List of top Questions asked in KEAM- 2025

With usual notations for a rigid body in rotational motion about a fixed axis, its
If the kinetic energy of a moving body reduces to \(49\%\), then its velocity is reduced to
If a ball of mass 0.02 kg bowled by a bowler straight to a batsman is hit back with the same speed with an impulse of 2 Ns, then the speed of the ball bowled is
The ratio between the gravitational potential energies of 1 kg of mass on the surface of two planets having masses and radii in the ratio \(1 : 2\) and \(1 : 3\) respectively, is
If \(f_{s}\) and \(f_{k}\) represent the coefficients of static friction and kinetic friction of the relative motion between two surfaces in contact with area A, then
The false statement is
The velocity of a swimmer in the direction of flow of river is \(10 \, \text{kmh}^{-1}\) and that against the flow of river is \(6 \, \text{kmh}^{-1}\). The velocity of the swimmer in still water in \(\text{kmh}^{-1}\) is
The ratio of the distance of the sun from the earth to that of the moon from the earth is of the order of
If \(\theta\) is the angle of projection of an object for which the horizontal range is equal to the maximum height attained, then the value of \(\tan \theta\) is
The dimensional formula for the product of moment of inertia and the square of angular velocity is
If a freely falling body from the top of a tower takes 3 s and 5 s to cross the \(28^{th}\) floor and \(4^{th}\) floor respectively, then the height difference between these floors is \((g = 10 \, \text{ms}^{-2})\)
The integrating factor of the differential equation \((1 + x^{2})dy = (1 - 2xy)dx\) is
Consider the linear programming problem:
Maximize: \(z = \alpha x + 6y\)
Subject to the constraints
\(3x + 2y \leq 60\)
\(x + 2y \leq 40\)
\(x, y \geq 0\)
If every point in the line segment joining (20, 0) and (10, 15) is optimal solution of the L.P.P, then the value of \(\alpha\) is equal to
The general solution of the differential equation \((1 + y)dx - (1 - x)dy = 0\) is
The value of \(\int_{0}^{\pi/3}\frac{\tan t}{\cos t} dt\) is equal to
\(\int \frac{e^{x}}{e^{-x} + 3e^{x}} dx =\)
The value of \(\int_{-1}^{1}|x - 3|dx\) is equal to
The area of the region bounded by \(\frac{x^{2}}{16} + \frac{y^{2}}{25} = 1\) and the line segment joining (0,5) and (4,0) in the first quadrant is
\(\int \frac{x}{5-x^2} \, dx =\)
\(\int \frac{\sin 4\theta}{\sin 2\theta} \, d\theta =\)
The function \(f(x) = 2\cos x - x + 3\) is
If \(e^{x}(y + 2\sqrt{1 + x}) = 5\), then \(-\frac{dy}{dx}\) at \((0,3)\) is
If \([x]\) denotes the greatest integer less than or equal to \(x\) for \(x \in \mathbb{R}\), then the value of \(\lim_{x \to 0^{+}} \left[ 2[x] - \frac{x}{|x|} \right]\) is equal to
If \(y = \sec (\tan^{-1} x)\), then \(\frac{dy}{dx}\) at \(x = \sqrt{3}\) is equal to
\(\lim_{x \to 11} \frac{x - 11}{\sqrt{x^2 + 48} - 13} =\)