List of practice Questions

Through the point $ P(\alpha ,\,\beta ,\,\,\gamma ) $ a plane is drawn at right angles to OP to meet the coordinate axes are A, B,. C respectively. If $ OP=p, $ then equation of plane $ ABC$ is

At $ x=\frac{3}{2} $ the function $ f(x)=\frac{|2x-3|}{2x-3} $ is

If $ x\left[ \begin{matrix} -3 \\ 4 \\ \end{matrix} \right]+y\left[ \begin{matrix} 4 \\ 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 \\ -5 \\ \end{matrix} \right], $ then

Derivative of $ {{\log }_{10}}\,x $ with respect to $ {{x}^{2}} $ is

If the difference between the roots of $ {{x}^{2}}+ax-b=0 $ is equal to the difference between the roots of $ {{x}^{2}}-px+q=0, $ then $ {{a}^{2}}-{{p}^{2}} $ in terms of $b$ and $q$ is

If $ \frac{1+\cos A}{1-\cos A}=\frac{{{m}^{2}}}{{{n}^{2}}}, $ then $tan\, A$ =

If $ \left| \begin{matrix} 1 & 1 & 0 \\ 2 & 0 & 3 \\ 5 & -6 & x \\ \end{matrix} \right|=29, $ then $x$ is

$ \underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right) $ =

$ \int{\frac{1}{1+\cos \,\,ax}}\,\,dx $ is equal to

The direction cosines of two rays $ \overrightarrow{AB} $ and $ \overrightarrow{AC} $ are $ \left( \frac{1}{2},\frac{1}{2},-1 \right) $ and $ \left( \frac{2}{7},\frac{-3}{7},\frac{6}{7} \right). $ The direction ratios of one of the bisectors of angle $ \left( \overrightarrow{AB},\overrightarrow{AC} \right) $ are

The solution of the equation $ 2{{x}^{3}}-{{x}^{2}}-22x-24=0 $ when two of the roots are in the ratio $ 3:4, $ is

If $ {{I}_{m}}\left( \frac{z-1}{2z+1} \right)=-4, $ then locus of z is

If the foot of the perpendicular from $ (0,0,0) $ to a plane is $ (1,2,2), $ then the equation of the plane is

The angle between the pair of lines $ ({{x}^{2}}+{{y}^{2}}){{\sin }^{2}}\alpha ={{(x\,\cos \theta -y\,\sin \theta )}^{2}} $ is :

The value of $ {{\cos }^{2}}\left( \frac{\pi }{4}+\theta \right)-{{\sin }^{2}}\left( \frac{\pi }{4}-\theta \right) $ is

Which one of the following is a correct statement?

Which one of the following shows maximum value of paramagnetic behaviour?

The number of moles of $KMnO_4$ that will be needed to react with one mole of sulphite ion in acidic solution is

A beam of electron passes undeflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained, the electrons move

The finches of Galapagos Islands provide an evidence in favour of

Electric potential at the centre of a charged hollow metal sphere is

The enthalpy of hydrogenation of cyclohexene is $-119.5\, kJ\, mol ^{-1}$. If resonance energy of benzene is $-150.4\, kJ\, mol ^{-1}$, its enthalpy of hydrogenation would be

Growth rings are formed due to activity of

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is