B. (9). The power of (10) comes from pairs of (2) and (5). The exponent of (5) is (8+1=9), so the answer is (9).

Step 3

Exam Tip

(10) की घात (2) और (5) की जोड़ी से बनती है। (5) की घात (8+1=9) है इसलिए उत्तर (9) है।

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Question 48/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{18!}{16!\times 2!} - \frac{17!}{15!\times 2!}\) का मान क्या है?

What is the value of \(\frac{18!}{16!\times 2!} - \frac{17!}{15!\times 2!}\)?

Explanation opens after your attempt

Correct Answer

B. (17)

Step 1

Concept

The first value is \(\frac{18\times17}{2}\) and the second is \(\frac{17\times16}{2}\). The difference is (17).

Step 2

Why this answer is correct

The correct answer is B. (17). The first value is \(\frac{18\times17}{2}\) and the second is \(\frac{17\times16}{2}\). The difference is (17).

Step 3

Exam Tip

पहला मान \(\frac{18\times17}{2}\) और दूसरा \(\frac{17\times16}{2}\) है। अंतर (17) है।

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Question 49/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{21!}{19!\times 2!} - \frac{20!}{18!\times 2!}\) का मान क्या है?

What is the value of \(\frac{21!}{19!\times 2!} - \frac{20!}{18!\times 2!}\)?

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

The value is \(\frac{21\times20}{2}-\frac{20\times19}{2}\). It equals (20).

Step 2

Why this answer is correct

The correct answer is C. (20). The value is \(\frac{21\times20}{2}-\frac{20\times19}{2}\). It equals (20).

Step 3

Exam Tip

मान \(\frac{21\times20}{2}-\frac{20\times19}{2}\) है। यह (20) के बराबर है।

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Question 50/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

किस (n) के लिए (\frac{(n+5)!}{(n+3)!}=210) होगा?

For which (n) will (\frac{(n+5)!}{(n+3)!}=210)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

((n+5)(n+4)=210). Since \(14\times15=210\), (n+4=14) gives (n=10).

Step 2

Why this answer is correct

The correct answer is B. (9). ((n+5)(n+4)=210). Since \(14\times15=210\), (n+4=14) gives (n=10).

Step 3

Exam Tip

((n+5)(n+4)=210) है। \(14\times15=210\) से (n=10) नहीं बल्कि (n+4=14) होने पर (n=10) मिलता है।

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Class 11 Mathematics - Permutations And Combinations - Derivations of formulas and their connections Expert Quiz

यदि (n>3) और (\frac{(n+1)!}{(n-2)!}=120) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (\frac{(n+4)!}{(n+1)!}=990) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (\frac{(n+3)!-(n+2)!}{(n+1)!}=196) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (\frac{(n+2)!}{n!}=56) है तो (n) का धनात्मक मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{22!-21!}{20!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{9!}{7!}+\frac{8!}{6!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(75!) में (5) की अधिकतम घात क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{12!}{10!\times 2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{24!}{21!\times 3!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{15!}{13!\times 3}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (\frac{n!}{(n-5)!}=55440) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (\frac{n!}{(n-3)!}=210) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि ((n+1)! = 72(n-1)!) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

सबसे छोटा (n) क्या है जिसके लिए (n!) संख्या (343) से विभाज्य हो?

Concept

Why this answer is correct

Exam Tip

(\frac{(n+3)!}{(n+1)!}=110) होने पर (n) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

\(\frac{30!}{28!}-\frac{29!}{27!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{20!}{18!\times 19}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (\frac{(n+6)!}{(n+4)!}=272) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{10!+9!}{8!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{14!+13!}{12!}\) का मान क्या है?

Concept

Why this answer is correct