List of top Mathematics Questions asked in VITEEE

The focus of the curve $y^2 + 4x - 6y + 13 = 0$ is

If A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. then, I. P(not A) = 0.58 II. P(not B) = 0.52 III. P(A or B) = 0.47

The equation of the hyperbola with vertices (3,0), (-3,0) and semi-latus rectum 4 is given by:

The no. of points of discontinuity of the function f (x) = x - [x] in the interval (0, 7) are

Amplitude of $\frac{1+\sqrt{3}i}{\sqrt{3}+1}$ is :

What is the length of the projection of $3\hat{i}+4\hat{j}+5\hat{k}$ on the xy-plane ?

The combined equation of the asymptotes of the hyperbola $2x^2 + 5xy + 2y^2 + 4x + 5y = 0$ is -

The solution of $\frac{dv}{dt} +\frac{k}{m}v = -g$ is

The principal value of $sin^{-1} \left(sin \frac{5\pi}{3}\right)$ is

The vector equation of the symmetrical form of equation of straight line $\frac{x-5}{3} = \frac{y+4}{7} = \frac{z-6}{2}$ is

A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is ___________$\pi$ cm/s

For the LPP; maximise $z =x + 4y$ subject to the constraints $x + 2y \leq 2, x +2 y \ge 8, x, y \ge 0$

The interval in which the function $f\left(x\right) = \frac{4x^{2}+1}{x}$ is decreasing is :

If the parabola $y^2 = 4ax$ passes through the point $(1, -2)$, then the tangent at this point is

The volume V and depth x of water in a vessel are connected by the relation $V=5x-\frac{x^{2}}{6} $ and the volume of water is increasing, at the rate of $5 cm^{3}/sec,$ when x = 2 cm. The rate at which the depth of water is increasing, is

The value of x obtained from the equation $\begin{vmatrix}x+\alpha&\beta&\gamma\\ \gamma&x+\beta&\alpha\\ \alpha&\beta&x+\gamma\end{vmatrix}=0$ will be

$\quad\int_{0}^{1} \left[f \left(x\right)g'' \left(x\right)-f''\left(x\right)g \left(x\right)\right]$ dx is equal to : [Given f(0) = g(0) = 0]

If $z=\frac{7-i}{3-4i} \, then\, z^{14}=$

The area bounded by f (x) $=x^{2}, 0 \le x \le 1, g\left(x\right)=x+2,1\le x\le2$ and x- axis is

Let A be the centre of the circle $x^{2}+y^{2}-2x-4y-20=0,$ and B( 1,7) andD(4,-2) are points on the circle then, if tangents be drawn at B and D, which meet at C, then area of quadri 1 ateral A BCD is-

Equation $\frac{1}{r}=\frac{1}{8}+\frac{3}{8} cos\, \theta represents$

The solution of the differential equation log x $\frac{d y}{d x}+\frac{y}{x} =$ sin 2x is

A straight line parallel to the line 2x - y + 5 = 0 is also a tangent to the curve $y^{2}=4x+5.$ Then the point of contact is

Value of $\int\limits_{0}^{\pi /2} \frac{\sqrt{sin x}}{\sqrt{sin x}\sqrt{cos x}} $ dx is