For a set of observations, if the coefficient of variation is 25 and mean is 44 , then the variance is

The circle \(x^2+y^2+4 x-4 y+4=0\) touches...

The derivative of \(\operatorname{Sec}^{-1}\left(\frac{1}{2 x^2-1}\right)\) with respect to \(\sqrt{1-x^2}\) at \(x=\frac{1}{2}\) is

\(\begin{aligned} & \sin ^4 \frac{\pi}{8}+\sin ^4 \frac{2 \pi}{8}+\sin ^4 \frac{3 \pi}{8}+\sin ^4 \frac{4 \pi}{8} \\ & +\sin ^4 \frac{5 \pi}{8}+\sin ^4 \frac{6 \pi}{8}+\sin ^4 \frac{7 \pi}{8}=\end{aligned}\)

If \(y=\operatorname{Tan}^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)\) for \(0 < |x| < 1\), then \(\frac{d y}{d x}=\)

Let \(A B C D E F\) be a regular hexagon with the vertices \(A, B, C, D, E\) and \(F\) counter clockwise. Then, the vector \(\mathbf{A B}+\mathbf{B C}\) is equal parallel to

Let ' \(\mathrm{O}\) ' be the origin, \(\mathrm{A}\) and \(\mathrm{B}\) be two points with position vectors \(-3 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(4 \hat{i}-4 \hat{j}-3 \hat{k}\) respectively. Let \(P\) be a point such that the line drawn through \(P\) parallel to \(\overrightarrow{\mathrm{OB}}\) meets \(\mathrm{OA}\) in \(\mathrm{L}\) and another line through \(\mathrm{P}\) parallel to \(\overrightarrow{\mathrm{OA}}\) meets \(\mathrm{OB}\) in \(\mathrm{M}\). If \(\mathrm{L}\) divides \(\mathrm{OA}\) in the ratio \(2: 3\) and \(\mathrm{M}\) divides \(\mathrm{OB}\) in the ratio \(3: 2\), then the distance from 0 to \(\mathrm{P}\) is

The sides of an equilateral triangle are increasing at the rate of \(2 \mathrm{~cm} \mathrm{~s}^{-1}\). How fast does its area increase when its side is \(10 \mathrm{~cm}\) ?

The number of valence electrons present in an element with atomic number 117 is

Find the absolute maximum of \(x^{40}-x^{20}\) on the interval \([0,1]\).

The types of hybridisation on the five carbon atoms from left to right in pent-1-en-4-yne are

If \(A=\left[\begin{array}{cc}1 & -2 \\ 4 & 5\end{array}\right]\) and \(f(t)=t^2-3 t+7\), then \(f(A)+\left[\begin{array}{cc}3 & 6 \\ -12 & -9\end{array}\right]\) is equal to

\(100 \mathrm{~mL}\) of \(0.2 \mathrm{M}\) acetic acid is completely neutralised using a standard solution of \(\mathrm{NaOH}\). The volume of ethane obtained at STP after complete electrolysis of the resulting solution is