List of top Mathematics Questions

$ \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 _______

The number $(49^2 -4) (49^2 -49)$ is divisible by ..................

The constant term of the polynomial $\begin{vmatrix} {x+3}&{x} &{x+2}\\ {x}&{x+1}& {x-1} \\ {x+2}&{2x}&{3x+1}\\ \end{vmatrix} $ is ________

The order and degree of the differential equation y =$ \frac {dp}{dx}x +\sqrt {a^2p^2+b^2}$ where $ p=\frac {dy}{dx}$(here $a$ and $b$ are arbitrary constants) respectively are

Equation of the circle centered at $(4, 3)$ touching the circle $x^2+y^2-1$ externally, is _____

A simple graph contains $24$ edges. Degree of each vertex is $3$. The number of vertices is .................

If $A$ is a $3 \times 3$ nonsingular matrix and if $|A | = 3$, then $|(2A)^{-1}|$= _______

The area bounded by the curve $y = \sin x$ between $x = 0$ and $x = 2\pi $ given by