List of top Questions asked in KEAM- 2024

The integral \( \int \tan^5 x \sec^2 x \, dx \) is equal to:
The solution of \( \frac{dy}{\cos y} = dx \) is:
The correct electronic configuration of Tc (Z = 43) is:
Which of the following isoelectronic species has the smallest radius?
Which of the following molecule has the highest dipole moment?
If \( \left\lfloor x^2 \right\rfloor \) is the greatest integer less than or equal to \( x^2 \), then \[ \int_0^{\sqrt{2}} \left\lfloor x^2 \right\rfloor \, dx = \]
Let \( \left\lfloor x \right\rfloor \) be the greatest integer less than or equal to \( x \). Then \[ \lim_{x \to 0^-} \frac{x \left( \left\lfloor x \right\rfloor + |x| \right)}{|x|} \] is equal to:
For which one of the following equilibria, \( K_P = K_C \)?
If

\[ \int x e^{-x} \, dx = M e^{-x} + C, \quad \text{where } C \text{ is an arbitrary constant, then } M \text{ is equal to:} \]
The area enclosed by the curve \[ x = 3 \cos \theta, \quad y = 5 \sin \theta, \quad 0 \leq \theta \leq 2\pi, \] is equal to:
If \( \sec(\alpha + \beta) = \frac{\sqrt{7}}{\sqrt{3}} \), then \( \sin(\alpha + \beta) + \tan(\alpha + \beta) \) is equal to:
If \[ \sin^{-1} x + \cos^{-1} y = 0, \] then \( x^2 + y^2 \) is equal to:
In which of the following reaction Lindlar's catalyst is used?
If \( |x| \leq 1 \), then \( \sin \left( 2 \sin^{-1} x + \cos^{-1} x \right) \) is equal to:
Three dice are thrown simultaneously. The probability that all the three outcomes are the same number, is:
Which of the following aqueous mixture is a buffer solution?
The expression
\[ \frac{1 + \cos\left(\frac{\pi}{5}\right) + i \sin\left(\frac{\pi}{5}\right)}{1 + \cos\left(\frac{\pi}{5}\right) - i \sin\left(\frac{\pi}{5}\right)} \] is equal to:
Which of the following base is not present in RNA molecule?
The ratio of the velocities of the electron in the second, third and fourth Bohr’s orbits of the hydrogen atom is:
If \( f(x) = \frac{|x|}{1 + |x|}, \, x \in \mathbb{R} \), then \( f'(-2) \) is equal to:
When \( y = vx \), the differential equation \[ \frac{dy}{dx} = \frac{y}{x} + \frac{f\left( \frac{y}{x} \right)}{f'\left( \frac{y}{x} \right)} \] reduces to:
Find the TRUE statement of the algebraic operations of scalar and vector quantities.
The mutual inductance between a pair of coils A and B placed close to each other depends upon:

The limit: \[ \lim_{x \to 0} \frac{\sin \left( \pi \sin^2 x \right)}{x^2} \] is equal to:

Which one of the following phenomena does not occur when a white light falls on an equilateral glass prism?