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Mathematics Quiz - Class 11 Mathematics Permutations And...

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

(7!) का मान क्या है?

What is the value of (7!)?

Explanation opens after your attempt

Correct Answer

B. (5040)

Step 1

Concept

\(7!=7\times6\times5\times4\times3\times2\times1=5040\). Find a larger factorial by multiplying the previous factorial.

Step 2

Why this answer is correct

The correct answer is B. (5040). \(7!=7\times6\times5\times4\times3\times2\times1=5040\). Find a larger factorial by multiplying the previous factorial.

Step 3

Exam Tip

\(7!=7\times6\times5\times4\times3\times2\times1=5040\)। बड़े क्रमगुणित को पिछले क्रमगुणित से गुणा करके निकालें।

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

(8!) को (6!) की सहायता से कैसे लिखेंगे?

How can (8!) be written using (6!)?

Explanation opens after your attempt

Correct Answer

A. \(8\times7\times6!\)

Step 1

Concept

\(8!=8\times7\times6!\). Breaking a factorial down to a smaller factorial is an easy method.

Step 2

Why this answer is correct

The correct answer is A. \(8\times7\times6!\). \(8!=8\times7\times6!\). Breaking a factorial down to a smaller factorial is an easy method.

Step 3

Exam Tip

\(8!=8\times7\times6!\) होता है। क्रमगुणित को छोटे क्रमगुणित तक तोड़ना आसान तरीका है।

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

\(\frac{9!}{7!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (72)

Step 1

Concept

\(\frac{9!}{7!}=9\times8=72\). Cancel the common (7!) part.

Step 2

Why this answer is correct

The correct answer is B. (72). \(\frac{9!}{7!}=9\times8=72\). Cancel the common (7!) part.

Step 3

Exam Tip

\(\frac{9!}{7!}=9\times8=72\)। समान (7!) भाग को काट दें।

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

(6!+1!) का मान क्या होगा?

What will be the value of (6!+1!)?

Explanation opens after your attempt

Correct Answer

B. (721)

Step 1

Concept

(6!=720) and (1!=1), so the sum is (721). Find both factorials before adding.

Step 2

Why this answer is correct

The correct answer is B. (721). (6!=720) and (1!=1), so the sum is (721). Find both factorials before adding.

Step 3

Exam Tip

(6!=720) और (1!=1), इसलिए योग (721) है। जोड़ से पहले दोनों क्रमगुणित निकालें।

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

\(\frac{8!}{6!,2!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (28)

Step 1

Concept

\(\frac{8!}{6!,2!}=\frac{8\times7}{2}=28\). Expand the larger factorial up to the smaller one first.

Step 2

Why this answer is correct

The correct answer is B. (28). \(\frac{8!}{6!,2!}=\frac{8\times7}{2}=28\). Expand the larger factorial up to the smaller one first.

Step 3

Exam Tip

\(\frac{8!}{6!,2!}=\frac{8\times7}{2}=28\)। पहले बड़े क्रमगुणित को छोटे तक फैलाएं।

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

यदि (n=4), तो (n!) का मान क्या है?

If (n=4), what is the value of (n!)?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

Putting (n=4), (n!=4!=24). Substitute the variable first and then evaluate the factorial.

Step 2

Why this answer is correct

The correct answer is C. (24). Putting (n=4), (n!=4!=24). Substitute the variable first and then evaluate the factorial.

Step 3

Exam Tip

(n=4) रखने पर (n!=4!=24)। पहले चर का मान रखकर फिर क्रमगुणित निकालें।

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

(2!+4!-1!) का मान क्या है?

What is the value of (2!+4!-1!)?

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

(2!=2), (4!=24), and (1!=1), so the value is (25). Convert factorials into ordinary numbers.

Step 2

Why this answer is correct

The correct answer is C. (25). (2!=2), (4!=24), and (1!=1), so the value is (25). Convert factorials into ordinary numbers.

Step 3

Exam Tip

(2!=2), (4!=24) और (1!=1), इसलिए मान (25) है। क्रमगुणित को साधारण संख्याओं में बदलें।

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

\(\frac{10!}{9!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

\(\frac{10!}{9!}=10\) because \(10!=10\times9!\). In such questions, full expansion is not needed.

Step 2

Why this answer is correct

The correct answer is B. (10). \(\frac{10!}{9!}=10\) because \(10!=10\times9!\). In such questions, full expansion is not needed.

Step 3

Exam Tip

\(\frac{10!}{9!}=10\) क्योंकि \(10!=10\times9!\)। ऐसे सवाल में पूरा विस्तार लिखने की जरूरत नहीं होती।

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

\(4!\times3!\) का मान क्या है?

What is the value of \(4!\times3!\)?

Explanation opens after your attempt

Correct Answer

C. (144)

Step 1

Concept

(4!=24) and (3!=6), so the product is (144). First evaluate each factorial separately.

Step 2

Why this answer is correct

The correct answer is C. (144). (4!=24) and (3!=6), so the product is (144). First evaluate each factorial separately.

Step 3

Exam Tip

(4!=24) और (3!=6), इसलिए गुणनफल (144) है। पहले प्रत्येक क्रमगुणित अलग निकालें।

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

\(6\times5\times4\times3!\) किसके बराबर है?

\(6\times5\times4\times3!\) is equal to which of the following?

Explanation opens after your attempt

Correct Answer

A. (6!)

Step 1

Concept

\(6!=6\times5\times4\times3!\), so the given form is (6!). Recognizing expansions is important in factorial questions.

Step 2

Why this answer is correct

The correct answer is A. (6!). \(6!=6\times5\times4\times3!\), so the given form is (6!). Recognizing expansions is important in factorial questions.

Step 3

Exam Tip

\(6!=6\times5\times4\times3!\), इसलिए दिया गया रूप (6!) है। विस्तार पहचानना क्रमगुणित प्रश्नों में जरूरी है।

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

\(\frac{5!+4!}{4!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

\(\frac{5!+4!}{4!}=\frac{120+24}{24}=6\). Add the numerator correctly and then divide.

Step 2

Why this answer is correct

The correct answer is B. (6). \(\frac{5!+4!}{4!}=\frac{120+24}{24}=6\). Add the numerator correctly and then divide.

Step 3

Exam Tip

\(\frac{5!+4!}{4!}=\frac{120+24}{24}=6\)। अंश को सही तरह से जोड़कर भाग दें।

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

यदि (n!=720), तो (n) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

(6!=720), so (n=6). Remembering small factorial values helps answer quickly.

Step 2

Why this answer is correct

The correct answer is B. (6). (6!=720), so (n=6). Remembering small factorial values helps answer quickly.

Step 3

Exam Tip

(6!=720), इसलिए (n=6)। छोटे क्रमगुणित मान याद रखने से उत्तर जल्दी मिलता है।

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

((2+3)!) का मान क्या है?

What is the value of ((2+3)!)?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

First (2+3=5), then (5!=120). Evaluate the bracket first.

Step 2

Why this answer is correct

The correct answer is C. (120). First (2+3=5), then (5!=120). Evaluate the bracket first.

Step 3

Exam Tip

पहले (2+3=5), फिर (5!=120)। कोष्ठक की गणना पहले करें।

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

(7!-6!) का मान क्या है?

What is the value of (7!-6!)?

Explanation opens after your attempt

Correct Answer

A. (4320)

Step 1

Concept

(7!=5040) and (6!=720), so the difference is (4320). Write both factorials separately while subtracting.

Step 2

Why this answer is correct

The correct answer is A. (4320). (7!=5040) and (6!=720), so the difference is (4320). Write both factorials separately while subtracting.

Step 3

Exam Tip

(7!=5040) और (6!=720), इसलिए अंतर (4320) है। घटाते समय दोनों क्रमगुणित अलग लिखें।

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

\(\frac{6!}{5!}+2!\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

\(\frac{6!}{5!}=6\) and (2!=2), so the total is (8). Simplify the quotient first.

Step 2

Why this answer is correct

The correct answer is C. (8). \(\frac{6!}{5!}=6\) and (2!=2), so the total is (8). Simplify the quotient first.

Step 3

Exam Tip

\(\frac{6!}{5!}=6\) और (2!=2), इसलिए कुल (8) है। पहले भाग को सरल करें।

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

\(3!\times3!\) का मान क्या है?

