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Mathematics Quiz - Class 11 Mathematics Permutations And...

Question 1/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{18!}{15!}-\frac{17!}{14!} \) का मान क्या है?

What is the value of \( \frac{18!}{15!}-\frac{17!}{14!} \)?

Explanation opens after your attempt

Correct Answer

B. (816)

Step 1

Concept

The first term is \(18\cdot17\cdot16=4896\) and the second is \(17\cdot16\cdot15=4080\). The difference is (816).

Step 2

Why this answer is correct

The correct answer is B. (816). The first term is \(18\cdot17\cdot16=4896\) and the second is \(17\cdot16\cdot15=4080\). The difference is (816).

Step 3

Exam Tip

पहला पद \(18\cdot17\cdot16=4896\) और दूसरा \(17\cdot16\cdot15=4080\) है। अंतर (816) है।

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Question 2/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{15!}{11!\cdot4!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{15!}{11!\cdot4!} \)?

Explanation opens after your attempt

Correct Answer

C. (1365)

Step 1

Concept

\( \frac{15\cdot14\cdot13\cdot12}{4!}=1365 \). Use the correct value of (4!) in the denominator.

Step 2

Why this answer is correct

The correct answer is C. (1365). \( \frac{15\cdot14\cdot13\cdot12}{4!}=1365 \). Use the correct value of (4!) in the denominator.

Step 3

Exam Tip

\( \frac{15\cdot14\cdot13\cdot12}{4!}=1365 \) है। हर में (4!) का सही मान लगाएं।

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Question 3/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+4)!}{n!}=11880 ), तो (n) का मान क्या होगा?

If ( \frac{(n+4)!}{n!}=11880 ), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

It is ((n+4)(n+3)(n+2)(n+1)=11880), and \(12\cdot11\cdot10\cdot9=11880\). So (n=8).

Step 2

Why this answer is correct

The correct answer is C. (8). It is ((n+4)(n+3)(n+2)(n+1)=11880), and \(12\cdot11\cdot10\cdot9=11880\). So (n=8).

Step 3

Exam Tip

यह ((n+4)(n+3)(n+2)(n+1)=11880) है और \(12\cdot11\cdot10\cdot9=11880\)। इसलिए (n=8) है।

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Question 4/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+2)!+(n+1)!}{(n+1)!}=14 ), तो (n) का मान क्या है?

If ( \frac{(n+2)!+(n+1)!}{(n+1)!}=14 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (11)

Step 1

Concept

The simplified form is (n+3). Thus (n+3=14) and (n=11).

Step 2

Why this answer is correct

The correct answer is C. (11). The simplified form is (n+3). Thus (n+3=14) and (n=11).

Step 3

Exam Tip

सरल रूप (n+3) है। इसलिए (n+3=14) और (n=11)।

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Question 5/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

A. ((n+2)²)

Step 1

Concept

((n+3)!-(n+2)!=(n+2)!((n+3)-1)). This gives ((n+2)²).

Step 2

Why this answer is correct

The correct answer is A. ((n+2)²). ((n+3)!-(n+2)!=(n+2)!((n+3)-1)). This gives ((n+2)²).

Step 3

Exam Tip

((n+3)!-(n+2)!=(n+2)!((n+3)-1)) है। इससे ((n+2)²) मिलता है।

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Question 6/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+3)!-(n+2)!}{(n+1)!}=121 ), तो (n) का मान क्या होगा?

If ( \frac{(n+3)!-(n+2)!}{(n+1)!}=121 ), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

The simplified form is ((n+2)²). Therefore (n+2=11) and (n=9).

Step 2

Why this answer is correct

The correct answer is B. (9). The simplified form is ((n+2)²). Therefore (n+2=11) and (n=9).

Step 3

Exam Tip

सरल रूप ((n+2)²) है। इसलिए (n+2=11) और (n=9)।

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Question 7/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n!)²}{(n-2)!(n+2)!}=\frac{10}{21} ), तो (n) का मान क्या है?

If ( \frac{(n!)²}{(n-2)!(n+2)!}=\frac{10}{21} ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

The simplified form is ( \frac{n(n-1)}{(n+1)(n+2)} ). Putting (n=5) gives \( \frac{20}{42}=\frac{10}{21} \).

Step 2

Why this answer is correct

The correct answer is B. (5). The simplified form is ( \frac{n(n-1)}{(n+1)(n+2)} ). Putting (n=5) gives \( \frac{20}{42}=\frac{10}{21} \).

Step 3

Exam Tip

सरल रूप ( \frac{n(n-1)}{(n+1)(n+2)} ) है। (n=5) रखने पर \( \frac{20}{42}=\frac{10}{21} \) मिलता है।

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Question 8/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(20!) को विभाजित करने वाली (2) की अधिकतम घात क्या है?

