permutations_combinations se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
251 questions tagged with permutations_combinations.
What is the value of \(\frac{7!-6!}{6!}\)?
B. (6)
\(7!=7\times6!\), इसलिए (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6)। समान फैक्टोरियल बाहर लें। / Since \(7!=7\times6!\), (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6). Take the common factorial out.
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What is the value of \(\frac{10!}{8!}+\frac{4!}{2!}\)?
C. (102)
\(\frac{10!}{8!}=90\) और \(\frac{4!}{2!}=12\), इसलिए योग (102) है। समान फैक्टोरियल भाग काटें। / \(\frac{10!}{8!}=90\) and \(\frac{4!}{2!}=12\), so the sum is (102). Cancel common factorial parts.
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If (\frac{n!}{(n-2)!}=42), what is the value of (n)?
B. (7)
(\frac{n!}{(n-2)!}=n(n-1)), इसलिए (n(n-1)=42)। \(7\times6=42\), अतः (n=7)। / (\frac{n!}{(n-2)!}=n(n-1)), so (n(n-1)=42). Since \(7\times6=42\), (n=7).
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What is the value of \(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\)?
C. (71)
\(\frac{8!}{5!,3!}=56\) और \(\frac{6!}{4!,2!}=15\), इसलिए कुल (71) है। दोनों पदों को अलग हल करें। / \(\frac{8!}{5!,3!}=56\) and \(\frac{6!}{4!,2!}=15\), so the total is (71). Solve both terms separately.
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What is the simplified value of (\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!})?
B. (2)
पहला अनुपात (n+2) और दूसरा (n) है। अंतर ((n+2)-n=2) होगा। / The first ratio is (n+2) and the second is (n). The difference is ((n+2)-n=2).
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What is the value of \(\frac{5!}{3!}+\frac{5!}{4!}\)?
B. (25)
\(\frac{5!}{3!}=20\) और \(\frac{5!}{4!}=5\), इसलिए योग (25) है। हर अनुपात अलग-अलग सरल करें। / \(\frac{5!}{3!}=20\) and \(\frac{5!}{4!}=5\), so the sum is (25). Simplify each ratio separately.
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What is the value of \(\frac{6!}{3!}+4!\)?
C. (144)
\(\frac{6!}{3!}=120\) और (4!=24), इसलिए कुल (144) है। पहले भिन्न को सरल करें। / \(\frac{6!}{3!}=120\) and (4!=24), so the total is (144). Simplify the fraction first.
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If ((n+1)!=720), what is the value of (n)?
B. (5)
(720=6!), इसलिए (n+1=6) और (n=5)। छोटे फैक्टोरियल मान याद रखें। / Since (720=6!), (n+1=6) and (n=5). Remember small factorial values.
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If (n=3), what will be the value of (\frac{(n+2)!}{n!})?
B. (20)
(n=3) रखने पर \(\frac{5!}{3!}=5\times4=20\)। पहले चर का मान रखें। / Putting (n=3), \(\frac{5!}{3!}=5\times4=20\). Substitute the variable first.
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What is the value of \(\frac{9!}{7!}-5!\)?
A. (-48)
\(\frac{9!}{7!}=9\times8=72\) और (5!=120), इसलिए मान (-48) है। घटाव में चिह्न ध्यान से रखें। / \(\frac{9!}{7!}=9\times8=72\) and (5!=120), so the value is (-48). Keep the sign carefully in subtraction.
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If (\frac{(n+1)!}{n!}=8), what is the value of (n)?
B. (7)
(\frac{(n+1)!}{n!}=n+1), इसलिए (n+1=8) और (n=7)। पहले फैक्टोरियल अनुपात सरल करें। / (\frac{(n+1)!}{n!}=n+1), so (n+1=8) and (n=7). Simplify the factorial ratio first.
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What is \(\frac{8!}{8}\) equal to?
B. (7!)
\(8!=8\times7!\), इसलिए \(\frac{8!}{8}=7!\) है। सामान्य गुणक काटकर उत्तर मिल जाता है। / \(8!=8\times7!\), so \(\frac{8!}{8}=7!\). Cancel the common factor to get the answer.
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What is the value of \(3!+4!\times0!\)?
A. (30)
(0!=1), इसलिए \(4!\times0!=24\) और (3!+24=30)। गुणा को जोड़ से पहले करें। / (0!=1), so \(4!\times0!=24\) and (3!+24=30). Do multiplication before addition.
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What is the value of \(\frac{10!}{8!,2!}\)?
C. (45)
\(\frac{10!}{8!,2!}=\frac{10\times9}{2}=45\)। पहले (8!) काटें और फिर (2!) से भाग दें। / \(\frac{10!}{8!,2!}=\frac{10\times9}{2}=45\). First cancel (8!) and then divide by (2!).
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How can (15!) be written using (14!)?
B. \(15\times14!\)
\(15!=15\times14!\) होता है। यह ((n)!=n(n-1)!) का सीधा प्रयोग है। / \(15!=15\times14!\). This is a direct use of ((n)!=n(n-1)!).
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If (m=2!) and (n=4!), what is the value of (m+n)?
C. (26)
(m=2) और (n=24), इसलिए (m+n=26)। चर को क्रमगुणित मान से बदलें। / (m=2) and (n=24), so (m+n=26). Replace the variables with factorial values.
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What is the value of \(\frac{4!+1!}{5}\)?
C. (5)
(4!+1!=24+1=25), और \(\frac{25}{5}=5\)। अंश को पहले सरल करें। / (4!+1!=24+1=25), and \(\frac{25}{5}=5\). Simplify the numerator first.
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Which expansion correctly starts (9!)?
A. \(9\times8\times7\times\cdots\times1\)
(9!) में (9) से (1) तक गुणा होता है। क्रमगुणित में जोड़ या घटाव नहीं होता। / In (9!), numbers from (9) down to (1) are multiplied. Factorial does not use addition or subtraction.
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A. (696)
(6!=720) और (4!=24), इसलिए अंतर (696) है। सीधे घटाने से पहले दोनों क्रमगुणित निकालें। / (6!=720) and (4!=24), so the difference is (696). Find both factorials before subtracting directly.
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What is the simplified form of (\frac{(n+3)!}{(n+1)!})?
B. ((n+3)(n+2))
((n+3)!=(n+3)(n+2)(n+1)!), इसलिए शेष ((n+3)(n+2)) है। समान क्रमगुणित भाग काटें। / ((n+3)!=(n+3)(n+2)(n+1)!), so the remaining part is ((n+3)(n+2)). Cancel the common factorial part.
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What is the value of \(\frac{6!}{3!}\div5\)?
B. (24)
\(\frac{6!}{3!}=6\times5\times4=120\), और \(120\div5=24\)। भागों को क्रम से सरल करें। / \(\frac{6!}{3!}=6\times5\times4=120\), and \(120\div5=24\). Simplify the operations in order.
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What is the last factor in (5!)?
B. (1)
\(5!=5\times4\times3\times2\times1\), इसलिए अंतिम गुणक (1) है। क्रमगुणित हमेशा (1) तक जाता है। / \(5!=5\times4\times3\times2\times1\), so the last factor is (1). A factorial always goes down to (1).
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What is the difference between \(7!\div5!\) and (2!)?
B. (40)
\(7!\div5!=42\) और (2!=2), इसलिए अंतर (40) है। पहले दोनों भागों के मान निकालें। / \(7!\div5!=42\) and (2!=2), so the difference is (40). First find the values of both parts.
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If (p=0!) and (q=1!), what is the value of (p+q)?
C. (2)
(0!=1) और (1!=1), इसलिए (p+q=2)। (0!) और (1!) के मान बराबर हैं। / (0!=1) and (1!=1), so (p+q=2). The values of (0!) and (1!) are equal.
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What is the value of \(\frac{12!}{10!}\)?
C. (132)
\(\frac{12!}{10!}=12\times11=132\)। छोटे क्रमगुणित को काटने के बाद बचे गुणक गुणा करें। / \(\frac{12!}{10!}=12\times11=132\). After cancelling the smaller factorial, multiply the remaining factors.
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How can (8!) be written using (9!)?
A. \(\frac{9!}{9}\)
\(9!=9\times8!\), इसलिए \(8!=\frac{9!}{9}\)। बड़े क्रमगुणित से छोटा क्रमगुणित भी निकाला जा सकता है। / \(9!=9\times8!\), so \(8!=\frac{9!}{9}\). A smaller factorial can also be found from a larger factorial.
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What is the value of \(4!\times2!-3!\)?
C. (42)
\(4!\times2!-3!=24\times2-6=42\)। क्रमगुणित मानों को पहले संख्याओं में बदलें। / \(4!\times2!-3!=24\times2-6=42\). Convert factorial values into numbers first.
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What is the value of \(\frac{5!}{1!,4!}\)?
B. (5)
\(\frac{5!}{1!,4!}=\frac{5\times4!}{1\times4!}=5\)। (1!) का मान (1) होता है। / \(\frac{5!}{1!,4!}=\frac{5\times4!}{1\times4!}=5\). The value of (1!) is (1).
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\(14\times13!\) is equal to which of the following?
C. (14!)
\(14!=14\times13!\), इसलिए दिया गया गुणनफल (14!) है। यह मूल क्रमगुणित पहचान है। / \(14!=14\times13!\), so the given product is (14!). This is a basic factorial identity.
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What is the value of ((6-3)!\times2!)?
B. (12)
((6-3)!=3!=6) और (2!=2), इसलिए गुणनफल (12) है। कोष्ठक पहले हल करें। / ((6-3)!=3!=6) and (2!=2), so the product is (12). Solve the bracket first.
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