KEAM 2025 April 28 Question Paper (Available) :Download Solutions with Answer Key

Which of the following is not an EWG (Electron Withdrawing Group)?

• (A) CN
• (B) COOH
• (C) COOR
• (D) OCH\(_3\)

CrO\(_3\) is -------- oxide?

• (A) Chromium (III) oxide
• (B) Chromium (IV) oxide
• (C) Chromium (V) oxide
• (D) Chromium (VI) oxide

Radius order of Yb\(^{3+}\), La\(^{3+}\), Ce\(^{3+}\), Pm\(^{3+}\)?

• (A) Yb\(^{3+}\) \(>\) La\(^{3+}\) \(>\) Ce\(^{3+}\) \(>\) Pm\(^{3+}\)
• (B) Yb\(^{3+}\) \(<\) La\(^{3+}\) \(<\) Ce\(^{3+}\) \(<\) Pm\(^{3+}\)
• (C) Yb\(^{3+}\) \(>\) Ce\(^{3+}\) \(>\) Pm\(^{3+}\) \(>\) La\(^{3+}\)
• (D) Yb\(^{3+}\) \(<\) Ce\(^{3+}\) \(<\) Pm\(^{3+}\) \(<\) La\(^{3+}\)

For a first-order reaction, if the rate constant is \( k = 6.93 \times 10^{-3} \), what is the half-life (\( t_{1/2} \)) of the reaction?

• (A) \( t_{1/2} = \frac{0.693}{k} \)
• (B) \( t_{1/2} = \frac{1}{k} \)
• (C) \( t_{1/2} = \frac{2}{k} \)
• (D) \( t_{1/2} = k \)

A wave from a source having power 1 watt is incident on a surface of area 200 m\(^2\). What is the intensity of the wave?

• (A) \( I = \frac{P}{A} = \frac{1}{200} \)
• (B) \( I = P \times A \)
• (C) \( I = P + A \)
• (D) \( I = \frac{A}{P} \)

Increasing ionic radii of lanthanoids having +2 oxidation state?

• (A) La\(^{2+}\) \(<\) Ce\(^{2+}\) \(<\) Pr\(^{2+}\) \(<\) Nd\(^{2+}\)
• (B) Eu\(^{2+}\) \(<\) Sm\(^{2+}\) \(<\) Gd\(^{2+}\) \(<\) Tb\(^{2+}\)
• (C) La\(^{2+}\) \(<\) Nd\(^{2+}\) \(<\) Pr\(^{2+}\) \(<\) Eu\(^{2+}\)
• (D) Eu\(^{2+}\) \(<\) Gd\(^{2+}\) \(<\) Tb\(^{2+}\) \(<\) Dy\(^{2+}\)

Mobility is the ratio of drift velocity and ________?

• (A) Current
• (B) Electric field
• (C) Charge
• (D) Resistance

Ratio of wavelength of first two modes of open pipe

• (A) 2:1
• (B) 1:2
• (C) 1:1

If the mean kinetic energy of Helium is 5000 J at 400 K, then the kinetic energy of neon at 800 K is

• (A) 10000 J
• (B) 12500 J
• (C) 5000 J
• (D) 20000 J

A body starts from rest and is moving with a constant acceleration \( a \). The relation between instantaneous displacement and time is

• (A) \( s = ut + \frac{1}{2} at^2 \)
• (B) \( s = \frac{1}{2} at^2 \)
• (C) \( s = a t^2 \)
• (D) \( s = v t \)

Total kinetic energy of a satellite at height \( h \) is \( k \). Then total energy of the satellite is

• (A) \( -k \)
• (B) \( -2k \)
• (C) \( k \)
• (D) \( -3k \)

A farm roller of mass 100 kg is given a force of 300 N at a \( 30^\circ \) angle to the ground. Find net force acting on it in the vertical direction.

• (A) 150 N
• (B) 300 N
• (C) 250 N
• (D) 100 N

Radius of gyration of a disc about its diameter is?

• (A) \( \frac{r}{\sqrt{2}} \)
• (B) \( \frac{r}{\sqrt{3}} \)
• (C) \( \frac{r}{2} \)
• (D) \( \frac{r}{4} \)

Gyro magnetic ratio is?

• (A) \( \frac{M}{I} \)
• (B) \( \frac{I}{M} \)
• (C) \( \frac{q}{m} \)
• (D) \( \frac{m}{q} \)

Dimensional formula of Planck’s constant is similar to

• (A) Angular momentum
• (B) Linear momentum
• (C) Force
• (D) Velocity

The work done to move a charge of 3 C from A to B is 12 J. Find potential difference between A and B.

• (A) 4 V
• (B) 6 V
• (C) 12 V
• (D) 3 V

Resistivity of a wire is proportional to

• (A) Relaxation time
• (B) Area
• (C) Length
• (D) Temperature
• (E) Number density of electrons

If \( f(x) = \sin x e^{\sin x} \), find \( f'(x) \)

• (A) \( \cos x e^{\sin x} + \sin x e^{\sin x} \)
• (B) \( \cos x e^{\sin x} - \sin x e^{\sin x} \)
• (C) \( \cos x e^{\sin x} + e^{\sin x} \)
• (D) \( \cos x e^{\sin x} + \sin x e^{\cos x} \)

If \( \tan(x - y) = \frac{4}{5} \), \( \tan(x + y) = \frac{6}{5} \), then \( \tan(2x) = \)

• (A) \( \frac{11}{12} \)
• (B) \( \frac{12}{11} \)
• (C) \( \frac{13}{14} \)
• (D) \( \frac{14}{13} \)

Evaluate \( \int_1^3 [x - 1] \, dx \)

• (A) 4
• (B) 6
• (C) 8
• (D) 10

P(A) = 0.4, P(B/A) = 0.9. Then P(A ∩ B) is

• (A) 0.36
• (B) 0.54
• (C) 0.72
• (D) 0.84

Distance between two foci of the hyperbola \( x^2 - 4y^2 = 16 \) is

• (A) 4
• (B) 6
• (C) 8
• (D) 10

If \( |x + 3| < 2 \), then \( x \) lies in

• (A) \( (-5, -1) \)
• (B) \( (-2, 2) \)
• (C) \( (-4, -2) \)
• (D) \( (-1, 5)

If \( f(x) \) is continuous in \( \mathbb{R} \), \[ f(x) = \begin{cases} \frac{3x^2 - 12}{x - 2}, & x \neq 2
k, & x = 2 \end{cases} \]
find \( k \).

• (A) 3
• (B) 2
• (C) 4
• (D) 6

If \( 1, a, b, c, 16 \) is in G.P., then \( \sqrt[3]{abc} = \)

• (A) 4
• (B) 8
• (C) 16
• (D) 12

Evaluate \( \int \sin x \cdot \sin 2x \, dx \)

• (A) \( -\frac{1}{4} \cos 3x + \frac{1}{4} \cos x \)
• (B) \( -\frac{1}{4} \cos 3x - \frac{1}{4} \cos x \)
• (C) \( \frac{1}{4} \cos 3x + \frac{1}{4} \cos x \)
• (D) \( \frac{1}{4} \cos 3x - \frac{1}{4} \cos x \)