List of practice Questions

The value of $\sin^{-1}\left(\frac{4}{5}\right) +2\,\sin^{-1}\left(\frac{1}{3}\right)$ is equal to
The value of $\sec\left[\tan^{-1}\frac{b+a}{b-a}-\tan^{-1}\frac{a}{b}\right]$ =
The value of $pK_w$ of water
The value of $\left(\frac{\pi}{4} - \cos^{-1} \frac{4}{5}\right) $ is equal to
The value of $ \lim_{x \to \infty}\left(\frac{x^2 sin \left(\frac{1}{x}\right)-x} {1-|x|}\right)$ is
The value of objective function is maximum under linear constraints
The value of P so that the vectors $2 \hat i - \hat j + \hat k, \hat i + 2 \hat j - 3 \hat k$ and $3 \hat i + P \hat j + 5 \hat k$ are coplanar should be
The value of $\lim_{x \to0} \frac{sin^2x+cosx-1}{x^2}$ is
The value of $K_b$ is highest in case of
The value of $\int\limits_{0}^{\infty} \frac {x\,\tan^{-1}x} {(1+x^2)^2}$ dx is
The value of horizontal component of earths magnetic field at a place is $0.35\times10^{-4}$ tesla. If the angle of dip is $60^0$, the value of vertical component of earths magnetic field is about :
The value of ionisation energy of the hydrogen atom is
The value of g on earth's surface is $980\,cms^{-2}$. The value at a height of 64 km from surface of earth is
The value of gas constant R is 8.314 X. Here Xrepresents
The value of $\displaystyle \lim_{x \to 0} \frac{\sqrt{1-cos\,x^{2}}}{1-cos\,x}$ is
The value of $ \displaystyle\lim_{x \to 0} \frac{\cos \, x}{\pi - x}$ is
The value of $\frac{d}{dx} [x^n \log_a xe^x ] = $
The value of $\Delta =\begin{vmatrix} ^{10}C_4 & ^{10}C_5 & ^{11}C_m \\[0.3em] ^{11}C_6 & ^{11}C_7 &^{12}C_{m+2} \\[0.3em] ^{12}C_8 & ^{12}C_9 & ^{13}C_{m+4} \end{vmatrix}$ is equal to zero, where m is
The value of $\Delta =\begin{vmatrix} ^5C_0 & ^5C_3 & 14 \\[0.3em] ^5C_1 & ^5C_4 &1 \\[0.3em] ^5C_2 & ^5C_5 & 1 \end{vmatrix}$ is
The value of $\displaystyle\int_1^e 10^{\log_ex}$ is equal to
The value of $\cos \left\{ \sin^{-1} \frac{3}{5} \right\}$ is :
The value of $\cos \frac{\pi}{3}. \cos \frac{\pi}{7}. \cos \frac{2\pi}{7}\cos \frac{4\pi}{7} : $
The value of $\cot \left(cosec^{-1}\frac{5}{3}+\tan^{-1}\frac{2}{3}\right)$ is
The value of cot 5$^\circ$ cot 10$^\circ$_______cot 85$^\circ$ is
The value of $\left(\frac{\cos\left(\frac{\pi}{2} + x\right) + \sin\left(\frac{\pi}{2}+ x\right)}{\cos\left(\frac{\pi}{2} - x\right) - \sin\left(\frac{\pi}{2} - x\right)}\right)^{2} $ is