\(\frac{10!}{8!,2!}\) का मान क्या है?
What is the value of \(\frac{10!}{8!,2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (36)
B (40)
C (45)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(\frac{10!}{8!,2!}=\frac{10\times9}{2}=45\). First cancel (8!) and then divide by (2!).
Step 2
Why this answer is correct
The correct answer is C. (45). \(\frac{10!}{8!,2!}=\frac{10\times9}{2}=45\). First cancel (8!) and then divide by (2!).
Step 3
Exam Tip
\(\frac{10!}{8!,2!}=\frac{10\times9}{2}=45\)। पहले (8!) काटें और फिर (2!) से भाग दें।
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(15!) को (14!) की सहायता से कैसे लिखेंगे?
How can (15!) be written using (14!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (15+14!)
B \(15\times14!\)
C \(14\times15!\)
D \(\frac{14!}{15}\)
Explanation opens after your attempt
Correct Answer
B. \(15\times14!\)
Step 1
Concept
\(15!=15\times14!\). This is a direct use of ((n)!=n(n-1)!).
Step 2
Why this answer is correct
The correct answer is B. \(15\times14!\). \(15!=15\times14!\). This is a direct use of ((n)!=n(n-1)!).
Step 3
Exam Tip
\(15!=15\times14!\) होता है। यह ((n)!=n(n-1)!) का सीधा प्रयोग है।
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यदि (m=2!) और (n=4!), तो (m+n) का मान क्या है?
If (m=2!) and (n=4!), what is the value of (m+n)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (24)
B (25)
C (26)
D (28)
Explanation opens after your attempt
Step 1
Concept
(m=2) and (n=24), so (m+n=26). Replace the variables with factorial values.
Step 2
Why this answer is correct
The correct answer is C. (26). (m=2) and (n=24), so (m+n=26). Replace the variables with factorial values.
Step 3
Exam Tip
(m=2) और (n=24), इसलिए (m+n=26)। चर को क्रमगुणित मान से बदलें।
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\(\frac{4!+1!}{5}\) का मान क्या है?
What is the value of \(\frac{4!+1!}{5}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(4!+1!=24+1=25), and \(\frac{25}{5}=5\). Simplify the numerator first.
Step 2
Why this answer is correct
The correct answer is C. (5). (4!+1!=24+1=25), and \(\frac{25}{5}=5\). Simplify the numerator first.
Step 3
Exam Tip
(4!+1!=24+1=25), और \(\frac{25}{5}=5\)। अंश को पहले सरल करें।
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कौन सा विस्तार (9!) का सही विस्तार शुरू करता है?
Which expansion correctly starts (9!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A \(9\times8\times7\times\cdots\times1\)
B \(9+8+7+\cdots+1\)
C \(9\times9\times9\times\cdots\)
D \(9-8-7-\cdots-1\)
Explanation opens after your attempt
Correct Answer
A. \(9\times8\times7\times\cdots\times1\)
Step 1
Concept
In (9!), numbers from (9) down to (1) are multiplied. Factorial does not use addition or subtraction.
Step 2
Why this answer is correct
The correct answer is A. \(9\times8\times7\times\cdots\times1\). In (9!), numbers from (9) down to (1) are multiplied. Factorial does not use addition or subtraction.
Step 3
Exam Tip
(9!) में (9) से (1) तक गुणा होता है। क्रमगुणित में जोड़ या घटाव नहीं होता।
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(6!-4!) का मान क्या है?
What is the value of (6!-4!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (696)
B (700)
C (704)
D (716)
Explanation opens after your attempt
Step 1
Concept
(6!=720) and (4!=24), so the difference is (696). Find both factorials before subtracting directly.
Step 2
Why this answer is correct
The correct answer is A. (696). (6!=720) and (4!=24), so the difference is (696). Find both factorials before subtracting directly.
Step 3
Exam Tip
(6!=720) और (4!=24), इसलिए अंतर (696) है। सीधे घटाने से पहले दोनों क्रमगुणित निकालें।
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(\frac{(n+3)!}{(n+1)!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+3)!}{(n+1)!})?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (n+3)
B ((n+3)(n+2))
C ((n+2)(n+1))
D (n+1)
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 remaining part is ((n+3)(n+2)). Cancel the common factorial part.
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 remaining part is ((n+3)(n+2)). Cancel the common factorial part.
Step 3
Exam Tip
((n+3)!=(n+3)(n+2)(n+1)!), इसलिए शेष ((n+3)(n+2)) है। समान क्रमगुणित भाग काटें।
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\(\frac{6!}{3!}\div5\) का मान क्या है?
What is the value of \(\frac{6!}{3!}\div5\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (20)
B (24)
C (30)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!}{3!}=6\times5\times4=120\), and \(120\div5=24\). Simplify the operations in order.
Step 2
Why this answer is correct
The correct answer is B. (24). \(\frac{6!}{3!}=6\times5\times4=120\), and \(120\div5=24\). Simplify the operations in order.
Step 3
Exam Tip
\(\frac{6!}{3!}=6\times5\times4=120\), और \(120\div5=24\)। भागों को क्रम से सरल करें।
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(5!) में अंतिम गुणक कौन सा होता है?
What is the last factor in (5!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (0)
B (1)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(5!=5\times4\times3\times2\times1\), so the last factor is (1). A factorial always goes down to (1).
Step 2
Why this answer is correct
The correct answer is B. (1). \(5!=5\times4\times3\times2\times1\), so the last factor is (1). A factorial always goes down to (1).
Step 3
Exam Tip
\(5!=5\times4\times3\times2\times1\), इसलिए अंतिम गुणक (1) है। क्रमगुणित हमेशा (1) तक जाता है।
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\(7!\div5!\) और (2!) का अंतर क्या है?
What is the difference between \(7!\div5!\) and (2!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (38)
B (40)
C (42)
D (44)
Explanation opens after your attempt
Step 1
Concept
\(7!\div5!=42\) and (2!=2), so the difference is (40). First find the values of both parts.
Step 2
Why this answer is correct
The correct answer is B. (40). \(7!\div5!=42\) and (2!=2), so the difference is (40). First find the values of both parts.
Step 3
Exam Tip
\(7!\div5!=42\) और (2!=2), इसलिए अंतर (40) है। पहले दोनों भागों के मान निकालें।
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यदि (p=0!) और (q=1!), तो (p+q) का मान क्या है?
If (p=0!) and (q=1!), what is the value of (p+q)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(0!=1) and (1!=1), so (p+q=2). The values of (0!) and (1!) are equal.
Step 2
Why this answer is correct
The correct answer is C. (2). (0!=1) and (1!=1), so (p+q=2). The values of (0!) and (1!) are equal.
Step 3
Exam Tip
(0!=1) और (1!=1), इसलिए (p+q=2)। (0!) और (1!) के मान बराबर हैं।
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\(\frac{12!}{10!}\) का मान क्या है?
What is the value of \(\frac{12!}{10!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (110)
B (120)
C (132)
D (144)
Explanation opens after your attempt
Step 1
Concept
\(\frac{12!}{10!}=12\times11=132\). After cancelling the smaller factorial, multiply the remaining factors.
Step 2
Why this answer is correct
The correct answer is C. (132). \(\frac{12!}{10!}=12\times11=132\). After cancelling the smaller factorial, multiply the remaining factors.
Step 3
Exam Tip
\(\frac{12!}{10!}=12\times11=132\)। छोटे क्रमगुणित को काटने के बाद बचे गुणक गुणा करें।
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(8!) को (9!) की सहायता से कैसे लिखा जा सकता है?
How can (8!) be written using (9!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A \(\frac{9!}{9}\)
B \(\frac{9!}{8}\)
C \(9\times9!\)
D (9!-1)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9!}{9}\)
Step 1
Concept
\(9!=9\times8!\), so \(8!=\frac{9!}{9}\). A smaller factorial can also be found from a larger factorial.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9!}{9}\). \(9!=9\times8!\), so \(8!=\frac{9!}{9}\). A smaller factorial can also be found from a larger factorial.
Step 3
Exam Tip
\(9!=9\times8!\), इसलिए \(8!=\frac{9!}{9}\)। बड़े क्रमगुणित से छोटा क्रमगुणित भी निकाला जा सकता है।
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\(4!\times2!-3!\) का मान क्या है?
What is the value of \(4!\times2!-3!\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (36)
B (40)
C (42)
D (48)
Explanation opens after your attempt
Step 1
Concept
\(4!\times2!-3!=24\times2-6=42\). Convert factorial values into numbers first.
Step 2
Why this answer is correct
The correct answer is C. (42). \(4!\times2!-3!=24\times2-6=42\). Convert factorial values into numbers first.
Step 3
Exam Tip
\(4!\times2!-3!=24\times2-6=42\)। क्रमगुणित मानों को पहले संख्याओं में बदलें।
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\(\frac{5!}{1!,4!}\) का मान क्या है?
What is the value of \(\frac{5!}{1!,4!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (4)
B (5)
C (6)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(\frac{5!}{1!,4!}=\frac{5\times4!}{1\times4!}=5\). The value of (1!) is (1).
Step 2
Why this answer is correct
The correct answer is B. (5). \(\frac{5!}{1!,4!}=\frac{5\times4!}{1\times4!}=5\). The value of (1!) is (1).
Step 3
Exam Tip
\(\frac{5!}{1!,4!}=\frac{5\times4!}{1\times4!}=5\)। (1!) का मान (1) होता है।
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\(14\times13!\) किसके बराबर है?
\(14\times13!\) is equal to which of the following?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (12!)
B (13!)
C (14!)
D (15!)
Explanation opens after your attempt
Step 1
Concept
\(14!=14\times13!\), so the given product is (14!). This is a basic factorial identity.
Step 2
Why this answer is correct
The correct answer is C. (14!). \(14!=14\times13!\), so the given product is (14!). This is a basic factorial identity.
Step 3
Exam Tip
\(14!=14\times13!\), इसलिए दिया गया गुणनफल (14!) है। यह मूल क्रमगुणित पहचान है।
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((6-3)!\times2!) का मान क्या है?
What is the value of ((6-3)!\times2!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
((6-3)!=3!=6) and (2!=2), so the product is (12). Solve the bracket first.
Step 2
Why this answer is correct
The correct answer is B. (12). ((6-3)!=3!=6) and (2!=2), so the product is (12). Solve the bracket first.
Step 3
Exam Tip
((6-3)!=3!=6) और (2!=2), इसलिए गुणनफल (12) है। कोष्ठक पहले हल करें।
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किस विकल्प का मान (720) है?
Which option has value (720)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5!)
B (6!)
C (7!)
D (8!)
Explanation opens after your attempt
Step 1
Concept
(6!=720). Remembering values from (1!) to (7!) is useful for exams.
Step 2
Why this answer is correct
The correct answer is B. (6!). (6!=720). Remembering values from (1!) to (7!) is useful for exams.
Step 3
Exam Tip
(6!=720) होता है। परीक्षा के लिए (1!) से (7!) तक के मान याद रखना उपयोगी है।
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(6!) और (4!) का अनुपात क्या है?
What is the ratio of (6!) to (4!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (30:1)
B (20:1)
C (15:1)
D (10:1)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!}{4!}=6\times5=30\), so the ratio is (30:1). Cancel the common factorial in a ratio.
Step 2
Why this answer is correct
The correct answer is A. (30:1). \(\frac{6!}{4!}=6\times5=30\), so the ratio is (30:1). Cancel the common factorial in a ratio.
Step 3
Exam Tip
\(\frac{6!}{4!}=6\times5=30\), इसलिए अनुपात (30:1) है। अनुपात में समान क्रमगुणित काटें।
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\(2!\times3!\times4!\) का मान क्या है?
What is the value of \(2!\times3!\times4!\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (144)
B (216)
C (288)
D (48)
Explanation opens after your attempt
Step 1
Concept
(2!=2), (3!=6), and (4!=24), so the product is (288). Evaluate each term separately.
Step 2
Why this answer is correct
The correct answer is C. (288). (2!=2), (3!=6), and (4!=24), so the product is (288). Evaluate each term separately.
Step 3
Exam Tip
(2!=2), (3!=6) और (4!=24), इसलिए गुणनफल (288) है। हर पद अलग निकालें।
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(\frac{(n+2)!}{(n+1)!}+1) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+2)!}{(n+1)!}+1)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (n+2)
B (n+3)
C (2n+1)
D (1)
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+2)!}{(n+1)!}=n+2), so adding (1) gives (n+3). Simplify the fraction first.
Step 2
Why this answer is correct
The correct answer is B. (n+3). (\frac{(n+2)!}{(n+1)!}=n+2), so adding (1) gives (n+3). Simplify the fraction first.
Step 3
Exam Tip
(\frac{(n+2)!}{(n+1)!}=n+2), इसलिए (1) जोड़ने पर (n+3) मिलता है। पहले भिन्न को सरल करें।
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यदि (n!=5040), तो (n) का मान क्या है?
If (n!=5040), what is the value of (n)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(7!=5040), so (n=7). Remember small factorial values.
Step 2
Why this answer is correct
The correct answer is B. (7). (7!=5040), so (n=7). Remember small factorial values.
Step 3
Exam Tip
(7!=5040), इसलिए (n=7)। छोटे क्रमगुणित मान याद रखें।
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\(\frac{11!}{9!}\) का मान क्या है?
What is the value of \(\frac{11!}{9!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (99)
B (110)
C (121)
D (132)
Explanation opens after your attempt
Step 1
Concept
\(\frac{11!}{9!}=11\times10=110\). Cancel the common (9!) part.
Step 2
Why this answer is correct
The correct answer is B. (110). \(\frac{11!}{9!}=11\times10=110\). Cancel the common (9!) part.
Step 3
Exam Tip
\(\frac{11!}{9!}=11\times10=110\)। समान (9!) भाग को काट दें।
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(1!+4!+0!) का मान क्या है?
What is the value of (1!+4!+0!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (24)
B (25)
C (26)
D (27)
Explanation opens after your attempt
Step 1
Concept
(1!=1), (4!=24), and (0!=1), so the sum is (26). Both (0!) and (1!) are (1).
Step 2
Why this answer is correct
The correct answer is C. (26). (1!=1), (4!=24), and (0!=1), so the sum is (26). Both (0!) and (1!) are (1).
Step 3
Exam Tip
(1!=1), (4!=24) और (0!=1), इसलिए योग (26) है। (0!) और (1!) दोनों (1) होते हैं।
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\(\frac{7!}{7\times6!}\) का मान क्या है?
What is the value of \(\frac{7!}{7\times6!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (0)
B (1)
C (7)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(7!=7\times6!\), so numerator and denominator are the same. The quotient of equal non-zero quantities is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). \(7!=7\times6!\), so numerator and denominator are the same. The quotient of equal non-zero quantities is (1).
Step 3
Exam Tip
\(7!=7\times6!\), इसलिए अंश और हर समान हैं। समान अशून्य राशियों का भाग (1) होता है।
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(13!) को (11!) की सहायता से कैसे लिखेंगे?
How can (13!) be written using (11!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A \(13\times11!\)
B \(12\times11!\)
C \(13\times12\times11!\)
D (13+12+11!)
Explanation opens after your attempt
Correct Answer
C. \(13\times12\times11!\)
Step 1
Concept
\(13!=13\times12\times11!\). Write the larger factorial down to the smaller factorial.
Step 2
Why this answer is correct
The correct answer is C. \(13\times12\times11!\). \(13!=13\times12\times11!\). Write the larger factorial down to the smaller factorial.
Step 3
Exam Tip
\(13!=13\times12\times11!\) होता है। बड़े क्रमगुणित को छोटे क्रमगुणित तक लिखें।
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\(5!\div4!+3!\) का मान क्या है?
What is the value of \(5!\div4!+3!\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
\(5!\div4!=5\) and (3!=6), so the total is (11). Simplify the division first.
Step 2
Why this answer is correct
The correct answer is B. (11). \(5!\div4!=5\) and (3!=6), so the total is (11). Simplify the division first.
Step 3
Exam Tip
\(5!\div4!=5\) और (3!=6), इसलिए कुल (11) है। पहले भाग को सरल करें।
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(9!) में कुल कितने गुणक होते हैं?
How many factors are present in (9!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
(9!) has (9) factors from (9) down to (1). (n!) has (n) factors.
Step 2
Why this answer is correct
The correct answer is C. (9). (9!) has (9) factors from (9) down to (1). (n!) has (n) factors.
Step 3
Exam Tip
(9!) में (9) से (1) तक कुल (9) गुणक होते हैं। (n!) में (n) गुणक होते हैं।
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((5-1)!+2!) का मान क्या है?
What is the value of ((5-1)!+2!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (24)
B (26)
C (28)
D (30)
Explanation opens after your attempt
Step 1
Concept
((5-1)!=4!=24) and (2!=2), so the sum is (26). Solve the bracket first.
Step 2
Why this answer is correct
The correct answer is B. (26). ((5-1)!=4!=24) and (2!=2), so the sum is (26). Solve the bracket first.
Step 3
Exam Tip
((5-1)!=4!=24) और (2!=2), इसलिए योग (26) है। कोष्ठक पहले हल करें।
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(8!-7!) का मान क्या है?
What is the value of (8!-7!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (30240)
B (35280)
C (40320)
D (5040)
Explanation opens after your attempt
Correct Answer
B. (35280)
Step 1
Concept
(8!=40320) and (7!=5040), so the difference is (35280). Find both values before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (35280). (8!=40320) and (7!=5040), so the difference is (35280). Find both values before subtracting.
Step 3
Exam Tip
(8!=40320) और (7!=5040), इसलिए अंतर (35280) है। घटाने से पहले दोनों मान निकालें।
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