List of top Mathematics Questions

A mixture (40 litres) contains tonic and water in the ratio 3 : 1 to make the ratio 2 : 1, how much additional amount of water is required?

A man can row 4.5 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of the stream.

The value of $\int \frac {1}{1+ Cos \; 8x}dx$ is

The number of positive divisors of $252$ is

The equation of the plane passing through the mid point of the line of join of the points $(1, 2, 3)$ and $(3, 4, 5) $ and perpendicular to it is

The domain of the function $ f(x)=\frac{{{\cos }^{-1}}x}{[x]} $ is

The amplitude of $(1+i)^5$ is

If the extremities of a diagonal of a square are $ (1,-2,3) $ and $ (2,-3,5) $ then the length of the side is

The solutions of $ x+\sin \,5x=\sin 3x $ in $ \left( 0,\frac{\pi }{2} \right) $ are

If $ \alpha ,\beta ,\gamma $ are the roots of the equation $ {{x}^{3}}-7x+7=0, $ then $ \frac{1}{{{\alpha }^{4}}}+\frac{1}{{{\beta }^{4}}}+\frac{1}{{{\gamma }^{4}}} $ is

Let $A$ be a square matrix and $ {{A}^{T}} $ is its transpose, then $ A+{{A}^{T}} $ is

If $ P=(0,1,2),\,\,Q=(4,-2,1),O=(0,0,0), $ then $ \angle POQ $ is equal to

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

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 $ 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

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

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

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

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