What is the highest power of (2) that divides (20!)?

Explanation opens after your attempt

Correct Answer

D. (18)

Step 1

Concept

The exponent is \( \left\lfloor\frac{20}{2}\right\rfloor+\left\lfloor\frac{20}{4}\right\rfloor+\left\lfloor\frac{20}{8}\right\rfloor+\left\lfloor\frac{20}{16}\right\rfloor=18 \). Add all quotients for a prime exponent.

Step 2

Why this answer is correct

The correct answer is D. (18). The exponent is \( \left\lfloor\frac{20}{2}\right\rfloor+\left\lfloor\frac{20}{4}\right\rfloor+\left\lfloor\frac{20}{8}\right\rfloor+\left\lfloor\frac{20}{16}\right\rfloor=18 \). Add all quotients for a prime exponent.

Step 3

Exam Tip

घात \( \left\lfloor\frac{20}{2}\right\rfloor+\left\lfloor\frac{20}{4}\right\rfloor+\left\lfloor\frac{20}{8}\right\rfloor+\left\lfloor\frac{20}{16}\right\rfloor=18 \) है। अभाज्य घात के लिए सभी भागफल जोड़ें।

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Question 9/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(45!) के अंत में कितने शून्य होंगे?

How many zeros will be at the end of (45!)?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

The number of zeros is \( \left\lfloor\frac{45}{5}\right\rfloor+\left\lfloor\frac{45}{25}\right\rfloor=10 \). Do not forget the contribution of (25).

Step 2

Why this answer is correct

The correct answer is A. (10). The number of zeros is \( \left\lfloor\frac{45}{5}\right\rfloor+\left\lfloor\frac{45}{25}\right\rfloor=10 \). Do not forget the contribution of (25).

Step 3

Exam Tip

शून्यों की संख्या \( \left\lfloor\frac{45}{5}\right\rfloor+\left\lfloor\frac{45}{25}\right\rfloor=10 \) है। (25) के योगदान को न भूलें।

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Question 10/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

सबसे छोटा धनात्मक (n) क्या है जिसके लिए (n!) संख्या (1440) से विभाज्य हो?

What is the smallest positive (n) for which (n!) is divisible by (1440)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

\(1440=2^5\cdot3^2\cdot5\), and this requirement is first satisfied by (8!). For divisibility, check prime factors.

Step 2

Why this answer is correct

The correct answer is C. (8). \(1440=2^5\cdot3^2\cdot5\), and this requirement is first satisfied by (8!). For divisibility, check prime factors.

Step 3

Exam Tip

\(1440=2^5\cdot3^2\cdot5\) है और यह जरूरत पहली बार (8!) में पूरी होती है। विभाज्यता में अभाज्य गुणनखंड जांचें।

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Question 11/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{20!}{18!\cdot2!}+\frac{19!}{17!\cdot2!} \) का मान क्या है?

What is the value of \( \frac{20!}{18!\cdot2!}+\frac{19!}{17!\cdot2!} \)?

Explanation opens after your attempt

Correct Answer

C. (361)

Step 1

Concept

The two terms are (190) and (171). Their sum is (361).

Step 2

Why this answer is correct

The correct answer is C. (361). The two terms are (190) and (171). Their sum is (361).

Step 3

Exam Tip

दोनों पद (190) और (171) हैं। योग (361) है।

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Question 12/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{21!}{18!\cdot3!}-\frac{20!}{17!\cdot3!} \) का मान क्या है?

What is the value of \( \frac{21!}{18!\cdot3!}-\frac{20!}{17!\cdot3!} \)?

Explanation opens after your attempt

Correct Answer

C. (190)

Step 1

Concept

The first term is (1330) and the second is (1140). The difference is (190).

Step 2

Why this answer is correct

The correct answer is C. (190). The first term is (1330) and the second is (1140). The difference is (190).

Step 3

Exam Tip

पहला पद (1330) और दूसरा (1140) है। अंतर (190) है।

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Question 13/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{14!}{10!\cdot4!}\div\frac{13!}{9!\cdot4!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{14!}{10!\cdot4!}\div\frac{13!}{9!\cdot4!} \)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{7}{5}\)

Step 1

Concept

The two terms are (1001) and (715). The ratio is \( \frac{1001}{715}=\frac{7}{5} \).

Step 2

Why this answer is correct

The correct answer is B. \(\frac{7}{5}\). The two terms are (1001) and (715). The ratio is \( \frac{1001}{715}=\frac{7}{5} \).

Step 3

Exam Tip

दोनों पद (1001) और (715) हैं। अनुपात \( \frac{1001}{715}=\frac{7}{5} \) है।

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Question 14/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(2n)!}{(2n-4)!} ) का सही विस्तार कौन सा है?

Which is the correct expansion of ( \frac{(2n)!}{(2n-4)!} )?

Explanation opens after your attempt

Correct Answer

B. ((2n)(2n-1)(2n-2)(2n-3))

Step 1

Concept

We expand ((2n)!) up to ((2n)(2n-1)(2n-2)(2n-3)(2n-4)!). Therefore four factors remain.

Step 2

Why this answer is correct

The correct answer is B. ((2n)(2n-1)(2n-2)(2n-3)). We expand ((2n)!) up to ((2n)(2n-1)(2n-2)(2n-3)(2n-4)!). Therefore four factors remain.

Step 3

Exam Tip

((2n)!) को ((2n)(2n-1)(2n-2)(2n-3)(2n-4)!) तक फैलाते हैं। इसलिए चार गुणक बचते हैं।

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Question 15/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(2n)!}{(2n-4)!}=1680 ), तो (n) का मान क्या है?

If ( \frac{(2n)!}{(2n-4)!}=1680 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

It is ((2n)(2n-1)(2n-2)(2n-3)=1680). Since \(8\cdot7\cdot6\cdot5=1680\), (n=4).

Step 2

Why this answer is correct

The correct answer is B. (4). It is ((2n)(2n-1)(2n-2)(2n-3)=1680). Since \(8\cdot7\cdot6\cdot5=1680\), (n=4).

Step 3

Exam Tip

यह ((2n)(2n-1)(2n-2)(2n-3)=1680) है। \(8\cdot7\cdot6\cdot5=1680\), इसलिए (n=4)।

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Question 16/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(3n+2)!}{(3n)!} ) किसके बराबर है?

What is ( \frac{(3n+2)!}{(3n)!} ) equal to?

Explanation opens after your attempt

Correct Answer

A. ((3n+2)(3n+1))

Step 1

Concept

((3n+2)!=(3n+2)(3n+1)(3n)!). Therefore two factors remain.

Step 2

Why this answer is correct

The correct answer is A. ((3n+2)(3n+1)). ((3n+2)!=(3n+2)(3n+1)(3n)!). Therefore two factors remain.

Step 3

Exam Tip

((3n+2)!=(3n+2)(3n+1)(3n)!) है। इसलिए दो गुणक बचते हैं।

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Question 17/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(3n+2)!}{(3n)!}=182 ), तो (n) का मान क्या है?

If ( \frac{(3n+2)!}{(3n)!}=182 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

It is ((3n+2)(3n+1)=182), and \(14\cdot13=182\). Thus (3n+2=14) and (n=4).

Step 2

Why this answer is correct

The correct answer is B. (4). It is ((3n+2)(3n+1)=182), and \(14\cdot13=182\). Thus (3n+2=14) and (n=4).

Step 3

Exam Tip

यह ((3n+2)(3n+1)=182) है और \(14\cdot13=182\)। इसलिए (3n+2=14) और (n=4)।

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Question 18/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+4)!}{(n+2)!}-\frac{(n+3)!}{(n+1)!}=24 ), तो (n) का मान क्या है?

If ( \frac{(n+4)!}{(n+2)!}-\frac{(n+3)!}{(n+1)!}=24 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

The simplified form is (2(n+3)). Thus (2(n+3)=24) and (n=9).

Step 2

Why this answer is correct

The correct answer is C. (9). The simplified form is (2(n+3)). Thus (2(n+3)=24) and (n=9).

Step 3

Exam Tip

सरल रूप (2(n+3)) है। इसलिए (2(n+3)=24) और (n=9)।

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Question 19/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(n+5)!+(n+4)!}{(n+3)!} ) का सरल रूप क्या है?

What is the simplified form of ( \frac{(n+5)!+(n+4)!}{(n+3)!} )?

Explanation opens after your attempt

Correct Answer

A. ((n+4)(n+6))

Step 1

Concept

The numerator becomes ((n+4)!((n+5)+1)). Dividing gives ((n+4)(n+6)).

Step 2

Why this answer is correct

The correct answer is A. ((n+4)(n+6)). The numerator becomes ((n+4)!((n+5)+1)). Dividing gives ((n+4)(n+6)).

Step 3

Exam Tip

ऊपर ((n+4)!((n+5)+1)) बनता है। भाग देने पर ((n+4)(n+6)) मिलता है।

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Question 20/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+5)!+(n+4)!}{(n+3)!}=120 ), तो (n) का मान क्या है?

