\(\frac{9!}{5!,4!}\div\frac{6!}{4!,2!}\) का मान क्या है?
What is the value of \(\frac{9!}{5!,4!}\div\frac{6!}{4!,2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A \( \frac{21}{5}\)
B \( \frac{42}{5}\)
C \( \frac{28}{5}\)
D \( \frac{14}{5}\)
Explanation opens after your attempt
Correct Answer
B. \( \frac{42}{5}\)
Step 1
Concept
The first term is (126) and the second is (15). Thus \(\frac{126}{15}=\frac{42}{5}\).
Step 2
Why this answer is correct
The correct answer is B. \( \frac{42}{5}\). The first term is (126) and the second is (15). Thus \(\frac{126}{15}=\frac{42}{5}\).
Step 3
Exam Tip
पहला पद (126) और दूसरा (15) है। \(\frac{126}{15}=\frac{42}{5}\) मिलता है।
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\(\frac{8!}{7!}+\frac{7!}{6!}+\frac{6!}{5!}\) का मान क्या है?
What is the value of \(\frac{8!}{7!}+\frac{7!}{6!}+\frac{6!}{5!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (19)
B (20)
C (21)
D (22)
Explanation opens after your attempt
Step 1
Concept
The three terms are (8), (7), and (6) respectively. The sum is (8+7+6=21).
Step 2
Why this answer is correct
The correct answer is C. (21). The three terms are (8), (7), and (6) respectively. The sum is (8+7+6=21).
Step 3
Exam Tip
तीनों पद क्रमशः (8), (7) और (6) हैं। योग (8+7+6=21) है।
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\(\frac{5!,3!}{4!}\) का मान क्या है?
What is the value of \(\frac{5!,3!}{4!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (24)
B (30)
C (36)
D (42)
Explanation opens after your attempt
Step 1
Concept
\(\frac{5!}{4!}=5\) and (3!=6), so the value is (30). Simplify multiplication and division step by step.
Step 2
Why this answer is correct
The correct answer is B. (30). \(\frac{5!}{4!}=5\) and (3!=6), so the value is (30). Simplify multiplication and division step by step.
Step 3
Exam Tip
\(\frac{5!}{4!}=5\) और (3!=6), इसलिए मान (30) है। गुणन और भाग को क्रम से सरल करें।
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यदि (\frac{(n+3)!}{(n+1)!}=56), तो (n) का मान क्या है?
If (\frac{(n+3)!}{(n+1)!}=56), what is the value of (n)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(8\times7=56\), (n=5).
Step 2
Why this answer is correct
The correct answer is B. (5). (\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(8\times7=56\), (n=5).
Step 3
Exam Tip
(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2))। \(8\times7=56\), इसलिए (n=5)।
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(\frac{(n+2)!-(n+1)!}{n!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+2)!-(n+1)!}{n!})?
#factorial_notation
#permutations_combinations
#class_11
#medium
A ((n+1)2 )
B (n+2)
C ((n+1)n)
D (2n+1)
Explanation opens after your attempt
Correct Answer
A. ((n+1)2 )
Step 1
Concept
The numerator is ((n+1)![(n+2)-1]=(n+1)2 n!). After cancelling (n!), the result is ((n+1)2 ).
Step 2
Why this answer is correct
The correct answer is A. ((n+1)2 ). The numerator is ((n+1)![(n+2)-1]=(n+1)2 n!). After cancelling (n!), the result is ((n+1)2 ).
Step 3
Exam Tip
अंश ((n+1)![(n+2)-1]=(n+1)2 n!) है। (n!) कटने पर ((n+1)2 ) मिलता है।
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\(\frac{10!-9!}{8!}\) का मान क्या है?
What is the value of \(\frac{10!-9!}{8!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (72)
B (81)
C (90)
D (99)
Explanation opens after your attempt
Step 1
Concept
The numerator is (9!(10-1)=9\cdot9!). Thus \(\frac{9\cdot9!}{8!}=9\times9=81\).
Step 2
Why this answer is correct
The correct answer is B. (81). The numerator is (9!(10-1)=9\cdot9!). Thus \(\frac{9\cdot9!}{8!}=9\times9=81\).
Step 3
Exam Tip
अंश (9!(10-1)=9\cdot9!) है। \(\frac{9\cdot9!}{8!}=9\times9=81\) मिलता है।
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\(\frac{7!}{3!,4!}\times2!\) का मान क्या है?
What is the value of \(\frac{7!}{3!,4!}\times2!\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (35)
B (70)
C (105)
D (140)
Explanation opens after your attempt
Step 1
Concept
\(\frac{7!}{3!,4!}=35\) and (2!=2), so the product is (70). Simplify the fraction first.
Step 2
Why this answer is correct
The correct answer is B. (70). \(\frac{7!}{3!,4!}=35\) and (2!=2), so the product is (70). Simplify the fraction first.
Step 3
Exam Tip
\(\frac{7!}{3!,4!}=35\) और (2!=2), इसलिए गुणनफल (70) है। पहले भिन्न को सरल करें।
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\(\frac{6!}{2!,4!}+\frac{5!}{2!,3!}\) का मान क्या है?
What is the value of \(\frac{6!}{2!,4!}+\frac{5!}{2!,3!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (20)
B (25)
C (30)
D (35)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!}{2!,4!}=15\) and \(\frac{5!}{2!,3!}=10\), so the total is (25). Count the smaller terms separately.
Step 2
Why this answer is correct
The correct answer is B. (25). \(\frac{6!}{2!,4!}=15\) and \(\frac{5!}{2!,3!}=10\), so the total is (25). Count the smaller terms separately.
Step 3
Exam Tip
\(\frac{6!}{2!,4!}=15\) और \(\frac{5!}{2!,3!}=10\), इसलिए कुल (25) है। छोटे पदों को अलग-अलग गिनें।
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यदि (\frac{n!}{(n-1)!}+2=9), तो (n) का मान क्या है?
If (\frac{n!}{(n-1)!}+2=9), what is the value of (n)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(\frac{n!}{(n-1)!}=n), so (n+2=9). Therefore, (n=7).
Step 2
Why this answer is correct
The correct answer is C. (7). (\frac{n!}{(n-1)!}=n), so (n+2=9). Therefore, (n=7).
Step 3
Exam Tip
(\frac{n!}{(n-1)!}=n), इसलिए (n+2=9)। अतः (n=7) है।
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(\frac{(n+1)!-n!}{n!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+1)!-n!}{n!})?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (n-1)
B (n)
C (n+1)
D (1)
Explanation opens after your attempt
Step 1
Concept
Since ((n+1)!=(n+1)n!), the numerator is (n!{(n+1)-1}=nn!). Dividing gives (n).
Step 2
Why this answer is correct
The correct answer is B. (n). Since ((n+1)!=(n+1)n!), the numerator is (n!{(n+1)-1}=nn!). Dividing gives (n).
Step 3
Exam Tip
((n+1)!=(n+1)n!), इसलिए अंश (n!{(n+1)-1}=nn!) है। भाग देने पर (n) मिलता है।
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कौन सा रूप \(\frac{12!}{9!}\) के बराबर है?
Which expression is equal to \(\frac{12!}{9!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A \(12\times11\)
B \(12\times11\times10\)
C \(12\times10\times9\)
D \(11\times10\times9\)
Explanation opens after your attempt
Correct Answer
B. \(12\times11\times10\)
Step 1
Concept
\(\frac{12!}{9!}=12\times11\times10\). Since the denominator is (9!), the part up to (9!) cancels.
Step 2
Why this answer is correct
The correct answer is B. \(12\times11\times10\). \(\frac{12!}{9!}=12\times11\times10\). Since the denominator is (9!), the part up to (9!) cancels.
Step 3
Exam Tip
\(\frac{12!}{9!}=12\times11\times10\)। हर में (9!) होने से (9!) तक का भाग कट जाता है।
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\(\frac{11!}{9!,2!}\) का मान क्या है?
What is the value of \(\frac{11!}{9!,2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (45)
B (55)
C (66)
D (72)
Explanation opens after your attempt
Step 1
Concept
\(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\). Write the larger factorial up to (9!).
