List of top Questions asked in KEAM

Two solutions that are isotonic have same ......

Which of the following is used to convert sodium chromate to sodium dichromate in the preparation of potassium dichromate?

Magnitude and direction of acceleration changes for:

A couple can result in which type of motion:

If current through a single circular loop of radius 10 cm produces a magnetic field of \( B \, \text{Tesla} \) at the centre, what is the current through the loop?

If \( \vec{F} \) and \( \vec{S} \) represent force and displacement respectively, then which of the following statements is true:

First element in 3d series which shows +2, +3, +4, +6 oxidation state

What happens to a ferromagnetic material when its temperature is raised above Curie temperature?

Which force holds the nucleons together in the nucleus of the atom?

If the de Broglie wavelength of \( \alpha \)-particle and proton are equal, then the momentum \( P \) and kinetic energy \( E \) are related as:

A constant force acts on a body at rest, resulting it to move with constant acceleration. If power relates to time as \( P \propto t^n \), what is the value of \( n \)?

A body starting from rest moves with a constant acceleration of \( 2 \, \text{m/s}^2 \). What is the distance covered by the body in the interval between 5 s and 6 s?

Two lenses, one of focal length 20 cm and another of power 4D are placed together, what is the effective power of the combination?

If two planets A and B have their densities in the ratio 2:1 and radii in the ratio 1:2, what will be the ratio of escape velocities from their surfaces?

The range of the function \( f(x) = \frac{1}{7 + 4\sin x + 3\cos x} \).

Evaluate \( \int \frac{x^2 + 6x + 1}{(x+3)^2} \, dx \).

If \( \alpha^2 - \frac{1}{\alpha^2} = 2 \), find \( \left( \alpha + \frac{1}{\alpha} \right)^{16} \).

If \( 2 \cot^{-1} \left( \frac{4}{3} \right) = \cos^{-1} \left( \frac{x}{5} \right) \), find \( x \).

If \( Z = 1 + i \) and \( Z - 24\overline{Z} = \lambda Z^2 \), find \( \lambda \).

Find the value of \( \cot 10^\circ \times \cot 30^\circ \times \cot 45^\circ \times \cot 60^\circ \times \cot 80^\circ \)

If \( y = \frac{1}{3\sqrt{x}} \left( \frac{2}{x} - 3 \right) \), find the interval in which \( y \) is strictly decreasing.

Find the locus of \( Z = x + iy \) satisfying \[ \frac{\text{Re}(z)}{2 + i} + \frac{\text{Im}(z)}{1 + 2i} = \frac{3}{1 - 2i} \]

If the sum of the first two terms of a G.P. is 12 and the third term is 16, find the common ratio \( r \).

Max of \( Z = 7x + 10y \) subject to \( x + y \geq 3 \), \( x + 2y \geq 4 \), \( x, y \geq 0 \).

Evaluate \( \lim_{x \to 1} \frac{\sqrt{x+3} \cdot \sqrt{x-1}}{x-1} \)