List of top Mathematics Questions

The value of the integral $I=\int\limits^{6}_{{3}}$$\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}}dx$ is :

any three vectors such that $\vec{a}\cdot\vec{b} \ne 0, \vec{b}\cdot\vec{c} \ne 0,$ then $\vec{a}$ and $\vec{c}$ are :

All the values of m for which both roots of the equation $x^{2}-2mx+m^{2}-1=0$ are greater than -2but less than 4 lie in the interval :

If $A$ and fl are square matrices of size $n \times n$ such that $A^{2}-B^{2}=\left(A-B\right)\left(A+B\right)$, then which of the following will be always true ?

If x is real, the maximum value of $\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}$ is

$A B C$ is a triangle, right angled at $A .$ The resultant of the forces acting along $\overline{A B}, \overline{B C}$ with magnitudes $\frac{1}{A B}$ and $\frac{1}{A C}$ respectively is the force along $\overline{A D},$ where $D$ is the foot of the perpendicular from $A$ onto $B C$. The magnitude of the resultant is

If sin $\theta$ , cos $\theta$ , tan $\theta$ are in G.P. then $cos^{9} \theta + cos^{6}\theta + 3cos^{5}\theta- 1$ is equal to

A plane passes through $ (1 ,-2 ,1 )$ and is perpendicular to two planes $2x - 2y + z = 0$ and $x - y + 2z = 4, $ then the distance of the plane from the point $ (1, 2, 2)$ is

For x > 0, $ lim_{ x \to 0} \Bigg [ (sin \, x)^{1/x} + \bigg( \frac{1}{x}\bigg)^{sin \, x} \Bigg ] $ is

Let, $\overrightarrow{a}=\widehat{i}+2\widehat{j}+\widehat{k}, \overrightarrow{c}=\widehat{i}+\widehat{j}+\widehat{k}.$ A vector coplanar to $\overrightarrow{a}$ and $\overrightarrow{c}$ of magnitude $\frac{1}{\sqrt{3}},$ then the vector is

If a, b,c are the sides of a triangle ABC such that $x^2 - 2(a+b+c)x+3\lambda(ab+bc+ca)=0$ has real roots, then

If $r, s, t$ are prime numbers and p , q are the positive integers such th a t LCM of p , q is $r^2 s^4 t^2$ then the number of ordered pairs (p, q) is

f(x) is cubic polynomial with f(2) = 18 and f(1) = -1. Also f(x) has local maxima at x = -1 and f '(x) has local minima at x = 0, then

If $e_1$ is the eccentricity of the ellipse $\frac {x^2}{16}+\frac{y^2}{25}=1$ and $e_2$ is the eccentricity of the hyperbola passing through the foci of the ellipse and $e_1e_2=1$ then equation of the hyperbola is

If $a, b$ and $c \in N$ which one of the following is not true ?

If $2A+3B =\begin{bmatrix} {2}&{-1} &{4}\\ {3}&{2}& {5} \\ \end{bmatrix} $ and $A+2B \begin{bmatrix} {5}&{0} &{3}\\ {1}&{6}& {2} \\ \end{bmatrix} $then $B =$

Let $A$ and $B$ are two events and $P \left( A '\right)=0.3, P ( B )=0.4, P \left( A \cap B '\right)=0.5$, then $P ( A \cup B)$ is.

The point of intersection of the line $\frac{x-1}{3}=\frac{y+2}{4}=\frac{z-3}{-2}$ and plane $2 x-y+3 z-1= 0$ is.

The equation of plane passing through a point $A (2,-1,3)$ and parallel to the vectors $a =(3,0,-1)$ and $b =(-3,2,2)$ is: