List of top Mathematics Questions asked in VITEEE

If the normal at $(ap^2, 2ap)$ on the parabola $y^2 = 4ax,$ meets the parabola again at $(aq^2, 2aq)$, then

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

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

A box contains $9$ tickets numbered $1$ to $9$ inclusive. If $3$ tickets are drawn from the box one at a time, the probability that they are alternatively either {odd, even, odd} or {even, odd, even} is

The sum of the series $ \frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+... $ upto $ n $ term is

Let $A = \{1,2,3,....., n\}$ and $B = \{a,b,c\}$, then the number of functions from $A$ to $B$ that are onto 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 (x +y )sin u = $x^2y^2$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = $

The length of the straight line $x - 3y = 1$ intercepted by the hyperbola $x^2 - 4y^2 = 1$ is

The product of all values of $(\cos \alpha + i \sin \alpha)^{3/5}$ is equal to

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

If the rank of the matrix $\begin{bmatrix}-1 &2&5\\ 2&-4&a-4\\ 1&-2&a+1\end{bmatrix}$ is 1, then the value of $a$ is

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

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

If $ P\left(A\right)=\frac{1}{12}, P\left(B\right)=\frac{5}{12},$ and $P\left(B|A\right) =\frac{1}{15}$ then $p\left(A\cup B\right)$ is equal to

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

$If \, \, \vec{a}=\hat{i}+2\hat{j}+3\hat{k}, \, \vec{b}= \, -\hat{i}+2\hat{j}+\hat{k}$ 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

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

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

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 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

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

What is the least value of k such that the function x$^2$ + kx + 1 is strictly increasing on (1,2)

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