List of top Questions asked in KEAM

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:
Focal length of a convex lens of refractive index 1.5 is 3 cm. When the lens is immersed in water of refractive index \( \frac{4}{3} \), its focal length will be:
If \( f(x) = \frac{x}{1 - x} \), \( x \neq 1 \), then the inverse of \( f \) is:
The domain of the function \( f(x) = \sqrt{7 - 8x + x^2} \) is:
The molecule which has a see-saw structure is:
If \( x + iy = \frac{3 + 4i}{5 - 12i} \), then \( x + y \) is equal to
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:
If \( \sin x = \frac{3}{5} \), then the value of \( \sec x + \tan x \) is equal to:
If \( n \) small identical liquid drops, each having terminal velocity \( v \), merge together, then the terminal velocity of the bigger drop is:
If the parametric form of the circle is \( x = 3\cos\theta + 3 \) and \( y = 3\sin\theta \), then the Cartesian form of the equation of the circle is:
The half-life period of a first order reaction is 1000 seconds. Its rate constant is:
The integral \( \int_5^{10} \left\lfloor x \right\rfloor dx \) is equal to (where \( \left\lfloor x \right\rfloor \) denotes the greatest integer function):
The radius of the circle \( x^2 + y^2 - 2x - 4y - 4 = 0 \) is:
The quantum number which determines the shape of the subshell is:
A fibrous protein present in muscles is:
If \( f(x) = \frac{1}{2 - x} \) and \( g(x) = \frac{1}{1 - x} \), then the point(s) of discontinuity of the function \( g(f(x)) \) is (are):
If \( P(-3, 4) \) and \( Q(3, 1) \) are points on a straight line, then the slope of the straight line perpendicular to PQ is:
The general solution of the differential equation \[ 2y \tan x + \frac{dy}{dx} = 5 \sin x \] is:
The value of \( \int_{-2}^{2} x |x| \,dx \) is:
The velocity (\( v \))-time (\( t \)) graph for the motion of a body is a straight line making an angle \( 60^\circ \) with the time axis. Then the body is moving with an acceleration (in m\( s^{-2} \)) of:
If two dice are rolled simultaneously, then the probability that the difference of the numbers on the two dice equals to zero is
In a nuclear fusion process, the masses of the fusing nuclei are \( M_A \) and \( M_B \). Then the mass of the product nucleus \( M_C \) is related to \( M_A \) and \( M_B \) as
The electron concentration \( n_e \) and hole concentration \( n_h \) in semiconductor are related to the number of intrinsic charge concentration \( n_i \) as
An intrinsic semiconductor at \( T = 0 \, {K} \) behaves like

The energy stored in the capacitor after closing the key K is