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Class 11 Mathematics Medium Quiz

Mathematics Medium Class 11 Level 56

Level 56 • 50/50 questions • 35 seconds per question.

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Question 1/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

C. (30)

Explanation

Simple Explanation

(n=4) रखने पर \(\frac{6!}{4!}=6\times5=30\)। पहले चर का मान रखकर फैक्टोरियल अनुपात सरल करें। / Putting (n=4), \(\frac{6!}{4!}=6\times5=30\). Substitute the variable first and simplify the factorial ratio.

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Question 2/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{8!-7!}{6!}\) का मान क्या है?

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

Explanation opens after your attempt
Correct Answer

D. (49)

Explanation

Simple Explanation

अंश (7!(8-1)=7\cdot7!) है। \(\frac{7\cdot7!}{6!}=7\times7=49\) मिलेगा। / The numerator is (7!(8-1)=7\cdot7!). Thus \(\frac{7\cdot7!}{6!}=7\times7=49\).

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Question 3/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

If (\frac{n!}{(n-2)!}=56), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (8)

Explanation

Simple Explanation

(\frac{n!}{(n-2)!}=n(n-1))। \(8\times7=56\), इसलिए (n=8) है। / (\frac{n!}{(n-2)!}=n(n-1)). Since \(8\times7=56\), (n=8).

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Question 4/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{6!+5!}{4!}\) का मान क्या है?

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

Explanation opens after your attempt
Correct Answer

D. (35)

Explanation

Simple Explanation

अंश (720+120=840) है और (4!=24)। इसलिए मान \(\frac{840}{24}=35\) है। / The numerator is (720+120=840) and (4!=24). Therefore the value is \(\frac{840}{24}=35\).

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Question 5/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{9!}{6!}-\frac{7!}{5!}\) का मान क्या है?

What is the value of \(\frac{9!}{6!}-\frac{7!}{5!}\)?

Explanation opens after your attempt
Correct Answer

A. (462)

Explanation

Simple Explanation

\(\frac{9!}{6!}=504\) और \(\frac{7!}{5!}=42\), इसलिए अंतर (462) है। दोनों अनुपात अलग-अलग सरल करें। / \(\frac{9!}{6!}=504\) and \(\frac{7!}{5!}=42\), so the difference is (462). Simplify both ratios separately.

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Question 6/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\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

B. (2(n+2)2)

Explanation

Simple Explanation

पहला पद ((n+3)(n+2)) और दूसरा ((n+2)(n+1)) है। समान ((n+2)) लेने पर (2(n+2)2) मिलता है। / The first term is ((n+3)(n+2)) and the second is ((n+2)(n+1)). Taking common ((n+2)) gives (2(n+2)2).

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Question 7/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+2)!}{n!}=42), तो (n) का मान क्या है?

If (\frac{(n+2)!}{n!}=42), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (5)

Explanation

Simple Explanation

(\frac{(n+2)!}{n!}=(n+2)(n+1))। \(7\times6=42\), इसलिए (n=5) है। / (\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(7\times6=42\), (n=5).

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Question 8/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{12!}{10!,2!}+\frac{8!}{6!,2!}\) का मान क्या है?

What is the value of \(\frac{12!}{10!,2!}+\frac{8!}{6!,2!}\)?

Explanation opens after your attempt
Correct Answer

D. (94)

Explanation

Simple Explanation

पहला पद (66) और दूसरा पद (28) है। दोनों को जोड़ने पर (94) मिलता है। / The first term is (66) and the second term is (28). Adding them gives (94).

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Question 9/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

A. \(n^2\)

Explanation

Simple Explanation

((n+1)!-n!=n!{(n+1)-1}=n\cdot n!)। ((n-1)!) से भाग देने पर \(n^2\) मिलता है। / ((n+1)!-n!=n!{(n+1)-1}=n\cdot n!). Dividing by ((n-1)!) gives \(n^2\).

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Question 10/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{7!}{4!,3!}\times3!\) का मान क्या है?

What is the value of \(\frac{7!}{4!,3!}\times3!\)?

Explanation opens after your attempt
Correct Answer

C. (210)

Explanation

Simple Explanation

\(\frac{7!}{4!,3!}=35\) और (3!=6)। इसलिए गुणनफल \(35\times6=210\) है। / \(\frac{7!}{4!,3!}=35\) and (3!=6). Therefore the product is \(35\times6=210\).

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Question 11/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि \(x=\frac{8!}{6!}\) और \(y=\frac{5!}{3!}\), तो (x+y) का मान क्या है?

If \(x=\frac{8!}{6!}\) and \(y=\frac{5!}{3!}\), what is the value of (x+y)?

Explanation opens after your attempt
Correct Answer

C. (76)

Explanation

Simple Explanation

\(x=8\times7=56\) और \(y=5\times4=20\)। इसलिए (x+y=76) है। / \(x=8\times7=56\) and \(y=5\times4=20\). Therefore (x+y=76).

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Question 12/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

((n+5)!=(n+5)(n+4)(n+3)!)। इसलिए सरल रूप ((n+5)(n+4)) है। / ((n+5)!=(n+5)(n+4)(n+3)!). Therefore the simplified form is ((n+5)(n+4)).

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Question 13/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{11!-10!}{9!}\) का मान क्या है?

What is the value of \(\frac{11!-10!}{9!}\)?

Explanation opens after your attempt
Correct Answer

C. (100)

Explanation

Simple Explanation

अंश (10!(11-1)=10\cdot10!) है। \(\frac{10\cdot10!}{9!}=10\times10=100\) है। / The numerator is (10!(11-1)=10\cdot10!). Thus \(\frac{10\cdot10!}{9!}=10\times10=100\).

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Question 14/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{9!}{7!}\div\frac{6!}{5!}\) का मान क्या है?

What is the value of \(\frac{9!}{7!}\div\frac{6!}{5!}\)?

Explanation opens after your attempt
Correct Answer

B. (12)

Explanation

Simple Explanation

\(\frac{9!}{7!}=72\) और \(\frac{6!}{5!}=6\)। इसलिए भागफल (12) है। / \(\frac{9!}{7!}=72\) and \(\frac{6!}{5!}=6\). Therefore the quotient is (12).

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Question 15/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+1)!}{(n-1)!}=72), तो (n) का मान क्या है?

If (\frac{(n+1)!}{(n-1)!}=72), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

अनुपात (n(n+1)) के बराबर है। \(8\times9=72\), इसलिए (n=8) है। / The ratio equals (n(n+1)). Since \(8\times9=72\), (n=8).

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Question 16/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{5!,3!}{2!,4!}\) का मान क्या है?

What is the value of \(\frac{5!,3!}{2!,4!}\)?

Explanation opens after your attempt
Correct Answer

C. (15)

Explanation

Simple Explanation

\(\frac{5!}{4!}=5\) और \(\frac{3!}{2!}=3\)। इसलिए मान \(5\times3=15\) है। / \(\frac{5!}{4!}=5\) and \(\frac{3!}{2!}=3\). Hence the value is \(5\times3=15\).

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Question 17/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{8!}{5!}+\frac{6!}{4!}-4!\) का मान क्या है?

What is the value of \(\frac{8!}{5!}+\frac{6!}{4!}-4!\)?

Explanation opens after your attempt
Correct Answer

D. (342)

Explanation

Simple Explanation

\(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\) और (4!=24)। इसलिए (336+30-24=342) है। / \(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\), and (4!=24). Thus (336+30-24=342).

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Question 18/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+5)!}{(n+2)!}) में कितने क्रमागत गुणक बचते हैं?

How many consecutive factors remain in (\frac{(n+5)!}{(n+2)!})?

Explanation opens after your attempt
Correct Answer

B. (3)

Explanation

Simple Explanation

(\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3))। इसलिए तीन क्रमागत गुणक बचते हैं। / (\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3)). Therefore three consecutive factors remain.

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Question 19/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+3)!}{(n+1)!}=90), तो (n) का मान क्या है?

If (\frac{(n+3)!}{(n+1)!}=90), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2))। \(10\times9=90\), इसलिए (n=7) है। / (\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(10\times9=90\), (n=7).

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Question 20/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{13!}{11!,2!}-\frac{6!}{4!,2!}\) का मान क्या है?

What is the value of \(\frac{13!}{11!,2!}-\frac{6!}{4!,2!}\)?

Explanation opens after your attempt
Correct Answer

C. (63)

Explanation

Simple Explanation

पहला पद (78) और दूसरा पद (15) है। अंतर (78-15=63) है। / The first term is (78) and the second term is (15). The difference is (78-15=63).

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Question 21/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

B. \(n^2+3n+1\)

Explanation

Simple Explanation

(\frac{(n+2)!}{n!}=(n+2)(n+1)), फिर (1) घटेगा। सरल रूप \(n^2+3n+1\) है। / (\frac{(n+2)!}{n!}=(n+2)(n+1)), then (1) is subtracted. The simplified form is \(n^2+3n+1\).

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Question 22/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{10!}{8!}+\frac{7!}{6!}+0!\) का मान क्या है?

What is the value of \(\frac{10!}{8!}+\frac{7!}{6!}+0!\)?

Explanation opens after your attempt
Correct Answer

C. (98)

Explanation

Simple Explanation

\(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\) और (0!=1)। कुल (98) है। / \(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\), and (0!=1). The total is (98).

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Question 23/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

C. (n(n+1))

Explanation

Simple Explanation

पहला अनुपात (n) और दूसरा (n+1) है। इसलिए गुणनफल (n(n+1)) है। / The first ratio is (n) and the second is (n+1). Therefore the product is (n(n+1)).

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Question 24/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(\frac{n!}{(n-3)!}=n(n-1)(n-2))। \(7\times6\times5=210\), इसलिए (n=7) है। / (\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(7\times6\times5=210\), (n=7).

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Question 25/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{9!+8!}{7!}\) का मान क्या है?

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

Explanation opens after your attempt
Correct Answer

B. (80)

Explanation

Simple Explanation

अंश को (8!(9+1)) लिखा जा सकता है। \(\frac{10\cdot8!}{7!}=10\times8=80\) है। / The numerator can be written as (8!(9+1)). Thus \(\frac{10\cdot8!}{7!}=10\times8=80\).

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Question 26/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{6!}{3!,3!}+\frac{7!}{5!,2!}\) का मान क्या है?

What is the value of \(\frac{6!}{3!,3!}+\frac{7!}{5!,2!}\)?

Explanation opens after your attempt
Correct Answer

C. (41)

Explanation

Simple Explanation

पहला पद (20) और दूसरा (21) है। दोनों का योग (41) होगा। / The first term is (20) and the second is (21). Their sum is (41).

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Question 27/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

यह भाग (\frac{(n+4)!}{(n+2)!}) बन जाता है। इसलिए सरल रूप ((n+4)(n+3)) है। / This division becomes (\frac{(n+4)!}{(n+2)!}). Hence the simplified form is ((n+4)(n+3)).

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Question 28/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि \(a=\frac{7!-5!}{5!}\), तो (a) का मान क्या है?

If \(a=\frac{7!-5!}{5!}\), what is the value of (a)?

Explanation opens after your attempt
Correct Answer

B. (41)

Explanation

Simple Explanation

\(\frac{7!}{5!}=42\) और \(\frac{5!}{5!}=1\)। इसलिए (a=42-1=41) है। / \(\frac{7!}{5!}=42\) and \(\frac{5!}{5!}=1\). Therefore (a=42-1=41).

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Question 29/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+1)!}{(n-2)!}=60), तो (n) का मान क्या है?

If (\frac{(n+1)!}{(n-2)!}=60), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

(\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1))। \(5\times4\times3=60\), इसलिए (n=4) है। / (\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1)). Since \(5\times4\times3=60\), (n=4).

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Question 30/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{\frac{12!}{9!,3!}}{\frac{5!}{3!,2!}}\) का मान क्या है?

What is the value of \(\frac{\frac{12!}{9!,3!}}{\frac{5!}{3!,2!}}\)?

Explanation opens after your attempt
Correct Answer

C. (22)

Explanation

Simple Explanation

ऊपर का पद (220) और नीचे का पद (10) है। भाग देने पर (22) मिलता है। / The numerator term is (220) and the denominator term is (10). Dividing gives (22).

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Question 31/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

C. (n+4)

Explanation

Simple Explanation

अंश ((n+2)![(n+3)+1]) है। इसलिए सरल रूप (n+4) है। / The numerator is ((n+2)![(n+3)+1]). Therefore the simplified form is (n+4).

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Question 32/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{10!-8!}{8!}\) का मान क्या है?

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

Explanation opens after your attempt
Correct Answer

C. (89)

Explanation

Simple Explanation

\(\frac{10!}{8!}=90\) और \(\frac{8!}{8!}=1\)। इसलिए मान (90-1=89) है। / \(\frac{10!}{8!}=90\) and \(\frac{8!}{8!}=1\). Therefore the value is (90-1=89).

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Question 33/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(4!\times\frac{6!}{5!}-3!\) का मान क्या है?

What is the value of \(4!\times\frac{6!}{5!}-3!\)?

Explanation opens after your attempt
Correct Answer

C. (138)

Explanation

Simple Explanation

(4!=24), \(\frac{6!}{5!}=6\) और (3!=6)। इसलिए \(24\times6-6=138\) है। / (4!=24), \(\frac{6!}{5!}=6\), and (3!=6). Hence \(24\times6-6=138\).

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Question 34/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{11!}{8!,3!}-\frac{9!}{7!,2!}\) का मान क्या है?

What is the value of \(\frac{11!}{8!,3!}-\frac{9!}{7!,2!}\)?

Explanation opens after your attempt
Correct Answer

C. (129)

Explanation

Simple Explanation

पहला पद (165) और दूसरा (36) है। अंतर (129) मिलेगा। / The first term is (165) and the second is (36). The difference is (129).

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Question 35/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

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Correct Answer

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

Explanation

Simple Explanation

((n+5)!=(n+5)(n+4)(n+3)(n+2)!)। इसलिए तीन गुणक बचते हैं। / ((n+5)!=(n+5)(n+4)(n+3)(n+2)!). Therefore three factors remain.

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Question 36/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+4)!}{(n+2)!}=132), तो (n) का मान क्या है?

If (\frac{(n+4)!}{(n+2)!}=132), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (8)

Explanation

Simple Explanation

(\frac{(n+4)!}{(n+2)!}=(n+4)(n+3))। \(12\times11=132\), इसलिए (n=8) है। / (\frac{(n+4)!}{(n+2)!}=(n+4)(n+3)). Since \(12\times11=132\), (n=8).

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Question 37/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{7!}{5!}+\frac{5!}{2!,3!}+1!\) का मान क्या है?

What is the value of \(\frac{7!}{5!}+\frac{5!}{2!,3!}+1!\)?

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Correct Answer

C. (53)

Explanation

Simple Explanation

\(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\) और (1!=1)। कुल (53) है। / \(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\), and (1!=1). The total is (53).

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Question 38/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

B. ((n+2)(n+1))

Explanation

Simple Explanation

पहला अनुपात (n+2) और दूसरा (n+1) है। गुणनफल ((n+2)(n+1)) होगा। / The first ratio is (n+2) and the second is (n+1). The product is ((n+2)(n+1)).

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Question 39/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{8!,3!}{6!,2!}\) का मान क्या है?

What is the value of \(\frac{8!,3!}{6!,2!}\)?

Explanation opens after your attempt
Correct Answer

C. (168)

Explanation

Simple Explanation

\(\frac{8!}{6!}=56\) और \(\frac{3!}{2!}=3\)। इसलिए मान \(56\times3=168\) है। / \(\frac{8!}{6!}=56\) and \(\frac{3!}{2!}=3\). Therefore the value is \(56\times3=168\).

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Question 40/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{9!-7!}{7!}\) का मान क्या है?

What is the value of \(\frac{9!-7!}{7!}\)?

Explanation opens after your attempt
Correct Answer

C. (71)

Explanation

Simple Explanation

\(\frac{9!}{7!}=72\) और \(\frac{7!}{7!}=1\)। इसलिए (72-1=71) है। / \(\frac{9!}{7!}=72\) and \(\frac{7!}{7!}=1\). Hence (72-1=71).

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Question 41/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

B. (n+1)

Explanation

Simple Explanation

(n!=n(n-1)!), इसलिए अंश ((n-1)!(n+1)) है। भाग देने पर (n+1) मिलेगा। / Since (n!=n(n-1)!), the numerator is ((n-1)!(n+1)). Dividing gives (n+1).