If ( \frac{(n+5)!+(n+4)!}{(n+3)!}=120 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

The simplified form is ((n+4)(n+6)). Putting (n=6) gives \(10\cdot12=120\).

Step 2

Why this answer is correct

The correct answer is B. (6). The simplified form is ((n+4)(n+6)). Putting (n=6) gives \(10\cdot12=120\).

Step 3

Exam Tip

सरल रूप ((n+4)(n+6)) है। (n=6) रखने पर \(10\cdot12=120\) मिलता है।

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Question 21/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{12!}{8!\cdot4!}+\frac{12!}{9!\cdot3!} \) का मान क्या है?

What is the value of \( \frac{12!}{8!\cdot4!}+\frac{12!}{9!\cdot3!} \)?

Explanation opens after your attempt

Correct Answer

B. (715)

Step 1

Concept

The two terms are (495) and (220). Their sum is (715).

Step 2

Why this answer is correct

The correct answer is B. (715). The two terms are (495) and (220). Their sum is (715).

Step 3

Exam Tip

दोनों पद (495) और (220) हैं। योग (715) है।

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Question 22/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{10!}{5!\cdot5!}\times\frac{5}{9} \) का मान क्या है?

What is the value of \( \frac{10!}{5!\cdot5!}\times\frac{5}{9} \)?

Explanation opens after your attempt

Correct Answer

C. (140)

Step 1

Concept

The first part is (252). Then \(252\cdot\frac{5}{9}=140\).

Step 2

Why this answer is correct

The correct answer is C. (140). The first part is (252). Then \(252\cdot\frac{5}{9}=140\).

Step 3

Exam Tip

पहला भाग (252) है। \(252\cdot\frac{5}{9}=140\) मिलता है।

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Question 23/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{13!}{10!}-2\cdot\frac{12!}{10!} \) का मान क्या है?

What is the value of \( \frac{13!}{10!}-2\cdot\frac{12!}{10!} \)?

Explanation opens after your attempt

Correct Answer

B. (1452)

Step 1

Concept

The first term is (1716) and the second is \(2\cdot132=264\). The difference is (1452).

Step 2

Why this answer is correct

The correct answer is B. (1452). The first term is (1716) and the second is \(2\cdot132=264\). The difference is (1452).

Step 3

Exam Tip

पहला पद (1716) और दूसरा \(2\cdot132=264\) है। अंतर (1452) है।

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Question 24/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{9!+2\cdot8!}{7!} \) का मान क्या है?

What is the value of \( \frac{9!+2\cdot8!}{7!} \)?

Explanation opens after your attempt

Correct Answer

C. (88)

Step 1

Concept

\( \frac{9!}{7!}=72 \) and \( \frac{2\cdot8!}{7!}=16 \). The total is (88).

Step 2

Why this answer is correct

The correct answer is C. (88). \( \frac{9!}{7!}=72 \) and \( \frac{2\cdot8!}{7!}=16 \). The total is (88).

Step 3

Exam Tip

\( \frac{9!}{7!}=72 \) और \( \frac{2\cdot8!}{7!}=16 \) है। कुल (88) मिलता है।

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Question 25/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

A. (n(n+3))

Step 1

Concept

The numerator is ((n+3)(n+2)(n+1)n(n-1)!). After cancellation, (n(n+3)) remains.

Step 2

Why this answer is correct

The correct answer is A. (n(n+3)). The numerator is ((n+3)(n+2)(n+1)n(n-1)!). After cancellation, (n(n+3)) remains.

Step 3

Exam Tip

ऊपर ((n+3)(n+2)(n+1)n(n-1)!) है। काटने पर (n(n+3)) बचता है।

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Question 26/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+3)!}{(n-1)!(n+2)(n+1)}=108 ), तो (n) का मान क्या है?

If ( \frac{(n+3)!}{(n-1)!(n+2)(n+1)}=108 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

The simplified form is (n(n+3)). Since \(9\cdot12=108\), (n=9).

Step 2

Why this answer is correct

The correct answer is C. (9). The simplified form is (n(n+3)). Since \(9\cdot12=108\), (n=9).

Step 3

Exam Tip

सरल रूप (n(n+3)) है। \(9\cdot12=108\), इसलिए (n=9)।

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Question 27/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(25!) को विभाजित करने वाली (3) की अधिकतम घात क्या है?

What is the highest power of (3) that divides (25!)?

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

The exponent is \( \left\lfloor\frac{25}{3}\right\rfloor+\left\lfloor\frac{25}{9}\right\rfloor=10 \). Adding the contribution of (9) is necessary.

Step 2

Why this answer is correct

The correct answer is C. (10). The exponent is \( \left\lfloor\frac{25}{3}\right\rfloor+\left\lfloor\frac{25}{9}\right\rfloor=10 \). Adding the contribution of (9) is necessary.

Step 3

Exam Tip

घात \( \left\lfloor\frac{25}{3}\right\rfloor+\left\lfloor\frac{25}{9}\right\rfloor=10 \) है। (9) के योगदान को जोड़ना जरूरी है।

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Question 28/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

सबसे छोटा धनात्मक (n) क्या है जिसके लिए (n!) संख्या \(2^7\cdot3^4\cdot5\) से विभाज्य हो?

What is the smallest positive (n) for which (n!) is divisible by \(2^7\cdot3^4\cdot5\)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

(9!) contains exponent (7) of (2) and exponent (4) of (3). No smaller (n) satisfies this condition.

Step 2

Why this answer is correct

The correct answer is B. (9). (9!) contains exponent (7) of (2) and exponent (4) of (3). No smaller (n) satisfies this condition.

Step 3

Exam Tip

(9!) में (2) की घात (7) और (3) की घात (4) मिल जाती है। इससे छोटा (n) यह शर्त पूरी नहीं करता।

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Question 29/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{25!}{23!\cdot2!}-\frac{24!}{22!\cdot2!} \) का मान क्या है?

What is the value of \( \frac{25!}{23!\cdot2!}-\frac{24!}{22!\cdot2!} \)?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

The first term is (300) and the second is (276). The difference is (24).

Step 2

Why this answer is correct

The correct answer is C. (24). The first term is (300) and the second is (276). The difference is (24).

Step 3

Exam Tip

पहला पद (300) और दूसरा (276) है। अंतर (24) है।

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Question 30/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{16!}{12!\cdot4!}-\frac{15!}{12!\cdot3!} \) का मान क्या है?

What is the value of \( \frac{16!}{12!\cdot4!}-\frac{15!}{12!\cdot3!} \)?

Explanation opens after your attempt

Correct Answer

B. (1365)

Step 1

Concept

The first term is (1820) and the second is (455). The difference is (1365).

Step 2

Why this answer is correct

The correct answer is B. (1365). The first term is (1820) and the second is (455). The difference is (1365).

Step 3

Exam Tip

पहला पद (1820) और दूसरा (455) है। अंतर (1365) है।

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Question 31/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(n+1)!}{(n-3)!} ) का सही विस्तार कौन सा है?

Which is the correct expansion of ( \frac{(n+1)!}{(n-3)!} )?

Explanation opens after your attempt

Correct Answer

A. ((n+1)n(n-1)(n-2))

Step 1

Concept

We expand ((n+1)!) up to ((n+1)n(n-1)(n-2)(n-3)!). Therefore four factors remain.

Step 2

Why this answer is correct

The correct answer is A. ((n+1)n(n-1)(n-2)). We expand ((n+1)!) up to ((n+1)n(n-1)(n-2)(n-3)!). Therefore four factors remain.

Step 3

Exam Tip

((n+1)!) को ((n+1)n(n-1)(n-2)(n-3)!) तक फैलाते हैं। इसलिए चार गुणक बचते हैं।

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Question 32/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+1)!}{(n-3)!}=5040 ), तो (n) का मान क्या है?

If ( \frac{(n+1)!}{(n-3)!}=5040 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

It is ((n+1)n(n-1)(n-2)=5040). Since \(10\cdot9\cdot8\cdot7=5040\), (n=9).

Step 2

Why this answer is correct

The correct answer is C. (9). It is ((n+1)n(n-1)(n-2)=5040). Since \(10\cdot9\cdot8\cdot7=5040\), (n=9).

Step 3

Exam Tip

यह ((n+1)n(n-1)(n-2)=5040) है। \(10\cdot9\cdot8\cdot7=5040\), इसलिए (n=9)।

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Question 33/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The common factors ((n+1)n(n-1)) cancel out. Therefore \( \frac{n+2}{n-2} \) remains.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{n+2}{n-2}\). The common factors ((n+1)n(n-1)) cancel out. Therefore \( \frac{n+2}{n-2} \) remains.

Step 3

Exam Tip

समान गुणक ((n+1)n(n-1)) कट जाते हैं। इसलिए \( \frac{n+2}{n-2} \) बचता है।

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Question 34/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

The simplified form is \( \frac{n+2}{n-2} \). From \( \frac{n+2}{n-2}=2 \), we get (n=6).

Step 2

Why this answer is correct

The correct answer is C. (6). The simplified form is \( \frac{n+2}{n-2} \). From \( \frac{n+2}{n-2}=2 \), we get (n=6).

