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Mathematics Quiz - Class 11 Mathematics Hard Level 56 Quiz

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

\( \frac{12!}{9!} \) का मान क्या है?

What is the value of \( \frac{12!}{9!} \)?

Explanation opens after your attempt

Correct Answer

C. (1320)

Step 1

Concept

Writing (12!) as \(12\cdot11\cdot10\cdot9!\) gives (1320). In exams, expand the larger factorial up to the smaller factorial.

Step 2

Why this answer is correct

The correct answer is C. (1320). Writing (12!) as \(12\cdot11\cdot10\cdot9!\) gives (1320). In exams, expand the larger factorial up to the smaller factorial.

Step 3

Exam Tip

(12!) को \(12\cdot11\cdot10\cdot9!\) लिखने पर मान (1320) मिलता है। परीक्षा में बड़े फैक्टोरियल को छोटे फैक्टोरियल तक फैलाएं।

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

\( \frac{10!}{7!\cdot3!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{10!}{7!\cdot3!} \)?

Explanation opens after your attempt

Correct Answer

B. (120)

Step 1

Concept

Writing (10!) as \(10\cdot9\cdot8\cdot7!\) and dividing by (3!) gives (120). Cancel common factorials first.

Step 2

Why this answer is correct

The correct answer is B. (120). Writing (10!) as \(10\cdot9\cdot8\cdot7!\) and dividing by (3!) gives (120). Cancel common factorials first.

Step 3

Exam Tip

(10!) को \(10\cdot9\cdot8\cdot7!\) लिखकर (3!) से भाग देने पर (120) मिलता है। समान फैक्टोरियल पहले काटें।

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

\( \frac{8!-7!}{6!} \) का मान ज्ञात कीजिए।

Find the value of \( \frac{8!-7!}{6!} \).

Explanation opens after your attempt

Correct Answer

D. (49)

Step 1

Concept

(8!-7!=7!(8-1)) and \( \frac{7!}{6!}=7 \), so the value is (49). Take the common factor in subtraction.

Step 2

Why this answer is correct

The correct answer is D. (49). (8!-7!=7!(8-1)) and \( \frac{7!}{6!}=7 \), so the value is (49). Take the common factor in subtraction.

Step 3

Exam Tip

(8!-7!=7!(8-1)) और \( \frac{7!}{6!}=7 \), इसलिए मान (49) है। घटाव में सामान्य फैक्टर निकालें।

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

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

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

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

It gives ((n+2)(n+1)=90), and \(10\cdot9=90\), so (n=8). Recognizing consecutive factors is a quick method.

Step 2

Why this answer is correct

The correct answer is A. (8). It gives ((n+2)(n+1)=90), and \(10\cdot9=90\), so (n=8). Recognizing consecutive factors is a quick method.

Step 3

Exam Tip

यह ((n+2)(n+1)=90) देता है और \(10\cdot9=90\), इसलिए (n=8)। लगातार गुणकों को पहचानना तेज तरीका है।

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

यदि ( \frac{n!}{(n-3)!}=336 ), तो (n) का धनात्मक मान क्या है?

If ( \frac{n!}{(n-3)!}=336 ), what is the positive value of (n)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

It is (n(n-1)(n-2)=336), and \(8\cdot7\cdot6=336\). In such questions, look for three consecutive decreasing factors.

Step 2

Why this answer is correct

The correct answer is C. (8). It is (n(n-1)(n-2)=336), and \(8\cdot7\cdot6=336\). In such questions, look for three consecutive decreasing factors.

Step 3

Exam Tip

यह (n(n-1)(n-2)=336) है और \(8\cdot7\cdot6=336\)। ऐसे प्रश्नों में तीन लगातार घटते गुणक देखें।

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

( \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

B. ( (n+1)(n+3) )

Step 1

Concept

((n+1)!) is common in both terms, so the simplified form is ((n+1)(n+3)). Take the common factorial out first.

Step 2

Why this answer is correct

The correct answer is B. ( (n+1)(n+3) ). ((n+1)!) is common in both terms, so the simplified form is ((n+1)(n+3)). Take the common factorial out first.

Step 3

Exam Tip

दोनों पदों में ((n+1)!) सामान्य है, इसलिए सरल रूप ((n+1)(n+3)) है। पहले सामान्य फैक्टोरियल बाहर निकालें।

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

यदि ( \frac{(n+3)!-(n+2)!}{(n+1)!}=49 ), तो (n) का मान क्या होगा?

If ( \frac{(n+3)!-(n+2)!}{(n+1)!}=49 ), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

D. (5)

Step 1

Concept

The expression becomes ((n+2)²), so ((n+2)²=49) and (n=5). Simplify the subtraction first.

Step 2

Why this answer is correct

The correct answer is D. (5). The expression becomes ((n+2)²), so ((n+2)²=49) and (n=5). Simplify the subtraction first.

Step 3

Exam Tip

अभिव्यक्ति ((n+2)²) बनती है, इसलिए ((n+2)²=49) और (n=5)। पहले घटाव को सरल करें।

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

\( \frac{14!}{11!}\div\frac{7!}{4!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{14!}{11!}\div\frac{7!}{4!} \)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{52}{5} \)

Step 1

Concept

The value is \( \frac{14\cdot13\cdot12}{7\cdot6\cdot5}=\frac{52}{5} \). In division, expand both factorial ratios separately.

Step 2

Why this answer is correct

The correct answer is A. \( \frac{52}{5} \). The value is \( \frac{14\cdot13\cdot12}{7\cdot6\cdot5}=\frac{52}{5} \). In division, expand both factorial ratios separately.

Step 3

Exam Tip

मान \( \frac{14\cdot13\cdot12}{7\cdot6\cdot5}=\frac{52}{5} \) है। भाग में दोनों फैक्टोरियल अनुपात अलग-अलग फैलाएं।

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

\( \frac{9!}{6!\cdot2!} \) का मान क्या है?

What is the value of \( \frac{9!}{6!\cdot2!} \)?

Explanation opens after your attempt

Correct Answer

C. (252)

Step 1

Concept

Write (9!) as \(9\cdot8\cdot7\cdot6!\) and divide by (2!). This gives (252).

Step 2

Why this answer is correct

The correct answer is C. (252). Write (9!) as \(9\cdot8\cdot7\cdot6!\) and divide by (2!). This gives (252).

Step 3

Exam Tip

(9!) को \(9\cdot8\cdot7\cdot6!\) लिखें और (2!) से भाग दें। इससे मान (252) आता है।

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

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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

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

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

Explanation opens after your attempt

Correct Answer

D. (5)

Step 1

Concept

It gives ((2n+2)(2n+1)=132), and \(12\cdot11=132\), so (n=5). Match the consecutive factors first.

Step 2

Why this answer is correct

The correct answer is D. (5). It gives ((2n+2)(2n+1)=132), and \(12\cdot11=132\), so (n=5). Match the consecutive factors first.

Step 3

Exam Tip

यह ((2n+2)(2n+1)=132) देता है और \(12\cdot11=132\), इसलिए (n=5)। पहले लगातार गुणकों को मिलाएं।

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

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

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

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

(m!=m(m^-1)(m^-2)!), so (m) remains after cancellation. Expand the factorial exactly up to the needed limit.

Step 2

Why this answer is correct

The correct answer is A. (m). (m!=m(m^-1)(m^-2)!), so (m) remains after cancellation. Expand the factorial exactly up to the needed limit.

Step 3

Exam Tip

(m!=m(m^-1)(m^-2)!), इसलिए काटने पर (m) बचता है। फैक्टोरियल को ठीक उसी सीमा तक फैलाएं।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

The left side is (n(n-1)), so (n(n-1)=9n). Since (n>0), (n-1=9) and (n=10).

Step 2

Why this answer is correct

The correct answer is B. (10). The left side is (n(n-1)), so (n(n-1)=9n). Since (n>0), (n-1=9) and (n=10).

Step 3

Exam Tip

बायां पक्ष (n(n-1)) है, इसलिए (n(n-1)=9n)। (n>0) होने से (n-1=9) और (n=10)।

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

\( \frac{11!}{8!\cdot3!}\div\frac{10!}{7!\cdot3!} \) का मान क्या है?

What is the value of \( \frac{11!}{8!\cdot3!}\div\frac{10!}{7!\cdot3!} \)?

Explanation opens after your attempt

Correct Answer

C. \( \frac{11}{8} \)

Step 1

Concept

The first term is (165) and the second is (120), so the ratio is \( \frac{11}{8} \). Treat division as a ratio of fractions.

Step 2

Why this answer is correct

The correct answer is C. \( \frac{11}{8} \). The first term is (165) and the second is (120), so the ratio is \( \frac{11}{8} \). Treat division as a ratio of fractions.

Step 3

Exam Tip

पहला पद (165) और दूसरा (120) है, इसलिए अनुपात \( \frac{11}{8} \) है। भाग को भिन्न के अनुपात की तरह लें।

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

\( \frac{12!}{8!\cdot4!}-\frac{11!}{7!\cdot4!} \) का मान क्या है?

What is the value of \( \frac{12!}{8!\cdot4!}-\frac{11!}{7!\cdot4!} \)?

Explanation opens after your attempt

Correct Answer

A. (165)

Step 1

Concept

The two terms are (495) and (330), so the difference is (165). Simplify each term separately first.

Step 2

Why this answer is correct

The correct answer is A. (165). The two terms are (495) and (330), so the difference is (165). Simplify each term separately first.

Step 3

Exam Tip

दोनों पद क्रमशः (495) और (330) हैं, इसलिए अंतर (165) है। पहले हर पद को अलग सरल करें।

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

( \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

D. (n+2)

Step 1

Concept

((n+1)!=(n+1)n!), so the sum becomes ((n+2)n!). Dividing gives (n+2).

Step 2

Why this answer is correct

The correct answer is D. (n+2). ((n+1)!=(n+1)n!), so the sum becomes ((n+2)n!). Dividing gives (n+2).

Step 3

Exam Tip

((n+1)!=(n+1)n!) है, इसलिए योग ((n+2)n!) बनता है। भाग देने पर (n+2) मिलता है।

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

यदि ( \frac{(n+1)!+n!}{n!}=13 ), तो (n) का मान क्या है?

If ( \frac{(n+1)!+n!}{n!}=13 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (11)

Step 1

Concept

The simplified form is (n+2), so (n+2=13) and (n=11). Reduce the expression first.

Step 2

Why this answer is correct

The correct answer is C. (11). The simplified form is (n+2), so (n+2=13) and (n=11). Reduce the expression first.

Step 3

Exam Tip

सरल रूप (n+2) है, इसलिए (n+2=13) और (n=11)। पहले अभिव्यक्ति को छोटा करें।

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

\( \frac{15!}{13!}-\frac{14!}{12!} \) का मान क्या है?

What is the value of \( \frac{15!}{13!}-\frac{14!}{12!} \)?

Explanation opens after your attempt

Correct Answer

B. (28)

Step 1

Concept

The first value is \(15\cdot14=210\) and the second is \(14\cdot13=182\). The difference is (28).

Step 2

Why this answer is correct

The correct answer is B. (28). The first value is \(15\cdot14=210\) and the second is \(14\cdot13=182\). The difference is (28).

Step 3

Exam Tip

पहला मान \(15\cdot14=210\) और दूसरा \(14\cdot13=182\) है। अंतर (28) है।

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

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

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

Explanation opens after your attempt

Correct Answer

D. (180)

Step 1

Concept

The two terms are (120) and (60), so the sum is (180). In a mixed sum, solve each term separately.

Step 2

Why this answer is correct

The correct answer is D. (180). The two terms are (120) and (60), so the sum is (180). In a mixed sum, solve each term separately.

Step 3

Exam Tip

दोनों पद (120) और (60) हैं, इसलिए योग (180) है। मिश्रित योग में हर पद अलग हल करें।

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

यदि ( \frac{(n+4)!}{(n+2)!}+\frac{(n+3)!}{(n+1)!}=200 ), तो (n) का मान क्या है?

If ( \frac{(n+4)!}{(n+2)!}+\frac{(n+3)!}{(n+1)!}=200 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

The expression becomes (2(n+3)²), so (2(n+3)²=200). Thus (n+3=10) and (n=7).

Step 2

Why this answer is correct

The correct answer is C. (7). The expression becomes (2(n+3)²), so (2(n+3)²=200). Thus (n+3=10) and (n=7).

Step 3

Exam Tip

अभिव्यक्ति (2(n+3)²) बनती है, इसलिए (2(n+3)²=200)। इससे (n+3=10) और (n=7)।

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

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The upper ratio is ((n+3)(n+2)(n+1)). Dividing by (n+3) leaves ((n+2)(n+1)).