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Question 42/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (n=5), तो (\frac{(n+3)!}{(n+1)!}-\frac{(n+1)!}{n!}) का मान क्या है?

If (n=5), what is the value of (\frac{(n+3)!}{(n+1)!}-\frac{(n+1)!}{n!})?

Explanation opens after your attempt
Correct Answer

C. (50)

Explanation

Simple Explanation

(n=5) पर पहला पद \(\frac{8!}{6!}=56\) और दूसरा \(\frac{6!}{5!}=6\) है। अंतर (50) है। / For (n=5), the first term is \(\frac{8!}{6!}=56\) and the second is \(\frac{6!}{5!}=6\). The difference is (50).

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Question 43/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{6!}{2!,4!}\times\frac{4!}{3!}\) का मान क्या है?

What is the value of \(\frac{6!}{2!,4!}\times\frac{4!}{3!}\)?

Explanation opens after your attempt
Correct Answer

D. (60)

Explanation

Simple Explanation

पहला पद (15) और दूसरा (4) है। गुणनफल \(15\times4=60\) है। / The first term is (15) and the second is (4). The product is \(15\times4=60\).

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Question 44/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{14!}{12!}-\frac{13!}{11!}\) का मान क्या है?

What is the value of \(\frac{14!}{12!}-\frac{13!}{11!}\)?

Explanation opens after your attempt
Correct Answer

B. (26)

Explanation

Simple Explanation

\(\frac{14!}{12!}=14\times13=182\) और \(\frac{13!}{11!}=13\times12=156\)। अंतर (26) है। / \(\frac{14!}{12!}=14\times13=182\) and \(\frac{13!}{11!}=13\times12=156\). The difference is (26).

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Question 45/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+2)!-(n+1)!}{n!}=36), तो (n) का मान क्या है?

If (\frac{(n+2)!-(n+1)!}{n!}=36), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

सरल रूप ((n+1)2) है। ((n+1)2=36) से (n+1=6) और (n=5) है। / The simplified form is ((n+1)2). From ((n+1)2=36), (n+1=6) and (n=5).

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Question 46/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

C. (n+3)

Explanation

Simple Explanation

भिन्न को सरल करने पर (\frac{(n+3)!}{(n+2)!}) मिलता है। इसका मान (n+3) है। / Simplifying the fraction gives (\frac{(n+3)!}{(n+2)!}). Its value is (n+3).

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Question 47/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{10!}{6!,4!}+\frac{10!}{7!,3!}\) का मान क्या है?

What is the value of \(\frac{10!}{6!,4!}+\frac{10!}{7!,3!}\)?

Explanation opens after your attempt
Correct Answer

D. (330)

Explanation

Simple Explanation

पहला पद (210) और दूसरा पद (120) है। दोनों का योग (330) है। / The first term is (210) and the second term is (120). Their sum is (330).

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Question 48/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

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

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

Explanation opens after your attempt
Correct Answer

B. (2729)

Explanation

Simple Explanation

\(\frac{15!}{12!}=15\times14\times13=2730\) और \(\frac{12!}{12!}=1\)। इसलिए मान (2730-1=2729) है। / \(\frac{15!}{12!}=15\times14\times13=2730\) and \(\frac{12!}{12!}=1\). Therefore the value is (2730-1=2729).

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Question 49/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+4)!}{(n+1)!}=504), तो (n) का मान क्या है?

If (\frac{(n+4)!}{(n+1)!}=504), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2))। \(9\times8\times7=504\), इसलिए (n=5) है। / (\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)). Since \(9\times8\times7=504\), (n=5).

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Question 50/50 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+4)!}{(n+2)!}-\frac{(n+3)!}{(n+1)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+4)!}{(n+2)!}-\frac{(n+3)!}{(n+1)!})?

Explanation opens after your attempt
Correct Answer

A. (2(n+3))

Explanation

Simple Explanation

पहला पद ((n+4)(n+3)) और दूसरा ((n+3)(n+2)) है। अंतर लेने पर (2(n+3)) मिलता है। / The first term is ((n+4)(n+3)) and the second is ((n+3)(n+2)). Taking the difference gives (2(n+3)).

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