List of top Mathematics Questions asked in VITEEE

The length of the parabola y$^2$ = 12x cut off by the latus-rectum is

The value of $f(0)$ so that $\frac{\left(-e^{x} +2^{x}\right)}{x}$may be continuous at $x = 0$ is

Let [ ] denote the greatest integer function and f (x) = [tan$^2$ x]. Then

The shortest distance between the straight lines through the points $A_1 = (6, 2, 2)$ and $A_2 = (-4, 0, -1)$, in the directions of $(1, -2, 2)$ and $(3, -2, -2)$ is

$\begin{bmatrix}0&a\\ b&0\end{bmatrix}^{^4}=I$, then

Probability of getting positive integral roots of the equation x$^2$ - n = 0 for the integer n, 1 $\le$ n $\le$ 40 is

Solution of the differential equation $xdy - ydx - \sqrt{x^{2}+y^{2}}dx = 0$ is

If $\left|\frac{z-25}{z-1}\right|=5$ , the value of |z|

The center and radius of the sphere $x^2 + y^2 + z^2 + 3x - 4z + 1 = 0$ are

The simplified expression of sin ($tan^{-1} x$), for any real number $x$ is given by

Area enclosed by the curve $\pi\left[4\left(x-\sqrt{2}\right)^{2} +y^{2}\right]=8$ is

If $R$ be a relation defined as $aRb iff |a - b| > 0$, then the relation is

If $I =\int\frac{x^{5}}{\sqrt{1+x^{3}}}dx$ , then I is equal to

If \( A(\theta) = \left[ \begin{matrix} 1 & -\tan \theta \\ \end{matrix} \right] \) and \( AB = 1 \), then \[ (\cos \theta)B \] is equal to

If the probability density function of a random variable \( X \) is \( f(x) = \frac{x}{2} \) for \( 0 \leq x \leq 2 \), then \[ P(X>1.5 \mid X>1) \] is equal to

If \( x = -5 \) is a root of the equation \[ \begin{vmatrix} 2x+1 & 4 & 8 \\ 2 & 2x & 2 \\ 7 & 6 & 2x \end{vmatrix} = 0 \] then the other roots are

If the rank of the matrix \[ \begin{pmatrix} -1 & 2 & 5 \\ 2 & -4 & -4 \\ 1 & -2 & a + 1 \end{pmatrix} \] is 1, then the value of \( a \) is

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}or {even, odd} is

If \( P(A) = \frac{1}{2}, P(B) = \frac{5}{12} \) and \( P(B/A) = \frac{1}{15} \), then \[ P(A \cup B) \] is equal to

If \( x \sin \left( \frac{y}{x} \right) \, dy = \sin \left( \frac{y}{x} \right) - x \, dx \) and \( y(1) = \frac{\pi}{2} \), then the value of \( \cos \left( \frac{y}{x} \right) \) is

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

The value of \( \int_0^\infty \frac{dx}{(a^2 + x^2)^7} \) is equal to

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

The imaginary part of \( \frac{(1+i)^2}{i(2i-1)} \) is

If \( \vec{a} \) and \( \vec{b} \) are two unit vectors, then the vector \[ (\vec{a} + \vec{b}) \times (\vec{a} \times \vec{b}) \] is parallel to the vector