List of practice Questions

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 $A$ is a square matrix. $A'$ its transpose, then $ \frac{1}{2}(A-A') $ is
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
The maximum number of molecules is present in
Difference between $S$ and $ S^{2-} $ as $ S^{2-}$ has
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
The major product $P$ in the following reaction is $ C{{H}_{3}}-CH=C{{H}_{2}}\xrightarrow[Peroxide]{HI}P $
Which one of the following is the correct difference between rod cells and cone cells of our retina ?
Which one of the-following proved effective for biological control of nematodal diseases in plants ?
In the reaction, $ {PCl_{3(g)} + Cl_{2(g)} <=> PCl_{5(g)}}$ at equilibrium
Helium is used in balloons in place of hydrogen because it is
An octahedral complex is formed when hybrid orbitals of the following type are involved
When body tissues are injured resulting in the loss of blood, the process of blood clotting begins and the blood platelets release
Who among the following is recognised as the father of immunology ?
A transgenic food crop which may help in solving the problem of night blindness in developing countries is
Angular momentum of an electron in an orbit of H atom is proportional to