List of top Questions asked in KEAM

If the initial speed of the car moving at constant acceleration is halved, then the stopping distance \( S \) becomes:
The stress required to produce a fractional compression of 1.5% in a liquid having bulk modulus of \( 0.9 \times 10^9 \, {Nm}^{-2} \) is:

The line \(y = 5x + 7\) is perpendicular to the line joining the points \((2, 12)\) and \((12, k)\). Then the value of \(k\) 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 \[ f(x) = \frac{|5 - x|(x + 5)}{\tan(x - 5)} \quad {for} \quad x \neq 5. \] Then \[ \lim_{x \to 5} f(x) { is equal to:} \]
If a cell of 12 V emf delivers 2 A current in a circuit having a resistance of 5.8 \(\Omega\), then the internal resistance of the cell is:

A particle is moving along the curve \( y = 8x + \cos y \), where \( 0 \leq y \leq \pi \). If at a point the ordinate is changing 4 times as fast as the abscissa, then the coordinates of the point are:

The coefficient of \( x^{14}y \) in the expansion of \( (x^2 + \sqrt{y})^9 \) is:

A bag contains 10 green balls and 5 red balls. If two balls are selected randomly, then the probability that both are green balls, is:

The first term and the 6th term of a G.P. are 2 and \( \frac{64}{243} \) respectively. Then the sum of first 10 terms of the G.P. is:

Let \( A \) and \( B \) be two sets each containing more than one element. If \( n(A \times B) = 155 \), then \( n(A) \) is equal to:
The sum of the series \( \frac{1}{2^{10}} + \frac{1}{2^{11}} + \cdots + \frac{1}{2^{19}} \) is equal to:
For two sets \( A \) and \( B \), we have \( n(A \cup B) = 50 \), \( n(A \cap B) = 12 \), and \( n(A - B) = 15 \). Then \( n(B - A) \) is equal to:

Let \( f(x) = \log_e(x) \) and let \( g(x) = \frac{x - 2}{x^2 + 1} \). Then the domain of the composite function \( f \circ g \) is:

Let \( f(x) = \begin{cases} x^2 - \alpha, & \text{if } x < 1 \\ \beta x - 3, & \text{if } x \geq 1 \end{cases} \). If \( f \) is continuous at \( x = 1 \), then the value of \( \alpha + \beta \) is:

Let \[ A = \begin{pmatrix} 3 & -2 & 1 \\ -1 & 3 & -1 \end{pmatrix} \] and \[ B = \begin{pmatrix} 1 \\ \alpha \\ -1 \end{pmatrix}. \] If \[ AB = \begin{pmatrix} -2 \\ 6 \end{pmatrix}, \] then the value of \( \alpha \) is equal to:

The modulus of the complex number \[ \frac{(1 + i)^{10} (2 - i)^6}{(2i - 4)^4} \] is equal to:
When heat is supplied to the gas in an isochoric process, the supplied heat changes its:
When a current passing through a coil changes at a rate of 30 A s\(^{-1}\), the emf induced in the coil is 12 V. If the current passing through this coil changes at a rate of 20 A s\(^{-1}\), the emf induced in this coil is:
The integrating factor of the differential equation \[ x \frac{dy}{dx} + 2y = x e^x \] is:
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:
When a cricketer catches a ball in 30 s, the force required is 2.5 N. The force required to catch that ball in 50 s is:
A flywheel ensures a smooth ride on the vehicle because of its:
The force of gravity is a:
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: