List of top Questions asked in KEAM

If the point \( (2, k) \) lies on the circle \( (x - 2)^2 + (y + 1)^2 = 4 \), then the value of \( k \) is:
An electromagnetic wave is propagating in a medium with velocity \( \vec{v} = v \hat{i} \). The instantaneous oscillating magnetic field of this electromagnetic wave is along positive \( z \)-direction. Then the direction of the oscillating electric field is in the:
If the slope of the velocity-time graph of a moving particle is zero, then its acceleration is:
If \( f(x) = \lfloor x \rfloor \), where \( \lfloor x \rfloor \) denotes the greatest integer function, and if the domain of \( f \) is \( \{-3.01, 2.99\} \), then the range of \( f \) is
On heating an aldehyde with Fehling’s reagent, a reddish-brown precipitate is obtained due to the formation of
The probability that at least one of \( A \) or \( B \) occurs is 0.6. If \( A \) and \( B \) occur simultaneously with probability 0.2, then \( P(A') + P(B') \) is:

In the circuit given below, the current is: 

The eccentricity of an ellipse is \( \frac{1}{3} \) and its center is at the origin. If one of the directrices is \( x = 9 \), then the equation of the ellipse is:
The torque required to increase the angular speed of a uniform solid disc of mass 10 kg and diameter 0.5 m from zero to 120 rotations per minute in 5 sec is:
A steady current of 2 A is flowing through a conducting wire. The number of electrons flowing per second in it is:
A projectile is projected with a velocity of \( 20 \, {ms}^{-1} \) at an angle of 45° to the horizontal. After some time its velocity vector makes an angle of 30° to the horizontal. Its speed at this instant (in \( {ms}^{-1} \)) is:
260 g of an aqueous solution contains 60 g of urea (Molar mass = 60 g mol\(^{-1}\)). The molality of the solution is:
The general solution of the differential equation \( (x + y)^2 \frac{dy}{dx} = 1 \) is:
The solution of the differential equation \( x + y \frac{dy}{dx} = 0 \), given that at \( x = 0 \), \( y = 5 \), is:
Which of the following liquid pairs shows negative deviation from Raoult’s law?
The equation of the curve passing through \( (1, 0) \) and which has slope \( \left( 1 + \frac{y}{x} \right) \) at \( (x, y) \), is:
The order and degree of the following differential equation: \( \frac{d^2 y}{dx^2} - 2x = \sqrt{y} + \frac{dy}{dx} \), respectively, are:
The value of \( \int_{-1}^{1} x^2 \sin x \, dx \) is equal to:
The molarity of a solution containing 8 g of NaOH (Molar mass = 40 g mol\(^{-1}\)) in 250 mL solution is:
The area of the region bounded by the curve \( y = 3x^2 \) and the x-axis, between \( x = -1 \) and \( x = 1 \), is:
The value of \( \int_{\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\tan x + \sin x}{1 + \cos^2 x} \, dx \) is equal to:
If a continuous function \( f \) is defined as \[ f(x) = \left\{ \begin{array}{ll} ax + 1, & x < 2 \\ x^2 + 7, & x \geq 2 \end{array} \right. \] then the value of \( a \) is:
The derivative of \( t^2 + t \) with respect to \( t-1 \) at \( t = -2 \), is equal to:
The function \( f(x) = (x - 4)^2 (1 + x)^3 \) attains a local extremum at the point:
If \( f(x) = x|x| \), then \( f'(-1) + f'(1) \) is equal to: