class 11 se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
2918 questions tagged with class 11.
(\frac{(n+1)!}{(n-1)!}) is equal to which expression?
B. (n(n+1))
((n+1)!=(n+1)n(n-1)!). Therefore division gives (n(n+1)).
The correct answer is B. (n(n+1)). ((n+1)!=(n+1)n(n-1)!). Therefore division gives (n(n+1)).
((n+1)!=(n+1)n(n-1)!) होता है। इसलिए भाग देने पर (n(n+1)) मिलता है।
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What is the value of \(\frac{6!}{4!}-2!\)?
B. (28)
\(\frac{6!}{4!}=30\) and (2!=2), so the value is (28). Keep the order of division and subtraction in mind.
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.
\(\frac{6!}{4!}=30\) और (2!=2), इसलिए मान (28) है। भाग और घटाव का क्रम ध्यान रखें।
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What is the value of \(\frac{9!}{6!\cdot3!}\)?
C. (84)
\(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\). Canceling (6!) first makes the solution shorter.
The correct answer is C. (84). \(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\). Canceling (6!) first makes the solution shorter.
\(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\) होता है। पहले (6!) काटने से हल छोटा होता है।
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If (\frac{(n+2)!}{n!}=56), what is the value of (n)?
B. (6)
((n+2)(n+1)=56), so \(8\cdot7=56\) gives (n=6). Compare with consecutive numbers.
The correct answer is B. (6). ((n+2)(n+1)=56), so \(8\cdot7=56\) gives (n=6). Compare with consecutive numbers.
((n+2)(n+1)=56), इसलिए \(8\cdot7=56\) से (n=6)। लगातार संख्याओं से तुलना करें।
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How should \(\frac{7!}{4!}\) be correctly written as a product?
A. \(7\cdot6\cdot5\)
\(\frac{7!}{4!}=7\cdot6\cdot5\). The denominator (4!) cancels out.
The correct answer is A. \(7\cdot6\cdot5\). \(\frac{7!}{4!}=7\cdot6\cdot5\). The denominator (4!) cancels out.
\(\frac{7!}{4!}=7\cdot6\cdot5\) होता है। हर का (4!) कट जाता है।
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What is the simplified form of (\frac{(n+2)!}{(n+1)!}+\frac{(n+1)!}{n!})?
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.
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.
पहला पद (n+2) और दूसरा (n+1) है, इसलिए योग (2n+3) है। प्रत्येक भिन्न को अलग सरल करें।
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What is the value of \(\frac{4!+3!}{3!+2!}\)?
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.
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.
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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The value of \(\frac{13!}{11!}\) is equal to which of the following?
B. \(13\cdot12\)
\(\frac{13!}{11!}=13\cdot12\). Expand the numerator only up to the factorial in the denominator.
The correct answer is B. \(13\cdot12\). \(\frac{13!}{11!}=13\cdot12\). Expand the numerator only up to the factorial in the denominator.
\(\frac{13!}{11!}=13\cdot12\) होता है। हर में मौजूद फैक्टोरियल तक अंश को विस्तार दें।
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What is the value of \(\frac{8!-7!}{7!}\)?
B. (7)
\(8!-7!=8\cdot7!-7!=7\cdot7!\), so the value is (7). Take the common factorial in subtraction.
The correct answer is B. (7). \(8!-7!=8\cdot7!-7!=7\cdot7!\), so the value is (7). Take the common factorial in subtraction.
\(8!-7!=8\cdot7!-7!=7\cdot7!\), इसलिए मान (7) है। घटाव में सामान्य फैक्टोरियल निकालें।
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If (n!) has (n) as a natural number, which product does (n!) represent?
B. \(1\cdot2\cdot3\cdots n\)
(n!) means the product of all natural numbers from (1) to (n). A clear definition makes simplification easier.
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.
(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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What is the value of \(\frac{12!}{10!\cdot2}\)?
C. (66)
\(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\). Canceling (10!) first shortens the calculation.
The correct answer is C. (66). \(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\). Canceling (10!) first shortens the calculation.
\(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\) होता है। पहले (10!) काटने से गणना छोटी होती है।
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What is the value of \(\frac{6!}{3!\cdot3!}\)?
C. (20)
\(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\). Keep each factorial value correct.
The correct answer is C. (20). \(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\). Keep each factorial value correct.
\(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\) होता है। हर फैक्टोरियल का मान सही रखें।
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What is the value of \(\frac{7!}{5!}+3!\)?
C. (48)
\(\frac{7!}{5!}=42\) and (3!=6), so the total is (48). In mixed questions, evaluate each part separately.
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.
\(\frac{7!}{5!}=42\) और (3!=6), इसलिए कुल (48) है। मिश्रित प्रश्नों में हर भाग अलग निकालें।
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What is the difference between the values of \(\frac{11!}{9!}\) and \(\frac{8!}{6!}\)?
D. (74)
\(\frac{11!}{9!}=110\) and \(\frac{8!}{6!}=56\), so the difference is (110-56=54). Do the subtraction carefully after simplification.
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.
\(\frac{11!}{9!}=110\) 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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If (\frac{(n+1)!}{(n-1)!}=30), what is the value of (n)?
B. (5)
(\frac{(n+1)!}{(n-1)!}=n(n+1)), so (n(n+1)=30) gives (n=5). Reduce factorials first in such questions.
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.
(\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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Which is the correct simplified form of (\frac{(n+2)!}{n!})?
C. ((n+2)(n+1))
((n+2)!=(n+2)(n+1)n!). After canceling (n!), ((n+2)(n+1)) remains.
The correct answer is C. ((n+2)(n+1)). ((n+2)!=(n+2)(n+1)n!). After canceling (n!), ((n+2)(n+1)) remains.
((n+2)!=(n+2)(n+1)n!) होता है। (n!) कटने पर ((n+2)(n+1)) बचता है।
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What is the value of \(\frac{10!}{8!\cdot2!}\)?
A. (45)
\(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\). Cancel (8!) first.
The correct answer is A. (45). \(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\). Cancel (8!) first.
\(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\) होता है। पहले (8!) को काटें।
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Which is the correct form of (8!) in terms of (6!)?
A. \(8\cdot7\cdot6!\)
\(8!=8\cdot7\cdot6!\). Breaking a larger factorial down to a smaller factorial is useful.
The correct answer is A. \(8\cdot7\cdot6!\). \(8!=8\cdot7\cdot6!\). Breaking a larger factorial down to a smaller factorial is useful.
\(8!=8\cdot7\cdot6!\) होता है। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक तोड़ना उपयोगी है।
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What is the simplified form of (\frac{(n+4)!}{(n+2)!}-\frac{(n+3)!}{(n+1)!})?
A. (2(n+3))
The first term is ((n+4)(n+3)) and the second is ((n+3)(n+2)). Taking the difference gives (2(n+3)).
The correct answer is A. (2(n+3)). The first term is ((n+4)(n+3)) and the second is ((n+3)(n+2)). Taking the difference gives (2(n+3)).
पहला पद ((n+4)(n+3)) और दूसरा ((n+3)(n+2)) है। अंतर लेने पर (2(n+3)) मिलता है।
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If (\frac{(n+4)!}{(n+1)!}=504), what is the value of (n)?
B. (5)
(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)). Since \(9\times8\times7=504\), (n=5).
The correct answer is B. (5). (\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)). Since \(9\times8\times7=504\), (n=5).
(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2))। \(9\times8\times7=504\), इसलिए (n=5) है।
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What is the value of \(\frac{15!-12!}{12!}\)?
B. (2729)
\(\frac{15!}{12!}=15\times14\times13=2730\) and \(\frac{12!}{12!}=1\). Therefore the value is (2730-1=2729).
The correct answer is B. (2729). \(\frac{15!}{12!}=15\times14\times13=2730\) and \(\frac{12!}{12!}=1\). Therefore the value is (2730-1=2729).
\(\frac{15!}{12!}=15\times14\times13=2730\) और \(\frac{12!}{12!}=1\)। इसलिए मान (2730-1=2729) है।
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What is the value of \(\frac{10!}{6!,4!}+\frac{10!}{7!,3!}\)?
D. (330)
The first term is (210) and the second term is (120). Their sum is (330).
The correct answer is D. (330). The first term is (210) and the second term is (120). Their sum is (330).
पहला पद (210) और दूसरा पद (120) है। दोनों का योग (330) है।
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What is the simplified form of (\frac{\frac{(n+3)!}{n!}}{\frac{(n+2)!}{n!}})?
C. (n+3)
Simplifying the fraction gives (\frac{(n+3)!}{(n+2)!}). Its value is (n+3).
The correct answer is C. (n+3). Simplifying the fraction gives (\frac{(n+3)!}{(n+2)!}). Its value is (n+3).
भिन्न को सरल करने पर (\frac{(n+3)!}{(n+2)!}) मिलता है। इसका मान (n+3) है।
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If (\frac{(n+2)!-(n+1)!}{n!}=36), what is the value of (n)?
B. (5)
The simplified form is ((n+1)2). From ((n+1)2=36), (n+1=6) and (n=5).
The correct answer is B. (5). The simplified form is ((n+1)2). From ((n+1)2=36), (n+1=6) and (n=5).
सरल रूप ((n+1)2) है। ((n+1)2=36) से (n+1=6) और (n=5) है।
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What is the value of \(\frac{14!}{12!}-\frac{13!}{11!}\)?
B. (26)
\(\frac{14!}{12!}=14\times13=182\) and \(\frac{13!}{11!}=13\times12=156\). The difference is (26).
The correct answer is B. (26). \(\frac{14!}{12!}=14\times13=182\) and \(\frac{13!}{11!}=13\times12=156\). The difference is (26).
\(\frac{14!}{12!}=14\times13=182\) और \(\frac{13!}{11!}=13\times12=156\)। अंतर (26) है।
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What is the value of \(\frac{6!}{2!,4!}\times\frac{4!}{3!}\)?
D. (60)
The first term is (15) and the second is (4). The product is \(15\times4=60\).
The correct answer is D. (60). The first term is (15) and the second is (4). The product is \(15\times4=60\).
पहला पद (15) और दूसरा (4) है। गुणनफल \(15\times4=60\) है।
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If (n=5), what is the value of (\frac{(n+3)!}{(n+1)!}-\frac{(n+1)!}{n!})?
C. (50)
For (n=5), the first term is \(\frac{8!}{6!}=56\) and the second is \(\frac{6!}{5!}=6\). The difference is (50).
The correct answer is C. (50). For (n=5), the first term is \(\frac{8!}{6!}=56\) and the second is \(\frac{6!}{5!}=6\). The difference is (50).
(n=5) पर पहला पद \(\frac{8!}{6!}=56\) और दूसरा \(\frac{6!}{5!}=6\) है। अंतर (50) है।
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What is the simplified form of (\frac{n!+(n-1)!}{(n-1)!})?
B. (n+1)
Since (n!=n(n-1)!), the numerator is ((n-1)!(n+1)). Dividing gives (n+1).
The correct answer is B. (n+1). Since (n!=n(n-1)!), the numerator is ((n-1)!(n+1)). Dividing gives (n+1).
(n!=n(n-1)!), इसलिए अंश ((n-1)!(n+1)) है। भाग देने पर (n+1) मिलेगा।
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What is the value of \(\frac{9!-7!}{7!}\)?
C. (71)
\(\frac{9!}{7!}=72\) and \(\frac{7!}{7!}=1\). Hence (72-1=71).
The correct answer is C. (71). \(\frac{9!}{7!}=72\) and \(\frac{7!}{7!}=1\). Hence (72-1=71).
\(\frac{9!}{7!}=72\) और \(\frac{7!}{7!}=1\)। इसलिए (72-1=71) है।
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What is the value of \(\frac{8!,3!}{6!,2!}\)?
C. (168)
\(\frac{8!}{6!}=56\) and \(\frac{3!}{2!}=3\). Therefore the value is \(56\times3=168\).
The correct answer is C. (168). \(\frac{8!}{6!}=56\) and \(\frac{3!}{2!}=3\). Therefore the value is \(56\times3=168\).
\(\frac{8!}{6!}=56\) और \(\frac{3!}{2!}=3\)। इसलिए मान \(56\times3=168\) है।
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