Step 3

Exam Tip

सरल रूप \( \frac{n+2}{n-2} \) है। \( \frac{n+2}{n-2}=2 \) से (n=6) मिलता है।

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Question 35/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(30!) के अंत में कितने शून्य होंगे?

How many zeros will be at the end of (30!)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

The number of zeros is \( \left\lfloor\frac{30}{5}\right\rfloor+\left\lfloor\frac{30}{25}\right\rfloor=7 \). Add the extra contribution of (25).

Step 2

Why this answer is correct

The correct answer is B. (7). The number of zeros is \( \left\lfloor\frac{30}{5}\right\rfloor+\left\lfloor\frac{30}{25}\right\rfloor=7 \). Add the extra contribution of (25).

Step 3

Exam Tip

शून्यों की संख्या \( \left\lfloor\frac{30}{5}\right\rfloor+\left\lfloor\frac{30}{25}\right\rfloor=7 \) है। (25) का अतिरिक्त योगदान जोड़ें।

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Question 36/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{22!}{20!}\div\frac{11!}{9!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{22!}{20!}\div\frac{11!}{9!} \)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{21}{5}\)

Step 1

Concept

The value is \( \frac{22\cdot21}{11\cdot10}=\frac{21}{5} \). Expand and cancel both ratios in division.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{21}{5}\). The value is \( \frac{22\cdot21}{11\cdot10}=\frac{21}{5} \). Expand and cancel both ratios in division.

Step 3

Exam Tip

मान \( \frac{22\cdot21}{11\cdot10}=\frac{21}{5} \) है। भाग में दोनों अनुपातों को फैलाकर काटें।

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Question 37/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{7!\cdot9!}{8!\cdot6!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{7!\cdot9!}{8!\cdot6!} \)?

Explanation opens after your attempt

Correct Answer

B. (63)

Step 1

Concept

\( \frac{7!}{6!}=7 \) and \( \frac{9!}{8!}=9 \). Hence the value is (63).

Step 2

Why this answer is correct

The correct answer is B. (63). \( \frac{7!}{6!}=7 \) and \( \frac{9!}{8!}=9 \). Hence the value is (63).

Step 3

Exam Tip

\( \frac{7!}{6!}=7 \) और \( \frac{9!}{8!}=9 \) है। इसलिए मान (63) है।

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Question 38/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(n+4)!-(n+3)!}{(n+2)!} ) का सरल रूप क्या है?

What is the simplified form of ( \frac{(n+4)!-(n+3)!}{(n+2)!} )?

Explanation opens after your attempt

Correct Answer

A. ((n+3)²)

Step 1

Concept

((n+4)!-(n+3)!=(n+3)!((n+4)-1)). Therefore ((n+3)²) is obtained.

Step 2

Why this answer is correct

The correct answer is A. ((n+3)²). ((n+4)!-(n+3)!=(n+3)!((n+4)-1)). Therefore ((n+3)²) is obtained.

Step 3

Exam Tip

((n+4)!-(n+3)!=(n+3)!((n+4)-1)) है। इसलिए ((n+3)²) मिलता है।

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Question 39/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+4)!-(n+3)!}{(n+2)!}=144 ), तो (n) का मान क्या है?

If ( \frac{(n+4)!-(n+3)!}{(n+2)!}=144 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

The simplified form is ((n+3)²). Thus (n+3=12) and (n=9).

Step 2

Why this answer is correct

The correct answer is B. (9). The simplified form is ((n+3)²). Thus (n+3=12) and (n=9).

Step 3

Exam Tip

सरल रूप ((n+3)²) है। इसलिए (n+3=12) और (n=9)।

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Question 40/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(n+5)!}{(n+2)!}-\frac{(n+4)!}{(n+1)!} ) का सरल रूप क्या है?

What is the simplified form of ( \frac{(n+5)!}{(n+2)!}-\frac{(n+4)!}{(n+1)!} )?

Explanation opens after your attempt

Correct Answer

B. (3(n+4)(n+3))

Step 1

Concept

Taking common ((n+4)(n+3)), the difference is ((n+5)-(n+2)=3). The answer is (3(n+4)(n+3)).

Step 2

Why this answer is correct

The correct answer is B. (3(n+4)(n+3)). Taking common ((n+4)(n+3)), the difference is ((n+5)-(n+2)=3). The answer is (3(n+4)(n+3)).

Step 3

Exam Tip

सामान्य ((n+4)(n+3)) निकालने पर अंतर ((n+5)-(n+2)=3) है। उत्तर (3(n+4)(n+3)) है।

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Question 41/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+5)!}{(n+2)!}-\frac{(n+4)!}{(n+1)!}=396 ), तो (n) का मान क्या है?

