List of practice Questions

The angular amplitude of a simple pendulum is $\theta_{0}$. The maximum tension in its string will be

An engine pumps up $100 \,kg$ of water through a height of $10\, m$ in $5 s$. Given that the efficiency of engine is $60 \%$. If $g=10\, ms ^{-2}$, the power of the engine is

The slow rate of decomposition of fallen logs in nature is due to

Senescence as an active developmental cellular process in the growth and functioning of a flowering plant, is indicated in

Unisexuality of flowers prevents

Which one of the following is not observed in biodiversity hotspots ?

Endosperm is consumed by developing embryo in the seed of ....

The coefficient of $ {{x}^{r}} $ in the expansion of $ {{(1-x)}^{-2}} $ is

$ 3a{{\int_{0}^{1}{\left( \frac{ax-1}{a-1} \right)}}^{2}}\,\,dx $ is equal to

The number of solutions of $ \sin x=\sin 2x $ between $ \frac{-\pi }{2} $ and $ \frac{\pi }{2} $ is

If $A$ is a square matrix. $A'$ its transpose, then $ \frac{1}{2}(A-A') $ is

The foot of the perpendicular from $ (2,4,-1) $ to the line $ x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6) $

If $ \alpha ,\beta $ are the roots of the equation $ {{x}^{2}}+ax+b=0, $ then $ \frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}} $ is equal to

If $p^{th}$ term of an arithmetic progression is $q$ and the $q^{th}$ term is $p$, then $10^{th}$ term is

If $ y={{\sec }^{-1}}\left( \frac{1}{\sqrt{1-{{x}^{2}}}} \right), $ then $ \frac{dy}{dx} $ is equal to

If $ |a|<1, $ then $ 1+2a+3{{a}^{2}}+4{{a}^{3}}+..... $ is equal to

The distance between the planes $ 2x-2y+z+3=0 $ and $ 4x-4y+2z+5=0 $ is

$ \left| \begin{matrix} 1 & x & y+z \\ 1 & y & z+x \\ 1 & z & x+y \\ \end{matrix} \right| $ is equal to

The standard deviation of the first n natural numbers is

$ \frac{1}{3!}+\frac{2}{5!}+\frac{3}{7!}+... $ is equal to

Difference between $S$ and $ S^{2-} $ as $ S^{2-}$ has

The maximum number of molecules is present in

Two radioactive materials $X_1$, and $X_2$ have decay constants 5$\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X$_1$ to that X$_2$ will be 1/e after a time

A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of $3 \times 10^6 \, ms^{-1}. $ The velocity of the particle is (mass of electron=$9.1 \times 10^{-31} \, kg) $

Two simple harmonic motions of angular frequency 100 and 1000 rad $s^1$ have the same displacement amplitude. The ratio of their maximum acceleration is