यदि (\frac{n!+(n-1)!}{(n-1)!}=9) हो, तो (n) का मान क्या है?
If (\frac{n!+(n-1)!}{(n-1)!}=9), what is the value of (n)?
#factorial notation
#class 11
#medium
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The simplified form of the fraction is (n+1), so (n+1=9) gives (n=8). First take the common factorial.
Step 2
Why this answer is correct
The correct answer is C. (8). The simplified form of the fraction is (n+1), so (n+1=9) gives (n=8). First take the common factorial.
Step 3
Exam Tip
भिन्न का सरल रूप (n+1) है, इसलिए (n+1=9) से (n=8)। पहले सामान्य फैक्टोरियल निकालें।
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यदि (\frac{(m+2)!}{m!}=90) हो, तो (m) का मान क्या है?
If (\frac{(m+2)!}{m!}=90), what is the value of (m)?
#factorial notation
#factorial equation
#class 11
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(\frac{(m+2)!}{m!}=(m+2)(m+1)), so \(10\cdot9=90\) gives (m=8). Identify the product of consecutive numbers.
Step 2
Why this answer is correct
The correct answer is C. (8). (\frac{(m+2)!}{m!}=(m+2)(m+1)), so \(10\cdot9=90\) gives (m=8). Identify the product of consecutive numbers.
Step 3
Exam Tip
(\frac{(m+2)!}{m!}=(m+2)(m+1)), इसलिए \(10\cdot9=90\) से (m=8)। लगातार संख्याओं का गुणनफल पहचानें।
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(8!) को (6!) के रूप में लिखने पर सही रूप कौन सा है?
Which is the correct form of (8!) in terms of (6!)?
#factorial notation
#simplification
#class 11
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A \(8\cdot7\cdot6!\)
B \(8\cdot6!\)
C \(7\cdot6!\)
D (8+7+6!)
Explanation opens after your attempt
Correct Answer
A. \(8\cdot7\cdot6!\)
Step 1
Concept
\(8!=8\cdot7\cdot6!\). Breaking a larger factorial down to a smaller factorial is useful.
Step 2
Why this answer is correct
The correct answer is A. \(8\cdot7\cdot6!\). \(8!=8\cdot7\cdot6!\). Breaking a larger factorial down to a smaller factorial is useful.
Step 3
Exam Tip
\(8!=8\cdot7\cdot6!\) होता है। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक तोड़ना उपयोगी है।
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\(\frac{14!}{12!\cdot2!}\) का मान क्या है?
What is the value of \(\frac{14!}{12!\cdot2!}\)?
#factorial notation
#simplification
#class 11
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A (78)
B (84)
C (91)
D (96)
Explanation opens after your attempt
Step 1
Concept
\(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\). Expand the larger factorial only up to the smaller factorial.
Step 2
Why this answer is correct
The correct answer is C. (91). \(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\). Expand the larger factorial only up to the smaller factorial.
Step 3
Exam Tip
\(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\) होता है। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक ही फैलाएं।
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\(\frac{8!}{4!\cdot2!\cdot2!}\) का मान क्या है?
What is the value of \(\frac{8!}{4!\cdot2!\cdot2!}\)?
#factorial notation
#calculation
#class 11
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A (420)
B (360)
C (280)
D (210)
Explanation opens after your attempt
Step 1
Concept
\(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\). Cancel (4!) first and calculate with smaller factors.
Step 2
Why this answer is correct
The correct answer is A. (420). \(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\). Cancel (4!) first and calculate with smaller factors.
Step 3
Exam Tip
\(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\) होता है। पहले (4!) काटकर छोटे पदों में गणना करें।
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सबसे छोटा प्राकृतिक (k) क्या है जिसके लिए (k!), (72) से विभाज्य हो?
What is the least natural (k) for which (k!) is divisible by (72)?
#factorial notation
#divisibility
#class 11
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(72=2^3\cdot3^2\), and (6!) contains these factors. In such questions, use prime factorization of the number.
Step 2
Why this answer is correct
The correct answer is C. (6). \(72=2^3\cdot3^2\), and (6!) contains these factors. In such questions, use prime factorization of the number.
Step 3
Exam Tip
\(72=2^3\cdot3^2\) है और (6!) में ये गुणनखंड मिल जाते हैं। ऐसे प्रश्नों में संख्या का अभाज्य गुणनखंडन करें।
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\(\frac{10!}{8!\cdot2!}\) का मान क्या होगा?
What is the value of \(\frac{10!}{8!\cdot2!}\)?
#factorial notation
#calculation
#class 11
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A (45)
B (55)
C (90)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\). Cancel (8!) first.
Step 2
Why this answer is correct
The correct answer is A. (45). \(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\). Cancel (8!) first.
Step 3
Exam Tip
\(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\) होता है। पहले (8!) को काटें।
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\(\frac{15!}{13!}-5!\) का मान क्या है?
What is the value of \(\frac{15!}{13!}-5!\)?
#factorial notation
#subtraction
#class 11
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A (84)
B (90)
C (96)
D (100)
Explanation opens after your attempt
Step 1
Concept
\(\frac{15!}{13!}=15\cdot14=210\) and (5!=120), so the difference is (90). Simplify the factorial ratio first.
Step 2
Why this answer is correct
The correct answer is B. (90). \(\frac{15!}{13!}=15\cdot14=210\) and (5!=120), so the difference is (90). Simplify the factorial ratio first.
Step 3
Exam Tip
\(\frac{15!}{13!}=15\cdot14=210\) और (5!=120), इसलिए अंतर (90) है। पहले फैक्टोरियल अनुपात को सरल करें।
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(\frac{(n+2)!}{n!}) का सही सरल रूप कौन सा है?
Which is the correct simplified form of (\frac{(n+2)!}{n!})?
#factorial notation
#algebraic simplification
#class 11
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A (n+2)
B (2n+2)
C ((n+2)(n+1))
D (n(n+2))
Explanation opens after your attempt
Correct Answer
C. ((n+2)(n+1))
Step 1
Concept
((n+2)!=(n+2)(n+1)n!). After canceling (n!), ((n+2)(n+1)) remains.
Step 2
Why this answer is correct
The correct answer is C. ((n+2)(n+1)). ((n+2)!=(n+2)(n+1)n!). After canceling (n!), ((n+2)(n+1)) remains.
Step 3
Exam Tip
((n+2)!=(n+2)(n+1)n!) होता है। (n!) कटने पर ((n+2)(n+1)) बचता है।
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\(\frac{11!}{8!\cdot3!}\) का मान क्या है?
What is the value of \(\frac{11!}{8!\cdot3!}\)?
#factorial notation
#calculation
#class 11
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A (145)
B (155)
C (165)
D (175)
Explanation opens after your attempt
Step 1
Concept
\(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\). Do not forget that (3!=6).
Step 2
Why this answer is correct
The correct answer is C. (165). \(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\). Do not forget that (3!=6).
Step 3
Exam Tip
\(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\) होता है। (3!) को (6) मानना न भूलें।
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यदि (\frac{(n+1)!}{(n-1)!}=30) हो, तो (n) का मान क्या है?
If (\frac{(n+1)!}{(n-1)!}=30), what is the value of (n)?
#factorial equation
#class 11
#medium
50 50-50 2 wrong hide
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+1)!}{(n-1)!}=n(n+1)), so (n(n+1)=30) gives (n=5). Reduce factorials first in such questions.
Step 2
Why this answer is correct
The correct answer is B. (5). (\frac{(n+1)!}{(n-1)!}=n(n+1)), so (n(n+1)=30) gives (n=5). Reduce factorials first in such questions.
Step 3
Exam Tip
(\frac{(n+1)!}{(n-1)!}=n(n+1)), इसलिए (n(n+1)=30) से (n=5)। ऐसे प्रश्नों में पहले फैक्टोरियल घटाएं।
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\(\frac{11!}{9!}\) और \(\frac{8!}{6!}\) के मानों का अंतर क्या है?
What is the difference between the values of \(\frac{11!}{9!}\) and \(\frac{8!}{6!}\)?
#factorial notation
#difference
#class 11
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A (54)
B (56)
C (62)
D (74)
Explanation opens after your attempt
Step 1
Concept
\(\frac{11!}{9!}=110\) and \(\frac{8!}{6!}=56\), so the difference is (110-56=54). Do the subtraction carefully after simplification.
Step 2
Why this answer is correct
The correct answer is D. (74). \(\frac{11!}{9!}=110\) and \(\frac{8!}{6!}=56\), so the difference is (110-56=54). Do the subtraction carefully after simplification.
Step 3
Exam Tip
\(\frac{11!}{9!}=110\) और \(\frac{8!}{6!}=56\), इसलिए अंतर (54) नहीं बल्कि (110-56=54) है। गणना के बाद घटाव सावधानी से करें।
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\(\frac{7!+6!}{6!+5!}\) का मान क्या है?
What is the value of \(\frac{7!+6!}{6!+5!}\)?
#factorial notation
#ratio
#class 11
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The numerator is \(7!+6!=8\cdot6!\) and the denominator is \(6!+5!=7\cdot5!\), so careful direct calculation is needed. Substitute values to avoid mistakes.
Step 2
Why this answer is correct
The correct answer is B. (7). The numerator is \(7!+6!=8\cdot6!\) and the denominator is \(6!+5!=7\cdot5!\), so careful direct calculation is needed. Substitute values to avoid mistakes.
Step 3
Exam Tip
ऊपर \(7!+6!=8\cdot6!\) और नीचे \(6!+5!=7\cdot5!\) है, इसलिए मान \(8\cdot6!/7\cdot5!=48/7\) नहीं है। सीधे मान रखने पर सही गणना करें।
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\(\frac{18!}{16!\cdot2}\) का मान क्या है?
What is the value of \(\frac{18!}{16!\cdot2}\)?
#factorial notation
#cancellation
#class 11
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A (136)
B (144)
C (153)
D (162)
Explanation opens after your attempt
Step 1
Concept
\(\frac{18!}{16!\cdot2}=\frac{18\cdot17}{2}=153\). Cancel (16!) first and then divide.
Step 2
Why this answer is correct
The correct answer is C. (153). \(\frac{18!}{16!\cdot2}=\frac{18\cdot17}{2}=153\). Cancel (16!) first and then divide.
Step 3
Exam Tip
\(\frac{18!}{16!\cdot2}=\frac{18\cdot17}{2}=153\) होता है। पहले (16!) काटें फिर भाग दें।
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\(\frac{7!}{5!}+3!\) का मान क्या है?
What is the value of \(\frac{7!}{5!}+3!\)?
#factorial notation
#addition
#class 11
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A (36)
B (42)
C (48)
D (54)
Explanation opens after your attempt
Step 1
Concept
\(\frac{7!}{5!}=42\) and (3!=6), so the total is (48). In mixed questions, evaluate each part separately.
Step 2
Why this answer is correct
The correct answer is C. (48). \(\frac{7!}{5!}=42\) and (3!=6), so the total is (48). In mixed questions, evaluate each part separately.
Step 3
Exam Tip
\(\frac{7!}{5!}=42\) और (3!=6), इसलिए कुल (48) है। मिश्रित प्रश्नों में हर भाग अलग निकालें।
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(\frac{(n+4)!}{(n+1)!}) में कितने लगातार गुणनखंड बचते हैं?
How many consecutive factors remain in (\frac{(n+4)!}{(n+1)!})?
#factorial notation
#expansion
#class 11
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)), so three factors remain. Reduce the numerator up to the denominator factorial.
Step 2
Why this answer is correct
The correct answer is B. (3). (\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)), so three factors remain. Reduce the numerator up to the denominator factorial.
Step 3
Exam Tip
(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)), इसलिए तीन गुणनखंड बचते हैं। हर के फैक्टोरियल तक अंश को घटाएं।
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\(\frac{6!}{3!\cdot3!}\) का मान क्या होगा?
What is the value of \(\frac{6!}{3!\cdot3!}\)?
#factorial notation
#combination base
#class 11
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A (10)
B (15)
C (20)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\). Keep each factorial value correct.
Step 2
Why this answer is correct
The correct answer is C. (20). \(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\). Keep each factorial value correct.
Step 3
Exam Tip
\(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\) होता है। हर फैक्टोरियल का मान सही रखें।
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\(\frac{3!+2!+1!}{0!}\) का मान क्या है?
What is the value of \(\frac{3!+2!+1!}{0!}\)?
#factorial notation
#zero factorial
#class 11
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A (8)
B (9)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
(3!+2!+1!=6+2+1=9) and (0!=1), so the value is (9). Always take (0!) as (1).
Step 2
Why this answer is correct
The correct answer is B. (9). (3!+2!+1!=6+2+1=9) and (0!=1), so the value is (9). Always take (0!) as (1).
Step 3
Exam Tip
(3!+2!+1!=6+2+1=9) और (0!=1), इसलिए मान (9) है। (0!) को हमेशा (1) लें।
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\(\frac{12!}{10!\cdot2}\) का मान क्या है?
What is the value of \(\frac{12!}{10!\cdot2}\)?
#factorial notation
#simplification
#class 11
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A (54)
B (60)
C (66)
D (72)
Explanation opens after your attempt
Step 1
Concept
\(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\). Canceling (10!) first shortens the calculation.
Step 2
Why this answer is correct
The correct answer is C. (66). \(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\). Canceling (10!) first shortens the calculation.
Step 3
Exam Tip
\(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\) होता है। पहले (10!) काटने से गणना छोटी होती 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)!})?
#factorial notation
#factoring
#class 11
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A (n+1)
B (n+2)
C (n+3)
D (2n+3)
Explanation opens after your attempt
Step 1
Concept
((n+3)!-(n+2)!=(n+3)(n+2)!-(n+2)!=(n+2)(n+2)!). Therefore the value is (n+2).
Step 2
Why this answer is correct
The correct answer is B. (n+2). ((n+3)!-(n+2)!=(n+3)(n+2)!-(n+2)!=(n+2)(n+2)!). Therefore the value is (n+2).
Step 3
Exam Tip
((n+3)!-(n+2)!=(n+3)(n+2)!-(n+2)!=(n+2)(n+2)!)। इसलिए मान (n+2) है।
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यदि (n!) में (n) प्राकृतिक संख्या है, तो (n!) किस गुणनफल को दर्शाता है?
If (n!) has (n) as a natural number, which product does (n!) represent?
#factorial definition
#class 11
#notation
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A \(1+2+\cdots+n\)
B \(1\cdot2\cdot3\cdots n\)
C \(n+n+\cdots+n\)
D \(n^2\)
Explanation opens after your attempt
Correct Answer
B. \(1\cdot2\cdot3\cdots n\)
Step 1
Concept
(n!) means the product of all natural numbers from (1) to (n). A clear definition makes simplification easier.
Step 2
Why this answer is correct
The correct answer is B. \(1\cdot2\cdot3\cdots n\). (n!) means the product of all natural numbers from (1) to (n). A clear definition makes simplification easier.
Step 3
Exam Tip
(n!) का अर्थ (1) से (n) तक की सभी प्राकृतिक संख्याओं का गुणनफल है। परिभाषा स्पष्ट हो तो सरलीकरण आसान होता है।
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यदि (a!=5040) हो, तो ((a-4)!) का मान क्या है?
If (a!=5040), what is the value of ((a-4)!)?
#factorial notation
#value based
#class 11
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A (1)
B (2)
C (3!)
D (4!)
Explanation opens after your attempt
Step 1
Concept
(5040=7!), so (a=7) and ((a-4)!=3!). First identify the variable from the given value.
Step 2
Why this answer is correct
The correct answer is C. (3!). (5040=7!), so (a=7) and ((a-4)!=3!). First identify the variable from the given value.
Step 3
Exam Tip
(5040=7!), इसलिए (a=7) और ((a-4)!=3!)। दिए मान से पहले चर पहचानें।
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\(\frac{16!}{14!}+\frac{5!}{4!}\) का मान क्या है?
What is the value of \(\frac{16!}{14!}+\frac{5!}{4!}\)?
#factorial notation
#sum
#class 11
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A (235)
B (240)
C (245)
D (250)
Explanation opens after your attempt
Step 1
Concept
\(\frac{16!}{14!}=16\cdot15=240\) and \(\frac{5!}{4!}=5\), so the sum is (245). Simplify the ratios separately.
Step 2
Why this answer is correct
The correct answer is C. (245). \(\frac{16!}{14!}=16\cdot15=240\) and \(\frac{5!}{4!}=5\), so the sum is (245). Simplify the ratios separately.
Step 3
Exam Tip
\(\frac{16!}{14!}=16\cdot15=240\) और \(\frac{5!}{4!}=5\), इसलिए योग (245) है। अनुपातों को अलग-अलग सरल करें।
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(\frac{(n+1)!}{(n-2)!}) का सही विस्तार कौन सा है?
Which is the correct expansion of (\frac{(n+1)!}{(n-2)!})?
#factorial notation
#expansion
#class 11
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A (n(n+1))
B ((n+1)n(n-1))
C ((n+1)(n-1))
D (n(n-1)(n-2))
Explanation opens after your attempt
Correct Answer
B. ((n+1)n(n-1))
Step 1
Concept
((n+1)!=(n+1)n(n-1)(n-2)!). After canceling ((n-2)!), ((n+1)n(n-1)) remains.
Step 2
Why this answer is correct
The correct answer is B. ((n+1)n(n-1)). ((n+1)!=(n+1)n(n-1)(n-2)!). After canceling ((n-2)!), ((n+1)n(n-1)) remains.
Step 3
Exam Tip
((n+1)!=(n+1)n(n-1)(n-2)!) होता है। इसलिए समान ((n-2)!) कटने पर ((n+1)n(n-1)) बचता है।
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\(\frac{8!-7!}{7!}\) का मान क्या है?
What is the value of \(\frac{8!-7!}{7!}\)?
#factorial notation
#subtraction
#class 11
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(8!-7!=8\cdot7!-7!=7\cdot7!\), so the value is (7). Take the common factorial in subtraction.
Step 2
Why this answer is correct
The correct answer is B. (7). \(8!-7!=8\cdot7!-7!=7\cdot7!\), so the value is (7). Take the common factorial in subtraction.
Step 3
Exam Tip
\(8!-7!=8\cdot7!-7!=7\cdot7!\), इसलिए मान (7) है। घटाव में सामान्य फैक्टोरियल निकालें।
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\(\frac{13!}{11!}\) का मान किसके बराबर है?
The value of \(\frac{13!}{11!}\) is equal to which of the following?
#factorial notation
#ratio
#class 11
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A (13+12)
B \(13\cdot12\)
C \(13\cdot11\)
D \(12\cdot11\)
Explanation opens after your attempt
Correct Answer
B. \(13\cdot12\)
Step 1
Concept
\(\frac{13!}{11!}=13\cdot12\). Expand the numerator only up to the factorial in the denominator.
Step 2
Why this answer is correct
The correct answer is B. \(13\cdot12\). \(\frac{13!}{11!}=13\cdot12\). Expand the numerator only up to the factorial in the denominator.
Step 3
Exam Tip
\(\frac{13!}{11!}=13\cdot12\) होता है। हर में मौजूद फैक्टोरियल तक अंश को विस्तार दें।
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\(\frac{4!+3!}{3!+2!}\) का मान क्या है?
What is the value of \(\frac{4!+3!}{3!+2!}\)?
#factorial notation
#careful calculation
#class 11
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The numerator is (24+6=30) and denominator is (6+2=8), so the value is \(\frac{15}{4}\). If options do not match, recalculation is necessary first.
Step 2
Why this answer is correct
The correct answer is A. (3). The numerator is (24+6=30) and denominator is (6+2=8), so the value is \(\frac{15}{4}\). If options do not match, recalculation is necessary first.
Step 3
Exam Tip
ऊपर (24+6=30) और नीचे (6+2=8) नहीं, बल्कि (3!+2!=6+2=8), इसलिए मान \(\frac{15}{4}\) है। विकल्पों में सही मान नहीं हो तो पहले पुनर्गणना जरूरी है।
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(\frac{(n+2)!}{(n+1)!}+\frac{(n+1)!}{n!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+2)!}{(n+1)!}+\frac{(n+1)!}{n!})?
#factorial notation
#algebraic expression
#class 11
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A (2n+1)
B (2n+2)
C (2n+3)
D \(n^2+3n\)
Explanation opens after your attempt
Step 1
Concept
The first term is (n+2) and the second is (n+1), so the sum is (2n+3). Simplify each fraction separately.
Step 2
Why this answer is correct
The correct answer is C. (2n+3). The first term is (n+2) and the second is (n+1), so the sum is (2n+3). Simplify each fraction separately.
Step 3
Exam Tip
पहला पद (n+2) और दूसरा (n+1) है, इसलिए योग (2n+3) है। प्रत्येक भिन्न को अलग सरल करें।
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\(\frac{7!}{4!}\) को गुणनफल के रूप में सही तरीके से कैसे लिखेंगे?
How should \(\frac{7!}{4!}\) be correctly written as a product?
#factorial notation
#expansion
#class 11
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A \(7\cdot6\cdot5\)
B \(7\cdot6\cdot5\cdot4\)
C \(6\cdot5\cdot4\)
D (7+6+5)
Explanation opens after your attempt
Correct Answer
A. \(7\cdot6\cdot5\)
Step 1
Concept
\(\frac{7!}{4!}=7\cdot6\cdot5\). The denominator (4!) cancels out.
Step 2
Why this answer is correct
The correct answer is A. \(7\cdot6\cdot5\). \(\frac{7!}{4!}=7\cdot6\cdot5\). The denominator (4!) cancels out.
Step 3
Exam Tip
\(\frac{7!}{4!}=7\cdot6\cdot5\) होता है। हर का (4!) कट जाता है।
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यदि (\frac{(n+2)!}{n!}=56) हो, तो (n) का मान क्या है?
If (\frac{(n+2)!}{n!}=56), what is the value of (n)?
#factorial equation
#class 11
#medium
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
((n+2)(n+1)=56), so \(8\cdot7=56\) gives (n=6). Compare with consecutive numbers.
Step 2
Why this answer is correct
The correct answer is B. (6). ((n+2)(n+1)=56), so \(8\cdot7=56\) gives (n=6). Compare with consecutive numbers.
Step 3
Exam Tip
((n+2)(n+1)=56), इसलिए \(8\cdot7=56\) से (n=6)। लगातार संख्याओं से तुलना करें।
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\(\frac{9!}{6!\cdot3!}\) का मान क्या है?
What is the value of \(\frac{9!}{6!\cdot3!}\)?
#factorial notation
#combination form
#class 11
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A (56)
B (72)
C (84)
D (96)
Explanation opens after your attempt
Step 1
Concept
\(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\). Canceling (6!) first makes the solution shorter.
Step 2
Why this answer is correct
The correct answer is C. (84). \(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\). Canceling (6!) first makes the solution shorter.
Step 3
Exam Tip
\(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\) होता है। पहले (6!) काटने से हल छोटा होता है।
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\(\frac{6!}{4!}-2!\) का मान क्या है?
What is the value of \(\frac{6!}{4!}-2!\)?
#factorial notation
#mixed operation
#class 11
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A (26)
B (28)
C (30)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6!}{4!}=30\) and (2!=2), so the value is (28). Keep the order of division and subtraction in mind.
Step 2
Why this answer is correct
The correct answer is B. (28). \(\frac{6!}{4!}=30\) and (2!=2), so the value is (28). Keep the order of division and subtraction in mind.
Step 3
Exam Tip
\(\frac{6!}{4!}=30\) और (2!=2), इसलिए मान (28) है। भाग और घटाव का क्रम ध्यान रखें।
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(\frac{(n+1)!}{(n-1)!}) किसके बराबर है?
(\frac{(n+1)!}{(n-1)!}) is equal to which expression?
#factorial notation
#identity
#class 11
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A (n+1)
B (n(n+1))
C (n(n-1))
D ((n+1)(n-1))
Explanation opens after your attempt
Correct Answer
B. (n(n+1))
Step 1
Concept
((n+1)!=(n+1)n(n-1)!). Therefore division gives (n(n+1)).
Step 2
Why this answer is correct
The correct answer is B. (n(n+1)). ((n+1)!=(n+1)n(n-1)!). Therefore division gives (n(n+1)).
Step 3
Exam Tip
((n+1)!=(n+1)n(n-1)!) होता है। इसलिए भाग देने पर (n(n+1)) मिलता है।
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\(\frac{4!\cdot5}{5!}\) का मान क्या है?
What is the value of \(\frac{4!\cdot5}{5!}\)?
#factorial notation
#cancellation
#class 11
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A (1)
B (4)
C (5)
D (20)
Explanation opens after your attempt
Step 1
Concept
Since \(5!=5\cdot4!\), \(\frac{4!\cdot5}{5!}=1\). Write a factorial using the nearest smaller factorial.
Step 2
Why this answer is correct
The correct answer is A. (1). Since \(5!=5\cdot4!\), \(\frac{4!\cdot5}{5!}=1\). Write a factorial using the nearest smaller factorial.
Step 3
Exam Tip
क्योंकि \(5!=5\cdot4!\), इसलिए \(\frac{4!\cdot5}{5!}=1\)। फैक्टोरियल को निकट छोटे फैक्टोरियल से लिखें।
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\(3!\cdot4!\) का मान क्या है?
What is the value of \(3!\cdot4!\)?
#factorial notation
#product
#class 11
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A (120)
B (132)
C (144)
D (156)
Explanation opens after your attempt
Step 1
Concept
(3!=6) and (4!=24), so the product is (144). Memorize small factorials.
Step 2
Why this answer is correct
The correct answer is C. (144). (3!=6) and (4!=24), so the product is (144). Memorize small factorials.
Step 3
Exam Tip
(3!=6) और (4!=24), इसलिए गुणनफल (144) है। छोटे फैक्टोरियल याद रखें।
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\(\frac{8!}{5!\cdot3!}\) का मान क्या होगा?
What is the value of \(\frac{8!}{5!\cdot3!}\)?
#factorial notation
#calculation
#class 11
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A (48)
B (54)
C (56)
D (64)
Explanation opens after your attempt
Step 1
Concept
\(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\). Cancel the common factorial first.
Step 2
Why this answer is correct
The correct answer is C. (56). \(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\). Cancel the common factorial first.
Step 3
Exam Tip
\(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\) होता है। पहले समान फैक्टोरियल काटें।
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यदि (n!=120) हो, तो ((n-2)!) का मान क्या है?
If (n!=120), what is the value of ((n-2)!)?
#factorial notation
#value finding
#class 11
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A (2)
B (3)
C (6)
D (24)
Explanation opens after your attempt
Step 1
Concept
(120=5!), so (n=5) and ((n-2)!=3!=6). Identify (n) first.
Step 2
Why this answer is correct
The correct answer is C. (6). (120=5!), so (n=5) and ((n-2)!=3!=6). Identify (n) first.
Step 3
Exam Tip
(120=5!), इसलिए (n=5) और ((n-2)!=3!=6)। पहले (n) पहचानें।
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\(\frac{7!}{3!\cdot4!}\) का मान क्या है?
What is the value of \(\frac{7!}{3!\cdot4!}\)?
#factorial notation
#combination form
#class 11
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A (21)
B (28)
C (35)
D (42)
Explanation opens after your attempt
Step 1
Concept
\(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\). Cancel (4!) and calculate.
Step 2
Why this answer is correct
The correct answer is C. (35). \(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\). Cancel (4!) and calculate.
Step 3
Exam Tip
\(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\) होता है। (4!) काटकर गणना करें।
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\(\frac{5!}{2!}+1!\) का मान क्या है?
What is the value of \(\frac{5!}{2!}+1!\)?
#factorial notation
#mixed operation
#class 11
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A (59)
B (60)
C (61)
D (62)
Explanation opens after your attempt
Step 1
Concept
\(\frac{5!}{2!}=60\) and (1!=1), so the value is (61). Both (1!) and (0!) equal (1).
Step 2
Why this answer is correct
The correct answer is C. (61). \(\frac{5!}{2!}=60\) and (1!=1), so the value is (61). Both (1!) and (0!) equal (1).
Step 3
Exam Tip
\(\frac{5!}{2!}=60\) और (1!=1), इसलिए मान (61) है। (1!) और (0!) दोनों (1) होते हैं।
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(\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!})?
#factorial notation
#algebraic simplification
#class 11
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A (1)
B (2)
C (n)
D (n+1)
Explanation opens after your attempt
Step 1
Concept
The first term is (n+2) and the second is (n), so the difference is (2). Simplifying separately reduces mistakes.
Step 2
Why this answer is correct
The correct answer is B. (2). The first term is (n+2) and the second is (n), so the difference is (2). Simplifying separately reduces mistakes.
Step 3
Exam Tip
पहला पद (n+2) और दूसरा (n) है, इसलिए अंतर (2) है। अलग-अलग सरलीकरण करने से गलती कम होती है।
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किस मान के लिए ((n-3)!) परिभाषित होगा, यदि (n) पूर्णांक है?
For which value will ((n-3)!) be defined if (n) is an integer?
#factorial notation
#domain
#class 11
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A (n=1)
B (n=2)
C (n=3)
D (n=-3)
Explanation opens after your attempt
Step 1
Concept
Factorial is defined for non-negative integers, so \(n-3\ge0\). Among the given options, (n=3) is correct.
Step 2
Why this answer is correct
The correct answer is C. (n=3). Factorial is defined for non-negative integers, so \(n-3\ge0\). Among the given options, (n=3) is correct.
Step 3
Exam Tip
फैक्टोरियल गैर-ऋणात्मक पूर्णांक के लिए परिभाषित होता है, इसलिए \(n-3\ge0\)। दिए विकल्पों में (n=3) सही है।
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\(\frac{9!}{8!}+\frac{6!}{5!}\) का मान क्या है?
What is the value of \(\frac{9!}{8!}+\frac{6!}{5!}\)?
#factorial notation
#sum
#class 11
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A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(\frac{9!}{8!}=9\) and \(\frac{6!}{5!}=6\), so the sum is (15). Reduce simple ratios quickly.
Step 2
Why this answer is correct
The correct answer is C. (15). \(\frac{9!}{8!}=9\) and \(\frac{6!}{5!}=6\), so the sum is (15). Reduce simple ratios quickly.
Step 3
Exam Tip
\(\frac{9!}{8!}=9\) और \(\frac{6!}{5!}=6\), इसलिए योग (15) है। सरल अनुपातों को तुरंत घटाएं।
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\(2!\cdot3!+4!\) का मान क्या है?
What is the value of \(2!\cdot3!+4!\)?
#factorial notation
#order of operations
#class 11
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A (30)
B (36)
C (42)
D (48)
Explanation opens after your attempt
Step 1
Concept
\(2!\cdot3!=2\cdot6=12\) and (4!=24), so the total is (36). Do multiplication before addition.
Step 2
Why this answer is correct
The correct answer is B. (36). \(2!\cdot3!=2\cdot6=12\) and (4!=24), so the total is (36). Do multiplication before addition.
Step 3
Exam Tip
\(2!\cdot3!=2\cdot6=12\) और (4!=24), इसलिए कुल (36) है। गुणा को जोड़ से पहले करें।
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(\frac{(n+3)!}{n!}) का पूर्ण विस्तार कौन सा है?
Which is the complete expansion of (\frac{(n+3)!}{n!})?
#factorial notation
#expansion
#class 11
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A (n+3)
B ((n+3)(n+2))
C ((n+3)(n+2)(n+1))
D ((n+3)(n+1)n)
Explanation opens after your attempt
Correct Answer
C. ((n+3)(n+2)(n+1))
Step 1
Concept
((n+3)!=(n+3)(n+2)(n+1)n!). After canceling (n!), three factors remain.
Step 2
Why this answer is correct
The correct answer is C. ((n+3)(n+2)(n+1)). ((n+3)!=(n+3)(n+2)(n+1)n!). After canceling (n!), three factors remain.
Step 3
Exam Tip
((n+3)!=(n+3)(n+2)(n+1)n!) होता है। इसलिए (n!) कटने पर तीन गुणनखंड बचते हैं।
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\(\frac{10!}{7!\cdot3!}\) का मान क्या है?
What is the value of \(\frac{10!}{7!\cdot3!}\)?
#factorial notation
#calculation
#class 11
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? Hint Small clue
A (90)
B (100)
C (110)
D (120)
Explanation opens after your attempt
Step 1
Concept
\(\frac{10!}{7!\cdot3!}=\frac{10\cdot9\cdot8}{6}=120\). Reduce the large factorial to three factors.
Step 2
Why this answer is correct
The correct answer is D. (120). \(\frac{10!}{7!\cdot3!}=\frac{10\cdot9\cdot8}{6}=120\). Reduce the large factorial to three factors.
Step 3
Exam Tip
\(\frac{10!}{7!\cdot3!}=\frac{10\cdot9\cdot8}{6}=120\) होता है। बड़े फैक्टोरियल को तीन पदों तक घटाएं।
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\(\frac{6!-5!}{4!}\) का मान क्या होगा?
What is the value of \(\frac{6!-5!}{4!}\)?
#factorial notation
#subtraction ratio
#class 11
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? Hint Small clue
A (20)
B (24)
C (25)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(6!-5!=6\cdot5!-5!=5\cdot5!\), and \(\frac{5\cdot5!}{4!}=25\). Take the common factorial first.
Step 2
Why this answer is correct
The correct answer is C. (25). \(6!-5!=6\cdot5!-5!=5\cdot5!\), and \(\frac{5\cdot5!}{4!}=25\). Take the common factorial first.
Step 3
Exam Tip
\(6!-5!=6\cdot5!-5!=5\cdot5!\), और \(\frac{5\cdot5!}{4!}=25\)। पहले सामान्य फैक्टोरियल निकालें।
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(\frac{(n+2)!+(n+1)!}{(n+1)!}) का सरल रूप क्या है?
What is the simplified form of (\frac{(n+2)!+(n+1)!}{(n+1)!})?
#factorial notation
#algebra
#class 11
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A (n+2)
B (n+3)
C (2n+3)
D \(n^2+3n\)
Explanation opens after your attempt
Step 1
Concept
((n+2)!+(n+1)!=(n+2)(n+1)!+(n+1)!=(n+3)(n+1)!). Therefore the value is (n+3).
Step 2
Why this answer is correct
The correct answer is B. (n+3). ((n+2)!+(n+1)!=(n+2)(n+1)!+(n+1)!=(n+3)(n+1)!). Therefore the value is (n+3).
Step 3
Exam Tip
((n+2)!+(n+1)!=(n+2)(n+1)!+(n+1)!=(n+3)(n+1)!)। इसलिए मान (n+3) है।
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\(\frac{12!}{9!}\) में कितने लगातार गुणनखंड बचते हैं?
How many consecutive factors remain in \(\frac{12!}{9!}\)?
#factorial notation
#expansion
#class 11
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A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(\frac{12!}{9!}=12\cdot11\cdot10\), so three factors remain. Cancel the numerator up to the denominator factorial.
Step 2
Why this answer is correct
The correct answer is B. (3). \(\frac{12!}{9!}=12\cdot11\cdot10\), so three factors remain. Cancel the numerator up to the denominator factorial.
Step 3
Exam Tip
\(\frac{12!}{9!}=12\cdot11\cdot10\), इसलिए तीन गुणनखंड बचते हैं। हर के फैक्टोरियल तक अंश को काटें।
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यदि (r!=24) हो, तो ((r+1)!) का मान क्या होगा?
If (r!=24), what will be the value of ((r+1)!)?
#factorial notation
#value based
#class 11
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A (60)
B (96)
C (100)
D (120)
Explanation opens after your attempt
Step 1
Concept
(24=4!), so (r=4) and ((r+1)!=5!=120). First find the variable from the given factorial.
Step 2
Why this answer is correct
The correct answer is D. (120). (24=4!), so (r=4) and ((r+1)!=5!=120). First find the variable from the given factorial.
Step 3
Exam Tip
(24=4!), इसलिए (r=4) और ((r+1)!=5!=120)। पहले दिए फैक्टोरियल से चर का मान निकालें।
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(\frac{(n+1)!}{(n+1)n!}) का मान क्या है?
What is the value of (\frac{(n+1)!}{(n+1)n!})?
#factorial notation
#cancellation
#class 11
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A (0)
B (1)
C (n)
D (n+1)
Explanation opens after your attempt
Step 1
Concept
((n+1)!=(n+1)n!), so the whole fraction becomes (1). Remembering this identity saves time.
Step 2
Why this answer is correct
The correct answer is B. (1). ((n+1)!=(n+1)n!), so the whole fraction becomes (1). Remembering this identity saves time.
Step 3
Exam Tip
((n+1)!=(n+1)n!), इसलिए पूरी भिन्न (1) बनती है। पहचान सूत्र याद रखने से समय बचता है।
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