List of top Questions asked in KEAM- 2025

The line segment joining the points $(-3,\,1)$ and $(1,\,1)$ is the transverse axis of a hyperbola. If the length of the conjugate axis is 4, then the equation of the hyperbola is

The coordinates of the focus and the vertex of a parabola, respectively, are $(-1,\,4)$ and $(3,\,4)$. Then the equation of the parabola is

Let $ABCD$ be a rectangle. If $\overrightarrow{AB} = 5\hat{i} + 4\hat{j} - 3\hat{k}$ and $\overrightarrow{AD} = 3\hat{i} + 2\hat{j} - \hat{k}$, then the length of $BD$ is

Let $\vec{a} = \alpha\,\hat{i} - 3\hat{j} - 2\hat{k}$ and $\vec{c} = \hat{i} - 2\hat{j} + 2\hat{k}$. If the projection of $\vec{a}$ on $\vec{c}$ is 2, then the value of $\alpha$ is

The line $x + y = 2$ touches a circle. If the centre of the circle is at $(-4,\,0)$, then the radius of the circle is

The area of the triangle bounded by the lines $x = 4$, $y = -4$ and $y = x$ is

The equation of the line passing through the point $(-4,\,2)$ and the centre of the circle $2x^2 + 2y^2 - 8y = 7$ is

Let $A(-1,\,2)$, $B(1,\,-2)$ and $C(-2,\,-2)$ be vertices of the triangle $ABC$. The equation of the line passing through $C$ and parallel to $AB$ is

\(x = \frac{1 + \cos 2\theta}{\tan \theta - \sec \theta}\) and \(y = \frac{\tan \theta + \sec \theta}{\sec^2 \theta}\), then \(\frac{y}{x} =\)

If \(\cos^{-1} x - \sin^{-1} x = \frac{\pi}{6}\), then \(x\) is equal to

\(\sin 60^{\circ} - \sin 80^{\circ} + \sin 100^{\circ} - \sin 120^{\circ} =\)

If the ratio of the Young's moduli and densities of two rods of different materials are respectively, \(3:2\) and \(3:1\), then the ratio of the velocities of sound in the rods is

If the period of a simple pendulum of length \(l\) is 5 seconds, then the period of the pendulum of length \(\frac{l}{4}\) is

If the heat supplied to an ideal gas is used up entirely to do work on the surrounding, then the process is called

The mean free path of a molecule is inversely proportional to

The product of the pressure P and volume V of an ideal gas in a container is related to the translational part of the internal energy, E as

Two particles A and B move in concentric circles with radii in the ratio \(2:1\). If for every completion of one circle of A, B completes 5 circles, then the ratio of their respective orbital velocities is

The amount of heat to be withdrawn from 3 kg of water at \(0^{\circ}C\) to obtain 3 kg of ice at \(0^{\circ}C\) in an icemaker is (latent heat of fusion of ice is \(80 \text{ kcal/kg}\))

If the ultimate strength and fracture points are far apart in a stress - strain curve of a material, then the material is said to be

Four identical point masses are placed at the corners of a square ABCD and the centre of mass lies at the centre O of the square. If the mass at B is removed, then the centre of mass lies at the point

Heat is conducted through a uniform rod ABC of length 1 m keeping the end A at \(100^{\circ}C\). If the temperature at the point B at a distance 0.4 m from the end A is \(80^{\circ}C\) and that at the other end C is \(40^{\circ}C\), then the ratio of heat conducted through AB to that through BC is

If a black body at a temperature T radiates the maximum energy at a wavelength \(\lambda_{m}\), then to radiate the maximum energy at the wavelength \(\frac{\lambda_{m}}{3}\), its temperature should be

If a satellite of mass M is spinning about its own axis and revolves around the earth in a circular orbit, then it does not have

If the moment of inertia of a solid sphere of mass M and radius R about its diameter is I, then that of another sphere of mass 2M and radius 2R about its diameter is