यदि (a=6!) और (b=5!), तो \(\frac{a}{b}\) का मान क्या है?
If (a=6!) and (b=5!), what is the value of \(\frac{a}{b}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5)
B (6)
C (7)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(\frac{a}{b}=\frac{6!}{5!}=6\). Cancel the common part in a factorial ratio.
Step 2
Why this answer is correct
The correct answer is B. (6). \(\frac{a}{b}=\frac{6!}{5!}=6\). Cancel the common part in a factorial ratio.
Step 3
Exam Tip
\(\frac{a}{b}=\frac{6!}{5!}=6\)। क्रमगुणित अनुपात में समान भाग काटें।
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\(\frac{6!+5!}{5!}\) का मान क्या है?
What is the value of \(\frac{6!+5!}{5!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!+5!}{5!}=\frac{720+120}{120}=7\). Write the sum in the numerator correctly.
Step 2
Why this answer is correct
The correct answer is C. (7). \(\frac{6!+5!}{5!}=\frac{720+120}{120}=7\). Write the sum in the numerator correctly.
Step 3
Exam Tip
\(\frac{6!+5!}{5!}=\frac{720+120}{120}=7\)। अंश का योग सही लिखें।
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कौन सा रूप \(7\times6\times5\) के बराबर है?
Which form is equal to \(7\times6\times5\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A \(\frac{7!}{4!}\)
B \(\frac{7!}{5!}\)
C \(\frac{6!}{4!}\)
D \(\frac{5!}{7!}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{7!}{4!}\)
Step 1
Concept
\(7!=7\times6\times5\times4!\), so \(\frac{7!}{4!}=7\times6\times5\). Choose the denominator according to the remaining factors.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7!}{4!}\). \(7!=7\times6\times5\times4!\), so \(\frac{7!}{4!}=7\times6\times5\). Choose the denominator according to the remaining factors.
Step 3
Exam Tip
\(7!=7\times6\times5\times4!\), इसलिए \(\frac{7!}{4!}=7\times6\times5\)। शेष गुणकों के अनुसार हर चुनें।
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\(3!\times5!\) का मान क्या है?
What is the value of \(3!\times5!\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (720)
B (600)
C (840)
D (900)
Explanation opens after your attempt
Step 1
Concept
(3!=6) and (5!=120), so the product is (720). Evaluate both factorials before multiplying.
Step 2
Why this answer is correct
The correct answer is A. (720). (3!=6) and (5!=120), so the product is (720). Evaluate both factorials before multiplying.
Step 3
Exam Tip
(3!=6) और (5!=120), इसलिए गुणनफल (720) है। गुणा से पहले दोनों क्रमगुणित निकालें।
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(\frac{(n+5)!}{(n+4)!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+5)!}{(n+4)!})?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (n+3)
B (n+4)
C (n+5)
D (1)
Explanation opens after your attempt
Step 1
Concept
((n+5)!=(n+5)(n+4)!), so the simplified form is (n+5). Cancel the adjacent factorial.
Step 2
Why this answer is correct
The correct answer is C. (n+5). ((n+5)!=(n+5)(n+4)!), so the simplified form is (n+5). Cancel the adjacent factorial.
Step 3
Exam Tip
((n+5)!=(n+5)(n+4)!), इसलिए सरल रूप (n+5) है। पास वाला क्रमगुणित काट दें।
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(4!+5!-3!) का मान क्या है?
What is the value of (4!+5!-3!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (132)
B (138)
C (144)
D (150)
Explanation opens after your attempt
Step 1
Concept
(4!=24), (5!=120), and (3!=6), so the value is (138). Write the factorial values first.
Step 2
Why this answer is correct
The correct answer is B. (138). (4!=24), (5!=120), and (3!=6), so the value is (138). Write the factorial values first.
Step 3
Exam Tip
(4!=24), (5!=120) और (3!=6), इसलिए मान (138) है। पहले क्रमगुणित मान लिखें।
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यदि (x=4!) और (y=3!), तो (xy) का मान क्या है?
If (x=4!) and (y=3!), what is the value of (xy)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (120)
B (132)
C (144)
D (156)
Explanation opens after your attempt
Step 1
Concept
(x=24) and (y=6), so (xy=144). Substitute the values of variables and then multiply.
Step 2
Why this answer is correct
The correct answer is C. (144). (x=24) and (y=6), so (xy=144). Substitute the values of variables and then multiply.
Step 3
Exam Tip
(x=24) और (y=6), इसलिए (xy=144) है। चर का मान रखने के बाद गुणा करें।
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\(\frac{8!}{3!,5!}\) का मान क्या है?
What is the value of \(\frac{8!}{3!,5!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (54)
B (56)
C (58)
D (60)
Explanation opens after your attempt
Step 1
Concept
\(\frac{8!}{3!,5!}=\frac{8\times7\times6}{6}=56\). Cancel each factorial carefully.
Step 2
Why this answer is correct
The correct answer is B. (56). \(\frac{8!}{3!,5!}=\frac{8\times7\times6}{6}=56\). Cancel each factorial carefully.
Step 3
Exam Tip
\(\frac{8!}{3!,5!}=\frac{8\times7\times6}{6}=56\)। हर फैक्टोरियल को सावधानी से काटें।
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(7!+0!) का मान क्या है?
What is the value of (7!+0!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5040)
B (5041)
C (5042)
D (5039)
Explanation opens after your attempt
Step 1
Concept
(7!=5040) and (0!=1), so the sum is (5041). Do not ignore the term with (0!).
Step 2
Why this answer is correct
The correct answer is B. (5041). (7!=5040) and (0!=1), so the sum is (5041). Do not ignore the term with (0!).
Step 3
Exam Tip
(7!=5040) और (0!=1), इसलिए योग (5041) है। (0!) वाले पद को न छोड़ें।
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\(11\times10\times9!\) किसके बराबर है?
\(11\times10\times9!\) is equal to which of the following?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (9!)
B (10!)
C (11!)
D (12!)
Explanation opens after your attempt
Step 1
Concept
\(11!=11\times10\times9!\), so the given form is (11!). Recognizing factorial expansion is the key point.
Step 2
Why this answer is correct
The correct answer is C. (11!). \(11!=11\times10\times9!\), so the given form is (11!). Recognizing factorial expansion is the key point.
Step 3
Exam Tip
\(11!=11\times10\times9!\), इसलिए दिया गया रूप (11!) है। क्रमगुणित विस्तार पहचानना मुख्य बात है।
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\(5!\times0!\) का मान क्या है?
What is the value of \(5!\times0!\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (0)
B (1)
C (120)
D (121)
Explanation opens after your attempt
Step 1
Concept
(5!=120) and (0!=1), so the product is (120). It is necessary to take (0!) as (1).
Step 2
Why this answer is correct
The correct answer is C. (120). (5!=120) and (0!=1), so the product is (120). It is necessary to take (0!) as (1).
Step 3
Exam Tip
(5!=120) और (0!=1), इसलिए गुणनफल (120) है। (0!) को (1) मानना जरूरी है।
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\(\frac{9!}{6!,3!}\) का मान क्या है?
What is the value of \(\frac{9!}{6!,3!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (72)
B (84)
C (96)
D (108)
Explanation opens after your attempt
Step 1
Concept
\(\frac{9!}{6!,3!}=\frac{9\times8\times7}{6}=84\). Breaking the larger factorial down to the smaller one is easy.
Step 2
Why this answer is correct
The correct answer is B. (84). \(\frac{9!}{6!,3!}=\frac{9\times8\times7}{6}=84\). Breaking the larger factorial down to the smaller one is easy.
Step 3
Exam Tip
\(\frac{9!}{6!,3!}=\frac{9\times8\times7}{6}=84\)। बड़े क्रमगुणित को छोटे तक तोड़ना आसान है।
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यदि (n=5), तो ((n-2)!) का मान क्या है?
If (n=5), what is the value of ((n-2)!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (2)
B (4)
C (6)
D (24)
Explanation opens after your attempt
Step 1
Concept
(n-2=3), so ((n-2)!=3!=6). First evaluate the bracket.
Step 2
Why this answer is correct
The correct answer is C. (6). (n-2=3), so ((n-2)!=3!=6). First evaluate the bracket.
Step 3
Exam Tip
(n-2=3), इसलिए ((n-2)!=3!=6)। पहले कोष्ठक का मान निकालें।
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\(\frac{10!}{7!}\) का मान क्या है?
What is the value of \(\frac{10!}{7!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (540)
B (720)
C (840)
D (900)
Explanation opens after your attempt
Step 1
Concept
\(\frac{10!}{7!}=10\times9\times8=720\). Cancel the smaller factorial and multiply only the remaining factors.
Step 2
Why this answer is correct
The correct answer is B. (720). \(\frac{10!}{7!}=10\times9\times8=720\). Cancel the smaller factorial and multiply only the remaining factors.
Step 3
Exam Tip
\(\frac{10!}{7!}=10\times9\times8=720\)। छोटे क्रमगुणित को काटकर केवल बचे गुणकों को गुणा करें।
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(2!+6!) का मान क्या है?
What is the value of (2!+6!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (722)
B (720)
C (724)
D (726)
Explanation opens after your attempt
Step 1
Concept
(2!=2) and (6!=720), so the sum is (722). Find each factorial value before adding.
Step 2
Why this answer is correct
The correct answer is A. (722). (2!=2) and (6!=720), so the sum is (722). Find each factorial value before adding.
Step 3
Exam Tip
(2!=2) और (6!=720), इसलिए योग (722) है। जोड़ने से पहले हर क्रमगुणित का मान निकालें।
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(6!) को (4!) की सहायता से कैसे लिखा जाएगा?
How will (6!) be written using (4!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A \(6\times4!\)
B \(5\times4!\)
C \(6\times5\times4!\)
D (6+5+4!)
Explanation opens after your attempt
Correct Answer
C. \(6\times5\times4!\)
Step 1
Concept
\(6!=6\times5\times4!\). Expand the factorial down to a smaller factorial.
Step 2
Why this answer is correct
The correct answer is C. \(6\times5\times4!\). \(6!=6\times5\times4!\). Expand the factorial down to a smaller factorial.
Step 3
Exam Tip
\(6!=6\times5\times4!\) होता है। क्रमगुणित को छोटे क्रमगुणित तक फैलाएं।
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\(\frac{12!}{11!}\) का सरल मान क्या है?
What is the simplified value of \(\frac{12!}{11!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (11)
B (12)
C (132)
D (23)
Explanation opens after your attempt
Step 1
Concept
\(12!=12\times11!\), so division leaves (12). Consecutive factorials cancel directly.
Step 2
Why this answer is correct
The correct answer is B. (12). \(12!=12\times11!\), so division leaves (12). Consecutive factorials cancel directly.
Step 3
Exam Tip
\(12!=12\times11!\), इसलिए भाग देने पर (12) बचता है। पास-पास के क्रमगुणित सीधे कटते हैं।
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(8!) का मान क्या है?
What is the value of (8!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (5040)
B (40320)
C (362880)
D (720)
Explanation opens after your attempt
Correct Answer
B. (40320)
Step 1
Concept
\(8!=8\times7!\) and (7!=5040), so the value is (40320). Find a larger factorial using the previous factorial.
Step 2
Why this answer is correct
The correct answer is B. (40320). \(8!=8\times7!\) and (7!=5040), so the value is (40320). Find a larger factorial using the previous factorial.
Step 3
Exam Tip
\(8!=8\times7!\) और (7!=5040), इसलिए मान (40320) है। बड़े क्रमगुणित को पिछले क्रमगुणित से निकालें।
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\(12\times11\times10!\) किसके बराबर है?
\(12\times11\times10!\) is equal to which of the following?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (10!)
B (11!)
C (12!)
D (13!)
Explanation opens after your attempt
Step 1
Concept
\(12!=12\times11\times10!\), so the given form is (12!). Recognize factorial expansion down to a smaller factorial.
Step 2
Why this answer is correct
The correct answer is C. (12!). \(12!=12\times11\times10!\), so the given form is (12!). Recognize factorial expansion down to a smaller factorial.
Step 3
Exam Tip
\(12!=12\times11\times10!\), इसलिए दिया गया रूप (12!) है। क्रमगुणित विस्तार को छोटे क्रमगुणित तक पहचानें।
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(7!) को (5!) की सहायता से कैसे लिखेंगे?
How can (7!) be written using (5!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A \(7\times5!\)
B \(6\times5!\)
C (7+6+5!)
D \(7\times6\times5!\)
Explanation opens after your attempt
Correct Answer
D. \(7\times6\times5!\)
Step 1
Concept
\(7!=7\times6\times5!\). Expand the larger factorial down to the smaller factorial.
Step 2
Why this answer is correct
The correct answer is D. \(7\times6\times5!\). \(7!=7\times6\times5!\). Expand the larger factorial down to the smaller factorial.
Step 3
Exam Tip
\(7!=7\times6\times5!\) होता है। बड़े क्रमगुणित को छोटे क्रमगुणित तक विस्तार करें।
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(2!+5!) का मान क्या है?
What is the value of (2!+5!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (120)
B (121)
C (122)
D (124)
Explanation opens after your attempt
Step 1
Concept
(2!=2) and (5!=120), so the sum is (122). Do not forget the smaller factorial while adding.
Step 2
Why this answer is correct
The correct answer is C. (122). (2!=2) and (5!=120), so the sum is (122). Do not forget the smaller factorial while adding.
Step 3
Exam Tip
(2!=2) और (5!=120), इसलिए योग (122) है। जोड़ते समय छोटे क्रमगुणित को न भूलें।
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\(\frac{5!}{2!,3!}\) का मान क्या है?
What is the value of \(\frac{5!}{2!,3!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\). Keep the correct value of each factorial.
Step 2
Why this answer is correct
The correct answer is C. (10). \(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\). Keep the correct value of each factorial.
Step 3
Exam Tip
\(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\)। हर क्रमगुणित का सही मान रखें।
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\(9\times8!\) किसके बराबर है?
\(9\times8!\) is equal to which of the following?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (7!)
B (8!)
C (9!)
D (10!)
Explanation opens after your attempt
Step 1
Concept
\(9!=9\times8!\), so the given form is (9!). This is a basic factorial identity.
Step 2
Why this answer is correct
The correct answer is C. (9!). \(9!=9\times8!\), so the given form is (9!). This is a basic factorial identity.
Step 3
Exam Tip
\(9!=9\times8!\), इसलिए दिया गया रूप (9!) है। यह क्रमगुणित की मूल पहचान है।
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\(4!\div2!\) और (3!) का योग क्या है?
What is the sum of \(4!\div2!\) and (3!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (16)
B (18)
C (20)
D (24)
Explanation opens after your attempt
Step 1
Concept
\(4!\div2!=12\) and (3!=6), so the sum is (18). Simplify the division and factorial separately.
Step 2
Why this answer is correct
The correct answer is B. (18). \(4!\div2!=12\) and (3!=6), so the sum is (18). Simplify the division and factorial separately.
Step 3
Exam Tip
\(4!\div2!=12\) और (3!=6), इसलिए योग (18) है। भाग और क्रमगुणित दोनों को अलग-अलग सरल करें।
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(\frac{(n+4)!}{(n+3)!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+4)!}{(n+3)!})?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (n+2)
B (n+3)
C (n+4)
D (1)
Explanation opens after your attempt
Step 1
Concept
((n+4)!=(n+4)(n+3)!), so the simplified form is (n+4). Cancel the adjacent factorial part.
Step 2
Why this answer is correct
The correct answer is C. (n+4). ((n+4)!=(n+4)(n+3)!), so the simplified form is (n+4). Cancel the adjacent factorial part.
Step 3
Exam Tip
((n+4)!=(n+4)(n+3)!), इसलिए सरल रूप (n+4) है। क्रमगुणित में पास वाला भाग काटें।
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(6!+0!-1!) का मान क्या है?
What is the value of (6!+0!-1!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (718)
B (719)
C (720)
D (721)
Explanation opens after your attempt
Step 1
Concept
(6!=720), (0!=1), and (1!=1), so the value is (720). (0!) and (1!) are equal.
Step 2
Why this answer is correct
The correct answer is C. (720). (6!=720), (0!=1), and (1!=1), so the value is (720). (0!) and (1!) are equal.
Step 3
Exam Tip
(6!=720), (0!=1) और (1!=1), इसलिए मान (720) है। (0!) और (1!) दोनों बराबर हैं।
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\(\frac{11!}{10!}\) का मान क्या है?
What is the value of \(\frac{11!}{10!}\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (10)
B (11)
C (21)
D (110)
Explanation opens after your attempt
Step 1
Concept
\(\frac{11!}{10!}=11\) because \(11!=11\times10!\). Consecutive factorials cancel easily.
Step 2
Why this answer is correct
The correct answer is B. (11). \(\frac{11!}{10!}=11\) because \(11!=11\times10!\). Consecutive factorials cancel easily.
Step 3
Exam Tip
\(\frac{11!}{10!}=11\) क्योंकि \(11!=11\times10!\)। लगातार क्रमगुणित आसानी से कटते हैं।
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(5!) को (3!) की सहायता से कैसे लिखेंगे?
How can (5!) be written using (3!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A \(5\times4\times3!\)
B \(5\times3!\)
C \(4\times3!\)
D (5+4+3!)
Explanation opens after your attempt
Correct Answer
A. \(5\times4\times3!\)
Step 1
Concept
\(5!=5\times4\times3!\). It is correct to stop the expansion and write a smaller factorial.
Step 2
Why this answer is correct
The correct answer is A. \(5\times4\times3!\). \(5!=5\times4\times3!\). It is correct to stop the expansion and write a smaller factorial.
Step 3
Exam Tip
\(5!=5\times4\times3!\) होता है। बीच में रुककर छोटा क्रमगुणित लिखना सही है।
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((4-2)!) का मान क्या है?
What is the value of ((4-2)!)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (1)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
First (4-2=2), then (2!=2). Solve the bracket first.
Step 2
Why this answer is correct
The correct answer is B. (2). First (4-2=2), then (2!=2). Solve the bracket first.
Step 3
Exam Tip
पहले (4-2=2), फिर (2!=2)। कोष्ठक को पहले हल करें।
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यदि (x=5!) और (y=4!), तो (x-y) का मान क्या है?
If (x=5!) and (y=4!), what is the value of (x-y)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (96)
B (100)
C (108)
D (120)
Explanation opens after your attempt
Step 1
Concept
(x=120) and (y=24), so (x-y=96). Replace variables by their factorial values first.
Step 2
Why this answer is correct
The correct answer is A. (96). (x=120) and (y=24), so (x-y=96). Replace variables by their factorial values first.
Step 3
Exam Tip
(x=120) और (y=24), इसलिए (x-y=96)। चर को पहले उनके क्रमगुणित मान से बदलें।
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