Level 56 • 50/50 questions • 40 seconds per question.
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B. (5040)
\(7!=7\times6\times5\times4\times3\times2\times1=5040\)। बड़े क्रमगुणित को पिछले क्रमगुणित से गुणा करके निकालें। / \(7!=7\times6\times5\times4\times3\times2\times1=5040\). Find a larger factorial by multiplying the previous factorial.
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How can (8!) be written using (6!)?
A. \(8\times7\times6!\)
\(8!=8\times7\times6!\) होता है। क्रमगुणित को छोटे क्रमगुणित तक तोड़ना आसान तरीका है। / \(8!=8\times7\times6!\). Breaking a factorial down to a smaller factorial is an easy method.
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What is the value of \(\frac{9!}{7!}\)?
B. (72)
\(\frac{9!}{7!}=9\times8=72\)। समान (7!) भाग को काट दें। / \(\frac{9!}{7!}=9\times8=72\). Cancel the common (7!) part.
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What will be the value of (6!+1!)?
B. (721)
(6!=720) और (1!=1), इसलिए योग (721) है। जोड़ से पहले दोनों क्रमगुणित निकालें। / (6!=720) and (1!=1), so the sum is (721). Find both factorials before adding.
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What is the value of \(\frac{8!}{6!,2!}\)?
B. (28)
\(\frac{8!}{6!,2!}=\frac{8\times7}{2}=28\)। पहले बड़े क्रमगुणित को छोटे तक फैलाएं। / \(\frac{8!}{6!,2!}=\frac{8\times7}{2}=28\). Expand the larger factorial up to the smaller one first.
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If (n=4), what is the value of (n!)?
C. (24)
(n=4) रखने पर (n!=4!=24)। पहले चर का मान रखकर फिर क्रमगुणित निकालें। / Putting (n=4), (n!=4!=24). Substitute the variable first and then evaluate the factorial.
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What is the value of (2!+4!-1!)?
C. (25)
(2!=2), (4!=24) और (1!=1), इसलिए मान (25) है। क्रमगुणित को साधारण संख्याओं में बदलें। / (2!=2), (4!=24), and (1!=1), so the value is (25). Convert factorials into ordinary numbers.
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What is the value of \(\frac{10!}{9!}\)?
B. (10)
\(\frac{10!}{9!}=10\) क्योंकि \(10!=10\times9!\)। ऐसे सवाल में पूरा विस्तार लिखने की जरूरत नहीं होती। / \(\frac{10!}{9!}=10\) because \(10!=10\times9!\). In such questions, full expansion is not needed.
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What is the value of \(4!\times3!\)?
C. (144)
(4!=24) और (3!=6), इसलिए गुणनफल (144) है। पहले प्रत्येक क्रमगुणित अलग निकालें। / (4!=24) and (3!=6), so the product is (144). First evaluate each factorial separately.
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\(6\times5\times4\times3!\) is equal to which of the following?
A. (6!)
\(6!=6\times5\times4\times3!\), इसलिए दिया गया रूप (6!) है। विस्तार पहचानना क्रमगुणित प्रश्नों में जरूरी है। / \(6!=6\times5\times4\times3!\), so the given form is (6!). Recognizing expansions is important in factorial questions.
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What is the value of \(\frac{5!+4!}{4!}\)?
B. (6)
\(\frac{5!+4!}{4!}=\frac{120+24}{24}=6\)। अंश को सही तरह से जोड़कर भाग दें। / \(\frac{5!+4!}{4!}=\frac{120+24}{24}=6\). Add the numerator correctly and then divide.
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If (n!=720), what is the value of (n)?
B. (6)
(6!=720), इसलिए (n=6)। छोटे क्रमगुणित मान याद रखने से उत्तर जल्दी मिलता है। / (6!=720), so (n=6). Remembering small factorial values helps answer quickly.
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What is the value of ((2+3)!)?
C. (120)
पहले (2+3=5), फिर (5!=120)। कोष्ठक की गणना पहले करें। / First (2+3=5), then (5!=120). Evaluate the bracket first.
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A. (4320)
(7!=5040) और (6!=720), इसलिए अंतर (4320) है। घटाते समय दोनों क्रमगुणित अलग लिखें। / (7!=5040) and (6!=720), so the difference is (4320). Write both factorials separately while subtracting.
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What is the value of \(\frac{6!}{5!}+2!\)?
C. (8)
\(\frac{6!}{5!}=6\) और (2!=2), इसलिए कुल (8) है। पहले भाग को सरल करें। / \(\frac{6!}{5!}=6\) and (2!=2), so the total is (8). Simplify the quotient first.
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What is the value of \(3!\times3!\)?
D. (36)
(3!=6), इसलिए \(3!\times3!=6\times6=36\)। समान क्रमगुणित को पहले एक बार निकालें। / (3!=6), so \(3!\times3!=6\times6=36\). Evaluate the repeated factorial once first.
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What is the value of \(\frac{7!}{4!}\)?
A. (210)
\(\frac{7!}{4!}=7\times6\times5=210\)। छोटे क्रमगुणित को काटकर गणना कम करें। / \(\frac{7!}{4!}=7\times6\times5=210\). Cancel the smaller factorial to reduce calculation.
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What is the value of (1!+2!+3!)?
B. (9)
(1!=1), (2!=2) और (3!=6), इसलिए योग (9) है। क्रमगुणित को जोड़ने से पहले उनका मान निकालें। / (1!=1), (2!=2), and (3!=6), so the sum is (9). Evaluate factorials before adding them.
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What is the simplified form of (\frac{(n+3)!}{(n+2)!})?
C. (n+3)
((n+3)!=(n+3)(n+2)!), इसलिए भाग देने पर (n+3) बचेगा। पास-पास वाले क्रमगुणित सीधे कटते हैं। / ((n+3)!=(n+3)(n+2)!), so division leaves (n+3). Nearby factorials cancel directly.
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\(8\times7\times6\times5!\) is equal to which of the following?
B. (8!)
\(8!=8\times7\times6\times5!\) होता है। क्रमगुणित विस्तार को अंतिम फैक्टोरियल से जोड़ें। / \(8!=8\times7\times6\times5!\). Match the factorial expansion with the last factorial part.
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What is the value of \(\frac{4!+2!}{2!}\)?
C. (13)
\(\frac{4!+2!}{2!}=\frac{24+2}{2}=13\)। जोड़ वाले अंश को पहले पूरा करें। / \(\frac{4!+2!}{2!}=\frac{24+2}{2}=13\). Complete the addition in the numerator first.
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What is the value of \(5!\div3!\)?
C. (20)
\(5!\div3!=\frac{5!}{3!}=5\times4=20\)। भाग को भिन्न के रूप में लिखकर हल करें। / \(5!\div3!=\frac{5!}{3!}=5\times4=20\). Write division as a fraction to solve.
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If (a=3!) and (b=2!), what is the value of (a+b)?
C. (8)
(a=6) और (b=2), इसलिए (a+b=8)। चर वाले प्रश्नों में पहले मान निकालें। / (a=6) and (b=2), so (a+b=8). In variable questions, find the values first.
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What is the simplified value of \(\frac{9!}{6!}\)?
A. (504)
\(\frac{9!}{6!}=9\times8\times7=504\)। छोटे क्रमगुणित तक विस्तार करें और काटें। / \(\frac{9!}{6!}=9\times8\times7=504\). Expand down to the smaller factorial and cancel.
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B. (25)
(0!=1) और (4!=24), इसलिए योग (25) है। (0!) को (1) लेना याद रखें। / (0!=1) and (4!=24), so the sum is (25). Remember to take (0!) as (1).
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How can (10!) be written using (8!)?
B. \(10\times9\times8!\)
\(10!=10\times9\times8!\) होता है। बड़े क्रमगुणित को छोटे क्रमगुणित से जोड़कर लिखें। / \(10!=10\times9\times8!\). Write the larger factorial in terms of the smaller factorial.
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What is the simplified form of (\frac{(n+1)!}{(n-1)!})?
B. (n(n+1))
((n+1)!=(n+1)n(n-1)!), इसलिए शेष (n(n+1)) है। समान क्रमगुणित भाग काटें। / ((n+1)!=(n+1)n(n-1)!), so the remaining part is (n(n+1)). Cancel the common factorial part.
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What is the value of \(2!\times5!\)?
C. (240)
(2!=2) और (5!=120), इसलिए गुणनफल (240) है। पहले क्रमगुणित मान निकालें। / (2!=2) and (5!=120), so the product is (240). First find the factorial values.
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What is the value of \(\frac{6!}{4!}+0!\)?
C. (31)
\(\frac{6!}{4!}=6\times5=30\) और (0!=1), इसलिए कुल (31) है। (0!) को सही मान दें। / \(\frac{6!}{4!}=6\times5=30\) and (0!=1), so the total is (31). Use the correct value of (0!).
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What is the ratio of (4!) to (3!)?
A. (4:1)
\(\frac{4!}{3!}=4\), इसलिए अनुपात (4:1) है। अनुपात के लिए दोनों पदों को (3!) से काटें। / \(\frac{4!}{3!}=4\), so the ratio is (4:1). For the ratio, cancel both terms by (3!).
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B. (114)
(5!=120) और (3!=6), इसलिए अंतर (114) है। घटाव करते समय क्रमगुणित का मान पहले निकालें। / (5!=120) and (3!=6), so the difference is (114). Find factorial values before subtracting.
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What is the value of \(\frac{3!+0!}{1!}\)?
B. (7)
(3!+0!=6+1=7) और (1!=1), इसलिए मान (7) है। (0!) और (1!) दोनों (1) होते हैं। / (3!+0!=6+1=7) and (1!=1), so the value is (7). Both (0!) and (1!) are (1).
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B. (4!)
\(4!=4\times3\times2\times1=24\)। छोटे क्रमगुणित मान याद रखना उपयोगी है। / \(4!=4\times3\times2\times1=24\). Remembering small factorial values is useful.
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How can (9!) be written using (10!)?
