KEAM 2026 Engineering April 18 Question Paper: Download Answer Key with Solutions PDF

If two planets A and B have their densities in the ratio 2:1 and radii in the ratio 1:2, what will be the ratio of escape velocities from their surfaces?

Three bulbs of power 10 W, 25 W, and 50 W are connected parallel across a voltage source \( V \). What is the effective power of the combination?

Two lenses, one of focal length 20 cm and another of power 4D are placed together, what is the effective power of the combination?

A constant force acts on a body at rest, resulting it to move with constant acceleration. If power relates to time as \( P \propto t^n \), what is the value of \( n \)?

Which force holds the nucleons together in the nucleus of the atom?

If the de Broglie wavelength of \( \alpha \)-particle and proton are equal, then the momentum \( P \) and kinetic energy \( E \) are related as:

• (A) \( P_{\alpha} = P_{p} \)
• (B) \( P_{\alpha} > P_{p} \)
• (C) \( E_{\alpha} = E_{p} \)
• (D) \( E_{\alpha} > E_{p} \)

A body starting from rest moves with a constant acceleration of \( 2 \, m/s^2 \). What is the distance covered by the body in the interval between 5 s and 6 s?

If current through a single circular loop of radius 10 cm produces a magnetic field of \( B \, Tesla \) at the centre, what is the current through the loop?

What happens to a ferromagnetic material when its temperature is raised above Curie temperature?

If \( \vec{F} \) and \( \vec{S} \) represent force and displacement respectively, then which of the following statements is true:

• (A) Work is maximum when \( \vec{F} \) and \( \vec{S} \) are at right angles
• (B) Work is positive when \( \vec{F} \) and \( \vec{S} \) are at obtuse angle
• (C) Work is negative when \( \vec{F} \) and \( \vec{S} \) are at acute angle
• (D) Work is zero if \( \vec{F} \) and \( \vec{S} \) are in opposite direction
• (E) Area under \( \vec{F} \)-\( \vec{S} \) graph gives work done

Magnitude and direction of acceleration changes for:

• (A) Simple harmonic motion
• (B) Body falling under gravity at low altitude
• (C) Body falling under gravity at high altitude
• (D) Circular motion with constant speed
• (E) Body falling in a viscous liquid

A couple can result in which type of motion:

• (A) Translational motion
• (B) Vibrational motion
• (C) Both translation and vibration motion
• (D) Rotational motion

First element in 3d series which shows +2, +3, +4, +6 oxidation state

• (A) Cr
• (B) Mn
• (C) Fe
• (D) Co
• (E) Ni

Which of the following is used to convert sodium chromate to sodium dichromate in the preparation of potassium dichromate?

• (A) \( Na_2CO_3 \)
• (B) \( NaOH \)
• (C) \( KClO_3 \)
• (D) \( H_2SO_4 \)
• (E) \( H_2O_2 \)

Which of the following series in hydrogen spectrum corresponds to UV radiation?

• (A) Lyman
• (B) Balmer
• (C) Pachen
• (D) Brackett

When CO is reacted with \( H_2 \) at 573 K, methanol is formed. Which is the catalyst used in this process?

• (A) Pd-BaSO₄
• (B) Ni-CrO₃
• (C) ZnO - Cr₂O₃
• (D) Pt-BaSO₄
• (E) CuO - Cr₂O₃

Which of these have the least bond length (in pm)?

• (A) \( O_2 \)
• (B) \( Cl_2 \)
• (C) \( Br_2 \)
• (D) HF
• (E) \( F_2 \)

Two solutions that are isotonic have same ______ .

• (A) Same boiling point
• (B) Same freezing point
• (C) Same vapour pressure
• (D) Same osmotic pressure
• (E) Same solubilities

2-methyl propene is obtained as product when sodium methoxide reacts with

• (A) 2-chloropropane
• (B) Isobutyl bromide
• (C) tert-butyl bromide
• (D) n-butyl bromide
• (E) sec-butyl bromide

Find the alkene which gives 2 mol of acetone by ozonolysis.

Benzene diazonium salt in the presence of Cu/HBr will give bromobenzene (C\(_6\)H\(_5\)Br) and release nitrogen gas (N\(_2\)). This reaction is known as:

Which aldehyde does not give Fehling test?

• (A) Methanal
• (B) Propanal
• (C) Ethanal
• (D) Butanal
• (E) Phenylmethanal

What is the name of the element which is known as Eka-Aluminium?

Evaluate the integral:
\[ \int \left( 27x^3 (1 - x^3)^{\frac{1}{3}} \right) dx \]

• (A) \( \frac{27}{4} (1 - x^3)^{\frac{4}{3}} + C \)
• (B) \( \frac{27}{5} (1 - x^3)^{\frac{5}{3}} + C \)
• (C) \( -\frac{27}{4} (1 - x^3)^{\frac{4}{3}} + C \)
• (D) \( -\frac{27}{5} (1 - x^3)^{\frac{5}{3}} + C \)

Solve the equation:
\[ \frac{(3x - 4)^2}{9} - \frac{(4x - 3)^2}{8} = 1 \] (length of the latus rectum)

Given that \( |AB| = 21 \) and \( |A^{-1}| = 7 \), find \( |B| \).

Find the number of combinations of 3-lettered numbers that can be created by 3, 4, 5, and 7 with repeating. The three digits cannot be equal to zero.

Evaluate the integral: \[ \int_0^1 \frac{t}{(t + 1)^3} \, dt \]

• (A) \( \frac{1}{8} \)
• (B) \( \frac{1}{4} \)
• (C) \( \frac{1}{2} \)
• (D) \( \frac{1}{16} \)

The 1st and 20th term of a GP are 512 and \( \frac{1}{1024} \), respectively. Find the common ratio.

Evaluate the integral: \[ \int 16x^3 \log_e x \, dx \]

• (A) \( \frac{4x^4}{\ln x} \)
• (B) \( 16x^4 \ln x - 4x^4 \)
• (C) \( 4x^4 \ln x - \frac{4x^4}{\ln x} \)
• (D) \( 4x^4 \ln x + \frac{4x^4}{\ln x} \)

If \( ay = x + b \) is the equation of the line passing through the points (-5, -2) and (4, 7), then the value of \( 2a + b \) is equal to:

• (A) 1
• (B) 3
• (C) 5
• (D) -3
• (E) -1

The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0, -4) is

• (A) \( 5x + 2y = 21 \)
• (B) \( 5x + 2y = 0 \)
• (C) \( 2x - 5y = 21 \)
• (D) \( 5x - 2y = 21 \)
• (E) \( 2x + 3y = 21 \)

The end-points of a diameter of a circle are \( (-1, 4) \) and \( (5, 4) \). Then the equation of the circle is

• (A) \( (x - 3)^2 + y^2 = 9 \)
• (B) \( (x - 3)^2 + (y + 4)^2 = 3 \)
• (C) \( (x - 2)^2 + (y - 4)^2 = 9 \)
• (D) \( (x + 3)^2 + (y + 4)^2 = 9 \)
• (E) \( (x - 3)^2 + (y - 4)^2 = 4 \)

A 3-digit number greater than 500 is to be made with the numbers 3, 4, 5, and 7. Find the number of possible ways.

Given: \( P(B) = 0.8 \) and \( P(A \cup B) = 0.8 \), find \( P(A' \cup B') \).