List of top Mathematics Questions asked in VITEEE

The area (in square unit) of the circle which touches the lines $4 x+3 y=15$ and $4 x+3 y=5$ is

The pairs of straight lines $x^{2}-3xy+2y^{2}=0 $ and $x^{2}-3xy+2y^{2}+x-2=0$ form a

The number of subsets of $\{1, 2, 3, ..., 9\} $containing at least one odd number is

In a $\Delta A B C \frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4 b^{2} c^{2}}$ equals

$cos^{-1} \left(\frac{-1}{2}\right)-2 sin^{-1}\left(\frac{1}{2}\right)+3 cos^{-1}\left(\frac{-1}{\sqrt{2}}\right)-4 tan^{-1 }\left(-1\right) $ equals

The equations of the circle which pass through the origin and makes intercepts of lengths $4$ and $8$ on the $x$ and $y$-axes respectively are

The point $(3, -4)$ lies on both the circles $x^{2}+y^{2}-2x+8y+13=0$ and $x^{2}+y^{2}-4x+6y+11=0 $ Then, the angle between the circles is

If $f: R \rightarrow R$ is defined by $f(x)=\begin{cases}\frac{2 \sin x-\sin 2 x}{2 x \cos x}, & \text { if } x \neq 0 \\ a, & \text { if } x=0\end{cases}$ then the value of a so that f is continuous at $0$ is

The directrix of the parabola y$^2$ + 4x + 3 = 0 is

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

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

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

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

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

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

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

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

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