What is the value of \(3!\times3!\)?

Explanation opens after your attempt

Correct Answer

D. (36)

Step 1

Concept

(3!=6), so \(3!\times3!=6\times6=36\). Evaluate the repeated factorial once first.

Step 2

Why this answer is correct

The correct answer is D. (36). (3!=6), so \(3!\times3!=6\times6=36\). Evaluate the repeated factorial once first.

Step 3

Exam Tip

(3!=6), इसलिए \(3!\times3!=6\times6=36\)। समान क्रमगुणित को पहले एक बार निकालें।

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

\(\frac{7!}{4!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

A. (210)

Step 1

Concept

\(\frac{7!}{4!}=7\times6\times5=210\). Cancel the smaller factorial to reduce calculation.

Step 2

Why this answer is correct

The correct answer is A. (210). \(\frac{7!}{4!}=7\times6\times5=210\). Cancel the smaller factorial to reduce calculation.

Step 3

Exam Tip

\(\frac{7!}{4!}=7\times6\times5=210\)। छोटे क्रमगुणित को काटकर गणना कम करें।

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

(1!+2!+3!) का मान क्या है?

What is the value of (1!+2!+3!)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

(1!=1), (2!=2), and (3!=6), so the sum is (9). Evaluate factorials before adding them.

Step 2

Why this answer is correct

The correct answer is B. (9). (1!=1), (2!=2), and (3!=6), so the sum is (9). Evaluate factorials before adding them.

Step 3

Exam Tip

(1!=1), (2!=2) और (3!=6), इसलिए योग (9) है। क्रमगुणित को जोड़ने से पहले उनका मान निकालें।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (n+3)

Step 1

Concept

((n+3)!=(n+3)(n+2)!), so division leaves (n+3). Nearby factorials cancel directly.

Step 2

Why this answer is correct

The correct answer is C. (n+3). ((n+3)!=(n+3)(n+2)!), so division leaves (n+3). Nearby factorials cancel directly.

Step 3

Exam Tip

((n+3)!=(n+3)(n+2)!), इसलिए भाग देने पर (n+3) बचेगा। पास-पास वाले क्रमगुणित सीधे कटते हैं।

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

\(8\times7\times6\times5!\) किसके बराबर है?

\(8\times7\times6\times5!\) is equal to which of the following?

Explanation opens after your attempt

Correct Answer

B. (8!)

Step 1

Concept

\(8!=8\times7\times6\times5!\). Match the factorial expansion with the last factorial part.

Step 2

Why this answer is correct

The correct answer is B. (8!). \(8!=8\times7\times6\times5!\). Match the factorial expansion with the last factorial part.

Step 3

Exam Tip

\(8!=8\times7\times6\times5!\) होता है। क्रमगुणित विस्तार को अंतिम फैक्टोरियल से जोड़ें।

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

\(\frac{4!+2!}{2!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. (13)

Step 1

Concept

\(\frac{4!+2!}{2!}=\frac{24+2}{2}=13\). Complete the addition in the numerator first.

Step 2

Why this answer is correct

The correct answer is C. (13). \(\frac{4!+2!}{2!}=\frac{24+2}{2}=13\). Complete the addition in the numerator first.

Step 3

Exam Tip

\(\frac{4!+2!}{2!}=\frac{24+2}{2}=13\)। जोड़ वाले अंश को पहले पूरा करें।

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

\(5!\div3!\) का मान क्या है?

What is the value of \(5!\div3!\)?

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

\(5!\div3!=\frac{5!}{3!}=5\times4=20\). Write division as a fraction to solve.

Step 2

Why this answer is correct

The correct answer is C. (20). \(5!\div3!=\frac{5!}{3!}=5\times4=20\). Write division as a fraction to solve.

Step 3

Exam Tip

\(5!\div3!=\frac{5!}{3!}=5\times4=20\)। भाग को भिन्न के रूप में लिखकर हल करें।

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

यदि (a=3!) और (b=2!), तो (a+b) का मान क्या है?

If (a=3!) and (b=2!), what is the value of (a+b)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

(a=6) and (b=2), so (a+b=8). In variable questions, find the values first.

Step 2

Why this answer is correct

The correct answer is C. (8). (a=6) and (b=2), so (a+b=8). In variable questions, find the values first.

Step 3

Exam Tip

(a=6) और (b=2), इसलिए (a+b=8)। चर वाले प्रश्नों में पहले मान निकालें।

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

\(\frac{9!}{6!}\) का सरल मान क्या है?

What is the simplified value of \(\frac{9!}{6!}\)?

Explanation opens after your attempt

Correct Answer

A. (504)

Step 1

Concept

\(\frac{9!}{6!}=9\times8\times7=504\). Expand down to the smaller factorial and cancel.

Step 2

Why this answer is correct

The correct answer is A. (504). \(\frac{9!}{6!}=9\times8\times7=504\). Expand down to the smaller factorial and cancel.

Step 3

Exam Tip

\(\frac{9!}{6!}=9\times8\times7=504\)। छोटे क्रमगुणित तक विस्तार करें और काटें।

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

(0!+4!) का मान क्या है?

What is the value of (0!+4!)?

Explanation opens after your attempt

Correct Answer

B. (25)

Step 1

Concept

(0!=1) and (4!=24), so the sum is (25). Remember to take (0!) as (1).

Step 2

Why this answer is correct

The correct answer is B. (25). (0!=1) and (4!=24), so the sum is (25). Remember to take (0!) as (1).

Step 3

Exam Tip

(0!=1) और (4!=24), इसलिए योग (25) है। (0!) को (1) लेना याद रखें।

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

(10!) को (8!) की सहायता से कैसे लिखेंगे?

How can (10!) be written using (8!)?

Explanation opens after your attempt

Correct Answer

B. \(10\times9\times8!\)

Step 1

Concept

\(10!=10\times9\times8!\). Write the larger factorial in terms of the smaller factorial.

Step 2

Why this answer is correct

The correct answer is B. \(10\times9\times8!\). \(10!=10\times9\times8!\). Write the larger factorial in terms of the smaller factorial.

Step 3

Exam Tip

\(10!=10\times9\times8!\) होता है। बड़े क्रमगुणित को छोटे क्रमगुणित से जोड़कर लिखें।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (n(n+1))

Step 1

Concept

((n+1)!=(n+1)n(n-1)!), so the remaining part is (n(n+1)). Cancel the common factorial part.

Step 2

Why this answer is correct

The correct answer is B. (n(n+1)). ((n+1)!=(n+1)n(n-1)!), so the remaining part is (n(n+1)). Cancel the common factorial part.

Step 3

Exam Tip

((n+1)!=(n+1)n(n-1)!), इसलिए शेष (n(n+1)) है। समान क्रमगुणित भाग काटें।

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

\(2!\times5!\) का मान क्या है?

What is the value of \(2!\times5!\)?

Explanation opens after your attempt

Correct Answer

C. (240)

Step 1

Concept

(2!=2) and (5!=120), so the product is (240). First find the factorial values.

Step 2

Why this answer is correct

The correct answer is C. (240). (2!=2) and (5!=120), so the product is (240). First find the factorial values.

Step 3

Exam Tip

(2!=2) और (5!=120), इसलिए गुणनफल (240) है। पहले क्रमगुणित मान निकालें।

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

\(\frac{6!}{4!}+0!\) का मान क्या है?

What is the value of \(\frac{6!}{4!}+0!\)?

Explanation opens after your attempt

Correct Answer

C. (31)

Step 1

Concept

\(\frac{6!}{4!}=6\times5=30\) and (0!=1), so the total is (31). Use the correct value of (0!).

Step 2

Why this answer is correct

The correct answer is C. (31). \(\frac{6!}{4!}=6\times5=30\) and (0!=1), so the total is (31). Use the correct value of (0!).

Step 3

Exam Tip

\(\frac{6!}{4!}=6\times5=30\) और (0!=1), इसलिए कुल (31) है। (0!) को सही मान दें।

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

(4!) और (3!) का अनुपात क्या है?

What is the ratio of (4!) to (3!)?

Explanation opens after your attempt

Correct Answer

A. (4:1)

Step 1

Concept

\(\frac{4!}{3!}=4\), so the ratio is (4:1). For the ratio, cancel both terms by (3!).

Step 2

Why this answer is correct

The correct answer is A. (4:1). \(\frac{4!}{3!}=4\), so the ratio is (4:1). For the ratio, cancel both terms by (3!).

Step 3

Exam Tip

\(\frac{4!}{3!}=4\), इसलिए अनुपात (4:1) है। अनुपात के लिए दोनों पदों को (3!) से काटें।

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

(5!-3!) का मान क्या है?

What is the value of (5!-3!)?

Explanation opens after your attempt

Correct Answer

B. (114)

Step 1

Concept

(5!=120) and (3!=6), so the difference is (114). Find factorial values before subtracting.

Step 2

Why this answer is correct

The correct answer is B. (114). (5!=120) and (3!=6), so the difference is (114). Find factorial values before subtracting.

Step 3

Exam Tip

(5!=120) और (3!=6), इसलिए अंतर (114) है। घटाव करते समय क्रमगुणित का मान पहले निकालें।

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

\(\frac{3!+0!}{1!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

(3!+0!=6+1=7) and (1!=1), so the value is (7). Both (0!) and (1!) are (1).

Step 2

Why this answer is correct

The correct answer is B. (7). (3!+0!=6+1=7) and (1!=1), so the value is (7). Both (0!) and (1!) are (1).

Step 3

Exam Tip

(3!+0!=6+1=7) और (1!=1), इसलिए मान (7) है। (0!) और (1!) दोनों (1) होते हैं।

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

किसका मान (24) है?

Which one has value (24)?

Explanation opens after your attempt

Correct Answer

B. (4!)

Step 1

Concept

\(4!=4\times3\times2\times1=24\). Remembering small factorial values is useful.

Step 2

Why this answer is correct

The correct answer is B. (4!). \(4!=4\times3\times2\times1=24\). Remembering small factorial values is useful.

Step 3

Exam Tip

\(4!=4\times3\times2\times1=24\)। छोटे क्रमगुणित मान याद रखना उपयोगी है।

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

(9!) को (10!) की सहायता से कैसे लिखेंगे?

How can (9!) be written using (10!)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{10!}{10}\)

Step 1

Concept

\(10!=10\times9!\), so \(9!=\frac{10!}{10}\). The reverse relation is also useful in factorials.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{10!}{10}\). \(10!=10\times9!\), so \(9!=\frac{10!}{10}\). The reverse relation is also useful in factorials.

Step 3

Exam Tip

\(10!=10\times9!\), इसलिए \(9!=\frac{10!}{10}\)। उलटा संबंध भी क्रमगुणित में काम आता है।

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

\(\frac{8!}{4!,4!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (70)

Step 1

Concept

\(\frac{8!}{4!,4!}=\frac{8\times7\times6\times5}{4\times3\times2\times1}=70\). Cancel factorials to make the numbers smaller.

Step 2

Why this answer is correct

The correct answer is B. (70). \(\frac{8!}{4!,4!}=\frac{8\times7\times6\times5}{4\times3\times2\times1}=70\). Cancel factorials to make the numbers smaller.

Step 3

Exam Tip

\(\frac{8!}{4!,4!}=\frac{8\times7\times6\times5}{4\times3\times2\times1}=70\)। क्रमगुणित काटकर संख्या छोटी करें।

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

(6!) में (6) से (1) तक कितने गुणक होते हैं?

How many factors from (6) to (1) are present in (6!)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

\(6!=6\times5\times4\times3\times2\times1\), which has (6) factors. (n!) has (n) factors.

Step 2

Why this answer is correct

The correct answer is B. (6). \(6!=6\times5\times4\times3\times2\times1\), which has (6) factors. (n!) has (n) factors.

Step 3

Exam Tip

\(6!=6\times5\times4\times3\times2\times1\), इसमें (6) गुणक हैं। (n!) में (n) गुणक होते हैं।

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

\(\frac{7!}{5!}+1!\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (43)

Step 1

Concept

\(\frac{7!}{5!}=7\times6=42\) and (1!=1), so the total is (43). Simplify the quotient first.

Step 2

Why this answer is correct

The correct answer is B. (43). \(\frac{7!}{5!}=7\times6=42\) and (1!=1), so the total is (43). Simplify the quotient first.

Step 3

Exam Tip

\(\frac{7!}{5!}=7\times6=42\) और (1!=1), इसलिए कुल (43) है। पहले भाग को सरल करें।

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

\(3!\times4!-4!\) का मान क्या है?

What is the value of \(3!\times4!-4!\)?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

\(3!\times4!-4!=6\times24-24=120\). You may also factor out the common term (4!).

Step 2

Why this answer is correct

The correct answer is C. (120). \(3!\times4!-4!=6\times24-24=120\). You may also factor out the common term (4!).

Step 3

Exam Tip

\(3!\times4!-4!=6\times24-24=120\)। समान पद (4!) को अलग लेकर भी हल कर सकते हैं।

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

यदि (x=5!) और (y=4!), तो (x-y) का मान क्या है?

If (x=5!) and (y=4!), what is the value of (x-y)?

Explanation opens after your attempt

Correct Answer

A. (96)

Step 1

Concept

(x=120) and (y=24), so (x-y=96). Replace variables by their factorial values first.

Step 2

Why this answer is correct

The correct answer is A. (96). (x=120) and (y=24), so (x-y=96). Replace variables by their factorial values first.

Step 3

Exam Tip

(x=120) और (y=24), इसलिए (x-y=96)। चर को पहले उनके क्रमगुणित मान से बदलें।

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

((4-2)!) का मान क्या है?

What is the value of ((4-2)!)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

First (4-2=2), then (2!=2). Solve the bracket first.

Step 2

Why this answer is correct

The correct answer is B. (2). First (4-2=2), then (2!=2). Solve the bracket first.

Step 3

Exam Tip

पहले (4-2=2), फिर (2!=2)। कोष्ठक को पहले हल करें।

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

(5!) को (3!) की सहायता से कैसे लिखेंगे?

How can (5!) be written using (3!)?

Explanation opens after your attempt

Correct Answer

A. \(5\times4\times3!\)

Step 1

Concept

\(5!=5\times4\times3!\). It is correct to stop the expansion and write a smaller factorial.

Step 2

Why this answer is correct

The correct answer is A. \(5\times4\times3!\). \(5!=5\times4\times3!\). It is correct to stop the expansion and write a smaller factorial.

Step 3

Exam Tip

\(5!=5\times4\times3!\) होता है। बीच में रुककर छोटा क्रमगुणित लिखना सही है।

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

\(\frac{11!}{10!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

B. (11)

Step 1

Concept

\(\frac{11!}{10!}=11\) because \(11!=11\times10!\). Consecutive factorials cancel easily.

Step 2

Why this answer is correct

The correct answer is B. (11). \(\frac{11!}{10!}=11\) because \(11!=11\times10!\). Consecutive factorials cancel easily.

Step 3

Exam Tip

\(\frac{11!}{10!}=11\) क्योंकि \(11!=11\times10!\)। लगातार क्रमगुणित आसानी से कटते हैं।

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

(6!+0!-1!) का मान क्या है?

What is the value of (6!+0!-1!)?

Explanation opens after your attempt

Correct Answer

C. (720)

Step 1

Concept

(6!=720), (0!=1), and (1!=1), so the value is (720). (0!) and (1!) are equal.

Step 2

Why this answer is correct

The correct answer is C. (720). (6!=720), (0!=1), and (1!=1), so the value is (720). (0!) and (1!) are equal.

Step 3

Exam Tip

(6!=720), (0!=1) और (1!=1), इसलिए मान (720) है। (0!) और (1!) दोनों बराबर हैं।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (n+4)

Step 1

Concept

((n+4)!=(n+4)(n+3)!), so the simplified form is (n+4). Cancel the adjacent factorial part.

Step 2

Why this answer is correct

The correct answer is C. (n+4). ((n+4)!=(n+4)(n+3)!), so the simplified form is (n+4). Cancel the adjacent factorial part.

Step 3

Exam Tip

((n+4)!=(n+4)(n+3)!), इसलिए सरल रूप (n+4) है। क्रमगुणित में पास वाला भाग काटें।

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

\(4!\div2!\) और (3!) का योग क्या है?

What is the sum of \(4!\div2!\) and (3!)?

Explanation opens after your attempt

Correct Answer

B. (18)

Step 1

Concept

\(4!\div2!=12\) and (3!=6), so the sum is (18). Simplify the division and factorial separately.

Step 2

Why this answer is correct

The correct answer is B. (18). \(4!\div2!=12\) and (3!=6), so the sum is (18). Simplify the division and factorial separately.

Step 3

Exam Tip

\(4!\div2!=12\) और (3!=6), इसलिए योग (18) है। भाग और क्रमगुणित दोनों को अलग-अलग सरल करें।

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

\(9\times8!\) किसके बराबर है?

\(9\times8!\) is equal to which of the following?

Explanation opens after your attempt

Correct Answer

C. (9!)

Step 1

Concept

\(9!=9\times8!\), so the given form is (9!). This is a basic factorial identity.

Step 2

Why this answer is correct

The correct answer is C. (9!). \(9!=9\times8!\), so the given form is (9!). This is a basic factorial identity.

Step 3

Exam Tip

\(9!=9\times8!\), इसलिए दिया गया रूप (9!) है। यह क्रमगुणित की मूल पहचान है।

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

\(\frac{5!}{2!,3!}\) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

\(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\). Keep the correct value of each factorial.

Step 2

Why this answer is correct

The correct answer is C. (10). \(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\). Keep the correct value of each factorial.

Step 3

Exam Tip

\(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\)। हर क्रमगुणित का सही मान रखें।

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

(2!+5!) का मान क्या है?

What is the value of (2!+5!)?

Explanation opens after your attempt

Correct Answer

C. (122)

Step 1

Concept

(2!=2) and (5!=120), so the sum is (122). Do not forget the smaller factorial while adding.

Step 2

Why this answer is correct

The correct answer is C. (122). (2!=2) and (5!=120), so the sum is (122). Do not forget the smaller factorial while adding.

Step 3

Exam Tip

(2!=2) और (5!=120), इसलिए योग (122) है। जोड़ते समय छोटे क्रमगुणित को न भूलें।

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

(7!) को (5!) की सहायता से कैसे लिखेंगे?

How can (7!) be written using (5!)?

Explanation opens after your attempt

Correct Answer

D. \(7\times6\times5!\)

Step 1

Concept

\(7!=7\times6\times5!\). Expand the larger factorial down to the smaller factorial.

Step 2

Why this answer is correct

The correct answer is D. \(7\times6\times5!\). \(7!=7\times6\times5!\). Expand the larger factorial down to the smaller factorial.

Step 3

Exam Tip

\(7!=7\times6\times5!\) होता है। बड़े क्रमगुणित को छोटे क्रमगुणित तक विस्तार करें।

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

\(12\times11\times10!\) किसके बराबर है?

\(12\times11\times10!\) is equal to which of the following?

Explanation opens after your attempt

Correct Answer

C. (12!)

Step 1

Concept

\(12!=12\times11\times10!\), so the given form is (12!). Recognize factorial expansion down to a smaller factorial.

Step 2

Why this answer is correct

The correct answer is C. (12!). \(12!=12\times11\times10!\), so the given form is (12!). Recognize factorial expansion down to a smaller factorial.

Step 3

Exam Tip

\(12!=12\times11\times10!\), इसलिए दिया गया रूप (12!) है। क्रमगुणित विस्तार को छोटे क्रमगुणित तक पहचानें।

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Class 11 Mathematics - Permutations And Combinations - Factorial notation Easy Quiz

(7!) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(8!) को (6!) की सहायता से कैसे लिखेंगे?

Concept

Why this answer is correct

Exam Tip

\(\frac{9!}{7!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(6!+1!) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

\(\frac{8!}{6!,2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (n=4), तो (n!) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(2!+4!-1!) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{10!}{9!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(4!\times3!\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(6\times5\times4\times3!\) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

\(\frac{5!+4!}{4!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (n!=720), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

((2+3)!) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(7!-6!) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{6!}{5!}+2!\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(3!\times3!\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{7!}{4!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(1!+2!+3!) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

\(8\times7\times6\times5!\) किसके बराबर है?

Concept

Why this answer is correct