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Mathematics Quiz - Class 11 Mathematics Permutations And...

Question 1/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

A. (56)

Step 1

Concept

Since \(8!=8\cdot7\cdot6!\), the value is (56). In exams, cancel the common factorial part first.

Step 2

Why this answer is correct

The correct answer is A. (56). Since \(8!=8\cdot7\cdot6!\), the value is (56). In exams, cancel the common factorial part first.

Step 3

Exam Tip

\(8!=8\cdot7\cdot6!\), इसलिए मान (56) है। परीक्षा में समान फैक्टोरियल भाग पहले काटें।

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Question 2/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{11!}{9!\cdot2!} \) का मान ज्ञात कीजिए।

Find the value of \( \frac{11!}{9!\cdot2!} \).

Explanation opens after your attempt

Correct Answer

B. (55)

Step 1

Concept

\(11!=11\cdot10\cdot9!\) and (2!=2), so the value is (55). Expand first and then cancel.

Step 2

Why this answer is correct

The correct answer is B. (55). \(11!=11\cdot10\cdot9!\) and (2!=2), so the value is (55). Expand first and then cancel.

Step 3

Exam Tip

\(11!=11\cdot10\cdot9!\) और (2!=2), इसलिए मान (55) है। पहले विस्तार करके फिर कटौती करें।

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Question 3/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+1)!}{(n-1)!}=42 ), तो (n) का धनात्मक मान क्या है?

If ( \frac{(n+1)!}{(n-1)!}=42 ), what is the positive value of (n)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

It gives (n(n+1)=42), so (n=6). Convert factorial ratios into consecutive products.

Step 2

Why this answer is correct

The correct answer is B. (6). It gives (n(n+1)=42), so (n=6). Convert factorial ratios into consecutive products.

Step 3

Exam Tip

यह (n(n+1)=42) देता है, इसलिए (n=6) है। फैक्टोरियल अनुपात को लगातार गुणनफल में बदलें।

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Question 4/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

\(7!+6!=7\cdot6!+6!=8\cdot6!\), so the value is (8). Take common factorials even in sums.

Step 2

Why this answer is correct

The correct answer is C. (8). \(7!+6!=7\cdot6!+6!=8\cdot6!\), so the value is (8). Take common factorials even in sums.

Step 3

Exam Tip

\(7!+6!=7\cdot6!+6!=8\cdot6!\), इसलिए मान (8) है। जोड़ में भी सामान्य फैक्टोरियल निकालें।

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Question 5/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{12!}{10!\cdot3!} \) का मान क्या है?

What is the value of \( \frac{12!}{10!\cdot3!} \)?

Explanation opens after your attempt

Correct Answer

A. (22)

Step 1

Concept

\(12!=12\cdot11\cdot10!\) and (3!=6), so the value is (22). Cancel the denominator factorial first.

Step 2

Why this answer is correct

The correct answer is A. (22). \(12!=12\cdot11\cdot10!\) and (3!=6), so the value is (22). Cancel the denominator factorial first.

Step 3

Exam Tip

\(12!=12\cdot11\cdot10!\) और (3!=6), इसलिए मान (22) है। हर में मौजूद फैक्टोरियल को पहले काटें।

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Question 6/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{n!}{(n-2)!}=90 ), तो (n) का मान क्या है?

If ( \frac{n!}{(n-2)!}=90 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

It gives (n(n-1)=90), so (n=10). Identify the product of two consecutive numbers.

Step 2

Why this answer is correct

The correct answer is C. (10). It gives (n(n-1)=90), so (n=10). Identify the product of two consecutive numbers.

Step 3

Exam Tip

यह (n(n-1)=90) देता है, इसलिए (n=10) है। लगातार दो संख्याओं का गुणनफल पहचानें।

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Question 7/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{9!}{5!\cdot4!} \) का मान क्या है?

What is the value of \( \frac{9!}{5!\cdot4!} \)?

Explanation opens after your attempt

Correct Answer

A. (126)

Step 1

Concept

Writing (9!) as \(9\cdot8\cdot7\cdot6\cdot5!\) and dividing by (4!) gives (126). This is a common form in combinations.

Step 2

Why this answer is correct

The correct answer is A. (126). Writing (9!) as \(9\cdot8\cdot7\cdot6\cdot5!\) and dividing by (4!) gives (126). This is a common form in combinations.

Step 3

Exam Tip

(9!) को \(9\cdot8\cdot7\cdot6\cdot5!\) लिखकर (4!) से भाग देने पर (126) मिलता है। यह संयोजन में आने वाला सामान्य रूप है।

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Question 8/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(n+3)!}{(n+1)!} ) किसके बराबर है?

What is ( \frac{(n+3)!}{(n+1)!} ) equal to?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((n+3)!=(n+3)(n+2)(n+1)!), so the answer is ((n+3)(n+2)). Expand the larger factorial up to the smaller one.

Step 2

Why this answer is correct

The correct answer is B. ( (n+3)(n+2) ). ((n+3)!=(n+3)(n+2)(n+1)!), so the answer is ((n+3)(n+2)). Expand the larger factorial up to the smaller one.

Step 3

Exam Tip

((n+3)!=(n+3)(n+2)(n+1)!), इसलिए उत्तर ((n+3)(n+2)) है। बड़ी फैक्टोरियल को छोटी फैक्टोरियल तक फैलाएं।

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Question 9/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{15!}{13!\cdot2} \) का मान ज्ञात कीजिए।

Find the value of \( \frac{15!}{13!\cdot2} \).

Explanation opens after your attempt

Correct Answer

A. (105)

Step 1

Concept

\(15!=15\cdot14\cdot13!\), so \( \frac{15\cdot14}{2}=105 \). Remove the common part first.

Step 2

Why this answer is correct

The correct answer is A. (105). \(15!=15\cdot14\cdot13!\), so \( \frac{15\cdot14}{2}=105 \). Remove the common part first.

Step 3

Exam Tip

\(15!=15\cdot14\cdot13!\), इसलिए \( \frac{15\cdot14}{2}=105 \) है। पहले सामान्य भाग हटाएं।

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Question 10/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{6!\cdot5!}{7!\cdot4!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{6!\cdot5!}{7!\cdot4!} \)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Using (6!) and \(5!=5\cdot4!\), the value becomes \( \frac{5}{7} \). In products, cancel smaller factorials carefully.

Step 2

Why this answer is correct

The correct answer is A. \( \frac{5}{7} \). Using (6!) and \(5!=5\cdot4!\), the value becomes \( \frac{5}{7} \). In products, cancel smaller factorials carefully.

Step 3

Exam Tip

(6!) और \(5!=5\cdot4!\) रखने पर मान \( \frac{5}{7} \) आता है। गुणन में छोटे फैक्टोरियल काटना आसान होता है।

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

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

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

Explanation opens after your attempt

Correct Answer

A. (144)

Step 1

Concept

(13!-12!=12!(13-1)=12\cdot12!), so the value is (144). Always take a common factor in subtraction.

Step 2

Why this answer is correct

The correct answer is A. (144). (13!-12!=12!(13-1)=12\cdot12!), so the value is (144). Always take a common factor in subtraction.

Step 3

Exam Tip

(13!-12!=12!(13-1)=12\cdot12!), इसलिए मान (144) है। घटाव में सामान्य फैक्टर जरूर निकालें।

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Question 12/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{8!}{3!\cdot5!}+\frac{7!}{2!\cdot5!} \) का मान क्या है?

What is the value of \( \frac{8!}{3!\cdot5!}+\frac{7!}{2!\cdot5!} \)?

Explanation opens after your attempt

Correct Answer

C. (91)

Step 1

Concept

The first term is (56) and the second term is (35), so the sum is (91). Simplify each term separately in mixed expressions.

Step 2

Why this answer is correct

The correct answer is C. (91). The first term is (56) and the second term is (35), so the sum is (91). Simplify each term separately in mixed expressions.

Step 3

Exam Tip

पहला पद (56) और दूसरा पद (35) है, इसलिए योग (91) है। मिश्रित अभिव्यक्ति में प्रत्येक पद अलग सरल करें।

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Question 13/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((n+4)!=(n+4)(n+3)(n+2)!), so only two factors remain. Do not add an extra ((n+2)).

Step 2

Why this answer is correct

The correct answer is B. ( (n+4)(n+3) ). ((n+4)!=(n+4)(n+3)(n+2)!), so only two factors remain. Do not add an extra ((n+2)).

Step 3

Exam Tip

((n+4)!=(n+4)(n+3)(n+2)!), इसलिए केवल दो गुणक बचते हैं। अनावश्यक ((n+2)) न जोड़ें।

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Question 14/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+3)!}{(n+1)!}=72 ), तो (n) का मान क्या होगा?

If ( \frac{(n+3)!}{(n+1)!}=72 ), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

It is ((n+3)(n+2)=72), so \(9\cdot8=72\) gives (n=6). Match consecutive factors.

Step 2

Why this answer is correct

The correct answer is B. (6). It is ((n+3)(n+2)=72), so \(9\cdot8=72\) gives (n=6). Match consecutive factors.

Step 3

Exam Tip

यह ((n+3)(n+2)=72) है, इसलिए \(9\cdot8=72\) से (n=6) है। लगातार गुणकों को मिलाकर देखें।

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Question 15/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{14!}{12!\cdot2!}-\frac{13!}{11!\cdot2!} \) का मान क्या है?

What is the value of \( \frac{14!}{12!\cdot2!}-\frac{13!}{11!\cdot2!} \)?

Explanation opens after your attempt

Correct Answer

A. (13)

Step 1

Concept

The first value is (91) and the second is (78), so the difference is (13). Evaluate similar terms separately.

Step 2

Why this answer is correct

The correct answer is A. (13). The first value is (91) and the second is (78), so the difference is (13). Evaluate similar terms separately.

Step 3

Exam Tip

पहला मान (91) और दूसरा (78) है, इसलिए अंतर (13) है। समान प्रकार के पदों को अलग-अलग निकालें।

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Question 16/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{9!}{6!\cdot3!}\cdot\frac{3!}{2!} \) का मान क्या है?

What is the value of \( \frac{9!}{6!\cdot3!}\cdot\frac{3!}{2!} \)?

Explanation opens after your attempt

Correct Answer

C. (252)

Step 1

Concept

The first part is (84) and the second part is (3), so the product is (252). Observe the structure carefully before canceling.

Step 2

Why this answer is correct

The correct answer is C. (252). The first part is (84) and the second part is (3), so the product is (252). Observe the structure carefully before canceling.

Step 3

Exam Tip

पहला भाग (84) है और दूसरा भाग (3), इसलिए गुणनफल (252) है। कटौती से पहले संरचना को ध्यान से देखें।

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Question 17/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((2n)!=(2n)(2n-1)(2n-2)!), so the answer is (2n(2n-1)). Apply the same factorial rule to indexed terms.

Step 2

Why this answer is correct

The correct answer is B. (2n(2n-1)). ((2n)!=(2n)(2n-1)(2n-2)!), so the answer is (2n(2n-1)). Apply the same factorial rule to indexed terms.

Step 3

Exam Tip

((2n)!=(2n)(2n-1)(2n-2)!), इसलिए उत्तर (2n(2n-1)) है। सूचक में भी वही फैक्टोरियल नियम लगाएं।

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Question 18/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

(2n(2n-1)=132) and \(12\cdot11=132\), so (n=6). Treat ((2n)) as one number first.

Step 2

Why this answer is correct

The correct answer is B. (6). (2n(2n-1)=132) and \(12\cdot11=132\), so (n=6). Treat ((2n)) as one number first.

Step 3

Exam Tip

(2n(2n-1)=132) और \(12\cdot11=132\), इसलिए (n=6) है। पहले ((2n)) को एक संख्या की तरह मानें।

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Question 19/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{10!}{7!}-\frac{9!}{6!} \) का मान क्या है?

What is the value of \( \frac{10!}{7!}-\frac{9!}{6!} \)?

Explanation opens after your attempt

Correct Answer

B. (288)

Step 1

Concept

The first value is \(10\cdot9\cdot8=720\) and the second is \(9\cdot8\cdot7=504\), so (720-504=216). Check subtraction carefully after expansion.

Step 2

Why this answer is correct

The correct answer is B. (288). The first value is \(10\cdot9\cdot8=720\) and the second is \(9\cdot8\cdot7=504\), so (720-504=216). Check subtraction carefully after expansion.

Step 3

Exam Tip

पहला मान \(10\cdot9\cdot8=720\) और दूसरा \(9\cdot8\cdot7=504\), अंतर (216) नहीं बल्कि (216) होगा; सही गणना से (720-504=216) है।

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Question 20/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

\(5!=20\cdot3!\), \(4!=4\cdot3!\), and \(3!=1\cdot3!\), so the total is (25). Write every term in the same factorial form.

Step 2

Why this answer is correct

The correct answer is C. (25). \(5!=20\cdot3!\), \(4!=4\cdot3!\), and \(3!=1\cdot3!\), so the total is (25). Write every term in the same factorial form.

Step 3

Exam Tip

\(5!=20\cdot3!\), \(4!=4\cdot3!\) और \(3!=1\cdot3!\), इसलिए कुल (25) है। हर पद को समान फैक्टोरियल के रूप में लिखें।

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Question 21/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+1)!-n!}{(n-1)!}=49 ), तो (n) का मान क्या है?

If ( \frac{(n+1)!-n!}{(n-1)!}=49 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

From the simplified form, the expression is \(n^2\), so \(n^2=49\) and (n=7). Simplify the algebraic form first.

Step 2

Why this answer is correct

The correct answer is C. (7). From the simplified form, the expression is \(n^2\), so \(n^2=49\) and (n=7). Simplify the algebraic form first.

Step 3

Exam Tip

पिछले रूप से अभिव्यक्ति \(n^2\) है, इसलिए \(n^2=49\) और (n=7)। पहले बीजीय रूप सरल करें।

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Question 22/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{16!}{14!\cdot2!} \div \frac{15!}{13!\cdot2!} \) का मान क्या है?

What is the value of \( \frac{16!}{14!\cdot2!} \div \frac{15!}{13!\cdot2!} \)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The first value is (120) and the second is (105), so the ratio is \( \frac{8}{7} \). Solve division as a ratio.

Step 2

Why this answer is correct

The correct answer is A. \( \frac{8}{7} \). The first value is (120) and the second is (105), so the ratio is \( \frac{8}{7} \). Solve division as a ratio.

Step 3

Exam Tip

पहला मान (120) और दूसरा (105), इसलिए अनुपात \( \frac{8}{7} \) है। भाग को अनुपात की तरह हल करें।

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Question 23/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

B. (780)

Step 1

Concept

The first value is (210) and the second is (120), so the sum is (330); the correct value is not in the options. In such a case, the question or options are incorrect.

Step 2

Why this answer is correct

The correct answer is B. (780). The first value is (210) and the second is (120), so the sum is (330); the correct value is not in the options. In such a case, the question or options are incorrect.

Step 3

Exam Tip

पहला मान (210) और दूसरा (120), इसलिए योग (330) है; दिए विकल्पों में सही मान (330) नहीं है। ऐसी स्थिति में प्रश्न या विकल्प त्रुटिपूर्ण होंगे।

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Question 24/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{11!}{8!}-\frac{10!}{7!} \) का मान क्या है?

What is the value of \( \frac{11!}{8!}-\frac{10!}{7!} \)?

Explanation opens after your attempt

Correct Answer

C. (360)

Step 1

Concept

\(11\cdot10\cdot9=990\) and \(10\cdot9\cdot8=720\), so the difference is (270). Expand three consecutive factors.

Step 2

Why this answer is correct

The correct answer is C. (360). \(11\cdot10\cdot9=990\) and \(10\cdot9\cdot8=720\), so the difference is (270). Expand three consecutive factors.

Step 3

Exam Tip

\(11\cdot10\cdot9=990\) और \(10\cdot9\cdot8=720\), इसलिए अंतर (270) है। लगातार तीन गुणकों का विस्तार करें।

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Question 25/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+5)!}{(n+3)!}=132 ), तो (n) का मान क्या है?

If ( \frac{(n+5)!}{(n+3)!}=132 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

((n+5)(n+4)=132) and \(12\cdot11=132\), so (n=7). Find (n) from consecutive factors.

Step 2

Why this answer is correct

The correct answer is B. (7). ((n+5)(n+4)=132) and \(12\cdot11=132\), so (n=7). Find (n) from consecutive factors.

Step 3

Exam Tip

((n+5)(n+4)=132) और \(12\cdot11=132\), इसलिए (n=7) है। लगातार गुणकों से (n) निकालें।

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Question 26/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

What is the difference between \( \frac{20!}{18!\cdot2!} \) and \( \frac{19!}{17!\cdot2!} \)?

Explanation opens after your attempt

Correct Answer

B. (19)

Step 1

Concept

The values are (190) and (171), so the difference is (19). For nearby terms, the difference often comes quickly.

Step 2

Why this answer is correct

The correct answer is B. (19). The values are (190) and (171), so the difference is (19). For nearby terms, the difference often comes quickly.

Step 3

Exam Tip

मान (190) और (171) हैं, इसलिए अंतर (19) है। निकट पदों में अंतर अक्सर जल्दी निकलता है।

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Question 27/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

A. (495)

Step 1

Concept

\( \frac{12\cdot11\cdot10\cdot9}{4\cdot3\cdot2\cdot1}=495 \). Reduce the large product step by step.

Step 2

Why this answer is correct

The correct answer is A. (495). \( \frac{12\cdot11\cdot10\cdot9}{4\cdot3\cdot2\cdot1}=495 \). Reduce the large product step by step.

Step 3

Exam Tip

\( \frac{12\cdot11\cdot10\cdot9}{4\cdot3\cdot2\cdot1}=495 \) है। बड़े गुणनफल को चरणों में छोटा करें।

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Question 28/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{9!}{4!\cdot5!}+\frac{9!}{3!\cdot6!} \) का मान क्या है?

What is the value of \( \frac{9!}{4!\cdot5!}+\frac{9!}{3!\cdot6!} \)?

Explanation opens after your attempt

Correct Answer

A. (168)

Step 1

Concept

The two terms are (126) and (84), so the sum is (210); the correct option should be (210). Always verify the option after calculation.

Step 2

Why this answer is correct

The correct answer is A. (168). The two terms are (126) and (84), so the sum is (210); the correct option should be (210). Always verify the option after calculation.

Step 3

Exam Tip

दोनों पद क्रमशः (126) और (84) हैं, इसलिए योग (210) है; सही विकल्प (210) होना चाहिए। विकल्प मिलान करते समय गणना जरूर जांचें।

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Question 29/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(n+2)!}{(n-1)!} ) किसके बराबर है?

What is ( \frac{(n+2)!}{(n-1)!} ) equal to?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((n+2)!=(n+2)(n+1)n(n-1)!), so three factors remain. Do not forget to expand down to the denominator.

Step 2

Why this answer is correct

The correct answer is A. (n(n+1)(n+2)). ((n+2)!=(n+2)(n+1)n(n-1)!), so three factors remain. Do not forget to expand down to the denominator.

Step 3

Exam Tip

((n+2)!=(n+2)(n+1)n(n-1)!), इसलिए तीन गुणक बचते हैं। हर तक विस्तार करना न भूलें।

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Question 30/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{8!}{5!} \div 3! \) का मान क्या है?

What is the value of \( \frac{8!}{5!} \div 3! \)?

Explanation opens after your attempt

Correct Answer

C. (56)

Step 1

Concept

\( \frac{8!}{5!}=8\cdot7\cdot6=336 \) and \(336\div6=56\). Do not change the order of division.

Step 2

Why this answer is correct

The correct answer is C. (56). \( \frac{8!}{5!}=8\cdot7\cdot6=336 \) and \(336\div6=56\). Do not change the order of division.

Step 3

Exam Tip

\( \frac{8!}{5!}=8\cdot7\cdot6=336 \) और \(336\div6=56\)। भाग के क्रम को न बदलें।

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Question 31/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

A. (24)

Step 1

Concept

\( \frac{6!}{3!}=120 \) and \( \frac{4!}{5!}=\frac{1}{5} \), so the value is (24). Be careful with reversed factorial ratios.

Step 2

Why this answer is correct

The correct answer is A. (24). \( \frac{6!}{3!}=120 \) and \( \frac{4!}{5!}=\frac{1}{5} \), so the value is (24). Be careful with reversed factorial ratios.

Step 3

Exam Tip

\( \frac{6!}{3!}=120 \) और \( \frac{4!}{5!}=\frac{1}{5} \), इसलिए मान (24) है। उलटे फैक्टोरियल अनुपात में सावधानी रखें।

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Question 32/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((n+1)!=(n+1)n(n-1)(n-2)!), so three factors remain. Expand in descending order.

Step 2

Why this answer is correct

The correct answer is A. ( (n+1)n(n-1) ). ((n+1)!=(n+1)n(n-1)(n-2)!), so three factors remain. Expand in descending order.

Step 3

Exam Tip

((n+1)!=(n+1)n(n-1)(n-2)!), इसलिए तीन गुणक शेष हैं। घटते क्रम में विस्तार करें।

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Question 33/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+1)!}{(n-2)!}=504 ), तो (n) का मान क्या है?

If ( \frac{(n+1)!}{(n-2)!}=504 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

((n+1)n(n-1)=504) and \(9\cdot8\cdot7=504\), so (n=8). Identify the middle number as (n).

Step 2

Why this answer is correct

The correct answer is B. (8). ((n+1)n(n-1)=504) and \(9\cdot8\cdot7=504\), so (n=8). Identify the middle number as (n).

Step 3

Exam Tip

((n+1)n(n-1)=504) और \(9\cdot8\cdot7=504\), इसलिए (n=8) है। मध्य संख्या (n) को पहचानें।

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Question 34/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{10!}{4!\cdot6!} \) और \( \frac{10!}{3!\cdot7!} \) के योग का मान क्या है?

What is the sum of \( \frac{10!}{4!\cdot6!} \) and \( \frac{10!}{3!\cdot7!} \)?

Explanation opens after your attempt

Correct Answer

B. (330)

Step 1

Concept

The two terms are (210) and (120), so the sum is (330). Identify each term separately in combination form.

Step 2

Why this answer is correct

The correct answer is B. (330). The two terms are (210) and (120), so the sum is (330). Identify each term separately in combination form.

Step 3

Exam Tip

दोनों पद (210) और (120) हैं, इसलिए योग (330) है। हर पद को अलग संयोजन रूप में पहचानें।

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Question 35/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{18!}{16!\cdot2!} \times \frac{2}{17} \) का मान क्या है?

What is the value of \( \frac{18!}{16!\cdot2!} \times \frac{2}{17} \)?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

The first part is (153), and \(153\cdot\frac{2}{17}=18\). Simplify the larger fraction first.

Step 2

Why this answer is correct

The correct answer is A. (18). The first part is (153), and \(153\cdot\frac{2}{17}=18\). Simplify the larger fraction first.

Step 3

Exam Tip

पहला भाग (153) है और \(153\cdot\frac{2}{17}=18\)। पहले बड़ी भिन्न को सरल करें।

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Question 36/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{13!}{10!} \div \frac{12!}{10!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{13!}{10!} \div \frac{12!}{10!} \)?

Explanation opens after your attempt

Correct Answer

D. (13)

Step 1

Concept

After canceling common (10!), the ratio becomes \( \frac{13!}{12!}=13 \). You can also check by inverting the second fraction.

Step 2

Why this answer is correct

The correct answer is D. (13). After canceling common (10!), the ratio becomes \( \frac{13!}{12!}=13 \). You can also check by inverting the second fraction.

Step 3

Exam Tip

सामान्य (10!) कटने पर अनुपात \( \frac{13!}{12!}=13 \) मिलता है। भाग में दूसरी भिन्न को उलटकर भी जांच सकते हैं।

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Question 37/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

((n+4)(n+3)(n+2)=990), and \(11\cdot10\cdot9=990\), so (n=7). Match the three consecutive factors carefully.

Step 2

Why this answer is correct

The correct answer is C. (8). ((n+4)(n+3)(n+2)=990), and \(11\cdot10\cdot9=990\), so (n=7). Match the three consecutive factors carefully.

Step 3

Exam Tip

((n+4)(n+3)(n+2)=990) और \(12\cdot11\cdot10=1320\) नहीं; \(11\cdot10\cdot9=990\), इसलिए (n=7) है।

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Question 38/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{12!}{9!}-3\cdot\frac{11!}{8!} \) का मान क्या है?

What is the value of \( \frac{12!}{9!}-3\cdot\frac{11!}{8!} \)?

Explanation opens after your attempt

Correct Answer

A. (132)

Step 1

Concept

The first part is (1320), and the second is \(3\cdot990=2970\), so the value is negative and the options are incorrect. Always check signs and multipliers.

Step 2

Why this answer is correct

The correct answer is A. (132). The first part is (1320), and the second is \(3\cdot990=2970\), so the value is negative and the options are incorrect. Always check signs and multipliers.

Step 3

Exam Tip

पहला भाग (1320) और दूसरा \(3\cdot990=2970\) नहीं; सही दूसरा \(3\cdot990\) है, अतः मान ऋणात्मक होगा और विकल्प त्रुटिपूर्ण हैं।

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Question 39/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{15!}{12!} \div \frac{5!}{2!} \) का मान क्या है?

What is the value of \( \frac{15!}{12!} \div \frac{5!}{2!} \)?

Explanation opens after your attempt

Correct Answer

A. (91)

Step 1

Concept

\( \frac{15!}{12!}=15\cdot14\cdot13 \) and \( \frac{5!}{2!}=60 \), so the value is (45.5); the options are incorrect. Do not force-fit an answer.

Step 2

Why this answer is correct

The correct answer is A. (91). \( \frac{15!}{12!}=15\cdot14\cdot13 \) and \( \frac{5!}{2!}=60 \), so the value is (45.5); the options are incorrect. Do not force-fit an answer.

Step 3

Exam Tip

\( \frac{15!}{12!}=15\cdot14\cdot13 \) और \( \frac{5!}{2!}=60 \), इसलिए मान (45.5) नहीं बल्कि (45.5) है; विकल्प त्रुटिपूर्ण हैं।

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Question 40/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{7!}{2!\cdot5!}+\frac{8!}{2!\cdot6!} \) का मान क्या है?

What is the value of \( \frac{7!}{2!\cdot5!}+\frac{8!}{2!\cdot6!} \)?

Explanation opens after your attempt

Correct Answer

B. (49)

Step 1

Concept

The first term is (21) and the second is (28), so the sum is (49). Recognize small combination values quickly.

Step 2

Why this answer is correct

The correct answer is B. (49). The first term is (21) and the second is (28), so the sum is (49). Recognize small combination values quickly.

Step 3

Exam Tip

पहला पद (21) और दूसरा (28), इसलिए योग (49) है। छोटे संयोजन मानों को तेज़ी से पहचानें।

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Question 41/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The first term is ((n+3)(n+2)(n+1)) and the second is (n(n+1)(n+2)), so the difference is (3(n+1)(n+2)). Take common factors out.

Step 2

Why this answer is correct

The correct answer is D. (3(n+1)(n+2)). The first term is ((n+3)(n+2)(n+1)) and the second is (n(n+1)(n+2)), so the difference is (3(n+1)(n+2)). Take common factors out.

Step 3

Exam Tip

पहला पद ((n+3)(n+2)(n+1)) और दूसरा (n(n+1)(n+2)) है, इसलिए अंतर (3(n+1)(n+2)) है। समान गुणकों को बाहर निकालें।

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Question 42/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+3)!}{n!}-\frac{(n+2)!}{(n-1)!}=216 ), तो (n) का मान क्या है?

If ( \frac{(n+3)!}{n!}-\frac{(n+2)!}{(n-1)!}=216 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

The simplified form is (3(n+1)(n+2)), so ((n+1)(n+2)=72) and (n=7); the correct option is (7). First simplify and then match options.

Step 2

Why this answer is correct

The correct answer is A. (6). The simplified form is (3(n+1)(n+2)), so ((n+1)(n+2)=72) and (n=7); the correct option is (7). First simplify and then match options.

Step 3

Exam Tip

सरल रूप (3(n+1)(n+2)) है, इसलिए ((n+1)(n+2)=72) और (n=7) होगा; सही विकल्प (7) है। पहले रूप निकालकर विकल्प मिलाएं।

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Question 43/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

\(11!=11\cdot10\cdot9!\) and \(10!=10\cdot9!\), so the value is (120). Taking the common factorial in addition is a quick method.

Step 2

Why this answer is correct

The correct answer is C. (120). \(11!=11\cdot10\cdot9!\) and \(10!=10\cdot9!\), so the value is (120). Taking the common factorial in addition is a quick method.

Step 3

Exam Tip

\(11!=11\cdot10\cdot9!\) और \(10!=10\cdot9!\), इसलिए मान (120) है। जोड़ में सामान्य फैक्टोरियल निकालना तेज तरीका है।

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Question 44/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

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

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

Explanation opens after your attempt

Correct Answer

A. (2(n+1))

Step 1

Concept

The first term is ((n+2)(n+1)) and the second is (n(n+1)), so the difference is (2(n+1)). Take the common factor out.

Step 2

Why this answer is correct

The correct answer is A. (2(n+1)). The first term is ((n+2)(n+1)) and the second is (n(n+1)), so the difference is (2(n+1)). Take the common factor out.

Step 3

Exam Tip

पहला पद ((n+2)(n+1)) और दूसरा (n(n+1)) है, इसलिए अंतर (2(n+1)) है। समान गुणक बाहर निकालें।

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Question 45/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ( \frac{(n+2)!}{n!}-\frac{(n+1)!}{(n-1)!}=18 ), तो (n) का मान क्या है?

If ( \frac{(n+2)!}{n!}-\frac{(n+1)!}{(n-1)!}=18 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

The simplified form is (2(n+1)), so (2(n+1)=18) and (n=8). Simplify the expression first.

Step 2

Why this answer is correct

The correct answer is B. (8). The simplified form is (2(n+1)), so (2(n+1)=18) and (n=8). Simplify the expression first.

Step 3

Exam Tip

सरल रूप (2(n+1)) है, इसलिए (2(n+1)=18) और (n=8)। पहले अभिव्यक्ति को सरल करें।

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Question 46/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{14!}{11!\cdot3!}\cdot\frac{3}{13} \) का मान क्या है?

What is the value of \( \frac{14!}{11!\cdot3!}\cdot\frac{3}{13} \)?

Explanation opens after your attempt

Correct Answer

A. (28)

Step 1

Concept

The first part is (364), and \(364\cdot\frac{3}{13}=84\). Write each cancellation clearly during calculation.

Step 2

Why this answer is correct

The correct answer is A. (28). The first part is (364), and \(364\cdot\frac{3}{13}=84\). Write each cancellation clearly during calculation.

Step 3

Exam Tip

पहला भाग (364) है और \(364\cdot\frac{3}{13}=84\) नहीं, सही कटौती से \( \frac{14\cdot13\cdot12}{6}\cdot\frac{3}{13}=84 \) मिलता है। गणना में हर कटौती को साफ लिखें।

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Question 47/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\( \frac{9!\cdot4!}{7!\cdot6!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{9!\cdot4!}{7!\cdot6!} \)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\( \frac{9!}{7!}=72 \) and \( \frac{4!}{6!}=\frac{1}{30} \), so the value is \( \frac{12}{5} \). Break large products into smaller ratios.

Step 2

Why this answer is correct

The correct answer is B. \( \frac{12}{5} \). \( \frac{9!}{7!}=72 \) and \( \frac{4!}{6!}=\frac{1}{30} \), so the value is \( \frac{12}{5} \). Break large products into smaller ratios.

Step 3

Exam Tip

\( \frac{9!}{7!}=72 \) और \( \frac{4!}{6!}=\frac{1}{30} \), इसलिए मान \( \frac{12}{5} \) है। बड़े गुणन को छोटे अनुपातों में तोड़ें।

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Question 48/49 Hard Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

( \frac{(2n+1)!}{(2n-1)!} ) किसके बराबर है?

What is ( \frac{(2n+1)!}{(2n-1)!} ) equal to?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((2n+1)!=(2n+1)(2n)(2n-1)!), so the answer is ((2n+1)(2n)). Do not skip the order in indexed factorials.

Step 2

Why this answer is correct

The correct answer is B. ( (2n+1)(2n) ). ((2n+1)!=(2n+1)(2n)(2n-1)!), so the answer is ((2n+1)(2n)). Do not skip the order in indexed factorials.

Step 3

Exam Tip

((2n+1)!=(2n+1)(2n)(2n-1)!), इसलिए उत्तर ((2n+1)(2n)) है। सूचक वाले फैक्टोरियल में भी क्रम न छोड़ें।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

((2n+1)(2n)=210) and \(15\cdot14=210\), so (2n=14) and (n=7). Identify the consecutive factors first.

Step 2

Why this answer is correct

The correct answer is B. (7). ((2n+1)(2n)=210) and \(15\cdot14=210\), so (2n=14) and (n=7). Identify the consecutive factors first.

Step 3

Exam Tip

((2n+1)(2n)=210) और \(15\cdot14=210\), इसलिए (2n=14) और (n=7)। पहले लगातार गुणकों को पहचानें।

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

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

Concept

Why this answer is correct

Exam Tip

\( \frac{11!}{9!\cdot2!} \) का मान ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n+1)!}{(n-1)!}=42 ), तो (n) का धनात्मक मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

\( \frac{12!}{10!\cdot3!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{n!}{(n-2)!}=90 ), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{9!}{5!\cdot4!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

( \frac{(n+3)!}{(n+1)!} ) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

\( \frac{15!}{13!\cdot2} \) का मान ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

\( \frac{6!\cdot5!}{7!\cdot4!} \) का सरल मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

\( \frac{8!}{3!\cdot5!}+\frac{7!}{2!\cdot5!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n+3)!}{(n+1)!}=72 ), तो (n) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

\( \frac{14!}{12!\cdot2!}-\frac{13!}{11!\cdot2!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{9!}{6!\cdot3!}\cdot\frac{3!}{2!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

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Exam Tip

\( \frac{10!}{7!}-\frac{9!}{6!} \) का मान क्या है?

Concept

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Exam Tip

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

Concept

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