List of top Questions asked in KEAM

Given $ Z_1 = \frac{1}{2} + \frac{\sqrt{3}}{2}i, \quad Z_2 = -\frac{1}{2} - \frac{\sqrt{3}}{2}i, \quad \text{and} \quad w = Z_1 + Z_2, \quad \text{find} \, w. $
Find the log $ K $ value, if $ \Delta G = -11.4 $ and $ 2.303 \cdot RT = 5.7 \times 10^1 $.
Which complex has dsp$^2$ hybridisation?
Find the half-life of a first order reaction if $ K = 2.31 \times 10^5 \, \text{s}^{-1} $.
Find the term independent of $ x $ in $ \left( 2x - \frac{5}{x^2} \right)^6 $
Evaluate the integral $ I = \int \frac{\sin 4x}{\sin 2x} \, dx $
If ABCD is a rectangle, $ AB = 5i + 4j - 3k $ and $ AD = 3i + 2j - k $, then find $ BD $.
Velocity of man swimming along the flow of river is 10 km/h and against the flow is 6 km/h. Velocity of man in still water is
If the torque on electric dipole placed with $30^\circ$ to electric field is $ \tau $, then what will be the torque if it is placed $45^\circ$ with electric field?
Mean free path is inversely proportional to (n = number density, d = diameter of particle)
4 masses are placed at 4 corners of square ABCD. If one mass is removed from the corner B, then the centre of mass lies in the line joining
Product of $ P $ and $ V $ of an ideal gas related to translational part of internal energy $ E $ as
Find object distance of concave mirror of $ R = 24 \, \text{cm} $ which gives magnification of 3.
The ratio of the velocity of light in a vacuum to that in a medium is?
Moment of inertia of solid sphere having mass M and radius R about an axis passing through diameter is I. Moment of inertia of sphere of mass 2M and radius 2R is:
Rectangular loop of side $a$ and carrying current $I$ is placed perpendicular to magnetic field. What will be the magnetic moment?
Given the set $ S = \{ a, b, c, d, e, f \} $, find the total number of subsets with an odd number of elements.
Solve the differential equation: $ (1 + y) \, dx = (1 + x) \, dy $
Find the limit: $ \lim_{x \to 11} \frac{x - 11}{\sqrt{49 + x^2} - 13} $
If $ \sum_{k=0}^{n+1} C_k^n = 512 $, find $ \sum_{k=0}^{n} C_k^n $.
If $ a, a r, a r^2 $ are in a geometric progression (G.P.), then find the value of: $ \left| a \quad a r \right| \quad \left| a r^2 \quad a r^3 \right| = \left| a r^3 \quad a r^6 \right| $
Find the limit: $ \lim_{x \to 0^+} 2 \left\lfloor x \right\rfloor - \frac{x}{|x|} $
Find the limit: $ \lim_{x \to 0^+} 2 \left\lfloor x \right\rfloor - \frac{x}{|x|} $
Find the domain of the function: $ f(x) = \sqrt{7 - 11x} $
Equation of parabola having focii (-3, 1) and (3, 1)