List of top Mathematics Questions

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

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

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

$ \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

The angle between the pair of lines $ ({{x}^{2}}+{{y}^{2}}){{\sin }^{2}}\alpha ={{(x\,\cos \theta -y\,\sin \theta )}^{2}} $ 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 value of $ {{\cos }^{2}}\left( \frac{\pi }{4}+\theta \right)-{{\sin }^{2}}\left( \frac{\pi }{4}-\theta \right) $ is

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

$ABC$ is a triangle $G$ is the centroid $ D$ is the mid- point of $BC$. If $A - (2, 3) $ and $G = (7, 5)$, then the point $D$ is

Let $ {{z}_{1}} $ and $ {{z}_{2}} $ be the roots of the equation $ {{z}^{2}}+pz+q=0 $ where p, q are real. The points represented by $ {{z}_{1}},{{z}_{2}} $ and the origin form an equilateral triangle, if

Given $ tan\text{ }A $ and $ tan\text{ B} $ are the roots of $ {{x}^{2}}-ax+b=0 $ . The value of $ {{\sin }^{2}}(A+B) $ is

The probability of choosing a number divisible by $6$ or $8$ from among $1$ to $90$ is

On the set $N$ of all natural numbers define the relation $R$ by $a R b$ if and only if the $G.C.D.$ of $a$ and $b$ is $2$, then $R$ is

When three dice are thrown the probability of getting a $4$ or $5$ so on each of the dice simultaneously is

The condition that the roots of the equation $ {{x}^{3}}+3p{{x}^{2}}+3qx+r=0 $ are in the Arithmetic Progression is:

If a line makes angles $ \frac{\pi }{3} $ and $ \frac{\pi }{4} $ with the $x$ and $y$-axis respectively, then the angle made by the line and $Z$-axis is

If $A =\begin{bmatrix} {1}&{-1} &{1}\\ {2}&{1}& {-3} \\ {1}&{1}&{1}\\ \end{bmatrix} ,10B \begin{bmatrix} {4}&{2} &{2}\\ {-5}&{0}& {\alpha} \\ {1}&{-2}&{3}\\ \end{bmatrix} $ and $B$ is the inverse of $A$, then the value of $\alpha$ is