Step 2
Why this answer is correct
The correct answer is B. (55). \(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\). Write the larger factorial up to (9!).
Step 3
Exam Tip
\(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\)। बड़े फैक्टोरियल को (9!) तक लिखें।
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\(\frac{8!}{4!}-\frac{7!}{4!}\) का मान क्या है?
What is the value of \(\frac{8!}{4!}-\frac{7!}{4!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (1260)
B (1470)
C (1680)
D (2016)
Explanation opens after your attempt
Step 1
Concept
(\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470). With a common denominator, combine the numerator.
Step 2
Why this answer is correct
The correct answer is B. (1470). (\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470). With a common denominator, combine the numerator.
Step 3
Exam Tip
(\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470)। समान हर होने पर अंश मिलाकर देखें।
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\(\frac{5!+3!}{4!}\) का मान क्या है?
What is the value of \(\frac{5!+3!}{4!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (4)
B (5)
C \(\frac{21}{4}\)
D (6)
Explanation opens after your attempt
Correct Answer
C. \(\frac{21}{4}\)
Step 1
Concept
The numerator is (120+6=126) and (4!=24). Hence the value is \(\frac{126}{24}=\frac{21}{4}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{21}{4}\). The numerator is (120+6=126) and (4!=24). Hence the value is \(\frac{126}{24}=\frac{21}{4}\).
Step 3
Exam Tip
अंश (120+6=126) है और (4!=24)। इसलिए मान \(\frac{126}{24}=\frac{21}{4}\) है।
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\(\frac{9!}{6!,3!}-\frac{7!}{5!,2!}\) का मान क्या है?
What is the value of \(\frac{9!}{6!,3!}-\frac{7!}{5!,2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (63)
B (84)
C (21)
D (105)
Explanation opens after your attempt
Step 1
Concept
\(\frac{9!}{6!,3!}=84\) and \(\frac{7!}{5!,2!}=21\), so the difference is (63). Evaluate both combination-like terms separately.
Step 2
Why this answer is correct
The correct answer is A. (63). \(\frac{9!}{6!,3!}=84\) and \(\frac{7!}{5!,2!}=21\), so the difference is (63). Evaluate both combination-like terms separately.
Step 3
Exam Tip
\(\frac{9!}{6!,3!}=84\) और \(\frac{7!}{5!,2!}=21\), इसलिए अंतर (63) है। दोनों संयोजन-जैसे पद अलग निकालें।
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यदि (\frac{(n+2)!}{n!}=30), तो (n) का मान क्या है?
If (\frac{(n+2)!}{n!}=30), what is the value of (n)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(6\times5=30\), (n=4).
Step 2
Why this answer is correct
The correct answer is B. (4). (\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(6\times5=30\), (n=4).
Step 3
Exam Tip
(\frac{(n+2)!}{n!}=(n+2)(n+1))। \(6\times5=30\), इसलिए (n=4)।
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(\frac{(n+3)!}{n!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+3)!}{n!})?
#factorial_notation
#permutations_combinations
#class_11
#medium
A ((n+3)(n+2)(n+1))
B (n+3)
C ((n+3)(n+1))
D ((n+2)(n+1))
Explanation opens after your attempt
Correct Answer
A. ((n+3)(n+2)(n+1))
Step 1
Concept
((n+3)!=(n+3)(n+2)(n+1)n!), so (n!) cancels. Three consecutive factors remain.
Step 2
Why this answer is correct
The correct answer is A. ((n+3)(n+2)(n+1)). ((n+3)!=(n+3)(n+2)(n+1)n!), so (n!) cancels. Three consecutive factors remain.
Step 3
Exam Tip
((n+3)!=(n+3)(n+2)(n+1)n!), इसलिए (n!) कट जाता है। क्रम से तीन गुणक बचते हैं।
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\(\frac{7!-6!}{6!}\) का मान क्या है?
What is the value of \(\frac{7!-6!}{6!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
Since \(7!=7\times6!\), (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6). Take the common factorial out.
Step 2
Why this answer is correct
The correct answer is B. (6). Since \(7!=7\times6!\), (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6). Take the common factorial out.
Step 3
Exam Tip
\(7!=7\times6!\), इसलिए (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6)। समान फैक्टोरियल बाहर लें।
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\(\frac{10!}{8!}+\frac{4!}{2!}\) का मान क्या है?
What is the value of \(\frac{10!}{8!}+\frac{4!}{2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (90)
B (96)
C (102)
D (108)
Explanation opens after your attempt
Step 1
Concept
\(\frac{10!}{8!}=90\) and \(\frac{4!}{2!}=12\), so the sum is (102). Cancel common factorial parts.
Step 2
Why this answer is correct
The correct answer is C. (102). \(\frac{10!}{8!}=90\) and \(\frac{4!}{2!}=12\), so the sum is (102). Cancel common factorial parts.
Step 3
Exam Tip
\(\frac{10!}{8!}=90\) और \(\frac{4!}{2!}=12\), इसलिए योग (102) है। समान फैक्टोरियल भाग काटें।
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यदि (\frac{n!}{(n-2)!}=42), तो (n) का मान क्या है?
If (\frac{n!}{(n-2)!}=42), what is the value of (n)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(\frac{n!}{(n-2)!}=n(n-1)), so (n(n-1)=42). Since \(7\times6=42\), (n=7).
Step 2
Why this answer is correct
The correct answer is B. (7). (\frac{n!}{(n-2)!}=n(n-1)), so (n(n-1)=42). Since \(7\times6=42\), (n=7).
Step 3
Exam Tip
(\frac{n!}{(n-2)!}=n(n-1)), इसलिए (n(n-1)=42)। \(7\times6=42\), अतः (n=7)।
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\(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\) का मान क्या है?
What is the value of \(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (56)
B (65)
C (71)
D (84)
Explanation opens after your attempt
Step 1
Concept
\(\frac{8!}{5!,3!}=56\) and \(\frac{6!}{4!,2!}=15\), so the total is (71). Solve both terms separately.
Step 2
Why this answer is correct
The correct answer is C. (71). \(\frac{8!}{5!,3!}=56\) and \(\frac{6!}{4!,2!}=15\), so the total is (71). Solve both terms separately.
Step 3
Exam Tip
\(\frac{8!}{5!,3!}=56\) और \(\frac{6!}{4!,2!}=15\), इसलिए कुल (71) है। दोनों पदों को अलग हल करें।
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(\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!}) का सरल मान क्या है?
What is the simplified value of (\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!})?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (1)
B (2)
C (n)
D (n+2)
Explanation opens after your attempt
Step 1
Concept
The first ratio is (n+2) and the second is (n). The difference is ((n+2)-n=2).
Step 2
Why this answer is correct
The correct answer is B. (2). The first ratio is (n+2) and the second is (n). The difference is ((n+2)-n=2).
Step 3
Exam Tip
पहला अनुपात (n+2) और दूसरा (n) है। अंतर ((n+2)-n=2) होगा।
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\(\frac{5!}{3!}+\frac{5!}{4!}\) का मान क्या है?
What is the value of \(\frac{5!}{3!}+\frac{5!}{4!}\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (20)
B (25)
C (30)
D (35)
Explanation opens after your attempt
Step 1
Concept
\(\frac{5!}{3!}=20\) and \(\frac{5!}{4!}=5\), so the sum is (25). Simplify each ratio separately.
Step 2
Why this answer is correct
The correct answer is B. (25). \(\frac{5!}{3!}=20\) and \(\frac{5!}{4!}=5\), so the sum is (25). Simplify each ratio separately.
Step 3
Exam Tip
\(\frac{5!}{3!}=20\) और \(\frac{5!}{4!}=5\), इसलिए योग (25) है। हर अनुपात अलग-अलग सरल करें।
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\(\frac{6!}{3!}+4!\) का मान क्या है?
What is the value of \(\frac{6!}{3!}+4!\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (120)
B (132)
C (144)
D (156)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!}{3!}=120\) and (4!=24), so the total is (144). Simplify the fraction first.
Step 2
Why this answer is correct
The correct answer is C. (144). \(\frac{6!}{3!}=120\) and (4!=24), so the total is (144). Simplify the fraction first.
Step 3
Exam Tip
\(\frac{6!}{3!}=120\) और (4!=24), इसलिए कुल (144) है। पहले भिन्न को सरल करें।
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यदि ((n+1)!=720), तो (n) का मान क्या है?
If ((n+1)!=720), what is the value of (n)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Since (720=6!), (n+1=6) and (n=5). Remember small factorial values.
Step 2
Why this answer is correct
The correct answer is B. (5). Since (720=6!), (n+1=6) and (n=5). Remember small factorial values.
Step 3
Exam Tip
(720=6!), इसलिए (n+1=6) और (n=5)। छोटे फैक्टोरियल मान याद रखें।
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यदि (n=3), तो (\frac{(n+2)!}{n!}) का मान क्या होगा?
If (n=3), what will be the value of (\frac{(n+2)!}{n!})?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (10)
B (20)
C (30)
D (60)
Explanation opens after your attempt
Step 1
Concept
Putting (n=3), \(\frac{5!}{3!}=5\times4=20\). Substitute the variable first.
Step 2
Why this answer is correct
The correct answer is B. (20). Putting (n=3), \(\frac{5!}{3!}=5\times4=20\). Substitute the variable first.
Step 3
Exam Tip
(n=3) रखने पर \(\frac{5!}{3!}=5\times4=20\)। पहले चर का मान रखें।
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\(\frac{9!}{7!}-5!\) का मान क्या है?
What is the value of \(\frac{9!}{7!}-5!\)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (-48)
B (48)
C (72)
D (120)
Explanation opens after your attempt
Step 1
Concept
\(\frac{9!}{7!}=9\times8=72\) and (5!=120), so the value is (-48). Keep the sign carefully in subtraction.
Step 2
Why this answer is correct
The correct answer is A. (-48). \(\frac{9!}{7!}=9\times8=72\) and (5!=120), so the value is (-48). Keep the sign carefully in subtraction.
Step 3
Exam Tip
\(\frac{9!}{7!}=9\times8=72\) और (5!=120), इसलिए मान (-48) है। घटाव में चिह्न ध्यान से रखें।
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यदि (\frac{(n+1)!}{n!}=8), तो (n) का मान क्या है?
If (\frac{(n+1)!}{n!}=8), what is the value of (n)?
#factorial_notation
#permutations_combinations
#class_11
#medium
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+1)!}{n!}=n+1), so (n+1=8) and (n=7). Simplify the factorial ratio first.
Step 2
Why this answer is correct
The correct answer is B. (7). (\frac{(n+1)!}{n!}=n+1), so (n+1=8) and (n=7). Simplify the factorial ratio first.
Step 3
Exam Tip
(\frac{(n+1)!}{n!}=n+1), इसलिए (n+1=8) और (n=7)। पहले फैक्टोरियल अनुपात सरल करें।
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\(\frac{8!}{8}\) किसके बराबर है?
What is \(\frac{8!}{8}\) equal to?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (6!)
B (7!)
C (8!)
D (9!)
Explanation opens after your attempt
Step 1
Concept
\(8!=8\times7!\), so \(\frac{8!}{8}=7!\). Cancel the common factor to get the answer.
Step 2
Why this answer is correct
The correct answer is B. (7!). \(8!=8\times7!\), so \(\frac{8!}{8}=7!\). Cancel the common factor to get the answer.
Step 3
Exam Tip
\(8!=8\times7!\), इसलिए \(\frac{8!}{8}=7!\) है। सामान्य गुणक काटकर उत्तर मिल जाता है।
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\(3!+4!\times0!\) का मान क्या है?
What is the value of \(3!+4!\times0!\)?
#factorial_notation
#permutations_combinations
#class_11
#easy
A (30)
B (24)
C (31)
D (29)
Explanation opens after your attempt
Step 1
Concept
(0!=1), so \(4!\times0!=24\) and (3!+24=30). Do multiplication before addition.
Step 2
Why this answer is correct
The correct answer is A. (30). (0!=1), so \(4!\times0!=24\) and (3!+24=30). Do multiplication before addition.
Step 3
Exam Tip
(0!=1), इसलिए \(4!\times0!=24\) और (3!+24=30)। गुणा को जोड़ से पहले करें।
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