B. \(\frac{10!}{10}\)
\(10!=10\times9!\), इसलिए \(9!=\frac{10!}{10}\)। उलटा संबंध भी क्रमगुणित में काम आता है। / \(10!=10\times9!\), so \(9!=\frac{10!}{10}\). The reverse relation is also useful in factorials.
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What is the value of \(\frac{8!}{4!,4!}\)?
B. (70)
\(\frac{8!}{4!,4!}=\frac{8\times7\times6\times5}{4\times3\times2\times1}=70\)। क्रमगुणित काटकर संख्या छोटी करें। / \(\frac{8!}{4!,4!}=\frac{8\times7\times6\times5}{4\times3\times2\times1}=70\). Cancel factorials to make the numbers smaller.
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How many factors from (6) to (1) are present in (6!)?
B. (6)
\(6!=6\times5\times4\times3\times2\times1\), इसमें (6) गुणक हैं। (n!) में (n) गुणक होते हैं। / \(6!=6\times5\times4\times3\times2\times1\), which has (6) factors. (n!) has (n) factors.
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What is the value of \(\frac{7!}{5!}+1!\)?
B. (43)
\(\frac{7!}{5!}=7\times6=42\) और (1!=1), इसलिए कुल (43) है। पहले भाग को सरल करें। / \(\frac{7!}{5!}=7\times6=42\) and (1!=1), so the total is (43). Simplify the quotient first.
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What is the value of \(3!\times4!-4!\)?
C. (120)
\(3!\times4!-4!=6\times24-24=120\)। समान पद (4!) को अलग लेकर भी हल कर सकते हैं। / \(3!\times4!-4!=6\times24-24=120\). You may also factor out the common term (4!).
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If (x=5!) and (y=4!), what is the value of (x-y)?
A. (96)
(x=120) और (y=24), इसलिए (x-y=96)। चर को पहले उनके क्रमगुणित मान से बदलें। / (x=120) and (y=24), so (x-y=96). Replace variables by their factorial values first.
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What is the value of ((4-2)!)?
B. (2)
पहले (4-2=2), फिर (2!=2)। कोष्ठक को पहले हल करें। / First (4-2=2), then (2!=2). Solve the bracket first.
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How can (5!) be written using (3!)?
A. \(5\times4\times3!\)
\(5!=5\times4\times3!\) होता है। बीच में रुककर छोटा क्रमगुणित लिखना सही है। / \(5!=5\times4\times3!\). It is correct to stop the expansion and write a smaller factorial.
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What is the value of \(\frac{11!}{10!}\)?
B. (11)
\(\frac{11!}{10!}=11\) क्योंकि \(11!=11\times10!\)। लगातार क्रमगुणित आसानी से कटते हैं। / \(\frac{11!}{10!}=11\) because \(11!=11\times10!\). Consecutive factorials cancel easily.
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What is the value of (6!+0!-1!)?
C. (720)
(6!=720), (0!=1) और (1!=1), इसलिए मान (720) है। (0!) और (1!) दोनों बराबर हैं। / (6!=720), (0!=1), and (1!=1), so the value is (720). (0!) and (1!) are equal.
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What is the simplified form of (\frac{(n+4)!}{(n+3)!})?
C. (n+4)
((n+4)!=(n+4)(n+3)!), इसलिए सरल रूप (n+4) है। क्रमगुणित में पास वाला भाग काटें। / ((n+4)!=(n+4)(n+3)!), so the simplified form is (n+4). Cancel the adjacent factorial part.
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What is the sum of \(4!\div2!\) and (3!)?
B. (18)
\(4!\div2!=12\) और (3!=6), इसलिए योग (18) है। भाग और क्रमगुणित दोनों को अलग-अलग सरल करें। / \(4!\div2!=12\) and (3!=6), so the sum is (18). Simplify the division and factorial separately.
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\(9\times8!\) is equal to which of the following?
C. (9!)
\(9!=9\times8!\), इसलिए दिया गया रूप (9!) है। यह क्रमगुणित की मूल पहचान है। / \(9!=9\times8!\), so the given form is (9!). This is a basic factorial identity.
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What is the value of \(\frac{5!}{2!,3!}\)?
C. (10)
\(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\)। हर क्रमगुणित का सही मान रखें। / \(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\). Keep the correct value of each factorial.
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C. (122)
(2!=2) और (5!=120), इसलिए योग (122) है। जोड़ते समय छोटे क्रमगुणित को न भूलें। / (2!=2) and (5!=120), so the sum is (122). Do not forget the smaller factorial while adding.
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How can (7!) be written using (5!)?
D. \(7\times6\times5!\)
\(7!=7\times6\times5!\) होता है। बड़े क्रमगुणित को छोटे क्रमगुणित तक विस्तार करें। / \(7!=7\times6\times5!\). Expand the larger factorial down to the smaller factorial.
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\(12\times11\times10!\) is equal to which of the following?
C. (12!)
\(12!=12\times11\times10!\), इसलिए दिया गया रूप (12!) है। क्रमगुणित विस्तार को छोटे क्रमगुणित तक पहचानें। / \(12!=12\times11\times10!\), so the given form is (12!). Recognize factorial expansion down to a smaller factorial.
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