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Mathematics Quiz - Class 11 Mathematics Medium Level 55 Quiz

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

यदि (\frac{(n+1)!}{n!}=8), तो (n) का मान क्या है?

If (\frac{(n+1)!}{n!}=8), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

(\frac{(n+1)!}{n!}=n+1), so (n+1=8) and (n=7). Simplify the factorial ratio first.

Step 2

Why this answer is correct

The correct answer is B. (7). (\frac{(n+1)!}{n!}=n+1), so (n+1=8) and (n=7). Simplify the factorial ratio first.

Step 3

Exam Tip

(\frac{(n+1)!}{n!}=n+1), इसलिए (n+1=8) और (n=7)। पहले फैक्टोरियल अनुपात सरल करें।

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

\(\frac{9!}{7!}-5!\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

A. (-48)

Step 1

Concept

\(\frac{9!}{7!}=9\times8=72\) and (5!=120), so the value is (-48). Keep the sign carefully in subtraction.

Step 2

Why this answer is correct

The correct answer is A. (-48). \(\frac{9!}{7!}=9\times8=72\) and (5!=120), so the value is (-48). Keep the sign carefully in subtraction.

Step 3

Exam Tip

\(\frac{9!}{7!}=9\times8=72\) और (5!=120), इसलिए मान (-48) है। घटाव में चिह्न ध्यान से रखें।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (20)

Step 1

Concept

Putting (n=3), \(\frac{5!}{3!}=5\times4=20\). Substitute the variable first.

Step 2

Why this answer is correct

The correct answer is B. (20). Putting (n=3), \(\frac{5!}{3!}=5\times4=20\). Substitute the variable first.

Step 3

Exam Tip

(n=3) रखने पर \(\frac{5!}{3!}=5\times4=20\)। पहले चर का मान रखें।

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

यदि ((n+1)!=720), तो (n) का मान क्या है?

If ((n+1)!=720), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

Since (720=6!), (n+1=6) and (n=5). Remember small factorial values.

Step 2

Why this answer is correct

The correct answer is B. (5). Since (720=6!), (n+1=6) and (n=5). Remember small factorial values.

Step 3

Exam Tip

(720=6!), इसलिए (n+1=6) और (n=5)। छोटे फैक्टोरियल मान याद रखें।

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

\(\frac{6!}{3!}+4!\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. (144)

Step 1

Concept

\(\frac{6!}{3!}=120\) and (4!=24), so the total is (144). Simplify the fraction first.

Step 2

Why this answer is correct

The correct answer is C. (144). \(\frac{6!}{3!}=120\) and (4!=24), so the total is (144). Simplify the fraction first.

Step 3

Exam Tip

\(\frac{6!}{3!}=120\) और (4!=24), इसलिए कुल (144) है। पहले भिन्न को सरल करें।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (25)

Step 1

Concept

\(\frac{5!}{3!}=20\) and \(\frac{5!}{4!}=5\), so the sum is (25). Simplify each ratio separately.

Step 2

Why this answer is correct

The correct answer is B. (25). \(\frac{5!}{3!}=20\) and \(\frac{5!}{4!}=5\), so the sum is (25). Simplify each ratio separately.

Step 3

Exam Tip

\(\frac{5!}{3!}=20\) और \(\frac{5!}{4!}=5\), इसलिए योग (25) है। हर अनुपात अलग-अलग सरल करें।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

The first ratio is (n+2) and the second is (n). The difference is ((n+2)-n=2).

Step 2

Why this answer is correct

The correct answer is B. (2). The first ratio is (n+2) and the second is (n). The difference is ((n+2)-n=2).

Step 3

Exam Tip

पहला अनुपात (n+2) और दूसरा (n) है। अंतर ((n+2)-n=2) होगा।

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

\(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\) का मान क्या है?

What is the value of \(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\)?

Explanation opens after your attempt

Correct Answer

C. (71)

Step 1

Concept

\(\frac{8!}{5!,3!}=56\) and \(\frac{6!}{4!,2!}=15\), so the total is (71). Solve both terms separately.

Step 2

Why this answer is correct

The correct answer is C. (71). \(\frac{8!}{5!,3!}=56\) and \(\frac{6!}{4!,2!}=15\), so the total is (71). Solve both terms separately.

Step 3

Exam Tip

\(\frac{8!}{5!,3!}=56\) और \(\frac{6!}{4!,2!}=15\), इसलिए कुल (71) है। दोनों पदों को अलग हल करें।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

(\frac{n!}{(n-2)!}=n(n-1)), so (n(n-1)=42). Since \(7\times6=42\), (n=7).

Step 2

Why this answer is correct

The correct answer is B. (7). (\frac{n!}{(n-2)!}=n(n-1)), so (n(n-1)=42). Since \(7\times6=42\), (n=7).

Step 3

Exam Tip

(\frac{n!}{(n-2)!}=n(n-1)), इसलिए (n(n-1)=42)। \(7\times6=42\), अतः (n=7)।

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

\(\frac{10!}{8!}+\frac{4!}{2!}\) का मान क्या है?

What is the value of \(\frac{10!}{8!}+\frac{4!}{2!}\)?

Explanation opens after your attempt

Correct Answer

C. (102)

Step 1

Concept

\(\frac{10!}{8!}=90\) and \(\frac{4!}{2!}=12\), so the sum is (102). Cancel common factorial parts.

Step 2

Why this answer is correct

The correct answer is C. (102). \(\frac{10!}{8!}=90\) and \(\frac{4!}{2!}=12\), so the sum is (102). Cancel common factorial parts.

Step 3

Exam Tip

\(\frac{10!}{8!}=90\) और \(\frac{4!}{2!}=12\), इसलिए योग (102) है। समान फैक्टोरियल भाग काटें।

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

\(\frac{7!-6!}{6!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

Since \(7!=7\times6!\), (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6). Take the common factorial out.

Step 2

Why this answer is correct

The correct answer is B. (6). Since \(7!=7\times6!\), (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6). Take the common factorial out.

Step 3

Exam Tip

\(7!=7\times6!\), इसलिए (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6)। समान फैक्टोरियल बाहर लें।

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

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((n+3)!=(n+3)(n+2)(n+1)n!), so (n!) cancels. Three consecutive factors remain.

Step 2

Why this answer is correct

The correct answer is A. ((n+3)(n+2)(n+1)). ((n+3)!=(n+3)(n+2)(n+1)n!), so (n!) cancels. Three consecutive factors remain.

Step 3

Exam Tip

((n+3)!=(n+3)(n+2)(n+1)n!), इसलिए (n!) कट जाता है। क्रम से तीन गुणक बचते हैं।

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

यदि (\frac{(n+2)!}{n!}=30), तो (n) का मान क्या है?

If (\frac{(n+2)!}{n!}=30), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

(\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(6\times5=30\), (n=4).

Step 2

Why this answer is correct

The correct answer is B. (4). (\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(6\times5=30\), (n=4).

Step 3

Exam Tip

(\frac{(n+2)!}{n!}=(n+2)(n+1))। \(6\times5=30\), इसलिए (n=4)।

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

\(\frac{9!}{6!,3!}-\frac{7!}{5!,2!}\) का मान क्या है?

What is the value of \(\frac{9!}{6!,3!}-\frac{7!}{5!,2!}\)?

Explanation opens after your attempt

Correct Answer

A. (63)

Step 1

Concept

\(\frac{9!}{6!,3!}=84\) and \(\frac{7!}{5!,2!}=21\), so the difference is (63). Evaluate both combination-like terms separately.

Step 2

Why this answer is correct

The correct answer is A. (63). \(\frac{9!}{6!,3!}=84\) and \(\frac{7!}{5!,2!}=21\), so the difference is (63). Evaluate both combination-like terms separately.

Step 3

Exam Tip

\(\frac{9!}{6!,3!}=84\) और \(\frac{7!}{5!,2!}=21\), इसलिए अंतर (63) है। दोनों संयोजन-जैसे पद अलग निकालें।

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

\(\frac{5!+3!}{4!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. \(\frac{21}{4}\)

Step 1

Concept

The numerator is (120+6=126) and (4!=24). Hence the value is \(\frac{126}{24}=\frac{21}{4}\).

Step 2

Why this answer is correct

The correct answer is C. \(\frac{21}{4}\). The numerator is (120+6=126) and (4!=24). Hence the value is \(\frac{126}{24}=\frac{21}{4}\).

Step 3

Exam Tip

अंश (120+6=126) है और (4!=24)। इसलिए मान \(\frac{126}{24}=\frac{21}{4}\) है।

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

\(\frac{8!}{4!}-\frac{7!}{4!}\) का मान क्या है?

What is the value of \(\frac{8!}{4!}-\frac{7!}{4!}\)?

Explanation opens after your attempt

Correct Answer

B. (1470)

Step 1

Concept

(\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470). With a common denominator, combine the numerator.

Step 2

Why this answer is correct

The correct answer is B. (1470). (\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470). With a common denominator, combine the numerator.

Step 3

Exam Tip

(\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470)। समान हर होने पर अंश मिलाकर देखें।

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

\(\frac{11!}{9!,2!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (55)

Step 1

Concept

\(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\). Write the larger factorial up to (9!).

Step 2

Why this answer is correct

The correct answer is B. (55). \(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\). Write the larger factorial up to (9!).

Step 3

Exam Tip

\(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\)। बड़े फैक्टोरियल को (9!) तक लिखें।

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

कौन सा रूप \(\frac{12!}{9!}\) के बराबर है?

Which expression is equal to \(\frac{12!}{9!}\)?

Explanation opens after your attempt

Correct Answer

B. \(12\times11\times10\)

Step 1

Concept

\(\frac{12!}{9!}=12\times11\times10\). Since the denominator is (9!), the part up to (9!) cancels.

Step 2

Why this answer is correct

The correct answer is B. \(12\times11\times10\). \(\frac{12!}{9!}=12\times11\times10\). Since the denominator is (9!), the part up to (9!) cancels.

Step 3

Exam Tip

\(\frac{12!}{9!}=12\times11\times10\)। हर में (9!) होने से (9!) तक का भाग कट जाता है।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (n)

Step 1

Concept

Since ((n+1)!=(n+1)n!), the numerator is (n!{(n+1)-1}=nn!). Dividing gives (n).

Step 2

Why this answer is correct

The correct answer is B. (n). Since ((n+1)!=(n+1)n!), the numerator is (n!{(n+1)-1}=nn!). Dividing gives (n).

Step 3

Exam Tip

((n+1)!=(n+1)n!), इसलिए अंश (n!{(n+1)-1}=nn!) है। भाग देने पर (n) मिलता है।

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

यदि (\frac{n!}{(n-1)!}+2=9), तो (n) का मान क्या है?

If (\frac{n!}{(n-1)!}+2=9), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

(\frac{n!}{(n-1)!}=n), so (n+2=9). Therefore, (n=7).

Step 2

Why this answer is correct

The correct answer is C. (7). (\frac{n!}{(n-1)!}=n), so (n+2=9). Therefore, (n=7).

Step 3

Exam Tip

(\frac{n!}{(n-1)!}=n), इसलिए (n+2=9)। अतः (n=7) है।

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

\(\frac{6!}{2!,4!}+\frac{5!}{2!,3!}\) का मान क्या है?

What is the value of \(\frac{6!}{2!,4!}+\frac{5!}{2!,3!}\)?

Explanation opens after your attempt

Correct Answer

B. (25)

Step 1

Concept

\(\frac{6!}{2!,4!}=15\) and \(\frac{5!}{2!,3!}=10\), so the total is (25). Count the smaller terms separately.

Step 2

Why this answer is correct

The correct answer is B. (25). \(\frac{6!}{2!,4!}=15\) and \(\frac{5!}{2!,3!}=10\), so the total is (25). Count the smaller terms separately.

Step 3

Exam Tip

\(\frac{6!}{2!,4!}=15\) और \(\frac{5!}{2!,3!}=10\), इसलिए कुल (25) है। छोटे पदों को अलग-अलग गिनें।

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

\(\frac{7!}{3!,4!}\times2!\) का मान क्या है?

What is the value of \(\frac{7!}{3!,4!}\times2!\)?

Explanation opens after your attempt

Correct Answer

B. (70)

Step 1

Concept

\(\frac{7!}{3!,4!}=35\) and (2!=2), so the product is (70). Simplify the fraction first.

Step 2

Why this answer is correct

The correct answer is B. (70). \(\frac{7!}{3!,4!}=35\) and (2!=2), so the product is (70). Simplify the fraction first.

Step 3

Exam Tip

\(\frac{7!}{3!,4!}=35\) और (2!=2), इसलिए गुणनफल (70) है। पहले भिन्न को सरल करें।

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

\(\frac{10!-9!}{8!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (81)

Step 1

Concept

The numerator is (9!(10-1)=9\cdot9!). Thus \(\frac{9\cdot9!}{8!}=9\times9=81\).

Step 2

Why this answer is correct

The correct answer is B. (81). The numerator is (9!(10-1)=9\cdot9!). Thus \(\frac{9\cdot9!}{8!}=9\times9=81\).

Step 3

Exam Tip

अंश (9!(10-1)=9\cdot9!) है। \(\frac{9\cdot9!}{8!}=9\times9=81\) मिलता है।

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

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

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

Explanation opens after your attempt

Correct Answer

A. ((n+1)²)

Step 1

Concept

The numerator is ((n+1)![(n+2)-1]=(n+1)²n!). After cancelling (n!), the result is ((n+1)²).

Step 2

Why this answer is correct

The correct answer is A. ((n+1)²). The numerator is ((n+1)![(n+2)-1]=(n+1)²n!). After cancelling (n!), the result is ((n+1)²).

Step 3

Exam Tip

अंश ((n+1)![(n+2)-1]=(n+1)²n!) है। (n!) कटने पर ((n+1)²) मिलता है।

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

यदि (\frac{(n+3)!}{(n+1)!}=56), तो (n) का मान क्या है?

If (\frac{(n+3)!}{(n+1)!}=56), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(8\times7=56\), (n=5).

Step 2

Why this answer is correct

The correct answer is B. (5). (\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(8\times7=56\), (n=5).

Step 3

Exam Tip

(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2))। \(8\times7=56\), इसलिए (n=5)।

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

\(\frac{5!,3!}{4!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (30)

Step 1

Concept

\(\frac{5!}{4!}=5\) and (3!=6), so the value is (30). Simplify multiplication and division step by step.

Step 2

Why this answer is correct

The correct answer is B. (30). \(\frac{5!}{4!}=5\) and (3!=6), so the value is (30). Simplify multiplication and division step by step.

Step 3

Exam Tip

\(\frac{5!}{4!}=5\) और (3!=6), इसलिए मान (30) है। गुणन और भाग को क्रम से सरल करें।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (21)

Step 1

Concept

The three terms are (8), (7), and (6) respectively. The sum is (8+7+6=21).

Step 2

Why this answer is correct

The correct answer is C. (21). The three terms are (8), (7), and (6) respectively. The sum is (8+7+6=21).

Step 3

Exam Tip

तीनों पद क्रमशः (8), (7) और (6) हैं। योग (8+7+6=21) है।

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

\(\frac{9!}{5!,4!}\div\frac{6!}{4!,2!}\) का मान क्या है?

What is the value of \(\frac{9!}{5!,4!}\div\frac{6!}{4!,2!}\)?

Explanation opens after your attempt

Correct Answer

B. \( \frac{42}{5}\)

Step 1

Concept

The first term is (126) and the second is (15). Thus \(\frac{126}{15}=\frac{42}{5}\).

Step 2

Why this answer is correct

The correct answer is B. \( \frac{42}{5}\). The first term is (126) and the second is (15). Thus \(\frac{126}{15}=\frac{42}{5}\).

Step 3

Exam Tip

पहला पद (126) और दूसरा (15) है। \(\frac{126}{15}=\frac{42}{5}\) मिलता है।

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

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((n+4)!=(n+4)(n+3)(n+2)!). After cancelling ((n+2)!), ((n+4)(n+3)) remains.

Step 2

Why this answer is correct

The correct answer is A. ((n+4)(n+3)). ((n+4)!=(n+4)(n+3)(n+2)!). After cancelling ((n+2)!), ((n+4)(n+3)) remains.

Step 3

Exam Tip

((n+4)!=(n+4)(n+3)(n+2)!)। ((n+2)!) कटने पर ((n+4)(n+3)) बचता है।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

(\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(6\times5\times4=120\), (n=6).

Step 2

Why this answer is correct

The correct answer is C. (6). (\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(6\times5\times4=120\), (n=6).

Step 3

Exam Tip

(\frac{n!}{(n-3)!}=n(n-1)(n-2))। \(6\times5\times4=120\), इसलिए (n=6)।

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

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

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

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

\(\frac{7!}{5!}=42\) and \(\frac{6!}{4!}=30\), so the difference is (12). Evaluate smaller ratios directly.

Step 2

Why this answer is correct

The correct answer is A. (12). \(\frac{7!}{5!}=42\) and \(\frac{6!}{4!}=30\), so the difference is (12). Evaluate smaller ratios directly.

Step 3

Exam Tip

\(\frac{7!}{5!}=42\) और \(\frac{6!}{4!}=30\), इसलिए अंतर (12) है। छोटे अनुपात सीधे निकालें।

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

\(\frac{4!+5!}{3!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (24)

Step 1

Concept

The numerator is (24+120=144) and (3!=6). Therefore, the value is (24).

Step 2

Why this answer is correct

The correct answer is B. (24). The numerator is (24+120=144) and (3!=6). Therefore, the value is (24).

Step 3

Exam Tip

अंश (24+120=144) है और (3!=6)। इसलिए मान (24) है।

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

\(\frac{12!}{10!,2!}-\frac{5!}{3!,2!}\) का मान क्या है?

What is the value of \(\frac{12!}{10!,2!}-\frac{5!}{3!,2!}\)?

Explanation opens after your attempt

Correct Answer

C. (56)

Step 1

Concept

\(\frac{12!}{10!,2!}=66\) and \(\frac{5!}{3!,2!}=10\), so the difference is (56). Keep the larger and smaller terms separate.

Step 2

Why this answer is correct

The correct answer is C. (56). \(\frac{12!}{10!,2!}=66\) and \(\frac{5!}{3!,2!}=10\), so the difference is (56). Keep the larger and smaller terms separate.

Step 3

Exam Tip

\(\frac{12!}{10!,2!}=66\) और \(\frac{5!}{3!,2!}=10\), इसलिए अंतर (56) है। बड़े और छोटे पद अलग रखें।

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

यदि (n(n-1)=72), तो (\frac{n!}{(n-2)!}) का मान क्या होगा?

If (n(n-1)=72), what will be the value of (\frac{n!}{(n-2)!})?

Explanation opens after your attempt

Correct Answer

B. (72)

Step 1

Concept

(\frac{n!}{(n-2)!}=n(n-1)). From the given condition, its value is (72).

Step 2

Why this answer is correct

The correct answer is B. (72). (\frac{n!}{(n-2)!}=n(n-1)). From the given condition, its value is (72).

Step 3

Exam Tip

(\frac{n!}{(n-2)!}=n(n-1))। दिए गए अनुसार इसका मान (72) है।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

The first ratio is (6) and the second is \(5\times4=20\). The product is \(6\times20=120\).

Step 2

Why this answer is correct

The correct answer is C. (120). The first ratio is (6) and the second is \(5\times4=20\). The product is \(6\times20=120\).

Step 3

Exam Tip

पहला अनुपात (6) और दूसरा \(5\times4=20\) है। गुणनफल \(6\times20=120\) है।

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

\(\frac{10!}{7!,3!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

\(\frac{10!}{7!,3!}=\frac{10\times9\times8}{6}=120\). Do not forget that (3!=6).

Step 2

Why this answer is correct

The correct answer is C. (120). \(\frac{10!}{7!,3!}=\frac{10\times9\times8}{6}=120\). Do not forget that (3!=6).

Step 3

Exam Tip

\(\frac{10!}{7!,3!}=\frac{10\times9\times8}{6}=120\)। (3!=6) रखना न भूलें।

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

\(\frac{7!+5!}{6!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

A. \(7+\frac{1}{6}\)

Step 1

Concept

\(\frac{7!}{6!}=7\) and \(\frac{5!}{6!}=\frac{1}{6}\), so the value is \(7+\frac{1}{6}\). Divide each term by the denominator separately.

Step 2

Why this answer is correct

The correct answer is A. \(7+\frac{1}{6}\). \(\frac{7!}{6!}=7\) and \(\frac{5!}{6!}=\frac{1}{6}\), so the value is \(7+\frac{1}{6}\). Divide each term by the denominator separately.

Step 3

Exam Tip

\(\frac{7!}{6!}=7\) और \(\frac{5!}{6!}=\frac{1}{6}\), इसलिए मान \(7+\frac{1}{6}\) है। पदों को हर से अलग-अलग भाग दें।

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

यदि \(a=\frac{8!}{6!}\) और (b=3!), तो (a-b) का मान क्या है?

If \(a=\frac{8!}{6!}\) and (b=3!), what is the value of (a-b)?

Explanation opens after your attempt

Correct Answer

B. (50)

Step 1

Concept

\(a=8\times7=56\) and (b=6), so (a-b=50). Find both values separately first.

Step 2

Why this answer is correct

The correct answer is B. (50). \(a=8\times7=56\) and (b=6), so (a-b=50). Find both values separately first.

Step 3

Exam Tip

\(a=8\times7=56\) और (b=6), इसलिए (a-b=50)। पहले दोनों मान अलग निकालें।

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

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((n+2)!=(n+2)(n+1)n(n-1)!). Hence after cancelling ((n-1)!), three factors remain.

Step 2

Why this answer is correct

The correct answer is A. ((n+2)(n+1)n). ((n+2)!=(n+2)(n+1)n(n-1)!). Hence after cancelling ((n-1)!), three factors remain.

Step 3

Exam Tip

((n+2)!=(n+2)(n+1)n(n-1)!)। इसलिए ((n-1)!) कटने पर तीन गुणक बचते हैं।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

The three ratios are (9), (8), and (7) respectively. Hence (9+8-7=10).

Step 2

Why this answer is correct

The correct answer is C. (10). The three ratios are (9), (8), and (7) respectively. Hence (9+8-7=10).

Step 3

Exam Tip

तीन अनुपात क्रमशः (9), (8) और (7) हैं। इसलिए (9+8-7=10) है।

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

यदि (\frac{(n+1)!}{(n-1)!}=20), तो (n) का मान क्या है?

If (\frac{(n+1)!}{(n-1)!}=20), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

This ratio is (n(n+1)). Since \(4\times5=20\), (n=4).

Step 2

Why this answer is correct

The correct answer is B. (4). This ratio is (n(n+1)). Since \(4\times5=20\), (n=4).

Step 3

Exam Tip

यह अनुपात (n(n+1)) है। \(4\times5=20\), इसलिए (n=4)।

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

\(\frac{8!}{6!}-\frac{5!}{4!}+2!\) का मान क्या है?

What is the value of \(\frac{8!}{6!}-\frac{5!}{4!}+2!\)?

Explanation opens after your attempt

Correct Answer

C. (53)

Step 1

Concept

\(\frac{8!}{6!}=56\), \(\frac{5!}{4!}=5\), and (2!=2). Thus (56-5+2=53).

Step 2

Why this answer is correct

The correct answer is C. (53). \(\frac{8!}{6!}=56\), \(\frac{5!}{4!}=5\), and (2!=2). Thus (56-5+2=53).

Step 3

Exam Tip

\(\frac{8!}{6!}=56\), \(\frac{5!}{4!}=5\) और (2!=2)। इसलिए (56-5+2=53) है।

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

\(\frac{7!}{4!,3!}+\frac{7!}{6!,1!}\) का मान क्या है?

What is the value of \(\frac{7!}{4!,3!}+\frac{7!}{6!,1!}\)?

Explanation opens after your attempt

Correct Answer

C. (42)

Step 1

Concept

The first term is (35) and the second term is (7). The total is (42).

Step 2

Why this answer is correct

The correct answer is C. (42). The first term is (35) and the second term is (7). The total is (42).

Step 3

Exam Tip

पहला पद (35) और दूसरा पद (7) है। कुल (42) मिलता है।

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

(\frac{(n+3)!}{n!}) में कुल कितने क्रमागत गुणक बचते हैं?

How many consecutive factors remain in (\frac{(n+3)!}{n!})?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

(\frac{(n+3)!}{n!}=(n+3)(n+2)(n+1)). Therefore, three consecutive factors remain.

Step 2

Why this answer is correct

The correct answer is B. (3). (\frac{(n+3)!}{n!}=(n+3)(n+2)(n+1)). Therefore, three consecutive factors remain.

Step 3

Exam Tip

(\frac{(n+3)!}{n!}=(n+3)(n+2)(n+1))। इसलिए तीन क्रमागत गुणक बचते हैं।

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

यदि \(x=\frac{9!}{7!}\) और \(y=\frac{6!}{4!}\), तो \(\frac{x}{y}\) का मान क्या है?

If \(x=\frac{9!}{7!}\) and \(y=\frac{6!}{4!}\), what is the value of \(\frac{x}{y}\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(x=72) and (y=30), so \(\frac{x}{y}=\frac{72}{30}=\frac{12}{5}\). Simplify the ratio at the end.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{12}{5}\). (x=72) and (y=30), so \(\frac{x}{y}=\frac{72}{30}=\frac{12}{5}\). Simplify the ratio at the end.

Step 3

Exam Tip

(x=72) और (y=30), इसलिए \(\frac{x}{y}=\frac{72}{30}=\frac{12}{5}\)। अनुपात को अंत में सरल करें।

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

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The first term is ((n+2)(n+1)) and the second is (n+1). Taking common ((n+1)) gives ((n+1)(n+3)).

Step 2

Why this answer is correct

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

Step 3

Exam Tip

पहला पद ((n+2)(n+1)) और दूसरा (n+1) है। समान ((n+1)) लेने पर ((n+1)(n+3)) मिलता है।

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

\(\frac{13!}{11!}-\frac{10!}{8!}\) का मान क्या है?

What is the value of \(\frac{13!}{11!}-\frac{10!}{8!}\)?

Explanation opens after your attempt

Correct Answer

B. (66)

Step 1

Concept

\(\frac{13!}{11!}=13\times12=156\) and \(\frac{10!}{8!}=10\times9=90\), so the difference is (66). Simplify both factorial ratios separately first.

Step 2

Why this answer is correct

The correct answer is B. (66). \(\frac{13!}{11!}=13\times12=156\) and \(\frac{10!}{8!}=10\times9=90\), so the difference is (66). Simplify both factorial ratios separately first.

Step 3

Exam Tip

\(\frac{13!}{11!}=13\times12=156\) और \(\frac{10!}{8!}=10\times9=90\), इसलिए अंतर (66) है। पहले दोनों फैक्टोरियल अनुपात अलग-अलग सरल करें।

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

यदि (\frac{(n+2)!}{(n-1)!}=210), तो (n) का मान क्या है?

If (\frac{(n+2)!}{(n-1)!}=210), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

(\frac{(n+2)!}{(n-1)!}=(n+2)(n+1)n). Since \(7\times6\times5=210\), (n=5).

Step 2

Why this answer is correct

The correct answer is B. (5). (\frac{(n+2)!}{(n-1)!}=(n+2)(n+1)n). Since \(7\times6\times5=210\), (n=5).

Step 3

Exam Tip

(\frac{(n+2)!}{(n-1)!}=(n+2)(n+1)n)। \(7\times6\times5=210\), इसलिए (n=5) है।

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

\(\frac{9!-8!}{7!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (64)

Step 1

Concept

The numerator is (8!(9-1)=8\cdot8!). Thus \(\frac{8\cdot8!}{7!}=8\times8=64\).

Step 2

Why this answer is correct

The correct answer is B. (64). The numerator is (8!(9-1)=8\cdot8!). Thus \(\frac{8\cdot8!}{7!}=8\times8=64\).

Step 3

Exam Tip

अंश (8!(9-1)=8\cdot8!) है। \(\frac{8\cdot8!}{7!}=8\times8=64\) मिलता है।

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

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

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

Explanation opens after your attempt

Correct Answer

B. ((n+4)(n+3)(n+2))

Step 1

Concept

((n+4)!=(n+4)(n+3)(n+2)(n+1)!), so ((n+1)!) cancels. Three consecutive factors remain.

Step 2

Why this answer is correct

The correct answer is B. ((n+4)(n+3)(n+2)). ((n+4)!=(n+4)(n+3)(n+2)(n+1)!), so ((n+1)!) cancels. Three consecutive factors remain.

Step 3

Exam Tip

((n+4)!=(n+4)(n+3)(n+2)(n+1)!), इसलिए ((n+1)!) कट जाता है। तीन क्रमागत गुणक बचते हैं।

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Class 11 Mathematics Medium Quiz

यदि (\frac{(n+1)!}{n!}=8), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{9!}{7!}-5!\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि ((n+1)!=720), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{6!}{3!}+4!\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

\(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

\(\frac{10!}{8!}+\frac{4!}{2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{7!-6!}{6!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि (\frac{(n+2)!}{n!}=30), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{9!}{6!,3!}-\frac{7!}{5!,2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{5!+3!}{4!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{8!}{4!}-\frac{7!}{4!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{11!}{9!,2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

कौन सा रूप \(\frac{12!}{9!}\) के बराबर है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि (\frac{n!}{(n-1)!}+2=9), तो (n) का मान क्या है?

Concept

Why this answer is correct