List of top Mathematics Questions asked in VITEEE

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

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

Let A and B are two fixed points in a plane then locus of another point C on the same plane then CA+CB = constant, \(>AB\) is

In a triangle ABC, the sides \(b\) and \(c\) are the roots of the equation \(x^2-61x+820=0\) and \(A=\tan^{-1}\left(\frac{4}{3}\right)\), then \(a^2\) is equal to

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

Argument of the complex number \(\left(\frac{-1-3i}{2+i}\right)\) is

The equation \(r^2 - 2\vec{r}\cdot\vec{c} + h = 0,\ |\vec{c}|>\sqrt{h}\), represents

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

Let $y$ be the number of people in a village at time $t$. Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then the population of the village at any fixed time $t$ is given by

The value of $\int^{^a}_{0}\sqrt{\frac{a-x}{x}}dx$ is

A spherical balloon is expanding. If the radius is increasing at the rate of $2$ centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is $5$ centimetres is

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