List of top Mathematics Questions

if the straight lines $ 2x+5ay-1=0 $ and $ 3x+7y+7=0 $ are mutually perpendicular, then value of $a$ is

If $A$ is a square matrix of order $3$ and if $ \det \,(A)=3, $ then $ \det \,[adj\,\,\{adj\,(adj\,A)\}] $ is equal to

If $ {{\tan }^{-1}}\,(1-x),\,\,{{\tan }^{-1}}\,(x) $ and $ {{\tan }^{-1}}\,(1+x) $ are in $A.P.$, then the value of $ {{x}^{3}}+{{x}^{2}} $ is equal to

$ \int_{0}^{\pi /2}{\frac{{{\sin }^{100}}x}{{{\sin }^{100}}x+{{\cos }^{100}}x}\,\,dx} $ is equal to

If $A$ and $B$ are square matrices of order $3$ such that $ det\text{ }A=1 $ and $ det\text{ }B=-1 $ then $ det\text{ (-10}\,\text{AB)} $ is equal to

Four arithmetic means between $-10$ and $25$ are inserted. Then the $5^{th}$ term in the series is

If $A$ and $B$ are square matrices of order 3 such that $det A = 1$ and $ det B = -1$, then $det (- 10 AB) = ? $

If $\begin{vmatrix} a_1 &b_1 &c_1 \\[0.3em] a_2 &b_2 &c_2 \\[0.3em] a_ 3&b_3 &c_3 \end{vmatrix}=\,\,\,\,3,\, $ then $ \begin{vmatrix} 3a_1 &9b_1 &3c_1 \\[0.3em] a_2 &3b_2 &c_2 \\[0.3em] 3a_ 3&9b_3 &3c_3 \end{vmatrix}=$,

$ \int{{{x}^{2}}\,{{7}^{x}}\,\,dx} $ is equal to

The dual of the statement $ (\sim p)\wedge [(\sim q)\wedge (p\vee q)\wedge ( \sim r)] $ is

The radius of the sphere $ |\,3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k}|=3 $ is

$ \underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{2}^{n+1}}+{{3}^{n+1}}}{{{2}^{n}}+{{3}^{n}}} $ is equal to

If $\vec{a}, \vec {b}$ and $\vec {c}$ are unit vectors, such that $\vec {a}+\vec {b} +\vec {c}=0$ then $3\vec {a}.\vec {b} +\vec {2b}.\vec {c} +\vec {c}.\vec {a}$

The foot of the perpendicular drawn from the origin to a plane is $ (1,-1,5) $ . The equation of the plane is

If $ A+B+C=\pi , $ then $ \tan \frac{A}{2}\tan \frac{B}{2}+\tan \frac{B}{2}\tan \frac{C}{2}+\tan \frac{C}{2}+\tan \frac{C}{2}\tan \frac{A}{2} $ is equal to

The centroid of the triangle formed by joining the mid points of the sides of a triangle with vertices $ (-1,-1),(2,4) $ and $ (-5,-6) $ is

The equation of the plane containing the lines $ \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{3} $ and $ \frac{x}{2}=\frac{y-2}{-1}=\frac{z+1}{3} $ is

The general solution of $1+\operatorname{Sin}^{2} x=3 \operatorname{Sin} x \cdot \operatorname{Cos} x, \operatorname{Tan} x \neq \frac{1}{2}$ is ......

A space vector makes the angles $150^\circ$ and $60^\circ$ with the positive direction of $X -$ and $Y-$axis. The angle made by the vector with the positive direction of $Z-$axis is .............

The derivative of $e^{ax} \cos\,bx$ with respect to $x$ is $re^{ax}$ $\cos\, (bx-Tan^{-1} \frac {b}{a})$ When $a >0, b > 0$,the value of $r$ is ............

The $n^{th}$ term of the series $1+3 + 7 + 13 + 21 + $ is $9901$. The value of $n$ is ................

The sum of all two digit natural numbers which leave a remainder $5$ when they are divided by $7$ is equal to

A wire of length $20\,cm$ is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is ____

If $m$ is the slope of one of the lines represented by $ax^2 + 2hxy + by^2 = 0,$ then $(h + bm)^2$ = ______

The line joining $A (2, -7)$ and $B(6, 5)$ is divided into $4$ equal parts by the points $ P,Q$ and $R$ such that $AQ = RP = QB$. The midpoint of $ PR$ is _______