KEAM 2026 Engineering April 17 Question Paper: Download Answer Key with Solutions PDF

In YDSE, when light of wavelength 700nm is used, a fringe width of 0.5mm is obtained. What happens when light of wavelength 500nm is used?

When light containing photon of energy \(2h\nu_0\) falls on a metal of work function \(h\nu_0\), electrons of velocity \(v_1\) are ejected. When photons of energy \(5h\nu_0\) is incident, velocity of electrons ejected is \(v_2\). What is the ratio \( \frac{v_1}{v_2} \)?

Consider a convex lens made of material of refractive index \( n = \frac{3}{2} \) and radius of curvature \( R \). What is the relation between focal length and radius?

• (A) \( f = \frac{R}{2} \)
• (B) \( f = \frac{R}{4} \)
• (C) \( f = \frac{R}{3} \)
• (D) \( f = \frac{2R}{3} \)

Kinetic energy of a particle of mass \( 1 \times 10^{31} \, kg \) and wavelength 63 nm (where \( h = 6.3 \times 10^{-34} \, Js \))

• (A) \( 1.56 \times 10^{-3} \, J \)
• (B) \( 1.34 \times 10^{-3} \, J \)
• (C) \( 1.00 \times 10^{-3} \, J \)
• (D) \( 2.46 \times 10^{-3} \, J \)

Dimension of Planck's constant is same as that of:

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

What is the number of significant figures in \( 420.00040 \times 10^{-3} \)?

Two metallic spheres of radii 1:2 are connected by a conducting wire. What is the ratio of electric field intensities at their surface?

What is the ratio of maximum height attained to the height attained at \( t = 1 \) s for a projectile of initial velocity \( u \) projected at an angle \( 30^\circ \) with horizontal?

If \( r_1 = \frac{c_p}{c_v} \) of a rigid diatomic gas and \( r_2 = \frac{c_p}{c_v} \) of a non-rigid diatomic gas, find \( r_1 \) and \( r_2 \).

If a body travels half of the total distance with velocity of \(20 \, km/hr\) and other half with velocity of \(30 \, km/hr\), find average velocity.

If an open pipe suddenly closed, the frequency of the third harmonic of the closed pipe is 50Hz more than the fundamental frequency of the open pipe. Find the fundamental frequency.

Given mass of neutron \( 1.0087 \, u \), mass of proton \( 1.0073 \, u \), mass of \( ^4He \) \( = 4.0018 \, u \), find the binding energy of He.

• (A) \( 27.8 \, MeV \)
• (B) \( 28.1 \, MeV \)
• (C) \( 29.5 \, MeV \)
• (D) \( 30.2 \, MeV \)

If \( I \), \( E \) and \( L \) are the moment of inertia, rotational kinetic energy, and angular momentum respectively, then:

• (A) \( I = \frac{E}{L} \)
• (B) \( 2E = \frac{I}{L} \)
• (C) \( L = \sqrt{2EI} \)
• (D) \( E = L = \frac{L}{I} \)

Kirchhoff's first and second laws are consequence of conservation of ----- and ----- respectively:

• (A) Energy and Charge
• (B) Charge and Energy
• (C) Angular momentum and energy of capacitance C

Two identical capacitors of capacitance \( C \) are connected in series. If the space between the plates of one of the capacitors is filled with a medium of dielectric constant \( k \), what is the effective capacitance?

If the ratio of escape velocities is 3:2 from two different planets A and B of radii in the ratio 2:3, find the ratio of acceleration due to gravity at the surface of A to that at the surface of B.

Find the velocity of wave given by \( y = 0.05 \sin \left( \frac{2\pi}{\lambda} (x - 200t) \right) \).

If work function of a metal is 6.6 eV, find the threshold wavelength.
Given \( h = 6.6 \times 10^{-34} \, J \cdot s \).

A circular loop is made from a wire of length 6m. If 2A current passes through the circular loop, what is the magnetic moment of the loop?

A galvanometer of 500Ω resistance is shunted such that only 4% of the current passes through the galvanometer. Find the shunt resistance.

• (A) 12.5Ω
• (B) 15Ω
• (C) 18Ω
• (D) 20Ω

If a body of mass 5 kg has a linear momentum of 4 kg⋅m/s, find the kinetic energy.

• (A) 4J
• (B) 8J
• (C) 16J
• (D) 32J

Find the relation between the wavelength of proton and electron, if both particles have the same kinetic energy.

A particle of charge equal to 10 times the charge of electrons revolves in a circle with frequency equal to 10 revolutions per second. Find the magnetic field at the centre of the circular path.

If \( I = 2 \, A, \, \phi = 10^{-2} \, Weber, \, N = 1000 \), calculate the self-inductance.

What should be connected in the circuit to remove ripples in AC?

What should be connected in the circuit to remove ripples in AC:

• (A) Capacitor in series with load resistance
• (B) Capacitor in parallel with load resistance
• (C) Inductor connected in parallel with load resistance
• (D) Inductor connected in series with load resistance

Bernoulli's principle is applicable for:

• (A) Non-compressible non-viscous fluid having stream line flow
• (B) Non-compressible non-viscous fluid having turbulent flow
• (C) Compressible viscous fluid having stream line flow
• (D) Compressible viscous fluid having turbulent flow

If power = 150 kW, torque = 100 Nm, find the angular velocity \(\omega\).

What is the ratio of the longest wavelength in Lyman and Balmer series?

A Carnot engine is working between 400K and 500K. If the output work is 1 kJ, what is the heat absorbed?

• (A) 2 kJ
• (B) 3 kJ
• (C) 4 kJ
• (D) 5 kJ

At a certain height \( h \) from the surface of Earth, the value of acceleration due to gravity is \( \frac{g}{9} \), where \( g \) is the acceleration due to gravity at the surface. What is the value of \( h \) in terms of the radius of Earth \( R \)?

• (A) \( \frac{R}{2} \)
• (B) \( \frac{R}{3} \)
• (C) \( 2R \)
• (D) \( 3R \)

If a proton is displaced by 5m in an electric field of \(50 \, N/C\), what is the work done by the electric field?

A particle of charge equal to 10 times the charge of an electron revolves in a circle with frequency equal to 10 revolutions per second. Find the magnetic field at the centre of the circular path.

Given \( I = 2A \), \( \phi = 10^{-2} \, weber \), \( N = 1000 \), calculate the self-inductance.

• (A) \( 0.5 \, H \)
• (B) \( 1.0 \, H \)
• (C) \( 1.5 \, H \)
• (D) \( 2.0 \, H \)

What should be connected in the circuit to remove ripples in AC:

• (A) Capacitor in series with load resistance
• (B) Capacitor in parallel with load resistance
• (C) Inductor connected in parallel with load resistance
• (D) Inductor connected in series with load resistance

Bernoulli's principle is applicable for:

• (A) Non-compressible non-viscous fluid having stream line flow
• (B) Non-compressible non-viscous fluid having turbulent flow
• (C) Compressible non-viscous fluid having stream line flow
• (D) Compressible viscous fluid having stream line flow

If \( I = 16 \, A \), electron density \( n = 5 \times 10^{23} \, m^{-3} \), and \( A = 1 \times 10^{-7} \, m^2 \), find the drift velocity.

Transformer core is laminated because:

• (A) To reduce eddy current loss
• (B) To reduce hysteresis loss
• (C) To reduce copper loss
• (D) To reduce core loss

For an elastic collision

• (A) both momentum and K.E is conserved
• (B) only K.E is conserved
• (C) only momentum is conserved
• (D) neither momentum nor K.E conserved

Current in a circuit is 0.6 A when an external resistance of \( 3 \, \Omega \) is connected. When the external resistance is changed to \( 6 \, \Omega \), current in the circuit becomes 0.4 A. Find the internal resistance of the cell.

Which of the following statement is correct for EM wave:

• (A) Velocity in vacuum is \( 3 \times 10^6 \, cm/s \)
• (B) They can travel in vacuum
• (C) Energy density of electric field and magnetic field are different
• (D) It contains electric field vibration only
• (E) It contains magnetic field vibration only

Transformer core is laminated because:

• (A) To reduce eddy current loss
• (B) To reduce hysteresis loss
• (C) To reduce copper loss
• (D) To reduce core loss

For an elastic collision

• (A) both momentum and K.E is conserved
• (B) only K.E is conserved
• (C) only momentum is conserved
• (D) neither momentum nor K.E is conserved

What is the IUPAC name of Mesityl oxide?

• (A) 4-methylpent-3-en-2-one
• (B) 2,4,6-Trimethylphenylacetone
• (C) 2,4,6-Trimethyl-3-penten-2-one
• (D) 2,4,6-Trimethyl-3-hexen-2-one

IUPAC name of Element number 105?

What is 1-chlorocyclohexene?

• (A) Vinylic Halide
• (B) Benzylic Halide
• (C) Allylic Halide

Decreasing order basic strength

• (A) \( NH_3 > CH_3NH_2 > (CH_3)_2NH > (CH_3)_3N \)
• (B) \( (CH_3)NH_2 > CH_3NH_2 > (CH_3)_2NH > NH_3 \)
• (C) \( CH_3NH_2 > (CH_3)_2NH > (CH_3)NH_2 > NH_3 \)

The KE of particle of mass \(1 \times 10^{-31}\) Kg and the de Broglie wavelength 63 nm (h = \(6.3 \times 10^{-34}\))

Which of the following have minimum and maximum threshold energy K, Na, Mg, Li?

Number of C−C, C−H, C=C in But-2-ene-1-yne respectively

There is 40 % C, 67% H2, find the empirical formula

Energy of \(2h\nu_0\) fall on a metal of work function \(h\nu_0\) cause velocity of \(v_1\), when \(5h\nu_0\) fall velocity ratio of \(v_1/v_2\)

• (A) \(v_1/v_2 = 1/5\)
• (B) \(v_1/v_2 = 5/1\)
• (C) \(v_1/v_2 = 1/25\)
• (D) \(v_1/v_2 = 25/1\)

The isomerism shown by the following compound:
\[ [Co(CN)_6][Cr(NH_3)_6] \quad [Co(CN)_6][Cr(NH_3)_6] \]

• (A) Ionisation isomerism
• (B) Coordinate isomerism
• (C) Linkage isomerism
• (D) Hydrate isomerism

P\(_4\) \(\rightarrow\) PH\(_3\) + H\(_2\)PO\(_2\)
Oxidation state of phosphorus change from -------- to -------- respectively.

Which 3d series of element has least enthalpy of atomization?

• (A) Sc
• (B) Mn
• (C) V
• (D) Cu
• (E) Zn

Ratio of between the maximum wavelength of Lyman and Balmer series.

• (A) \( \frac{5}{27} \)
• (B) \( \frac{27}{5} \)
• (C) \( \frac{4}{3} \)
• (D) \( \frac{36}{5} \)
• (E) \( \frac{5}{36} \)

The \( K_c \) of the reaction
\[ NH_3(g) + O_2(g) \rightleftharpoons 2NO(g) \]

at 1500 K is 0.1. What is the concentration of NO, when the initial concentration of \( N_2 \) and \( O_2 \) is 0.04 mol?

• (A) \( 1.09 \times 10^{-2} \, M \)
• (B) \( 10.9 \times 10^{-2} \, M \)
• (C) \( 2.18 \times 10^{-2} \, M \)
• (D) \( 1.09 \times 10^{-4} \, M \)
• (E) \( 2.18 \times 10^{-4} \, M \)

Which reagent gives as major product from phenol

• (A) \( Br_2 + CS_2, at 273 \, K \)
• (B) \( Br_2 + heat \)
• (C) Bromine water
• (D) \( Br_2 + CCl_4 at 273 \, K \)
• (E) \( Br_2 + acetone at 273 \, K \)

Hinsberg reagent is

• (A) p-toluene sulphonyl chloride
• (B) Benzene sulphonyl chloride
• (C) Phthalimide and KOH
• (D) Anhydrous ZnCl\(_2\) and conc HCl
• (E) Benzoyl chloride and NaOH

If ‘m’ is the molality, ‘M’ is the molarity, ‘d’ is the density in g/cm\(^3\) and ‘M\(_2\)’ is the molarity of solute. What is the relation between them?

Which of the following has highest pKa value?

• (A) CH\(_3\)COOH
• (B) F-CH\(_2\)-COOH
• (C) CN-CH\(_2\)-COOH
• (D) Cl-CH\(_2\)-COOH
• (E) NO\(_2\)-CH\(_2\)-COOH

Which of the following statements regarding the structure of CO\(_2\) is correct?

• (A) CO\(_2\) contains 1 C=O and 1 C=O and one lone pair in each oxygen
• (B) CO\(_2\) contains 2 C=O, and 2 lone pairs in each oxygen
• (C) CO\(_2\) contains 2 C=O, and 2 lone pairs in each oxygen
• (D) CO\(_2\) contains 1 C=O, and 1 C=O and two lone pairs in each oxygen atom
• (E) None of these

Which of the following has a planar structure with two lone pairs?

• (A) XeF\(_4\)
• (B) NiF\(_4\)
• (C) SF\(_4\)
• (D) SF\(_6\)
• (E) XeF\(_4\)

Lactose is composed of:

• (A) \( \alpha \)-D glucose and \( \beta \)-D fructose
• (B) \( \beta \)-D glucose and \( \beta \)-D galactose
• (C) 2 units of \( \alpha \)-D glucose
• (D) 2 units of \( \beta \)-D glucose
• (E) \( \alpha \)-D glucose and \( \beta \)-D galactose

Which of the following is allylic alcohol?

• (A) \( C_6H_5CH_2OH \)
• (B) \( CH_2 = CH - C(CH_3)_2OH \)
• (C) \( CH_2 - CH_2 - CH_2OH \)
• (D) \( CH_3 - CH_2 - CH_2 - OH \)

Relationship between \( t_{90} \) and \( t_{99} \) for a first order reaction:

• (A) \( t_{99} = 3t_{90} \)
• (B) \( t_{99} = 2t_{90} \)
• (C) \( t_{99} = 2.303t_{90} \)
• (D) \( t_{99} = 20.693t_{90} \)
• (E) \( t_{99} = 6.93t_{90} \)

Enthalpy of formation of \( C_6H_6 \), \( CO_2(g) \) and \( H_2O(l) \) are -393.5, -285.8 and +48.5 KJ/mol respectively. Find the enthalpy of combustion of \( C_6H_6 \):

• (A) 3267.4 KJ/mol
• (B) 3218.49 KJ/mol
• (C) 857.5 KJ/mol
• (D) 2361 KJ/mol
• (E) 2361 KJ/mol

Increasing order of metallic character

• (A) \( Na > Mg > Be > Si > P \)
• (B) \( Na > Be > P > Si > Mg \)
• (C) \( Mg > Be > P > Si > Na \)
• (D) \( P > Si > Be > Mg > Na \)
• (E) \( Mg > Si > Be > Na > P \)

(3, −4) and (4, −a) lie on line. Find a?

If \(y = 4\sqrt{x}\) then \(\frac{d^2y}{dx^2} =\)

The range of the function \( f(x) = \frac{1}{7 + 4\sin x + 3\cos x} \)

• (A) \( \left[ \frac{1}{14}, \frac{1}{4} \right] \)
• (B) \( \left[ \frac{1}{7}, \frac{1}{3} \right] \)
• (C) \( \left[ \frac{1}{3}, \frac{1}{7} \right] \)
• (D) \( \left[ \frac{1}{7}, 1 \right] \)

Number of words that can be formed starting and ending with the same letter from the word BANANA.

