\(\frac{10!}{9!}\) का मान क्या है?
What is the value of \(\frac{10!}{9!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (9)
B (10)
C (19)
D (90)
Explanation opens after your attempt
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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(2!+4!-1!) का मान क्या है?
What is the value of (2!+4!-1!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (23)
B (24)
C (25)
D (26)
Explanation opens after your attempt
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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यदि (n=4), तो (n!) का मान क्या है?
If (n=4), what is the value of (n!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (16)
B (20)
C (24)
D (32)
Explanation opens after your attempt
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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\(\frac{8!}{6!,2!}\) का मान क्या है?
What is the value of \(\frac{8!}{6!,2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (14)
B (28)
C (56)
D (64)
Explanation opens after your attempt
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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(6!+1!) का मान क्या होगा?
What will be the value of (6!+1!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (720)
B (721)
C (719)
D (722)
Explanation opens after your attempt
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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\(\frac{9!}{7!}\) का मान क्या है?
What is the value of \(\frac{9!}{7!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (63)
B (72)
C (90)
D (126)
Explanation opens after your attempt
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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(8!) को (6!) की सहायता से कैसे लिखेंगे?
How can (8!) be written using (6!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A \(8\times7\times6!\)
B (8+7+6!)
C \(8\times6!\)
D \(7\times6!\)
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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(7!) का मान क्या है?
What is the value of (7!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (720)
B (5040)
C (40320)
D (840)
Explanation opens after your attempt
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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(7!) में कुल कितने गुणक लिखे जाते हैं?
How many factors are written in (7!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(7!=7\times6\times5\times4\times3\times2\times1\), which has (7) factors. In (n!), factors run from (n) down to (1).
Step 2
Why this answer is correct
The correct answer is C. (7). \(7!=7\times6\times5\times4\times3\times2\times1\), which has (7) factors. In (n!), factors run from (n) down to (1).
Step 3
Exam Tip
\(7!=7\times6\times5\times4\times3\times2\times1\), इसमें (7) गुणक हैं। (n!) में (n) से (1) तक के गुणक आते हैं।
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\(\frac{2!+3!}{2!}\) का मान क्या है?
What is the value of \(\frac{2!+3!}{2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(\frac{2!+3!}{2!}=\frac{2+6}{2}=4\). Complete the addition in the numerator first.
Step 2
Why this answer is correct
The correct answer is C. (4). \(\frac{2!+3!}{2!}=\frac{2+6}{2}=4\). Complete the addition in the numerator first.
Step 3
Exam Tip
\(\frac{2!+3!}{2!}=\frac{2+6}{2}=4\)। अंश में जोड़ पहले पूरा करें।
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\(\frac{5!}{4!}+1\) का मान क्या है?
What is the value of \(\frac{5!}{4!}+1\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5)
B (6)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(\frac{5!}{4!}=5\), so (5+1=6). Simplify the quotient first and then add.
Step 2
Why this answer is correct
The correct answer is B. (6). \(\frac{5!}{4!}=5\), so (5+1=6). Simplify the quotient first and then add.
Step 3
Exam Tip
\(\frac{5!}{4!}=5\), इसलिए (5+1=6)। पहले भाग को सरल करके फिर जोड़ें।
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(8!) को (7!) की सहायता से कैसे लिखेंगे?
How can (8!) be written using (7!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (8+7!)
B \(8\times7!\)
C \(7\times8!\)
D \(\frac{7!}{8}\)
Explanation opens after your attempt
Correct Answer
B. \(8\times7!\)
Step 1
Concept
\(8!=8\times7!\). This is a basic factorial identity.
Step 2
Why this answer is correct
The correct answer is B. \(8\times7!\). \(8!=8\times7!\). This is a basic factorial identity.
Step 3
Exam Tip
\(8!=8\times7!\) होता है। यह फैक्टोरियल की मूल पहचान है।
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(3!+0!) का मान क्या है?
What is the value of (3!+0!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(3!=6) and (0!=1), so the sum is (7). Pay special attention in questions involving (0!).
Step 2
Why this answer is correct
The correct answer is B. (7). (3!=6) and (0!=1), so the sum is (7). Pay special attention in questions involving (0!).
Step 3
Exam Tip
(3!=6) और (0!=1), इसलिए योग (7) है। (0!) वाले सवाल में विशेष ध्यान रखें।
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((3+1)!) का मान क्या है?
What is the value of ((3+1)!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (4)
B (12)
C (24)
D (36)
Explanation opens after your attempt
Step 1
Concept
First calculate (3+1=4), then (4!=24). The expression inside the brackets is evaluated first.
Step 2
Why this answer is correct
The correct answer is C. (24). First calculate (3+1=4), then (4!=24). The expression inside the brackets is evaluated first.
Step 3
Exam Tip
पहले (3+1=4) करें, फिर (4!=24)। कोष्ठक के अंदर की गणना पहले होती है।
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यदि (n!=120), तो (n) का मान क्या है?
If (n!=120), what is the value of (n)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(5!=120), so (n=5). Small factorial values help answer quickly in exams.
Step 2
Why this answer is correct
The correct answer is B. (5). (5!=120), so (n=5). Small factorial values help answer quickly in exams.
Step 3
Exam Tip
(5!=120), इसलिए (n=5)। छोटे फैक्टोरियल मान परीक्षा में जल्दी उत्तर दिलाते हैं।
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\(\frac{4!}{0!}\) का मान क्या है?
What is the value of \(\frac{4!}{0!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (0)
B (1)
C (12)
D (24)
Explanation opens after your attempt
Step 1
Concept
(4!=24) and (0!=1), so the quotient is (24). Always take (0!) as (1).
Step 2
Why this answer is correct
The correct answer is D. (24). (4!=24) and (0!=1), so the quotient is (24). Always take (0!) as (1).
Step 3
Exam Tip
(4!=24) और (0!=1), इसलिए भागफल (24) है। (0!) हमेशा (1) रखें।
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\(\frac{7!}{7}\) का मान क्या है?
What is the value of \(\frac{7!}{7}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5!)
B (6!)
C (7!)
D (8!)
Explanation opens after your attempt
Step 1
Concept
\(7!=7\times6!\), so \(\frac{7!}{7}=6!\). Break the factorial into factors and cancel.
Step 2
Why this answer is correct
The correct answer is B. (6!). \(7!=7\times6!\), so \(\frac{7!}{7}=6!\). Break the factorial into factors and cancel.
Step 3
Exam Tip
\(7!=7\times6!\), इसलिए \(\frac{7!}{7}=6!\)। फैक्टोरियल को गुणनखंड में तोड़कर काटें।
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(6!) का मान क्या है?
What is the value of (6!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (120)
B (360)
C (720)
D (840)
Explanation opens after your attempt
Step 1
Concept
\(6!=6\times5\times4\times3\times2\times1=720\). If you remember (5!=120), then use \(6!=6\times120\).
Step 2
Why this answer is correct
The correct answer is C. (720). \(6!=6\times5\times4\times3\times2\times1=720\). If you remember (5!=120), then use \(6!=6\times120\).
Step 3
Exam Tip
\(6!=6\times5\times4\times3\times2\times1=720\)। (5!=120) याद हो तो \(6!=6\times120\) करें।
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\(5\times4\times3!\) किसके बराबर है?
\(5\times4\times3!\) is equal to which of the following?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (3!)
B (4!)
C (5!)
D (6!)
Explanation opens after your attempt
Step 1
Concept
\(5!=5\times4\times3!\), so the given form is (5!). Recognizing factorial expansion is important.
Step 2
Why this answer is correct
The correct answer is C. (5!). \(5!=5\times4\times3!\), so the given form is (5!). Recognizing factorial expansion is important.
Step 3
Exam Tip
\(5!=5\times4\times3!\), इसलिए दिया गया रूप (5!) है। फैक्टोरियल विस्तार को पहचानना जरूरी है।
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\(\frac{3!}{2!}\) का मान क्या है?
What is the value of \(\frac{3!}{2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(\frac{3!}{2!}=\frac{3\times2!}{2!}=3\). Cancel the common (2!).
Step 2
Why this answer is correct
The correct answer is B. (3). \(\frac{3!}{2!}=\frac{3\times2!}{2!}=3\). Cancel the common (2!).
Step 3
Exam Tip
\(\frac{3!}{2!}=\frac{3\times2!}{2!}=3\)। समान (2!) को काट दें।
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यदि (x=4!), तो (x) का मान क्या है?
If (x=4!), what is the value of (x)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (16)
B (20)
C (24)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(4!=4\times3\times2\times1=24\), so (x=24). In variable-based questions, first evaluate the factorial.
Step 2
Why this answer is correct
The correct answer is C. (24). \(4!=4\times3\times2\times1=24\), so (x=24). In variable-based questions, first evaluate the factorial.
Step 3
Exam Tip
\(4!=4\times3\times2\times1=24\), इसलिए (x=24)। चर वाले सवाल में पहले फैक्टोरियल का मान निकालें।
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(4!-3!) का मान क्या है?
What is the value of (4!-3!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (18)
B (12)
C (10)
D (6)
Explanation opens after your attempt
Step 1
Concept
(4!=24) and (3!=6), so the difference is (18). Do not treat the factorial sign as ordinary subtraction.
Step 2
Why this answer is correct
The correct answer is A. (18). (4!=24) and (3!=6), so the difference is (18). Do not treat the factorial sign as ordinary subtraction.
Step 3
Exam Tip
(4!=24) और (3!=6), इसलिए अंतर (18) है। फैक्टोरियल चिन्ह को साधारण घटाव न समझें।
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\(\frac{5!}{5}\) का मान क्या है?
What is the value of \(\frac{5!}{5}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (12)
B (20)
C (24)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(5!=5\times4!\), so \(\frac{5!}{5}=4!=24\). Cancel common factors in factorial expressions.
Step 2
Why this answer is correct
The correct answer is C. (24). \(5!=5\times4!\), so \(\frac{5!}{5}=4!=24\). Cancel common factors in factorial expressions.
Step 3
Exam Tip
\(5!=5\times4!\), इसलिए \(\frac{5!}{5}=4!=24\)। फैक्टोरियल में सामान्य गुणक काटें।
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\(6\times5\times4!\) किसके बराबर है?
\(6\times5\times4!\) is equal to which of the following?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5!)
B (6!)
C (7!)
D (4!)
Explanation opens after your attempt
Step 1
Concept
\(6!=6\times5\times4!\), so the given product is (6!). A factorial can be identified from the middle expansion too.
Step 2
Why this answer is correct
The correct answer is B. (6!). \(6!=6\times5\times4!\), so the given product is (6!). A factorial can be identified from the middle expansion too.
Step 3
Exam Tip
\(6!=6\times5\times4!\), इसलिए दिया गया गुणनफल (6!) है। फैक्टोरियल को बीच से भी पहचाना जा सकता है।
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(2!+2!+2!) का मान क्या है?
What is the value of (2!+2!+2!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (4)
B (6)
C (8)
D (12)
Explanation opens after your attempt
Step 1
Concept
(2!=2), so (2+2+2=6). Find the repeated factorial once first.
Step 2
Why this answer is correct
The correct answer is B. (6). (2!=2), so (2+2+2=6). Find the repeated factorial once first.
Step 3
Exam Tip
(2!=2), इसलिए (2+2+2=6)। दोहराए गए फैक्टोरियल को पहले एक बार निकालें।
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\(\frac{6!}{2!,4!}\) का मान क्या है?
What is the value of \(\frac{6!}{2!,4!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (10)
B (12)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!}{2!,4!}=\frac{6\times5}{2}=15\). Cancel the smaller factorial from the larger factorial.
Step 2
Why this answer is correct
The correct answer is C. (15). \(\frac{6!}{2!,4!}=\frac{6\times5}{2}=15\). Cancel the smaller factorial from the larger factorial.
Step 3
Exam Tip
\(\frac{6!}{2!,4!}=\frac{6\times5}{2}=15\)। बड़े फैक्टोरियल से छोटे फैक्टोरियल को काटें।
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\(3!\times0!\) का मान क्या है?
What is the value of \(3!\times0!\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (0)
B (3)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
(3!=6) and (0!=1), so the product is (6). Treating (0!) as (0) is a common mistake.
Step 2
Why this answer is correct
The correct answer is C. (6). (3!=6) and (0!=1), so the product is (6). Treating (0!) as (0) is a common mistake.
Step 3
Exam Tip
(3!=6) और (0!=1), इसलिए गुणनफल (6) है। (0!) को (0) समझना सामान्य गलती है।
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(7!) में (7) के बाद अगला गुणक कौन सा आता है?
In (7!), which factor comes immediately after (7)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (8)
B (7)
C (6)
D (1)
Explanation opens after your attempt
Step 1
Concept
\(7!=7\times6\times5\times4\times3\times2\times1\). In factorial notation, the numbers decrease step by step.
Step 2
Why this answer is correct
The correct answer is C. (6). \(7!=7\times6\times5\times4\times3\times2\times1\). In factorial notation, the numbers decrease step by step.
Step 3
Exam Tip
\(7!=7\times6\times5\times4\times3\times2\times1\)। फैक्टोरियल में संख्या घटती जाती है।
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\(\frac{4!+3!}{3!}\) का मान क्या है?
What is the value of \(\frac{4!+3!}{3!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(\frac{4!+3!}{3!}=\frac{24+6}{6}=5\). Simplify the numerator with addition first.
Step 2
Why this answer is correct
The correct answer is B. (5). \(\frac{4!+3!}{3!}=\frac{24+6}{6}=5\). Simplify the numerator with addition first.
Step 3
Exam Tip
\(\frac{4!+3!}{3!}=\frac{24+6}{6}=5\)। जोड़ वाले अंश को पहले सरल करें।
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(5!) और (4!) में कौन सा बड़ा है?
Which is greater between (5!) and (4!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (4!)
B दोनों बराबर / Both are equal
C (5!)
D तुलना नहीं हो सकती / Cannot be compared
Explanation opens after your attempt
Step 1
Concept
(5!=120) and (4!=24), so (5!) is greater. The factorial of a larger positive integer is generally larger.
Step 2
Why this answer is correct
The correct answer is C. (5!). (5!=120) and (4!=24), so (5!) is greater. The factorial of a larger positive integer is generally larger.
Step 3
Exam Tip
(5!=120) और (4!=24), इसलिए (5!) बड़ा है। बड़े धनात्मक पूर्णांक का फैक्टोरियल सामान्यतः बड़ा होता है।
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