Step 2

Why this answer is correct

The correct answer is D. ( (n+2)(n+1) ). The upper ratio is ((n+3)(n+2)(n+1)). Dividing by (n+3) leaves ((n+2)(n+1)).

Step 3

Exam Tip

ऊपर का अनुपात ((n+3)(n+2)(n+1)) है। (n+3) से भाग देने पर ((n+2)(n+1)) बचता है।

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

\( \frac{13!}{10!\cdot3!}-\frac{12!}{9!\cdot3!} \) का मान क्या है?

What is the value of \( \frac{13!}{10!\cdot3!}-\frac{12!}{9!\cdot3!} \)?

Explanation opens after your attempt

Correct Answer

B. (66)

Step 1

Concept

The first term is (286) and the second is (220), so the difference is (66). In such questions, write each term value and subtract.

Step 2

Why this answer is correct

The correct answer is B. (66). The first term is (286) and the second is (220), so the difference is (66). In such questions, write each term value and subtract.

Step 3

Exam Tip

पहला पद (286) और दूसरा (220) है, इसलिए अंतर (66) है। ऐसे प्रश्नों में हर पद का मान लिखकर घटाएं।

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

सबसे छोटा धनात्मक (n) क्या है जिसके लिए (n!) संख्या (72) से विभाज्य हो?

What is the smallest positive (n) for which (n!) is divisible by (72)?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

\(72=2^3\cdot3^2\), and (6!) contains all these factors. For divisibility, check prime factors.

Step 2

Why this answer is correct

The correct answer is A. (6). \(72=2^3\cdot3^2\), and (6!) contains all these factors. For divisibility, check prime factors.

Step 3

Exam Tip

\(72=2^3\cdot3^2\) है और (6!) में ये सभी गुणक मिल जाते हैं। विभाज्यता में अभाज्य गुणनखंड जांचें।

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

(18!) के अंत में कितने शून्य होंगे?

How many zeros will be at the end of (18!)?

Explanation opens after your attempt

Correct Answer

D. (3)

Step 1

Concept

The number of ending zeros comes from multiples of (5), and (18!) has (5,10,15). Therefore, there are (3) zeros.

Step 2

Why this answer is correct

The correct answer is D. (3). The number of ending zeros comes from multiples of (5), and (18!) has (5,10,15). Therefore, there are (3) zeros.

Step 3

Exam Tip

अंतिम शून्यों की संख्या (5) के गुणकों से मिलती है और (18!) में (5,10,15) हैं। इसलिए कुल (3) शून्य होंगे।

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

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

What is the highest power of (2) that divides (10!)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

The exponent is \( \left\lfloor\frac{10}{2}\right\rfloor+\left\lfloor\frac{10}{4}\right\rfloor+\left\lfloor\frac{10}{8}\right\rfloor=8 \). For prime exponents, add the quotients.

Step 2

Why this answer is correct

The correct answer is C. (8). The exponent is \( \left\lfloor\frac{10}{2}\right\rfloor+\left\lfloor\frac{10}{4}\right\rfloor+\left\lfloor\frac{10}{8}\right\rfloor=8 \). For prime exponents, add the quotients.

Step 3

Exam Tip

घात \( \left\lfloor\frac{10}{2}\right\rfloor+\left\lfloor\frac{10}{4}\right\rfloor+\left\lfloor\frac{10}{8}\right\rfloor=8 \) है। अभाज्य घात के लिए भागफल जोड़ें।

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

(25!) में (5) की अधिकतम घात क्या होगी?

What will be the highest power of (5) in (25!)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

The exponent is \( \left\lfloor\frac{25}{5}\right\rfloor+\left\lfloor\frac{25}{25}\right\rfloor=6 \). Do not forget higher multiples such as (25).

Step 2

Why this answer is correct

The correct answer is B. (6). The exponent is \( \left\lfloor\frac{25}{5}\right\rfloor+\left\lfloor\frac{25}{25}\right\rfloor=6 \). Do not forget higher multiples such as (25).

Step 3

Exam Tip

घात \( \left\lfloor\frac{25}{5}\right\rfloor+\left\lfloor\frac{25}{25}\right\rfloor=6 \) है। (25) जैसे उच्च गुणकों को न भूलें।

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

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

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

Explanation opens after your attempt

Correct Answer

C. \( \frac{n}{n+1} \)

Step 1

Concept

( \frac{n!}{(n-1)!}=n ) and ( \frac{n!}{(n+1)!}=\frac{1}{n+1} ), so the answer is \( \frac{n}{n+1} \). Break the ratio into two smaller parts.

Step 2

Why this answer is correct

The correct answer is C. \( \frac{n}{n+1} \). ( \frac{n!}{(n-1)!}=n ) and ( \frac{n!}{(n+1)!}=\frac{1}{n+1} ), so the answer is \( \frac{n}{n+1} \). Break the ratio into two smaller parts.

Step 3

Exam Tip

( \frac{n!}{(n-1)!}=n ) और ( \frac{n!}{(n+1)!}=\frac{1}{n+1} ), इसलिए उत्तर \( \frac{n}{n+1} \) है। अनुपात को दो छोटे भागों में तोड़ें।

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

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

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

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

The simplified form is \( \frac{n}{n+1} \), so \( \frac{n}{n+1}=\frac{5}{6} \). This gives (n=5).

Step 2

Why this answer is correct

The correct answer is A. (5). The simplified form is \( \frac{n}{n+1} \), so \( \frac{n}{n+1}=\frac{5}{6} \). This gives (n=5).

Step 3

Exam Tip

सरल रूप \( \frac{n}{n+1} \) है, इसलिए \( \frac{n}{n+1}=\frac{5}{6} \)। इससे (n=5) मिलता है।

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

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The numerator becomes ((n+2)(n+1)n(n-1)(n-2)!). After cancellation with the denominator, ((n+2)(n+1)) remains.

Step 2

Why this answer is correct

The correct answer is B. ( (n+2)(n+1) ). The numerator becomes ((n+2)(n+1)n(n-1)(n-2)!). After cancellation with the denominator, ((n+2)(n+1)) remains.

Step 3

Exam Tip

ऊपर ((n+2)(n+1)n(n-1)(n-2)!) बनता है। हर से काटने पर ((n+2)(n+1)) बचता है।

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

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

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

Explanation opens after your attempt

Correct Answer

D. (6)

Step 1

Concept

It is ((n+2)(n+1)n(n-1)=1680). Since \(8\cdot7\cdot6\cdot5=1680\), (n=6).

Step 2

Why this answer is correct

The correct answer is D. (6). It is ((n+2)(n+1)n(n-1)=1680). Since \(8\cdot7\cdot6\cdot5=1680\), (n=6).

Step 3

Exam Tip

यह ((n+2)(n+1)n(n-1)=1680) है। \(8\cdot7\cdot6\cdot5=1680\), इसलिए (n=6)।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (225)

Step 1

Concept

The first term is (120) and the second is (105), so the sum is (225). Find both parts separately before adding.

Step 2

Why this answer is correct

The correct answer is C. (225). The first term is (120) and the second is (105), so the sum is (225). Find both parts separately before adding.

Step 3

Exam Tip

पहला पद (120) और दूसरा (105) है, इसलिए योग (225) है। जोड़ने से पहले दोनों भाग अलग निकालें।

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

\( \frac{18!}{15!}\div\frac{6!}{3!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{18!}{15!}\div\frac{6!}{3!} \)?

Explanation opens after your attempt

Correct Answer

B. \( \frac{204}{5} \)

Step 1

Concept

The value is \( \frac{18\cdot17\cdot16}{6\cdot5\cdot4}=\frac{204}{5} \). In division, convert both sides into products of equal length.

Step 2

Why this answer is correct

The correct answer is B. \( \frac{204}{5} \). The value is \( \frac{18\cdot17\cdot16}{6\cdot5\cdot4}=\frac{204}{5} \). In division, convert both sides into products of equal length.

Step 3

Exam Tip

मान \( \frac{18\cdot17\cdot16}{6\cdot5\cdot4}=\frac{204}{5} \) है। भाग में दोनों पक्षों को समान लंबाई के गुणनफल में बदलें।

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

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

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

Explanation opens after your attempt

Correct Answer

A. (3n(3n-1))

Step 1

Concept

((3n)!=(3n)(3n-1)(3n-2)!), so the answer is (3n(3n-1)). Handle the indexed term as one unit.

Step 2

Why this answer is correct

The correct answer is A. (3n(3n-1)). ((3n)!=(3n)(3n-1)(3n-2)!), so the answer is (3n(3n-1)). Handle the indexed term as one unit.

Step 3

Exam Tip

((3n)!=(3n)(3n-1)(3n-2)!), इसलिए उत्तर (3n(3n-1)) है। सूचक वाले पद को एक इकाई की तरह संभालें।

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

यदि ( \frac{(3n)!}{(3n-2)!}=132 ), तो (n) का मान क्या है?

If ( \frac{(3n)!}{(3n-2)!}=132 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

D. (4)

Step 1

Concept

It is (3n(3n-1)=132), and \(12\cdot11=132\), so (3n=12). Hence (n=4).

Step 2

Why this answer is correct

The correct answer is D. (4). It is (3n(3n-1)=132), and \(12\cdot11=132\), so (3n=12). Hence (n=4).

Step 3

Exam Tip

यह (3n(3n-1)=132) है और \(12\cdot11=132\), इसलिए (3n=12)। अतः (n=4)।

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

( \frac{(2n)!}{(2n-3)!} ) का सही विस्तार कौन सा है?

Which is the correct expansion of ( \frac{(2n)!}{(2n-3)!} )?

Explanation opens after your attempt

Correct Answer

C. ( (2n)(2n-1)(2n-2) )

Step 1

Concept

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

Step 2

Why this answer is correct

The correct answer is C. ( (2n)(2n-1)(2n-2) ). We expand ((2n)!) up to ((2n)(2n-1)(2n-2)(2n-3)!). Therefore, three factors remain.

Step 3

Exam Tip

((2n)!) को ((2n)(2n-1)(2n-2)(2n-3)!) तक फैलाते हैं। इसलिए तीन गुणक शेष रहते हैं।

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

यदि ( \frac{(2n)!}{(2n-3)!}=720 ), तो (n) का मान क्या है?

If ( \frac{(2n)!}{(2n-3)!}=720 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

It is ((2n)(2n-1)(2n-2)=720). Since \(10\cdot9\cdot8=720\), (2n=10) and (n=5).

Step 2

Why this answer is correct

The correct answer is A. (5). It is ((2n)(2n-1)(2n-2)=720). Since \(10\cdot9\cdot8=720\), (2n=10) and (n=5).

Step 3

Exam Tip

यह ((2n)(2n-1)(2n-2)=720) है। \(10\cdot9\cdot8=720\), इसलिए (2n=10) और (n=5)।

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

\( \frac{9!}{7!} \), \( \frac{8!}{6!} \) से कितना अधिक है?

By how much is \( \frac{9!}{7!} \) greater than \( \frac{8!}{6!} \)?

Explanation opens after your attempt

Correct Answer

B. (16)

Step 1

Concept

The first value is (72) and the second is (56). The difference is (16).

Step 2

Why this answer is correct

The correct answer is B. (16). The first value is (72) and the second is (56). The difference is (16).

Step 3

Exam Tip

पहला मान (72) और दूसरा (56) है। अंतर (16) है।

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

\( \frac{4!\cdot8!}{5!\cdot7!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{4!\cdot8!}{5!\cdot7!} \)?

Explanation opens after your attempt

Correct Answer

D. \( \frac{8}{5} \)

Step 1

Concept

\( \frac{4!}{5!}=\frac{1}{5} \) and \( \frac{8!}{7!}=8 \), so the value is \( \frac{8}{5} \). Cancel separate ratios in multiplication.

Step 2

Why this answer is correct

The correct answer is D. \( \frac{8}{5} \). \( \frac{4!}{5!}=\frac{1}{5} \) and \( \frac{8!}{7!}=8 \), so the value is \( \frac{8}{5} \). Cancel separate ratios in multiplication.

Step 3

Exam Tip

\( \frac{4!}{5!}=\frac{1}{5} \) और \( \frac{8!}{7!}=8 \), इसलिए मान \( \frac{8}{5} \) है। गुणन में अलग-अलग अनुपात काटें।

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

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

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

Explanation opens after your attempt

Correct Answer

C. (2n)

Step 1

Concept

The first term is (n(n+1)) and the second is (n(n-1)). The difference is (2n).

