List of top Questions asked in KEAM

The resistance of a wire at 0 °C is 4 \(\Omega\). If the temperature coefficient of resistance of the material of the wire is \(5 \times 10^{-3} / ^\circ C\), then the resistance of a wire at 50 °C is:
Evaluate the integral:

\[ \int \frac{4x \cos \left( \sqrt{4x^2 + 7} \right)}{\sqrt{4x^2 + 7}} \, dx \]

The modulus of the complex number \[ \frac{(1 + i)^{10} (2 - i)^6}{(2i - 4)^4} \] is equal to:

The value of the limit \(\lim_{x \to 0} \frac{(2 + \cos 3x) \sin^2 x}{x \tan(2x)}\) is equal to:

There are 3 different mathematics books and 4 different physics books in a shelf. Then the number of ways these books can be arranged so that the mathematics books are together is:
If \[ \frac{1}{1 - \tan x} = \frac{3 + \sqrt{3}}{2}, \quad 0 \leq x \leq \frac{\pi}{2}, \] then the value of \( x \) is equal to:
Phenol can be converted to salicylaldehyde by:
The second term of a G.P. is \( \frac{1}{2} \). If the product of first five terms is 32, then the common ratio of the G.P. is:

The foci of the ellipse \(\frac{x^2}{49} + \frac{y^2}{24} = 1\) are:

The value of \[ \frac{\cos^{-1}(0) + \sin^{-1}\left( \frac{\sqrt{3}}{2} \right) + \cos^{-1}\left( \frac{1}{2} \right)}{\sin^{-1}(1) + \cos^{-1}\left( \frac{\sqrt{3}}{2} \right) + \sin^{-1}\left( \frac{1}{\sqrt{2}} \right)} \] is equal to:
Three capacitances 1 \(\mu\)F, 4 \(\mu\)F, and 5 \(\mu\)F are connected in parallel with a supply voltage. If the total charge flowing through the capacitors is 50 \(\mu\)C, then the supply voltage is:
If the fundamental frequency of the stretched string of length 1 m under a given tension is 3 Hz, then the fundamental frequency of the stretched string of length 0.75 m under the same tension is:
A ball is thrown vertically upwards with an initial speed of 20 ms\(^{-1}\). The velocity (in ms\(^{-1}\)) and acceleration (in ms\(^{-2}\)) at the highest point of its motion are respectively:
The product of the total electric flux emanating from a closed surface enclosing a charge \( q \) in free space is (\( \epsilon_0 \) - electrical permittivity of free space):

If \( a = \frac{1 + \tan \theta + \sec \theta}{2 \sec \theta} \) and \( b = \frac{\sin \theta}{1 - \sec \theta + \tan \theta} \), then \( \frac{a}{b} \) is equal to:

An external voltage \( V \) is supplied to a semiconductor diode having built-in potential \( V_0 \). The effective barrier height under forward bias is

Let \( S \) denote the set of all subsets of integers containing more than two numbers. A relation \( R \) on \( S \) is defined by:

\[ R = \{ (A, B) : \text{the sets } A \text{ and } B \text{ have at least two numbers in common} \}. \]

Then the relation \( R \) is:

If \( a = \tan^{-1}\left(\frac{4}{3}\right) \) and \( b = \tan^{-1}\left(\frac{1}{3}\right) \), where \( 0<a, b<\frac{\pi}{2} \), then \( a - b \) is:

The general solution of the differential equation \( \frac{dy}{dx} = xy - 2x - 2y + 4 \) is:

n number of electrons flowing in a copper wire for 1 minute constitute a current of 0.5 A. Twice the number of electrons flowing through the same wire for 20 s will constitute a current of:
The force of gravity is a:
The escape speed of the moon when compared with escape speed of the earth is approximately:

If \( 0 \leq x \leq 5 \), then the greatest value of \( \alpha \) and the least value of \( \beta \) satisfying the inequalities \( \alpha \leq 3x + 5 \leq \beta \) are, respectively,

1 g of ice at 0°C is converted into water by supplying a heat of 418.72 J. The quantity of heat that is used to increase the temperature of water from 0°C is (Latent heat of fusion of ice = \( 3.35 \times 10^5 \, {Jkg}^{-1} \)):
A block of 50 g mass is connected to a spring of spring constant 500 Nm\(^{-1}\). It is extended to the maximum and released. If the maximum speed of the block is 3 ms\(^{-1}\), then the length of extension is: