List of practice Questions

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
The value of $\cos 22 \frac{1^{\circ}}{2}$ is
The value of cos 20$^\circ$ cos 40$^\circ$ cos 60$^\circ$ cos 80$^\circ$ is equal to
The value of cos 9$^\circ$ - sin 9$^\circ$ is
The value of $\cos\left( 2 \cos^{-1} x + \sin^{-1} x\right) $ at $x = \frac{1}{5} $ is
The value of $\cos^2 \, 48^{\circ} - \sin^2 12^{\circ}$ is
The value of $\cos \frac{2\pi}{7} + \cos \frac{4 \pi}{7} + \cos \frac{6\pi}{7} $ is equal to
The value of $cos \,12^{\circ} + cos84^{\circ} + cos \,156^{\circ} + cos \,132^{\circ}$ is
The value of $\cos \, 1^{\circ} \, \cos \, 2^{\circ} \, \cos \, 3^{\circ} ... \cos \, 179^{\circ}$ is
The value of $\cos^{-1} \left(\cos \frac{7\pi}{6}\right) $ is
The value of $\cos \, 12^{\circ} + \cos \, 84^{\circ} + \cos \, 156^{\circ} + \cos \, 132^{\circ}$ is
The value of $\binom{30}{0}\binom{30}{10}-\binom{30}{1}\binom{30}{11}+\binom{30}{2}\binom{30}{12} .....+ \binom{30}{20}\binom{30}{30}$ is where $\binom{n}{r} = ^{n}C_{r}$
The value of $c$ in Rolle's theorem for the function $f(x) = x^3 - 3x$ in the interval $\left[0, \sqrt{3}\right]$ is
The value of azimuthal quantum number for electrons present in $6p$-orbitals is
The value of $2^{1/4}.4^{1/8}. 8^{1/6}....\infty $ is