List of top Questions asked in KEAM- 2025

Find the domain of the function: $ f(x) = \sqrt{7 - 11x} $
Three identical resistors are connected as triangle ABC. Voltage across AB = 12V. Find the ratio of current through AB to ACB:
Evaluate the following limit: $ \lim_{x \to 0} \frac{1 + \cos(4x)}{\tan(x)} $
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 limit: $ \lim_{x \to 11} \frac{x - 11}{\sqrt{49 + x^2} - 13} $
Product of $ P $ and $ V $ of an ideal gas related to translational part of internal energy $ E $ as
Equation of parabola having focii (-3, 1) and (3, 1)
If $ \sum_{k=0}^{n+1} C_k^n = 512 $, find $ \sum_{k=0}^{n} C_k^n $.
Find the term independent of $ x $ in $ \left( 2x - \frac{5}{x^2} \right)^6 $
If ABCD is a rectangle, $ AB = 5i + 4j - 3k $ and $ AD = 3i + 2j - k $, then find $ BD $.

If $ |\vec{a}| = 5 $, $ |\vec{b}| = 8 $, $ |\vec{a} - \vec{b}| = 7 $, find the angle between  $ \vec{a} $ and $ \vec{b} $.

Find object distance of concave mirror of $ R = 24 \, \text{cm} $ which gives magnification of 3.
Solve the following differential equation and integrate: $ \frac{dy}{dx} + \frac{2x}{1 + x^2} \cdot y = x $
Evaluate the integral: $ \int e^{-x} \cdot e^{3x} \, dx $
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| $
If maximum height and range are equal in projectile motion, then $ \tan \theta = ... $:
If the angular displacement in 10 seconds is $ 150^\circ $, find the number of revolutions in 10 seconds.
The orbital velocity of a satellite is $ V_0 $, at a height $ h = R $ (where $ R $ is the radius of the Earth) from the surface of the Earth. What is the relationship between $ V_0 $ and the escape velocity $ V_e $?
If $ F = 6\pi \eta x $, find the dimension of $ x $.

Find the incorrect statement: 
A) Isobaric - constant pressure 
B) Isochoric - constant volume 
C) Isothermal - constant temperature 
D) Adiabatic - involves heat exchange

Entropy decreases in which of the following reactions? $ \text{(A) } \text{Br}_2 (l) \to \text{Br}_2 (g) $ $ \text{(B) } \text{Br}_2 (g) \to \text{Br}_2 (l) $ $ \text{(C) } \text{Br}_2 (l) \to \text{Br}_2 (g) \text{ and } \text{Br}_2 (g) \to \text{Br}_2 (l) $
Find the area between the line $ y = x - 1 $, $ y = 0 $, $ -2 \leq y \leq 2 $.

Which of the following cannot form hydrogen bonding?
A) Phenol  
B) Diethyl ether 
C) Aniline 

1 torr = ________