• (A) 60
• (B) 72
• (C) 48
• (D) 36

Number of ways 3 boys and 4 girls can be arranged such that there is one girl between any 2 boys and one boy between any 2 girls.

If \( y = \frac{1 + \tan^2 x}{1 - \tan^2 x} \), find \( y' \left( \frac{\pi}{8} \right) \), where \( 0 < x < \frac{\pi}{4} \).

If \( \alpha = \frac{\pi}{4} \), find \( (\sin \alpha + \sin \beta)^2 + (\cos \alpha + \cos \beta)^2 \).

If \( y = \log_e (x^3 + 24) \), find \( \frac{dy}{dx} \) at \( y = \log_e 2 \).

Find \(\int_{-1}^{1} \frac{\log(1 + |x|)}{1 + |x|} \, dx\)

Find unit vector parallel to \(- (s + 4s) \hat{i} + (7 - 2s) \hat{j} + (3 + 4s) \hat{k}\)

Compute \( \int (\cot 2x + \cos 2x) \, dx \)

• (A) \( \frac{1}{2} \ln (\sin 2x) + \frac{1}{2} \sin 2x + C \)
• (B) \( \frac{1}{2} \ln (\sin 2x) + \frac{1}{2} \cos 2x + C \)
• (C) \( \ln (\sin 2x) + \sin 2x + C \)
• (D) \( \ln (\sin 2x) + \cos 2x + C \)

Compute \( \int \frac{\sqrt{x + 1}}{\sqrt{x}} \, dx \)

• (A) \( 2\sqrt{x+1} - \sqrt{x} + C \)
• (B) \( 2\sqrt{x+1} + \sqrt{x} + C \)
• (C) \( \sqrt{x+1} - \sqrt{x} + C \)
• (D) \( \sqrt{x+1} + \sqrt{x} + C \)

Solve \( 6(2x+3) + x > 53 - 2x \).

Evaluate \( \int \frac{x^2 + 6x + 1}{(x+3)^2} dx \).

Find \( \alpha \) if \[ \lim_{x \to 0} \frac{1 - \sec^2(\alpha x)}{\alpha x^2} = -3 \]

The distance of the point (10, 10, 10) from the Z-axis.

Find \(\int_{0}^{\frac{\pi}{2}} \sqrt{\cos x \sin 2x} \, dx\)

Find minimum value of \( \sin x \sin \left( x + \frac{\pi}{3} \right) \)

• (A) \( \frac{1}{2} \)
• (B) 0
• (C) 1
• (D) \( \frac{\sqrt{3}}{2} \)

Find the integral \( \int 2 \, dy = (y + \cos x) \, dx \)

• (A) \( y = \sin x + C \)
• (B) \( y = \cos x + C \)
• (C) \( y = x + C \)
• (D) \( y = \sin x + \cos x + C \)

If the area of the circle \( x^2 + y^2 + 8x - 6y + c = 0 \).

If \( n(B) = 61 \), \( n(A \cup B) = 99 \), \( n(A \cap B) = 28 \), find \( n(A') \).

Given that \( \vec{a} = 2\hat{i} - \lambda \hat{j} + 5\hat{k} \), \( \vec{b} = \mu \hat{i} + 7\hat{j} + 3\hat{k} \), and the midpoint of \( \overrightarrow{AB} = 3\hat{i} + 2\hat{j} + 4\hat{k} \), find \( \lambda + \mu \).

If \( \alpha^2 - \frac{1}{\alpha^2} = 2 \), find \( \left( \alpha + \frac{1}{\alpha} \right)^{16} \).

Maximum of \( f(x) = \alpha - 4x - x^2 \), find \(\alpha = ?\)

If \( (2 - x)^9 = a_0 + a_1x + \dots + a_9x^9 \), find \( a_1 + a_2 + \dots + a_8 \)

Given \( y = 4e^{-x} - 2e^{-2x} - e^{-3x} \), find \( y'' \).