Step 2

Why this answer is correct

The correct answer is C. (2n). The first term is (n(n+1)) and the second is (n(n-1)). The difference is (2n).

Step 3

Exam Tip

पहला पद (n(n+1)) और दूसरा (n(n-1)) है। अंतर (2n) है।

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

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

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

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

The simplified form is (2n), so (2n=18). Hence (n=9).

Step 2

Why this answer is correct

The correct answer is B. (9). The simplified form is (2n), so (2n=18). Hence (n=9).

Step 3

Exam Tip

सरल रूप (2n) है, इसलिए (2n=18)। अतः (n=9)।

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

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

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

Explanation opens after your attempt

Correct Answer

A. (3n(n+1))

Step 1

Concept

The terms become (n(n+1)(n+2)) and (n(n+1)(n-1)). The difference is (3n(n+1)).

Step 2

Why this answer is correct

The correct answer is A. (3n(n+1)). The terms become (n(n+1)(n+2)) and (n(n+1)(n-1)). The difference is (3n(n+1)).

Step 3

Exam Tip

पद (n(n+1)(n+2)) और (n(n+1)(n-1)) बनते हैं। अंतर (3n(n+1)) है।

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

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

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

Explanation opens after your attempt

Correct Answer

D. (8)

Step 1

Concept

The simplified form is (3n(n+1)), so (n(n+1)=72). Since \(8\cdot9=72\), (n=8).

Step 2

Why this answer is correct

The correct answer is D. (8). The simplified form is (3n(n+1)), so (n(n+1)=72). Since \(8\cdot9=72\), (n=8).

Step 3

Exam Tip

सरल रूप (3n(n+1)) है, इसलिए (n(n+1)=72)। \(8\cdot9=72\), इसलिए (n=8)।

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

( \frac{(n+5)!}{(n+1)!} ) के विस्तार में कितने लगातार गुणक बचते हैं?

How many consecutive factors remain in the expansion of ( \frac{(n+5)!}{(n+1)!} )?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

The expansion is ((n+5)(n+4)(n+3)(n+2)), so (4) factors remain. The factorial gap gives the number of factors.

Step 2

Why this answer is correct

The correct answer is B. (4). The expansion is ((n+5)(n+4)(n+3)(n+2)), so (4) factors remain. The factorial gap gives the number of factors.

Step 3

Exam Tip

विस्तार ((n+5)(n+4)(n+3)(n+2)) है, इसलिए (4) गुणक बचते हैं। फैक्टोरियल अंतर से गुणकों की संख्या मिलती है।

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

(n=3) होने पर ( \frac{(n+5)!}{(n+1)!} ) का मान क्या है?

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

Explanation opens after your attempt

Correct Answer

C. (1680)

Step 1

Concept

Putting (n=3) gives \( \frac{8!}{4!}=8\cdot7\cdot6\cdot5=1680 \). Understand the general form before substituting.

Step 2

Why this answer is correct

The correct answer is C. (1680). Putting (n=3) gives \( \frac{8!}{4!}=8\cdot7\cdot6\cdot5=1680 \). Understand the general form before substituting.

Step 3

Exam Tip

(n=3) रखने पर \( \frac{8!}{4!}=8\cdot7\cdot6\cdot5=1680 \)। मान रखने से पहले सामान्य रूप समझें।

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

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

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

Explanation opens after your attempt

Correct Answer

A. (171)

Step 1

Concept

The first term is (190) and the second is (19). The difference is (171).

Step 2

Why this answer is correct

The correct answer is A. (171). The first term is (190) and the second is (19). The difference is (171).

Step 3

Exam Tip

पहला पद (190) और दूसरा (19) है। अंतर (171) है।

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

\( \frac{11!}{5!\cdot6!}\div\frac{10!}{5!\cdot5!} \) का सरल मान क्या है?

What is the simplified value of \( \frac{11!}{5!\cdot6!}\div\frac{10!}{5!\cdot5!} \)?

Explanation opens after your attempt

Correct Answer

D. \( \frac{11}{6} \)

Step 1

Concept

The two terms are (462) and (252), so the ratio is \( \frac{11}{6} \). Reduce large values to a simple ratio.

Step 2

Why this answer is correct

The correct answer is D. \( \frac{11}{6} \). The two terms are (462) and (252), so the ratio is \( \frac{11}{6} \). Reduce large values to a simple ratio.

Step 3

Exam Tip

दोनों पद (462) और (252) हैं, इसलिए अनुपात \( \frac{11}{6} \) है। बड़े मानों को काटकर सरल अनुपात बनाएं।

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

यदि ( \frac{(n+4)!}{(n+2)!}=182 ), तो (n) का मान क्या है?

If ( \frac{(n+4)!}{(n+2)!}=182 ), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (10)

Step 1

Concept

It is ((n+4)(n+3)=182), and \(14\cdot13=182\). Therefore, (n+4=14) and (n=10).

Step 2

Why this answer is correct

The correct answer is B. (10). It is ((n+4)(n+3)=182), and \(14\cdot13=182\). Therefore, (n+4=14) and (n=10).

Step 3

Exam Tip

यह ((n+4)(n+3)=182) है और \(14\cdot13=182\)। इसलिए (n+4=14) और (n=10)।

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Question 48/50 Hard Mathematics Permutations and Combinations Class 11 Level 56

\(\frac{13!}{10!}+\frac{12!}{9!}\) का मान क्या है?

What is the value of \(\frac{13!}{10!}+\frac{12!}{9!}\)?

Explanation opens after your attempt

Correct Answer

A. (3036)

Step 1

Concept

The first term is \(13\cdot12\cdot11=1716\) and the second is \(12\cdot11\cdot10=1320\). The sum is (3036).

Step 2

Why this answer is correct

The correct answer is A. (3036). The first term is \(13\cdot12\cdot11=1716\) and the second is \(12\cdot11\cdot10=1320\). The sum is (3036).

Step 3

Exam Tip

पहला पद \(13\cdot12\cdot11=1716\) और दूसरा \(12\cdot11\cdot10=1320\) है। योग (3036) है।

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Question 49/50 Hard Mathematics Permutations and Combinations Class 11 Level 56

यदि \(\frac{(n+5)!}{(n+3)!}=210 \), तो (n) का मान क्या है?

If \( \frac{(n+5)!}{(n+3)!}=210\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

It gives \((n+5)(n+4)=210\), and \(15\cdot14=210\). Therefore, (n=10).

Step 2

Why this answer is correct

The correct answer is B. (9). It gives \((n+5)(n+4)=210\), and \(15\cdot14=210\). Therefore, (n=10).

Step 3

Exam Tip

यह \((n+5)(n+4)=210\) देता है और \(15\cdot14=210\)। इसलिए (n+5=15) और (n=10) नहीं, सही (n=10) है।

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Question 50/50 Hard Mathematics Permutations and Combinations Class 11 Level 56

\(\frac{21!}{19!\cdot2!}-\frac{18!}{16!\cdot2!}\) का मान क्या है?

What is the value of \(\frac{21!}{19!\cdot2!}-\frac{18!}{16!\cdot2!}\)?

Explanation opens after your attempt

Correct Answer

C. (72)

Step 1

Concept

The first term is (210) and the second is (153). The difference is (57).

Step 2

Why this answer is correct

The correct answer is C. (72). The first term is (210) and the second is (153). The difference is (57).

Step 3

Exam Tip

पहला पद (210) और दूसरा (153) है। अंतर (57) है।

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Class 11 Mathematics Hard Quiz

\( \frac{12!}{9!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{10!}{7!\cdot3!} \) का सरल मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{8!-7!}{6!} \) का मान ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{n!}{(n-3)!}=336 ), तो (n) का धनात्मक मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n+3)!-(n+2)!}{(n+1)!}=49 ), तो (n) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

\( \frac{14!}{11!}\div\frac{7!}{4!} \) का सरल मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{9!}{6!\cdot2!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

\( \frac{11!}{8!\cdot3!}\div\frac{10!}{7!\cdot3!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{12!}{8!\cdot4!}-\frac{11!}{7!\cdot4!} \) का मान क्या 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+1)!+n!}{n!}=13 ), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\( \frac{15!}{13!}-\frac{14!}{12!} \) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि ( \frac{(n+4)!}{(n+2)!}+\frac{(n+3)!}{(n+1)!}=200 ), तो (n) का मान क्या है?

Concept

Why this answer is correct

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

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

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