If ( \frac{(n+5)!}{(n+2)!}-\frac{(n+4)!}{(n+1)!}=396 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

The simplified form is (3(n+4)(n+3)). Since \(3\cdot12\cdot11=396\), (n=8).

Step 2

Why this answer is correct

The correct answer is B. (8). The simplified form is (3(n+4)(n+3)). Since \(3\cdot12\cdot11=396\), (n=8).

Step 3

Exam Tip

सरल रूप (3(n+4)(n+3)) है। \(3\cdot12\cdot11=396\), इसलिए (n=8)।

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Question 42/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n!)²}{(n-1)!(n+1)!}=\frac{11}{12} ), तो (n) का मान क्या है?

If ( \frac{(n!)²}{(n-1)!(n+1)!}=\frac{11}{12} ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

The simplified form is \( \frac{n}{n+1} \). From \( \frac{n}{n+1}=\frac{11}{12} \), we get (n=11).

Step 2

Why this answer is correct

The correct answer is B. (11). The simplified form is \( \frac{n}{n+1} \). From \( \frac{n}{n+1}=\frac{11}{12} \), we get (n=11).

Step 3

Exam Tip

सरल रूप \( \frac{n}{n+1} \) है। \( \frac{n}{n+1}=\frac{11}{12} \) से (n=11) मिलता है।

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Question 43/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{18!}{14!\cdot4!}\div\frac{17!}{13!\cdot4!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{18!}{14!\cdot4!}\div\frac{17!}{13!\cdot4!} \)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{153}{119}\)

Step 1

Concept

The two terms are (3060) and (2380). Their ratio is \( \frac{3060}{2380}=\frac{153}{119} \).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{153}{119}\). The two terms are (3060) and (2380). Their ratio is \( \frac{3060}{2380}=\frac{153}{119} \).

Step 3

Exam Tip

दोनों पद (3060) और (2380) हैं। उनका अनुपात \( \frac{3060}{2380}=\frac{153}{119} \) है।

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Question 44/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The first term is ((n+2)(n+1)) and the second is (n(n-1)). Adding gives \(2n^2+2n+2\).

Step 2

Why this answer is correct

The correct answer is B. \(2n^2+2n+2\). The first term is ((n+2)(n+1)) and the second is (n(n-1)). Adding gives \(2n^2+2n+2\).

Step 3

Exam Tip

पहला पद ((n+2)(n+1)) और दूसरा (n(n-1)) है। जोड़ने पर \(2n^2+2n+2\) मिलता है।

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Question 45/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+2)!}{n!}+\frac{n!}{(n-2)!}=114 ), तो (n) का मान क्या है?

If ( \frac{(n+2)!}{n!}+\frac{n!}{(n-2)!}=114 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

The simplified form is \(2n^2+2n+2\). Putting (n=7) gives (98+14+2=114).

Step 2

Why this answer is correct

The correct answer is B. (7). The simplified form is \(2n^2+2n+2\). Putting (n=7) gives (98+14+2=114).

Step 3

Exam Tip

सरल रूप \(2n^2+2n+2\) है। (n=7) रखने पर (98+14+2=114) मिलता है।

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Question 46/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{12!}{6!\cdot6!}-\frac{11!}{5!\cdot6!} \) का मान क्या है?

What is the value of \( \frac{12!}{6!\cdot6!}-\frac{11!}{5!\cdot6!} \)?

Explanation opens after your attempt

Correct Answer

C. (462)

Step 1

Concept

The first term is (924) and the second is (462). The difference is (462).

Step 2

Why this answer is correct

The correct answer is C. (462). The first term is (924) and the second is (462). The difference is (462).

Step 3

Exam Tip

पहला पद (924) और दूसरा (462) है। अंतर (462) है।

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Question 47/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(n+6)!}{(n+2)!}-\frac{(n+5)!}{(n+1)!} ) का सरल रूप क्या है?

What is the simplified form of ( \frac{(n+6)!}{(n+2)!}-\frac{(n+5)!}{(n+1)!} )?

Explanation opens after your attempt

Correct Answer

A. (4(n+5)(n+4)(n+3))

Step 1

Concept

Taking common ((n+5)(n+4)(n+3)), the difference is ((n+6)-(n+2)=4). Identify common factors first.

Step 2

Why this answer is correct

The correct answer is A. (4(n+5)(n+4)(n+3)). Taking common ((n+5)(n+4)(n+3)), the difference is ((n+6)-(n+2)=4). Identify common factors first.

