Question
If $^n{P_3}{ + ^n}{C_{n - 2}} = 14n$, then $n = $

Answer

a
(a) By inspection $n = 5$.

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

Similar questions

A company has two plants $\mathrm{A}$ and $\mathrm{B}$ to manufacture motorcycles. $60 \%$ motorcycles are manufactured at plant $\mathrm{A}$ and the remaining are manufactured at plant B. $80 \%$ of the motorcycles manufactured at plant $\mathrm{A}$ are rated of the standard quality, while $90 \%$ of the motorcycles manufactured at plant $B$ are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If $p$ is the probability that it was manufactured at plant $\mathrm{B}$, then $126 \mathrm{p}$ is
Let $S=\{1,2,3, \ldots, 40)$ and let $A$ be a subset of $S$ such that no two elements in $A$ have their sum divisible by 5 . What is the maximum number of elements possible in $A$ ?
Let $f: R \rightarrow R$ be a differentiable function that satisfies the relation $f ( x + y )= f ( x )+ f ( y )-1, \forall x$, $y \in R$. If $f ^{\prime}(0)=2$, then $|f(-2)|$ is equal to $.........$.
If $\lim \limits_{x \rightarrow 1} \frac{x+x^{2}+x^{3}+\ldots+x^{n}-n}{x-1}=820,(n \in N)$ then the value of $n$ is equal to
For real numbers $\alpha, \beta, \gamma$ and $\delta,$ if  $\int \frac{\left(x^{2}-1\right)+\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)}{\left(x^{4}+3 x^{2}+1\right) \tan ^{-1}\left(\frac{x^{2}+1}{x}\right)} d x$  $=\alpha \log _{e}\left(\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)\right)$ $+\beta \tan ^{-1}\left(\frac{\gamma\left(x^{2}-1\right)}{x}\right)+\delta \tan ^{-1}\left(\frac{x^{2}+1}{x}\right)+C$  where $C$ is an arbitrary constant, then the value of $10(\alpha+\beta \gamma+\delta)$ is equal to ....... .
If $tanA + cotA = 4$, then $tan^4A + cot^4A$ is equal to
Let $\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by $f(x)=\frac{4^x}{4^x+2}$ and $M=\int_{f(a)}^{f(1-a)} x \sin ^4(x(1-x)) d x,$ $N=\int_{f(a)}^{f(1-a)} \sin ^4(x(1-x)) d x ; a \neq \frac{1}{2} . \text { If }$ $\alpha \mathrm{M}=\beta \mathrm{N}, \alpha, \beta \in \mathbb{N}$, then the least value of $\alpha^2+\beta^2$ is equal to $ . . . . .$
Let $[t]$ denote the greatest integer function. If $\int \limits_0^{2.4}\left[x^2\right] d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}+\delta \sqrt{5}$, then $\alpha+\beta+\gamma+$ $\delta$ is equal to $..............$.
Number of rational roots of equation $x^{2016} -x^{2015} + x^{1008} + x^{1003} + 1 = 0,$ is equal to
If the constant term in the expansion of $\left(3 x^{3}-2 x^{2}+\frac{5}{x^{5}}\right)^{10}$ is $2^{k} . l$, where $l$ is an odd integer, then the value of $k$ is equal to