• (A) \( 4e^{-x} - 4e^{-2x} - 3e^{-3x} \)
• (B) \( 4e^{-x} - 2e^{-2x} - 6e^{-3x} \)
• (C) \( 4e^{-x} - 2e^{-2x} - 3e^{-3x} \)
• (D) \( 4e^{-x} - 2e^{-2x} - 5e^{-3x} \)

Given \( a_1 + a_2 + a_3 + a_4 = 960 \) and \( a_4 - 8a = a_1 \), find \( a_1 \).

• (A) 320
• (B) 240
• (C) 160
• (D) 120

Evaluate \( \lim_{x \to 0} \frac{x - \tan(3x)}{\sin(2x)} \)

Given \( y = \frac{1}{1 + \tan x} \), find \( f^{-1}(x) \), where \( 0 < x < \frac{\pi}{2} \).

Arithmetic mean & Geometric mean of 2 numbers \( a \) & \( b \) in the ratio 5:3. Find \( \frac{a^2 + b^2}{ab} \).

Find \(\int \frac{x \cos 2x}{\cos x - \sin x} \, dx\)

If 2 vectors \( 4\hat{i} + \ell \hat{j} - 6 \hat{k} \) and \( -6 \hat{i} + 12 \hat{j} + 9 \hat{k} \) are collinear, find \(\ell\).

Given the numbers 4, 7, \( x \), 13, 16, with a mean of 10, find the mean deviation about the mean.

• (A) 2.8
• (B) 3.2
• (C) 2.5
• (D) 3.0

Given \( (3\cos x - 2\sec x)^2 = 9\cos^2 x + 4\tan^2 x + k \), find \( k \).

• (A) 4
• (B) 5
• (C) 3
• (D) 6

Evaluate \( \lim_{x \to 1} \frac{\sqrt{x+3} \cdot \sqrt{x-1}}{x-1} \)

The coefficient of \( x^3 \) in \( (2+x)^n \) is 160. Find the coefficient of \( x^6 \) in \( (2-x^2)^n \).

If \( f(x) = x^2 - 10x \), \( g(x) = e^x + 5 \), find \( g(2x) - f(g(x)) \).

Max of \( Z = 7x + 10y \) subject to \( x + y \geq 3 \), \( x + 2y \geq 4 \), \( x, y \geq 0 \).

If \( |\mathbf{a} - \mathbf{b}| = \frac{\sqrt{3}}{2} \) where \( \mathbf{a} \) and \( \mathbf{b} \) are unit vectors, find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).

Find the value of \( \cot 10^\circ \times \cot 30^\circ \times \cot 45^\circ \times \cot 60^\circ \times \cot 80^\circ \)

If \( 2 \cot^{-1} \left( \frac{4}{3} \right) = \cos^{-1} \left( \frac{x}{5} \right) \), find \( x \).

• (A) 3
• (B) 4
• (C) 5
• (D) 6

Find the locus of \( Z = x + iy \) satisfying \[ \frac{Re(z)}{2 + i} + \frac{Im(z)}{1 + 2i} = \frac{3}{1 - 2i} \]

• (A) \( x^2 + y^2 = 1 \)
• (B) \( x^2 + y^2 = 9 \)
• (C) \( x^2 + y^2 = 4 \)
• (D) \( x^2 + y^2 = 25 \)

Find the equation of the curve \( (x, y) \) if \( \cos^{-1}(x-2) = \sin^{-1}(y+1) \).

If the sum of the first two terms of a G.P. is 12 and the third term is 16, find the common ratio \( r \).

If \( y = \frac{1}{3\sqrt{x}} \left( \frac{2}{x} - 3 \right) \), find the interval in which \( y \) is strictly decreasing.

If \( Z = 1 + i \) and \( Z - 24\overline{Z} = \lambda Z^2 \), find \( \lambda \).