NDA MATHEMATICS QUIZ

The shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-2}{1}=\frac{y-4}{1}=\frac{z-5}{5}$ is.

If the line through the points $A(k, 1,-1)$ and $B(2 k, 0,2)$ is perpendicular to the line through the points $B$ and $C(2+2 k, k, 1)$, then what is the value of $k$ ?

How many diagonals of a polygon dodecagon are possible?

The area of the region bounded by $X$-axis, $y^2=2 x, x=1$ and $x=4$ is

$\operatorname{Lt}_{x \rightarrow y} \frac{\tan x-\tan y}{x-y}$ equals

What is a vector of unit length orthogonal to both the vectors $\hat{i}+\hat{j}+\hat{k}$ and $2 \hat{i}+3 \hat{j}-\hat{k}$ ?

The term independent of a in the expansion of $\left(\sqrt{\frac{a}{3}}+\frac{3}{2 a^{2}}\right)^{10}$ is:

$\int_{0}^{\infty} \frac{d x}{x^{4}+13 x^{2}+36}=\ldots$

Solution of the differential equation $\frac{d x}{d y}=$ $e^{y-x}+y^{2} e^{-x}$ will be

If $\mathrm{P}=\left[\begin{array}{cc}a-i & i \\ -i & a-i\end{array}\right]$ where $\mathrm{i}^{2}=-1$ than which of the following is correct?