Step 3

Exam Tip

सामान्य ((n+5)(n+4)(n+3)) निकालने पर अंतर ((n+6)-(n+2)=4) है। पहले समान गुणकों को पहचानें।

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Question 48/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+6)!}{(n+2)!}-\frac{(n+5)!}{(n+1)!}=2880 ), तो (n) का मान क्या है?

If ( \frac{(n+6)!}{(n+2)!}-\frac{(n+5)!}{(n+1)!}=2880 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

The simplified form is (4(n+5)(n+4)(n+3)). Since \(4\cdot10\cdot9\cdot8=2880\), (n=5).

Step 2

Why this answer is correct

The correct answer is B. (5). The simplified form is (4(n+5)(n+4)(n+3)). Since \(4\cdot10\cdot9\cdot8=2880\), (n=5).

Step 3

Exam Tip

सरल रूप (4(n+5)(n+4)(n+3)) है। \(4\cdot10\cdot9\cdot8=2880\), इसलिए (n=5)।

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Question 49/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

सबसे छोटा धनात्मक (n) क्या है जिसके लिए (n!) संख्या \(2^8\cdot3^2\cdot5^2\) से विभाज्य हो?

What is the smallest positive (n) for which (n!) is divisible by \(2^8\cdot3^2\cdot5^2\)?

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

(10!) contains exponent (8) of (2) and exponent (2) of (5). (9!) does not contain \(5^2\), so (10) is minimum.

Step 2

Why this answer is correct

The correct answer is C. (10). (10!) contains exponent (8) of (2) and exponent (2) of (5). (9!) does not contain \(5^2\), so (10) is minimum.

Step 3

Exam Tip

(10!) में (2) की घात (8) और (5) की घात (2) मिलती है। (9!) में \(5^2\) नहीं आता, इसलिए (10) न्यूनतम है।

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Question 50/50 Expert Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(100!) को विभाजित करने वाली (7) की अधिकतम घात क्या है?

What is the highest power of (7) that divides (100!)?

Explanation opens after your attempt

Correct Answer

C. (16)

Step 1

Concept

The exponent is \( \left\lfloor\frac{100}{7}\right\rfloor+\left\lfloor\frac{100}{49}\right\rfloor=16 \). Always add the contribution of higher powers such as (49).

Step 2

Why this answer is correct

The correct answer is C. (16). The exponent is \( \left\lfloor\frac{100}{7}\right\rfloor+\left\lfloor\frac{100}{49}\right\rfloor=16 \). Always add the contribution of higher powers such as (49).

Step 3

Exam Tip

घात \( \left\lfloor\frac{100}{7}\right\rfloor+\left\lfloor\frac{100}{49}\right\rfloor=16 \) है। उच्च घातों जैसे (49) का योगदान जरूर जोड़ें।

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

\( \frac{18!}{15!}-\frac{17!}{14!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{15!}{11!\cdot4!} \) का सरल मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n+4)!}{n!}=11880 ), तो (n) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n+2)!+(n+1)!}{(n+1)!}=14 ), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n+3)!-(n+2)!}{(n+1)!}=121 ), तो (n) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n!)2}{(n-2)!(n+2)!}=\frac{10}{21} ), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(20!) को विभाजित करने वाली (2) की अधिकतम घात क्या है?

Concept

Why this answer is correct

Exam Tip

(45!) के अंत में कितने शून्य होंगे?

Concept

Why this answer is correct

Exam Tip

सबसे छोटा धनात्मक (n) क्या है जिसके लिए (n!) संख्या (1440) से विभाज्य हो?

Concept

Why this answer is correct

Exam Tip

\( \frac{20!}{18!\cdot2!}+\frac{19!}{17!\cdot2!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{21!}{18!\cdot3!}-\frac{20!}{17!\cdot3!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{14!}{10!\cdot4!}\div\frac{13!}{9!\cdot4!} \) का सरल मान क्या है?

Concept

Why this answer is correct

Exam Tip

( \frac{(2n)!}{(2n-4)!} ) का सही विस्तार कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(2n)!}{(2n-4)!}=1680 ), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

( \frac{(3n+2)!}{(3n)!} ) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(3n+2)!}{(3n)!}=182 ), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n+4)!}{(n+2)!}-\frac{(n+3)!}{(n+1)!}=24 ), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

( \frac{(n+5)!+(n+4)!}{(n+3)!} ) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n+5)!+(n+4)!}{(n+3)!}=120 ), तो (n) का मान क्या है?

Concept

Why this answer is correct

यदि ( \frac{(n!)²}{(n-2)!(n+2)!}=\frac{10}{21} ), तो (n) का मान क्या है?