List of top Questions asked in VITEEE

A table fan rotating at a speed of 2400 rpm is switched off and the resulting variation of revolution/minute with time is shown in figure. The total number of revolutions of the fan before it, comes to rest is

If \( f(x) = \left\{ \begin{array}{ll} mx + 1, & \text{for } x \leq \frac{\pi}{2}, \\ \sin x + n, & \text{for } x>\frac{\pi}{2}, \end{array} \right. \) is continuous at \( x = \frac{\pi}{2} \), then:

The value of the determinant \[ \begin{vmatrix} \cos \alpha & -\sin \alpha & 1 \\ \sin \alpha & \cos \alpha & 1 \\ \cos(\alpha + \beta) & -\sin(\alpha + \beta) & 1 \end{vmatrix} \] is:

The domain of the function \[ f(x) = \frac{\sqrt{4 - x^2}}{\sin^{-1}(2 - x)} \] is:

The general solution of the differential equation \[ (1 + y^2) \, dx + (1 + x^2) \, dy = 0 \] is:

The order and degree of the differential equation \[ \rho = \frac{\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^{3/2}}{\frac{d^2y}{dx^2}}, \] are respectively:

The relation \( R \) defined on the set of natural numbers as \( (a, b) : a \) differs from \( b \) by 3 is given by:

The sum of the series \[ 1 + \frac{1^2 + 2^2}{2!} + \frac{1^2 + 2^2 + 3^2}{3!} + \frac{1^2 + 2^2 + 3^2 + 4^2}{4!} + \dots \] is:

The coefficient of \( x^n \) in the expansion of \( \log_a(1 + x) \) is:

If a plane meets the coordinate axes at \( A \), \( B \), and \( C \) in such a way that the centroid of \( \triangle ABC \) is at the point \( (1, 2, 3) \), then the equation of the plane is:

The area lying in the first quadrant and bounded by the circle \( x^2 + y^2 = 4 \), the line \( x = \sqrt{3}y \), and the \( x \)-axis is:

The value of \[ \lim_{x \to \infty} \left( \frac{\pi}{2} - \tan^{-1} x \right)^{1/x} \] is:

\[ \int \frac{dx}{\sin x - \cos x + \sqrt{2}} = ? \]

The value of the integral \[ I = \int_0^1 \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \, dx \] is:

The value of the integral \[ I = \int_0^1 \left| x - \frac{1}{2} \right| \, dx \] is:

The eccentricity of the ellipse, which meets the straight line \( \frac{x}{7} + \frac{y}{2} = 1 \) on the axis of \( x \) and the straight line \( \frac{x}{3} - \frac{y}{5} = 1 \) on the axis of \( y \), and whose axes lie along the axes of coordinates, is:

If \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a>b) \] and \[ x^2 - y^2 = c^2 \] cut at right angles, then:

The equation of the conic with focus at \( (1, -1) \), directrix along \( x - y + 1 = 0 \), and eccentricity \( \sqrt{2} \) is:

There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelopes is:

If \[ A = \begin{pmatrix} 1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{pmatrix}, \] then the trace of matrix \( A \) is:

The maximum value of \( 4 \sin^2 x - 12 \sin x + 7 \) is:

A straight line through the point \( A(3, 4) \) is such that its intercept between the axes is bisected at \( A \). Its equation is:

The tangent at \( (1, 7) \) to the curve \( x^2 = y - 6 \) touches the circle \( x^2 + y^2 + 16x + 12y + c = 0 \) at:

The equation of the straight line through the intersection of the lines \( x - 2y = 1 \) and \( x + 3y = 2 \) and parallel to \( 3x + 4y = 0 \) is:

If \( \mathbf{a} = \mathbf{i} + \mathbf{j} + \mathbf{k}, \mathbf{b} = \mathbf{i} + 3\mathbf{j} + 5\mathbf{k}, \) and \( \mathbf{c} = 7\mathbf{i} + 9\mathbf{j} + 11\mathbf{k} \), then the area of the parallelogram having diagonals \( \mathbf{a} + \mathbf{b} \) and \( \mathbf{b} + \mathbf{c} \) is: