List of top Mathematics Questions asked in VITEEE

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

If \( A \) and \( B \) are events such that \( P(A) = 0.42 \), \( P(B) = 0.48 \), and \( P(A \cap B) = 0.16 \), then: I. \( P(\text{not } A) = 0.58 \)
II. \( P(\text{not } B) = 0.52 \)
III. \( P(A \cup B) = 0.47 \)

The connective in the statement: \[ "2 + 7>9 \, \text{or} \, 2 + 7<9" \] is:

The value of \[ \lim_{x \to 0} \frac{x^3 \cot x}{1 - \cos x} \] is:

The focus of the curve \( y^2 + 4x - 6y + 13 = 0 \) is:

If \( 12 \cot^2 \theta - 31 \csc \theta + 32 = 0 \), then the value of \( \sin \theta \) 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 no. of points of discontinuity of the function f (x) = x - [x] in the interval (0, 7) are

The eccentricity of the ellipse whose major axis is three times the minor axis is:

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

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

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

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

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

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

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

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

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

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 angle between a pair of tangents drawn from a point \( T \) to the curve \[ x^2 + y^2 + 4x - 6y - 9 = 3x + 1 \] is

If matrix \( A = \begin{pmatrix} 3 & 2 & 4 \\1 & 2 & -1 \end{pmatrix} \) and

The set of points of discontinuity of the function \[ f(x) = \sin (2 \sin x) \sin^2 x \] is given by

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