If ^n P_4 ;: ; ^n P_5 = 1:2, then n = - Vidyadip

MCQ

If ${}^n{P_4}\;:\;{}^n{P_5} = 1:2$, then $n = $

A
$4$
B
$5$
✓
$6$
D
$7$

✓

Answer

Correct option: C.

$6$

c
(c) $\frac{{n\;!}}{{(n - 4)\;!}} \times \frac{{(n - 5)\;!}}{{n\;!}} = \frac{1}{2}$

$\Rightarrow n - 4 = 2 $

$\Rightarrow n = 6$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from permutation and combination→permutation and combination — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

if $\text{f}(\text{x})=\text{x}^{100}+\text{x}^{99}+\dots+\text{x}+1,$ then f'(1) is equal to

The number of pairs of reals $(x, y)$ such that $x=x^2+y^2$ and $y=2 x y$ is

Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S=\left\{x \in Z: x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A=\{ x \in S : x$ is a multiple of $3$ $\}$. Then $P ( A )$ is equal to

$8^{th}$ term of the series $2\sqrt 2 + \sqrt 2 + 0 + .....$ will be

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw

For any two sets A and B, $\text{A}\cap\text{(A}\cup\text{B)}=$

The number of roots of the quadratic equation $8{\sec ^2}\theta - 6\sec \theta + 1 = 0$ is

Find median for the following distribution :-
Class Frequency
$10-20$ $180$
$20-30$ $82$
$30-40$ $34$
$40-50$ $180$
$50-60$ $136$
$60-70$ $23$
$70-80$ $50$

The orthocentre of the triangle formed by $(0, 0),\, (8, 0), \,(4 6)$ is

Let $f(x) = sinx + 2sin^2x + 3sin^3x + 4sin^4x+....\infty $ , then number of solution $(s)$ of equation $f(x) = 2$ in $x \in \left[ { - \pi ,\pi } \right] - \left\{ { \pm \frac{\pi }{2}} \right\}$ is