If ^ n + 1 C_3 = 2 ,^n C_2 , then n = - Vidyadip

MCQ

If $^{n + 1}{C_3} = 2{\,^n}{C_2},$ then $n =$

A
$3$
B
$4$
✓
$5$
D
$6$

✓

Answer

Correct option: C.

$5$

c
(c) $^{n + 1}{C_3} = 2\,.{\,^n}{C_2}$

==> $\frac{{(n + 1)!}}{{3!\,.\,(n - 2)!}} = 2\,.\,\frac{{n!}}{{2!.(n - 2)!}}$

==> $\frac{{n + 1}}{{3\,.\,2!}} = \frac{2}{{2!}}$

==> $n + 1 = 6\,\, \Rightarrow \,n = 5$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $f(x)$ satisfies $f(7 -x) = f(7 + x)\ \forall \,x\, \in \,R$ such that $f(x)$ has exactly $5$ real roots which are all distinct such that sum of the real roots is $S$ then $S/7$ is equal to

$\mathop {\lim }\limits_{x \to 0} \frac{{\log \cos x}}{x} = $

Words of length $10$ are formed using the letters, $A, B, C, D, E, F, G, H, I, J$. Let $x$ be the number of such words where no letter is repeated ; and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, $\frac{y}{9 x}=$

If the vertices of a triangle be $(2,1), (5,2)$ and $(3,4)$, then its circumcentre is

If $\frac{1}{{b - c}},\;\frac{1}{{c - a}},\;\frac{1}{{a - b}}$ be consecutive terms of an $A.P.$, then ${(b - c)^2},\;{(c - a)^2},\;{(a - b)^2}$ will be in

If for positive integers $r> 1, n > 2$, the coefficients of the $(3r)^{th}$ and $(r + 2)^{th}$ powers of $x$ in the expansion of $( 1 + x)^{2n}$ are equal, then $n$ is equal to

If three non-zero vectors are $a = {a_1}i + {a_2}j + {a_3}k,$ $b = {b_1}i + {b_2}j + {b_3}k$ and $c = {c_1}i + {c_2}j + {c_3}k.$ If $c$ is the unit vector perpendicular to the vectors $a$ and $ b$ and the angle between $a$ and $b $ is $\frac{\pi }{6},$ then ${\left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{a_2}}&{{a_3}}\\{{b_1}}&{{b_2}}&{{b_3}}\\{{c_1}}&{{c_2}}&{{c_3}}\end{array}\,} \right|^2}$ is equal to

For $\mathrm{x} \in \mathbb{R}$, let $\tan ^{-1}(\mathrm{x}) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Then the minimum value of the function $\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$ defined by $\mathrm{f}(\mathrm{x})=\int_0^{\mathrm{x} \mathrm{xmm}^{-1} \mathrm{x}} \frac{e^{(t-\cos x)}}{1+\mathrm{t}^{2023}} \mathrm{dt}$ is

Let $d \in R$, and $A = \left[ {\begin{array}{*{20}{c}} { - 2}&{4 + d}&{\left( {\sin \,\theta } \right) - 2}\\ 1&{\left( {\sin \,\theta } \right) + 2}&d\\ 5&{\left( {2\sin \,\theta } \right) - d}&{\left( { - \sin \,\theta } \right) + 2 + 2d} \end{array}} \right]$, $\theta \in \left[ {0,2\pi } \right]$. If the minimum value of det $(A)$ is $8$, then a value of $d$ is

The following system of linear equations $7 x+6 y-2 z=0$ ; $3 x+4 y+2 z=0$ ; ${x}-2{y}-6{z}=0,$ has