List of top Questions asked in VITEEE

The force between two short bar magnets with magnetic moments $ M_1 $ and $ M_2 $ whose centers are $ r $ meters apart is 8 N when their axes are in the same line. If the separation is increased to $ 2r $, the force between them is reduced to:

A given ray of light suffers minimum deviation in an equilateral prism $ P $. Additional prisms $ Q $ and $ R $ of identical shape and of the same material as $ P $ are now added as shown in the figure. The ray will now suffer:
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An $ \alpha $-particle of 10 MeV collides head-on with a copper nucleus ($ Z = 29 $) and is deflected back. The minimum distance of approach between the centers of the two is:

A and B are two metals with threshold frequencies $ 1.8 \times 10^{14} $ Hz and $ 2.2 \times 10^{14} $ Hz. Two identical photons of energy $ 0.825 $ eV each are incident on them. Then photoelectrons are emitted in (Take $ h = 6.6 \times 10^{-34} $ Js):

A car moves at a speed of $ 20 { m/s} $ on a banked track and describes an arc of a circle of radius $ 40\sqrt{3} $ m. The angle of banking is: (Take $ g = 10 { m/s}^2 $)

The P-V diagram of a diatomic ideal gas system undergoing a cyclic process is shown in the figure. The work done during the adiabatic process $ CD $ is (Use $ \gamma = 1.4 $):

What will be the maximum speed of a car on a road turn of radius 30m if the coefficient of friction between the tyres and the road is 0.4? (Take $ g = 9.8 { m/s}^2 $)

A person aiming to reach the exactly opposite point on the bank of a stream is swimming with speed of $ 0.5 $ m/s at an angle of $ 120^\circ $ with the direction of flow of water. The speed of water in the stream is:

The argument of the complex number \[ \left( \frac{i}{2} - \frac{2}{i} \right) \] is equal to:

The lines $$ p(p^2 + 1)x - y + q = 0 \quad {and} \quad (p^2 + 1)^2 x + (p^2 + 1)y + 2q = 0 $$ are perpendicular to a common line for:

The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:

If

and $(A + B)^2 = A^2 + B^2$ then $x + y$ is:

If $ |\mathbf{a}| = 3 $, $ |\mathbf{b}| = 4 $, then the value of $ \lambda $ for which $ \mathbf{a} + \lambda \mathbf{b} $ is perpendicular to $ \mathbf{a} - \lambda \mathbf{b} $ is:

The area of the parallelogram whose diagonals are \[ \mathbf{d_1} = \frac{3}{2} \hat{i} + \frac{1}{2} \hat{j} - \hat{k}, \quad \mathbf{d_2} = 2 \hat{i} - 6 \hat{j} + 8 \hat{k} \] is:

For which toy category has there been a continuous increase in production over the years?

Find the missing number in the sequence: \[ 285, 253, 221, 189, ? \]

If the vertex of a parabola is $ (2, -1) $ and the equation of its directrix is \[ 4x - 3y = 21, \] then the length of its latus rectum is:

Eccentricity of ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ if it passes through point $(9, 5)$ and $(12, 4)$ is:

The particular solution of \[ \log \frac{dy}{dx} = 3x + 4y, \quad y(0) = 0 \] is:

The angle between the two lines: \[ \frac{x + 1}{2} = \frac{y + 3}{2} = \frac{z - 4}{-1} \] \[ \frac{x - 4}{1} = \frac{y + 4}{2} = \frac{z + 1}{2} \] is:

What is the percentage drop in the production of Ludo from 1992 to 1994?

If \[ \left| \frac{\sec(x - y)}{\sec(x + y)} \right| = a \] then $ \frac{dy}{dx} $ is:

Evaluate the definite integral: \[ I = \int_{0}^{\frac{\pi}{2}} (\sqrt{\tan x} + \sqrt{\cot x})dx \]

The derivative of \[ \sin^{-1} \left(\frac{2x}{1 + x^2} \right) \] with respect to \[ \cos^{-1} \left(\frac{1 - x^2}{1 + x^2} \right) \] is equal to:

Evaluate the integral: \[ I = \int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx \]