\(\frac{(n+2)!}{(n+1)!}\times\frac{(n+1)!}{n!}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{(n+2)!}{(n+1)!}\times\frac{(n+1)!}{n!}\)?
Explanation opens after your attempt
Correct Answer
B. ((n+2)(n+1))
Step 1
Concept
The first ratio is (n+2) and the second is (n+1). The product is ((n+2)(n+1)).
Step 2
Why this answer is correct
The correct answer is B. ((n+2)(n+1)). The first ratio is (n+2) and the second is (n+1). The product is ((n+2)(n+1)).
Step 3
Exam Tip
पहला अनुपात (n+2) और दूसरा (n+1) है। गुणनफल ((n+2)(n+1)) होगा।
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\(\frac{7!}{5!}+\frac{5!}{2!,3!}+1!\) का मान क्या है?
What is the value of \(\frac{7!}{5!}+\frac{5!}{2!,3!}+1!\)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\), and (1!=1). The total is (53).
Step 2
Why this answer is correct
The correct answer is C. (53). \(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\), and (1!=1). The total is (53).
Step 3
Exam Tip
\(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\) और (1!=1)। कुल (53) है।
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यदि (\frac{(n+4)!}{(n+2)!}=132), तो (n) का मान क्या है?
If (\frac{(n+4)!}{(n+2)!}=132), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+4)!}{(n+2)!}=(n+4)(n+3)). Since \(12\times11=132\), (n=8).
Step 2
Why this answer is correct
The correct answer is B. (8). (\frac{(n+4)!}{(n+2)!}=(n+4)(n+3)). Since \(12\times11=132\), (n=8).
Step 3
Exam Tip
(\frac{(n+4)!}{(n+2)!}=(n+4)(n+3))। \(12\times11=132\), इसलिए (n=8) है।
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(\frac{(n+5)!}{(n+2)!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+5)!}{(n+2)!})?
Explanation opens after your attempt
Correct Answer
B. ((n+5)(n+4)(n+3))
Step 1
Concept
((n+5)!=(n+5)(n+4)(n+3)(n+2)!). Therefore three factors remain.
Step 2
Why this answer is correct
The correct answer is B. ((n+5)(n+4)(n+3)). ((n+5)!=(n+5)(n+4)(n+3)(n+2)!). Therefore three factors remain.
Step 3
Exam Tip
((n+5)!=(n+5)(n+4)(n+3)(n+2)!)। इसलिए तीन गुणक बचते हैं।
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\(\frac{11!}{8!,3!}-\frac{9!}{7!,2!}\) का मान क्या है?
What is the value of \(\frac{11!}{8!,3!}-\frac{9!}{7!,2!}\)?
Explanation opens after your attempt
Step 1
Concept
The first term is (165) and the second is (36). The difference is (129).
Step 2
Why this answer is correct
The correct answer is C. (129). The first term is (165) and the second is (36). The difference is (129).
Step 3
Exam Tip
पहला पद (165) और दूसरा (36) है। अंतर (129) मिलेगा।
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\(4!\times\frac{6!}{5!}-3!\) का मान क्या है?
What is the value of \(4!\times\frac{6!}{5!}-3!\)?
Explanation opens after your attempt
Step 1
Concept
(4!=24), \(\frac{6!}{5!}=6\), and (3!=6). Hence \(24\times6-6=138\).
Step 2
Why this answer is correct
The correct answer is C. (138). (4!=24), \(\frac{6!}{5!}=6\), and (3!=6). Hence \(24\times6-6=138\).
Step 3
Exam Tip
(4!=24), \(\frac{6!}{5!}=6\) और (3!=6)। इसलिए \(24\times6-6=138\) है।
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\(\frac{10!-8!}{8!}\) का मान क्या है?
What is the value of \(\frac{10!-8!}{8!}\)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{10!}{8!}=90\) and \(\frac{8!}{8!}=1\). Therefore the value is (90-1=89).
Step 2
Why this answer is correct
The correct answer is C. (89). \(\frac{10!}{8!}=90\) and \(\frac{8!}{8!}=1\). Therefore the value is (90-1=89).
Step 3
Exam Tip
\(\frac{10!}{8!}=90\) और \(\frac{8!}{8!}=1\)। इसलिए मान (90-1=89) है।
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(\frac{(n+3)!+(n+2)!}{(n+2)!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+3)!+(n+2)!}{(n+2)!})?
Explanation opens after your attempt
Step 1
Concept
The numerator is ((n+2)![(n+3)+1]). Therefore the simplified form is (n+4).
Step 2
Why this answer is correct
The correct answer is C. (n+4). The numerator is ((n+2)![(n+3)+1]). Therefore the simplified form is (n+4).
Step 3
Exam Tip
अंश ((n+2)![(n+3)+1]) है। इसलिए सरल रूप (n+4) है।
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\(\frac{\frac{12!}{9!,3!}}{\frac{5!}{3!,2!}}\) का मान क्या है?
What is the value of \(\frac{\frac{12!}{9!,3!}}{\frac{5!}{3!,2!}}\)?
Explanation opens after your attempt
Step 1
Concept
The numerator term is (220) and the denominator term is (10). Dividing gives (22).
Step 2
Why this answer is correct
The correct answer is C. (22). The numerator term is (220) and the denominator term is (10). Dividing gives (22).
Step 3
Exam Tip
ऊपर का पद (220) और नीचे का पद (10) है। भाग देने पर (22) मिलता है।
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यदि (\frac{(n+1)!}{(n-2)!}=60), तो (n) का मान क्या है?
If (\frac{(n+1)!}{(n-2)!}=60), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1)). Since \(5\times4\times3=60\), (n=4).
Step 2
Why this answer is correct
The correct answer is B. (4). (\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1)). Since \(5\times4\times3=60\), (n=4).
Step 3
Exam Tip
(\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1))। \(5\times4\times3=60\), इसलिए (n=4) है।
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यदि \(a=\frac{7!-5!}{5!}\), तो (a) का मान क्या है?
If \(a=\frac{7!-5!}{5!}\), what is the value of (a)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{7!}{5!}=42\) and \(\frac{5!}{5!}=1\). Therefore (a=42-1=41).
Step 2
Why this answer is correct
The correct answer is B. (41). \(\frac{7!}{5!}=42\) and \(\frac{5!}{5!}=1\). Therefore (a=42-1=41).
Step 3
Exam Tip
\(\frac{7!}{5!}=42\) और \(\frac{5!}{5!}=1\)। इसलिए (a=42-1=41) है।
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(\frac{\frac{(n+4)!}{n!}}{\frac{(n+2)!}{n!}}) का सरल रूप क्या है?
What is the simplified form of (\frac{\frac{(n+4)!}{n!}}{\frac{(n+2)!}{n!}})?
Explanation opens after your attempt
Correct Answer
B. ((n+4)(n+3))
Step 1
Concept
This division becomes (\frac{(n+4)!}{(n+2)!}). Hence the simplified form is ((n+4)(n+3)).
Step 2
Why this answer is correct
The correct answer is B. ((n+4)(n+3)). This division becomes (\frac{(n+4)!}{(n+2)!}). Hence the simplified form is ((n+4)(n+3)).
Step 3
Exam Tip
यह भाग (\frac{(n+4)!}{(n+2)!}) बन जाता है। इसलिए सरल रूप ((n+4)(n+3)) है।
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\(\frac{6!}{3!,3!}+\frac{7!}{5!,2!}\) का मान क्या है?
What is the value of \(\frac{6!}{3!,3!}+\frac{7!}{5!,2!}\)?
Explanation opens after your attempt
Step 1
Concept
The first term is (20) and the second is (21). Their sum is (41).
Step 2
Why this answer is correct
The correct answer is C. (41). The first term is (20) and the second is (21). Their sum is (41).
Step 3
Exam Tip
पहला पद (20) और दूसरा (21) है। दोनों का योग (41) होगा।
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\(\frac{9!+8!}{7!}\) का मान क्या है?
What is the value of \(\frac{9!+8!}{7!}\)?
Explanation opens after your attempt
Step 1
Concept
The numerator can be written as (8!(9+1)). Thus \(\frac{10\cdot8!}{7!}=10\times8=80\).
Step 2
Why this answer is correct
The correct answer is B. (80). The numerator can be written as (8!(9+1)). Thus \(\frac{10\cdot8!}{7!}=10\times8=80\).
Step 3
Exam Tip
अंश को (8!(9+1)) लिखा जा सकता है। \(\frac{10\cdot8!}{7!}=10\times8=80\) है।
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यदि (\frac{n!}{(n-3)!}=210), तो (n) का मान क्या है?
If (\frac{n!}{(n-3)!}=210), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
(\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(7\times6\times5=210\), (n=7).
Step 2
Why this answer is correct
The correct answer is B. (7). (\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(7\times6\times5=210\), (n=7).
Step 3
Exam Tip
(\frac{n!}{(n-3)!}=n(n-1)(n-2))। \(7\times6\times5=210\), इसलिए (n=7) है।
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\(\frac{n!}{(n-1)!}\times\frac{(n+1)!}{n!}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{n!}{(n-1)!}\times\frac{(n+1)!}{n!}\)?
Explanation opens after your attempt
Correct Answer
C. (n(n+1))
Step 1
Concept
The first ratio is (n) and the second is (n+1). Therefore the product is (n(n+1)).
Step 2
Why this answer is correct
The correct answer is C. (n(n+1)). The first ratio is (n) and the second is (n+1). Therefore the product is (n(n+1)).
Step 3
Exam Tip
पहला अनुपात (n) और दूसरा (n+1) है। इसलिए गुणनफल (n(n+1)) है।
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\(\frac{10!}{8!}+\frac{7!}{6!}+0!\) का मान क्या है?
What is the value of \(\frac{10!}{8!}+\frac{7!}{6!}+0!\)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\), and (0!=1). The total is (98).
Step 2
Why this answer is correct
The correct answer is C. (98). \(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\), and (0!=1). The total is (98).
Step 3
Exam Tip
\(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\) और (0!=1)। कुल (98) है।
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(\frac{(n+2)!-n!}{n!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+2)!-n!}{n!})?
Explanation opens after your attempt
Correct Answer
B. \(n^2+3n+1\)
Step 1
Concept
(\frac{(n+2)!}{n!}=(n+2)(n+1)), then (1) is subtracted. The simplified form is \(n^2+3n+1\).
Step 2
Why this answer is correct
The correct answer is B. \(n^2+3n+1\). (\frac{(n+2)!}{n!}=(n+2)(n+1)), then (1) is subtracted. The simplified form is \(n^2+3n+1\).
Step 3
Exam Tip
(\frac{(n+2)!}{n!}=(n+2)(n+1)), फिर (1) घटेगा। सरल रूप \(n^2+3n+1\) है।
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\(\frac{13!}{11!,2!}-\frac{6!}{4!,2!}\) का मान क्या है?
What is the value of \(\frac{13!}{11!,2!}-\frac{6!}{4!,2!}\)?
Explanation opens after your attempt
Step 1
Concept
The first term is (78) and the second term is (15). The difference is (78-15=63).
Step 2
Why this answer is correct
The correct answer is C. (63). The first term is (78) and the second term is (15). The difference is (78-15=63).
Step 3
Exam Tip
पहला पद (78) और दूसरा पद (15) है। अंतर (78-15=63) है।
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यदि (\frac{(n+3)!}{(n+1)!}=90), तो (n) का मान क्या है?
If (\frac{(n+3)!}{(n+1)!}=90), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(10\times9=90\), (n=7).
Step 2
Why this answer is correct
The correct answer is B. (7). (\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(10\times9=90\), (n=7).
Step 3
Exam Tip
(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2))। \(10\times9=90\), इसलिए (n=7) है।
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(\frac{(n+5)!}{(n+2)!}) में कितने क्रमागत गुणक बचते हैं?
How many consecutive factors remain in (\frac{(n+5)!}{(n+2)!})?
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3)). Therefore three consecutive factors remain.
Step 2
Why this answer is correct
The correct answer is B. (3). (\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3)). Therefore three consecutive factors remain.
Step 3
Exam Tip
(\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3))। इसलिए तीन क्रमागत गुणक बचते हैं।
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\(\frac{8!}{5!}+\frac{6!}{4!}-4!\) का मान क्या है?
What is the value of \(\frac{8!}{5!}+\frac{6!}{4!}-4!\)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\), and (4!=24). Thus (336+30-24=342).
Step 2
Why this answer is correct
The correct answer is D. (342). \(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\), and (4!=24). Thus (336+30-24=342).
Step 3
Exam Tip
\(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\) और (4!=24)। इसलिए (336+30-24=342) है।
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\(\frac{5!,3!}{2!,4!}\) का मान क्या है?
What is the value of \(\frac{5!,3!}{2!,4!}\)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{5!}{4!}=5\) and \(\frac{3!}{2!}=3\). Hence the value is \(5\times3=15\).
Step 2
Why this answer is correct
The correct answer is C. (15). \(\frac{5!}{4!}=5\) and \(\frac{3!}{2!}=3\). Hence the value is \(5\times3=15\).
Step 3
Exam Tip
\(\frac{5!}{4!}=5\) और \(\frac{3!}{2!}=3\)। इसलिए मान \(5\times3=15\) है।
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यदि (\frac{(n+1)!}{(n-1)!}=72), तो (n) का मान क्या है?
If (\frac{(n+1)!}{(n-1)!}=72), what is the value of (n)?
Explanation opens after your attempt
Step 1
Concept
The ratio equals (n(n+1)). Since \(8\times9=72\), (n=8).
Step 2
Why this answer is correct
The correct answer is C. (8). The ratio equals (n(n+1)). Since \(8\times9=72\), (n=8).
Step 3
Exam Tip
अनुपात (n(n+1)) के बराबर है। \(8\times9=72\), इसलिए (n=8) है।
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\(\frac{9!}{7!}\div\frac{6!}{5!}\) का मान क्या है?
What is the value of \(\frac{9!}{7!}\div\frac{6!}{5!}\)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{9!}{7!}=72\) and \(\frac{6!}{5!}=6\). Therefore the quotient is (12).
Step 2
Why this answer is correct
The correct answer is B. (12). \(\frac{9!}{7!}=72\) and \(\frac{6!}{5!}=6\). Therefore the quotient is (12).
Step 3
Exam Tip
\(\frac{9!}{7!}=72\) और \(\frac{6!}{5!}=6\)। इसलिए भागफल (12) है।
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\(\frac{11!-10!}{9!}\) का मान क्या है?
What is the value of \(\frac{11!-10!}{9!}\)?
Explanation opens after your attempt
Step 1
Concept
The numerator is (10!(11-1)=10\cdot10!). Thus \(\frac{10\cdot10!}{9!}=10\times10=100\).
Step 2
Why this answer is correct
The correct answer is C. (100). The numerator is (10!(11-1)=10\cdot10!). Thus \(\frac{10\cdot10!}{9!}=10\times10=100\).
Step 3
Exam Tip
अंश (10!(11-1)=10\cdot10!) है। \(\frac{10\cdot10!}{9!}=10\times10=100\) है।
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(\frac{(n+5)!}{(n+3)!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+5)!}{(n+3)!})?
Explanation opens after your attempt
Correct Answer
A. ((n+5)(n+4))
Step 1
Concept
((n+5)!=(n+5)(n+4)(n+3)!). Therefore the simplified form is ((n+5)(n+4)).
Step 2
Why this answer is correct
The correct answer is A. ((n+5)(n+4)). ((n+5)!=(n+5)(n+4)(n+3)!). Therefore the simplified form is ((n+5)(n+4)).
Step 3
Exam Tip
((n+5)!=(n+5)(n+4)(n+3)!)। इसलिए सरल रूप ((n+5)(n+4)) है।
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यदि \(x=\frac{8!}{6!}\) और \(y=\frac{5!}{3!}\), तो (x+y) का मान क्या है?
If \(x=\frac{8!}{6!}\) and \(y=\frac{5!}{3!}\), what is the value of (x+y)?
Explanation opens after your attempt
Step 1
Concept
\(x=8\times7=56\) and \(y=5\times4=20\). Therefore (x+y=76).
Step 2
Why this answer is correct
The correct answer is C. (76). \(x=8\times7=56\) and \(y=5\times4=20\). Therefore (x+y=76).
Step 3
Exam Tip
\(x=8\times7=56\) और \(y=5\times4=20\)। इसलिए (x+y=76) है।
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\(\frac{7!}{4!,3!}\times3!\) का मान क्या है?
What is the value of \(\frac{7!}{4!,3!}\times3!\)?
Explanation opens after your attempt
Step 1
Concept
\(\frac{7!}{4!,3!}=35\) and (3!=6). Therefore the product is \(35\times6=210\).
Step 2
Why this answer is correct
The correct answer is C. (210). \(\frac{7!}{4!,3!}=35\) and (3!=6). Therefore the product is \(35\times6=210\).
Step 3
Exam Tip
\(\frac{7!}{4!,3!}=35\) और (3!=6)। इसलिए गुणनफल \(35\times6=210\) है।
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(\frac{(n+1)!-n!}{(n-1)!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+1)!-n!}{(n-1)!})?
Explanation opens after your attempt
Correct Answer
A. \(n^2\)
Step 1
Concept
((n+1)!-n!=n!{(n+1)-1}=n\cdot n!). Dividing by ((n-1)!) gives \(n^2\).
Step 2
Why this answer is correct
The correct answer is A. \(n^2\). ((n+1)!-n!=n!{(n+1)-1}=n\cdot n!). Dividing by ((n-1)!) gives \(n^2\).
Step 3
Exam Tip
((n+1)!-n!=n!{(n+1)-1}=n\cdot n!)। ((n-1)!) से भाग देने पर \(n^2\) मिलता है।
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