List of practice Questions

The value of $\left[\tan^{-1} \left( \frac{1}{2}\right) + \tan^{-1} \left(\frac{1}{3}\right)\right] $ is :
The value of $\sum^{n}_{r =1} \frac{^nP_r}{r!} $ is :
The value of $sin50^{\circ} - sin70^{\circ} + sin10^{\circ}$ is equal to
The value of $\sin (\cot^{-1}x)$ is
The value of $\sin \left[ n \pi + (-1)^n \frac{\pi}{4} \right], n \in I$ is
The value of $sin \frac{\pi}{10}sin \frac{13\pi}{10}$ is
The value of $sin\left(45^{\circ}+\theta\right)-cos\left(45^{\circ}-\theta\right)$ is
The value of $\sin^{-1} \cos (sin^{-1}x)+\cos^{-1} \sin(\cos^{-1}x)$ is
The value of $\sin \, 20^{\circ} \, \sin \, 40^{\circ} \sin \, 60^{\circ} \, \sin \, 80^{\circ}$ is
The value of sin 10$^\circ$ + sin 20$^\circ$ + sin 40$^\circ$ + sin 50$^\circ$ = sin 70$^\circ$ + sin 80$^\circ$ is equal to
The value of sin 20$^\circ$ sin 40$^\circ$ sin 60$^\circ$ sin 80$^\circ$ is equal to
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