Level 57 • 50/50 questions • 40 seconds per question.
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B. (40320)
\(8!=8\times7!\) और (7!=5040), इसलिए मान (40320) है। बड़े क्रमगुणित को पिछले क्रमगुणित से निकालें। / \(8!=8\times7!\) and (7!=5040), so the value is (40320). Find a larger factorial using the previous factorial.
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What is the simplified value of \(\frac{12!}{11!}\)?
B. (12)
\(12!=12\times11!\), इसलिए भाग देने पर (12) बचता है। पास-पास के क्रमगुणित सीधे कटते हैं। / \(12!=12\times11!\), so division leaves (12). Consecutive factorials cancel directly.
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How will (6!) be written using (4!)?
C. \(6\times5\times4!\)
\(6!=6\times5\times4!\) होता है। क्रमगुणित को छोटे क्रमगुणित तक फैलाएं। / \(6!=6\times5\times4!\). Expand the factorial down to a smaller factorial.
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A. (722)
(2!=2) और (6!=720), इसलिए योग (722) है। जोड़ने से पहले हर क्रमगुणित का मान निकालें। / (2!=2) and (6!=720), so the sum is (722). Find each factorial value before adding.
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What is the value of \(\frac{10!}{7!}\)?
B. (720)
\(\frac{10!}{7!}=10\times9\times8=720\)। छोटे क्रमगुणित को काटकर केवल बचे गुणकों को गुणा करें। / \(\frac{10!}{7!}=10\times9\times8=720\). Cancel the smaller factorial and multiply only the remaining factors.
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If (n=5), what is the value of ((n-2)!)?
C. (6)
(n-2=3), इसलिए ((n-2)!=3!=6)। पहले कोष्ठक का मान निकालें। / (n-2=3), so ((n-2)!=3!=6). First evaluate the bracket.
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What is the value of \(\frac{9!}{6!,3!}\)?
B. (84)
\(\frac{9!}{6!,3!}=\frac{9\times8\times7}{6}=84\)। बड़े क्रमगुणित को छोटे तक तोड़ना आसान है। / \(\frac{9!}{6!,3!}=\frac{9\times8\times7}{6}=84\). Breaking the larger factorial down to the smaller one is easy.
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What is the value of \(5!\times0!\)?
C. (120)
(5!=120) और (0!=1), इसलिए गुणनफल (120) है। (0!) को (1) मानना जरूरी है। / (5!=120) and (0!=1), so the product is (120). It is necessary to take (0!) as (1).
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\(11\times10\times9!\) is equal to which of the following?
C. (11!)
\(11!=11\times10\times9!\), इसलिए दिया गया रूप (11!) है। क्रमगुणित विस्तार पहचानना मुख्य बात है। / \(11!=11\times10\times9!\), so the given form is (11!). Recognizing factorial expansion is the key point.
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B. (5041)
(7!=5040) और (0!=1), इसलिए योग (5041) है। (0!) वाले पद को न छोड़ें। / (7!=5040) and (0!=1), so the sum is (5041). Do not ignore the term with (0!).
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What is the value of \(\frac{8!}{3!,5!}\)?
B. (56)
\(\frac{8!}{3!,5!}=\frac{8\times7\times6}{6}=56\)। हर फैक्टोरियल को सावधानी से काटें। / \(\frac{8!}{3!,5!}=\frac{8\times7\times6}{6}=56\). Cancel each factorial carefully.
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If (x=4!) and (y=3!), what is the value of (xy)?
C. (144)
(x=24) और (y=6), इसलिए (xy=144) है। चर का मान रखने के बाद गुणा करें। / (x=24) and (y=6), so (xy=144). Substitute the values of variables and then multiply.
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What is the value of (4!+5!-3!)?
B. (138)
(4!=24), (5!=120) और (3!=6), इसलिए मान (138) है। पहले क्रमगुणित मान लिखें। / (4!=24), (5!=120), and (3!=6), so the value is (138). Write the factorial values first.
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What is the simplified form of (\frac{(n+5)!}{(n+4)!})?
C. (n+5)
((n+5)!=(n+5)(n+4)!), इसलिए सरल रूप (n+5) है। पास वाला क्रमगुणित काट दें। / ((n+5)!=(n+5)(n+4)!), so the simplified form is (n+5). Cancel the adjacent factorial.
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What is the value of \(3!\times5!\)?
A. (720)
(3!=6) और (5!=120), इसलिए गुणनफल (720) है। गुणा से पहले दोनों क्रमगुणित निकालें। / (3!=6) and (5!=120), so the product is (720). Evaluate both factorials before multiplying.
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Which form is equal to \(7\times6\times5\)?
A. \(\frac{7!}{4!}\)
\(7!=7\times6\times5\times4!\), इसलिए \(\frac{7!}{4!}=7\times6\times5\)। शेष गुणकों के अनुसार हर चुनें। / \(7!=7\times6\times5\times4!\), so \(\frac{7!}{4!}=7\times6\times5\). Choose the denominator according to the remaining factors.
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What is the value of \(\frac{6!+5!}{5!}\)?
C. (7)
\(\frac{6!+5!}{5!}=\frac{720+120}{120}=7\)। अंश का योग सही लिखें। / \(\frac{6!+5!}{5!}=\frac{720+120}{120}=7\). Write the sum in the numerator correctly.
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If (a=6!) and (b=5!), what is the value of \(\frac{a}{b}\)?
B. (6)
\(\frac{a}{b}=\frac{6!}{5!}=6\)। क्रमगुणित अनुपात में समान भाग काटें। / \(\frac{a}{b}=\frac{6!}{5!}=6\). Cancel the common part in a factorial ratio.
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B. (35280)
(8!=40320) और (7!=5040), इसलिए अंतर (35280) है। घटाने से पहले दोनों मान निकालें। / (8!=40320) and (7!=5040), so the difference is (35280). Find both values before subtracting.
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What is the value of ((5-1)!+2!)?
B. (26)
((5-1)!=4!=24) और (2!=2), इसलिए योग (26) है। कोष्ठक पहले हल करें। / ((5-1)!=4!=24) and (2!=2), so the sum is (26). Solve the bracket first.
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How many factors are present in (9!)?
C. (9)
(9!) में (9) से (1) तक कुल (9) गुणक होते हैं। (n!) में (n) गुणक होते हैं। / (9!) has (9) factors from (9) down to (1). (n!) has (n) factors.
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What is the value of \(5!\div4!+3!\)?
B. (11)
\(5!\div4!=5\) और (3!=6), इसलिए कुल (11) है। पहले भाग को सरल करें। / \(5!\div4!=5\) and (3!=6), so the total is (11). Simplify the division first.
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How can (13!) be written using (11!)?
C. \(13\times12\times11!\)
\(13!=13\times12\times11!\) होता है। बड़े क्रमगुणित को छोटे क्रमगुणित तक लिखें। / \(13!=13\times12\times11!\). Write the larger factorial down to the smaller factorial.
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What is the value of \(\frac{7!}{7\times6!}\)?
B. (1)
\(7!=7\times6!\), इसलिए अंश और हर समान हैं। समान अशून्य राशियों का भाग (1) होता है। / \(7!=7\times6!\), so numerator and denominator are the same. The quotient of equal non-zero quantities is (1).
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What is the value of (1!+4!+0!)?
C. (26)
(1!=1), (4!=24) और (0!=1), इसलिए योग (26) है। (0!) और (1!) दोनों (1) होते हैं। / (1!=1), (4!=24), and (0!=1), so the sum is (26). Both (0!) and (1!) are (1).
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What is the value of \(\frac{11!}{9!}\)?
B. (110)
\(\frac{11!}{9!}=11\times10=110\)। समान (9!) भाग को काट दें। / \(\frac{11!}{9!}=11\times10=110\). Cancel the common (9!) part.
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If (n!=5040), what is the value of (n)?
B. (7)
(7!=5040), इसलिए (n=7)। छोटे क्रमगुणित मान याद रखें। / (7!=5040), so (n=7). Remember small factorial values.
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What is the simplified form of (\frac{(n+2)!}{(n+1)!}+1)?
B. (n+3)
(\frac{(n+2)!}{(n+1)!}=n+2), इसलिए (1) जोड़ने पर (n+3) मिलता है। पहले भिन्न को सरल करें। / (\frac{(n+2)!}{(n+1)!}=n+2), so adding (1) gives (n+3). Simplify the fraction first.
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What is the value of \(2!\times3!\times4!\)?
C. (288)
(2!=2), (3!=6) और (4!=24), इसलिए गुणनफल (288) है। हर पद अलग निकालें। / (2!=2), (3!=6), and (4!=24), so the product is (288). Evaluate each term separately.
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What is the ratio of (6!) to (4!)?
A. (30:1)
\(\frac{6!}{4!}=6\times5=30\), इसलिए अनुपात (30:1) है। अनुपात में समान क्रमगुणित काटें। / \(\frac{6!}{4!}=6\times5=30\), so the ratio is (30:1). Cancel the common factorial in a ratio.
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B. (6!)
(6!=720) होता है। परीक्षा के लिए (1!) से (7!) तक के मान याद रखना उपयोगी है। / (6!=720). Remembering values from (1!) to (7!) is useful for exams.
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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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\(14\times13!\) 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 \(\frac{5!}{1!,4!}\)?
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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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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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 \(\frac{12!}{10!}\)?
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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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 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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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 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 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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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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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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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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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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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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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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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 \(\frac{8!}{8}\) 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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