List of top Mathematics Questions asked in VITEEE

If $\sin^{-1} x + \sin^{-1} y = \frac{\pi}{2}$ , then $\cos^{-1} x + \cos^{-1} y$ is equal to

$\frac{1+\tan ^{2} x}{1-\tan ^{2} x} d x$ is equal to

The function $f(x) = x^2 \; e^{-2} x, x > 0$. Then the maximum value of $f(x)$ is

If b$^2 \ge 4 ac$ for the equation $ax^4 + bx^2 + c = 0$, then all the roots of the equation will be real if

Let $A = \{1,2,3,....., n\}$ and $B = \{a,b,c\}$, then the number of functions from $A$ to $B$ that are onto is

The differential equation of the system of all circles of radius $r$ in the $xy$ plane is

If $x > 0$ and $\log_{3} x+\log_{3}\left(\sqrt{x}\right)+\log_{3}\left(\sqrt[4]{x}\right)+\log_{3}\sqrt[8]{x}+\log_{3}\left(\sqrt[16]{x}\right)+....=4,$ then x equals

If the normal to the curve $y = f(x)$ at $(3,4)$ makes an angle $\frac{3 \pi}{4}$ with the positive x-axis, then $f'(3)$ is equal to

The equation of a directrix of the ellipse $\frac{x^2}{16} + \frac{y^2}{25} = 1 $ is

An equation of the plane passing through the line of intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and passing through (1, 1, 1) is

If x = -9 is a root of A = $\begin{vmatrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{vmatrix}$ = 0, then other two root are

$If \, \, \vec{a}=\hat{i}+2\hat{j}+3\hat{k}, \, \vec{b}= \, -\hat{i}+2\hat{j}+\hat{k}$ and $\vec{c} \, = \, 3\hat{i}+\hat{j}$ then t such that $\vec{a}+t\vec{b}$ is at right angle to $\vec{c}$ will be equal to

If $\alpha \, and \, \beta$ are the roots of the equation ax+bx+c=0, then the value of $\alpha^{3} \, + \, \beta^{3}$ is

An equilateral triangle is inscribed in the parabola y$^2$ = 4x one of whose vertex is at the vertex of the parabola, the length of each side of the triangle is

The values of $\alpha$ for which the system of equation x + y + z = 1, x + 2y + 4z = $\alpha$, x + 4y + 10z = $\alpha^2$ is consistent are given by

Let A=$\begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 &t \\ 4&7-t&-6 \\ \end{bmatrix}$, then the values of t for which inverse of A does not exist

if $e^x \, =\, y+ \sqrt{1+y^2},$ then the value of y is

The volume of the tetrahedron with vertices P (-1, 2, 0), Q ( 2, 1, -3), R (1, 0, 1) and S (3, -2, 3) is

The length of the shortest distance between the lines $\vec{r}=3\hat{i}+5\hat{j}+7\hat{k}+\lambda(\hat{i}-2\hat{j}+\hat{k})$ and $\vec{r} = -\hat{i}-\hat{j}-\hat{k}+\mu (7\hat{i}-6\hat{j}+\hat{k})$ 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

In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding 6 ?

The particular integral of $\frac{d^2y}{dx^2}+2y=x^2$is

The value of the integral $\int\limits_{0}^{\frac{\pi}{2}} log \left(tan\,x\right)dx=$

The value of \( x \), for which the matrix \( A \) is singular, is: \[ A = \begin{pmatrix} 2 & x & -1 & 2 \\ 1 & x & 2x^2 \\ 1 & \frac{1}{x} & 2 \end{pmatrix} \]