List of top Questions asked in KEAM

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?
Find the term independent of $ x $ in $ \left( 2x - \frac{5}{x^2} \right)^6 $
If $ f(x) = \frac{\sqrt{x^4}}{\sqrt{x^2}} $, find $ f'(27) $.
Which of the following is mismatched pair?
Three identical resistors are connected as triangle ABC. Voltage across AB = 12V. Find the ratio of current through AB to ACB:
If maximum height and range are equal in projectile motion, then $ \tan \theta = ... $:
If $ f(x) = \frac{1}{x^2} $, $ u = f(x) $, and $ f'(x) $, then find $ \frac{du}{dx} $.
The ratio of the wavelength of two particles with energy $ E $ and $ 3E $ respectively, is:
Product of $ P $ and $ V $ of an ideal gas related to translational part of internal energy $ E $ as
Solve for $ \alpha $ if: $ \cos^{-1}(2 \sin \alpha) = \frac{47}{12} $
Find the half-life of a first order reaction if $ K = 2.31 \times 10^5 \, \text{s}^{-1} $.
If ABCD is a rectangle, $ AB = 5i + 4j - 3k $ and $ AD = 3i + 2j - k $, then find $ BD $.
Evaluate the integral: $ \int \frac{\sec^2(\sqrt{2x+5})}{\sqrt{2x+5}} \, dx $
Evaluate the integral $ I = \int \frac{\sin 4x}{\sin 2x} \, dx $
Evaluate the integral: $ \int e^{-x} \cdot e^{3x} \, dx $
Evaluate the integral: $ \int_0^\pi \frac{\tan x}{\cos x} \, dx = \int_0^\pi \frac{\sin x}{\cos^2 x} \, dx $
Evaluate the integral: $ \int_{-1}^1 |x - 3| \, dx $
What is the de Broglie wavelength of the particle having kinetic energy of $ 2E $?
If Young's modulus and densities are in the ratio 3:2 and 3:1 respectively, the ratio of velocity of sound is:
Find the value of $ \sin 60^\circ - \sin 80^\circ + \sin 100^\circ - \sin 120^\circ $
If $ \sum_{k=0}^{n+1} C_k^n = 512 $, find $ \sum_{k=0}^{n} C_k^n $.
Find the limit: $ \lim_{x \to 0^+} 2 \left\lfloor x \right\rfloor - \frac{x}{|x|} $
Which of the following are neutral?
If $ \mu_s $ and $ \mu_k $ are static and kinetic friction, then:
Equation of parabola having focii (-3, 1) and (3, 1)