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COMEDK UGET practice questions

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Question 1Engineering (UGET Engineering – 2026)

A particle moves along a straight line with velocity v = 3t² − 12t (SI units). At what time does the particle momentarily come to rest after t = 0?

  1. t = 3 s
  2. t = 4 s Correct answer.
  3. t = 2 s
  4. t = 6 s

Explanation

Setting v = 0 gives 3t² − 12t = 3t(t − 4) = 0, so t = 0 or t = 4 s. The nonzero instant of rest is t = 4 s.

Question 2Engineering (UGET Engineering – 2026)

The dimensional formula of the universal gravitational constant G is:

  1. [ML²T⁻²]
  2. [M⁻¹L³T⁻²] Correct answer.
  3. [ML³T⁻²]
  4. [M⁻¹L²T⁻²]

Explanation

From F = Gm₁m₂/r², we get G = Fr²/(m₁m₂), so its dimensions are [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²]. This is the standard result for the gravitational constant.

Question 3Engineering (UGET Engineering – 2026)

A block slides down a frictionless incline of angle 30° with acceleration a. If the same block slides down a frictionless incline of angle 60°, its acceleration becomes:

  1. a/2
  2. a√3 Correct answer.
  3. 2a
  4. a

Explanation

On a frictionless incline the acceleration is g sin θ. Since sin 60° = √3/2 and sin 30° = 1/2, the new acceleration is √3 times the old one, i.e. a√3.

Question 4Engineering (UGET Engineering – 2026)

An ideal gas undergoes an isothermal expansion at temperature T. Which statement about the gas is correct?

  1. Its internal energy decreases by the work done on the surroundings.
  2. No heat is exchanged with the surroundings.
  3. Its internal energy remains constant and it absorbs heat equal to the work done. Correct answer.
  4. Its internal energy increases because the volume increases.

Explanation

For an ideal gas, internal energy depends only on temperature, so isothermal means ΔU = 0. The first law then gives Q = W, so the heat absorbed equals the work done by the gas.

Question 5Engineering (UGET Engineering – 2026)

Two resistors of 6 Ω and 3 Ω are connected in parallel across a 12 V battery of negligible internal resistance. The total current drawn from the battery is:

  1. 4 A
  2. 6 A Correct answer.
  3. 1.33 A
  4. 2 A

Explanation

The parallel equivalent is (6×3)/(6+3) = 2 Ω. The current is I = V/R = 12/2 = 6 A, which also equals 2 A + 4 A through the branches.

Question 6Engineering (UGET Engineering – 2026)

A ray of light passes from glass (refractive index 1.5) into air. The critical angle for total internal reflection is closest to:

  1. 42° Correct answer.
  2. 30°
  3. 49°
  4. 60°

Explanation

The critical angle satisfies sin C = 1/n = 1/1.5 = 0.667, giving C ≈ 41.8°, close to 42°. This is the standard glass–air critical angle.

Question 7Engineering (UGET Engineering – 2026)

The number of significant figures in the measured value 0.004560 m is:

  1. 3
  2. 4 Correct answer.
  3. 7
  4. 6

Explanation

Leading zeros are not significant, but the trailing zero after the decimal point is. The significant digits are 4, 5, 6, and 0, giving four.

Question 8Engineering (UGET Engineering – 2026)

A body of mass 2 kg moving at 3 m/s collides head-on with a stationary body of mass 1 kg, and they stick together. The speed of the combined mass after collision is:

  1. 1 m/s
  2. 2 m/s Correct answer.
  3. 3 m/s
  4. 1.5 m/s

Explanation

Momentum is conserved in a perfectly inelastic collision: (2)(3) = (2+1)v, so v = 6/3 = 2 m/s. Kinetic energy is lost, but momentum is not.

Question 9Engineering (UGET Engineering – 2026)

The value of the integral ∫₀^{π/2} sin²x dx is:

  1. π
  2. π/4 Correct answer.
  3. π/2
  4. 1

Explanation

Using sin²x = (1 − cos 2x)/2, the integral becomes [x/2 − sin 2x/4] from 0 to π/2, which equals π/4. This is a standard definite integral result.

Question 10Engineering (UGET Engineering – 2026)

If the roots of the quadratic equation x² − 5x + k = 0 differ by 3, then the value of k is:

  1. 6
  2. 4 Correct answer.
  3. 5
  4. 3

Explanation

Let roots be α and α+3. Sum gives 2α+3 = 5, so α = 1 and roots are 1 and 4. Product k = 1×4 = 4.

Question 11Engineering (UGET Engineering – 2026)

The slope of the tangent to the curve y = x³ − 3x at the point where it crosses the y-axis is:

  1. −3 Correct answer.
  2. 1
  3. 3
  4. 0

Explanation

At the y-axis x = 0, giving the point (0, 0). The derivative is dy/dx = 3x² − 3, which at x = 0 equals −3.

Question 12Engineering (UGET Engineering – 2026)

A committee of 3 is to be chosen from 5 men and 4 women. The number of committees containing exactly 2 women is:

  1. 10
  2. 30 Correct answer.
  3. 60
  4. 40

Explanation

Choose 2 women from 4 in C(4,2) = 6 ways and 1 man from 5 in 5 ways, giving 6×5 = 30. The choices are independent, so we multiply.

Question 13Engineering (UGET Engineering – 2026)

The mean of five observations is 20. If one observation of value 30 is removed, the mean of the remaining observations is:

  1. 17.5 Correct answer.
  2. 15
  3. 20
  4. 18

Explanation

The total of all five is 5×20 = 100. Removing 30 leaves 70 for four observations, so the new mean is 70/4 = 17.5.

Question 14Engineering (UGET Engineering – 2026)

The distance of the point (3, 4) from the line 3x + 4y − 10 = 0 is:

  1. 1
  2. 3 Correct answer.
  3. 2
  4. 5

Explanation

The perpendicular distance is |3(3)+4(4)−10|/√(3²+4²) = |9+16−10|/5 = 15/5 = 3. The formula uses the absolute value of the numerator over the square root of the coefficient squares.

Question 15Engineering (UGET Engineering – 2026)

If the vectors a = 2i + 3j − k and b = i − j + 2k, then a·b equals:

  1. −3 Correct answer.
  2. 3
  3. 5
  4. −1

Explanation

The dot product is (2)(1) + (3)(−1) + (−1)(2) = 2 − 3 − 2 = −3. Each pair of corresponding components is multiplied and the results summed.

Question 16Engineering (UGET Engineering – 2026)

The period of the function f(x) = sin(3x) + cos(3x) is:

  1. 2π
  2. 3π
  3. π/3
  4. 2π/3 Correct answer.

Explanation

Both sin(3x) and cos(3x) have period 2π/3, so their sum has the same period. The common period is 2π divided by the coefficient 3.

Question 17Engineering (UGET Engineering – 2026)

The number of real solutions of the equation |x − 2| + |x + 2| = 4 is:

  1. Infinitely many Correct answer.
  2. Exactly two
  3. Zero
  4. Exactly one

Explanation

For any x with −2 ≤ x ≤ 2, the sum |x−2| + |x+2| equals the distance between −2 and 2, which is 4. Hence every x in that closed interval satisfies the equation, giving infinitely many solutions.

Question 18Engineering (UGET Engineering – 2026)

A satellite orbits Earth in a circular orbit of radius r. If the radius is increased to 4r, the orbital speed becomes:

  1. Unchanged
  2. Twice the original speed
  3. Half the original speed Correct answer.
  4. One-fourth the original speed

Explanation

Orbital speed is v = √(GM/r), so v ∝ 1/√r. Increasing r by a factor of 4 divides v by √4 = 2.

Question 19Engineering (UGET Engineering – 2026)

A charged particle enters a uniform magnetic field with velocity perpendicular to the field. Its path is a circle because the magnetic force:

  1. Acts along the velocity and increases speed
  2. Acts perpendicular to velocity and does no work, changing only direction Correct answer.
  3. Acts opposite to velocity and slows the particle
  4. Has a component along the field direction

Explanation

The magnetic force qv×B is always perpendicular to velocity, so it provides centripetal force without doing work. Speed stays constant while direction changes continuously, giving circular motion.

Question 20Engineering (UGET Engineering – 2026)

In a Young's double-slit experiment, the fringe width is β. If the separation between the slits is halved while everything else is unchanged, the new fringe width is:

  1. β/2
  2. 2β Correct answer.
  3. β
  4. 4β

Explanation

Fringe width is β = λD/d, so it is inversely proportional to slit separation d. Halving d doubles the fringe width to 2β.

Question 21Engineering (UGET Engineering – 2026)

The half-life of a radioactive sample is 10 days. The fraction of the original nuclei remaining after 30 days is:

  1. 1/3
  2. 1/4
  3. 1/8 Correct answer.
  4. 1/6

Explanation

Thirty days equals three half-lives. After each half-life the amount halves, so the remaining fraction is (1/2)³ = 1/8.

Question 22Engineering (UGET Engineering – 2026)

A particle executes simple harmonic motion with amplitude A. At what displacement from equilibrium is its kinetic energy equal to its potential energy?

  1. A/2
  2. A/√2 Correct answer.
  3. A√2
  4. A/4

Explanation

Total energy is ½kA², and potential energy is ½kx². Setting ½kx² = ½(½kA²) gives x² = A²/2, so x = A/√2.

Question 23Engineering (UGET Engineering – 2026)

An ideal gas is taken through a cyclic process consisting of two isochoric and two isobaric steps on a P–V diagram. The net work done by the gas in one complete cycle equals:

  1. The area enclosed by the cycle on the P–V diagram Correct answer.
  2. The change in internal energy over the cycle
  3. Zero because the process is cyclic
  4. The heat absorbed in the isochoric steps

Explanation

For any cyclic process the net work done by the gas is the area enclosed by the loop on a P–V diagram, taken with sign according to the direction of traversal. Internal energy change over a full cycle is zero, so net heat absorbed equals net work.

Question 24Engineering (UGET Engineering – 2026)

A capacitor of capacitance C is charged to potential V and then disconnected from the battery. A dielectric of constant K is now inserted to fill the space between the plates. Which quantity remains unchanged?

  1. Potential difference across the plates
  2. Charge on the plates Correct answer.
  3. Electric field between the plates
  4. Energy stored in the capacitor

Explanation

With the battery disconnected, no charge can flow, so Q stays fixed. Inserting the dielectric raises C to KC, which lowers V to V/K, reduces the field, and reduces stored energy to U/K.

Question 25Engineering (UGET Engineering – 2026)

Let f(x) = x³ − 3x² + 2. The function f has a local maximum at x = 0 and a local minimum at x = 2. The number of distinct real roots of f(x) = 0 is:

  1. 1
  2. 0
  3. 3 Correct answer.
  4. 2

Explanation

f(0) = 2 is a local maximum and f(2) = 8 − 12 + 2 = −2 is a local minimum, so the graph crosses the x-axis once left of 0, once between 0 and 2, and once right of 2. As x → ±∞ the cubic goes to ±∞, confirming three distinct real roots.

Question 26Engineering (UGET Engineering – 2026)

A block slides down a frictionless incline of height 5 m starting from rest. Taking g = 10 m/s², its speed at the bottom is:

  1. 50 m/s
  2. 5 m/s
  3. 10 m/s Correct answer.
  4. 20 m/s

Explanation

Conservation of mechanical energy gives mgh = ½mv², so v = √(2gh) = √(2 × 10 × 5) = √100 = 10 m/s. The mass cancels, so the answer does not depend on the block's mass.

Question 27Engineering (UGET Engineering – 2026)

Which of the following quantities is a scalar in classical mechanics?

  1. Electric charge Correct answer.
  2. Angular momentum
  3. Torque
  4. Displacement

Explanation

Electric charge has magnitude only and no direction, so it is a scalar. Displacement, torque and angular momentum all require a direction (or an axis) for their complete specification.

Question 28Engineering (UGET Engineering – 2026)

An object is placed 20 cm in front of a concave mirror of focal length 10 cm. The image formed is:

  1. Real, inverted and diminished
  2. Virtual, erect and diminished
  3. Real, inverted and of the same size Correct answer.
  4. Virtual, erect and magnified

Explanation

The object lies at the centre of curvature (2f = 20 cm), so the mirror forms a real, inverted image of the same size at the same position. Using 1/v + 1/u = 1/f with sign convention gives v = 20 cm and magnification −1.

Question 29Engineering (UGET Engineering – 2026)

The equivalent resistance of two resistors of 6 Ω and 3 Ω connected in parallel is:

  1. 4.5 Ω
  2. 9 Ω
  3. 0.5 Ω
  4. 2 Ω Correct answer.

Explanation

For parallel resistors, 1/R = 1/6 + 1/3 = 3/6 = 1/2, so R = 2 Ω. The parallel equivalent is always smaller than the smallest individual resistance.

Question 30Engineering (UGET Engineering – 2026)

The IUPAC name of CH₃–CH(CH₃)–CH₂–OH is:

  1. Propan-2-ol
  2. 2-Methylpropan-2-ol
  3. 2-Methylpropan-1-ol Correct answer.
  4. Butan-1-ol

Explanation

The longest chain containing the –OH carbon has three carbons, so the parent is propan-1-ol, and a methyl branch sits on carbon 2. Hence the name is 2-methylpropan-1-ol.

Question 31Engineering (UGET Engineering – 2026)

The pH of a 0.01 M aqueous solution of HCl at 25 °C is:

  1. 7
  2. 1
  3. 2 Correct answer.
  4. 12

Explanation

HCl is a strong acid that dissociates completely, giving [H⁺] = 0.01 = 10⁻² M. Therefore pH = −log(10⁻²) = 2.

Question 32Engineering (UGET Engineering – 2026)

Which of the following molecules has a linear shape according to VSEPR theory?

  1. NH₃
  2. CO₂ Correct answer.
  3. CH₄
  4. H₂O

Explanation

CO₂ has two bonding regions and no lone pairs on the central carbon, giving an AX₂ arrangement that is linear with a 180° bond angle. The other molecules have lone pairs or four bonding pairs producing bent, pyramidal or tetrahedral shapes.

Question 33Engineering (UGET Engineering – 2026)

A body moves along a straight line with velocity v = 3t² m/s. Its acceleration at t = 2 s is:

  1. 24 m/s²
  2. 4 m/s²
  3. 6 m/s²
  4. 12 m/s² Correct answer.

Explanation

Acceleration is the time derivative of velocity, so a = dv/dt = 6t. At t = 2 s, a = 12 m/s².

Question 34Engineering (UGET Engineering – 2026)

Two masses of 4 kg and 6 kg are connected by a light string over a frictionless pulley. Taking g = 10 m/s², the acceleration of the system is:

  1. 2 m/s² Correct answer.
  2. 10 m/s²
  3. 5 m/s²
  4. 1 m/s²

Explanation

For an Atwood machine, a = (m₂ − m₁)g/(m₁ + m₂) = (6 − 4)(10)/(10) = 2 m/s². The tension is then 4(10 + 2) = 48 N.

Question 35Engineering (UGET Engineering – 2026)

A wire of resistance R is stretched uniformly to twice its original length. Its new resistance is:

  1. R/4
  2. 2R
  3. R/2
  4. 4R Correct answer.

Explanation

Stretching keeps the volume constant, so doubling the length halves the cross-sectional area. Since R = ρL/A, both the length increase and the area decrease raise the resistance by a factor of 4.

Question 36Engineering (UGET Engineering – 2026)

A body of mass 0.5 kg is tied to a string of length 1 m and whirled in a vertical circle. The minimum speed at the top of the circle for the string to remain taut is (g = 10 m/s²):

  1. 5 m/s
  2. 10 m/s
  3. √10 m/s Correct answer.
  4. √5 m/s

Explanation

At the top, gravity alone supplies the centripetal force in the limiting case: mg = mv²/r, so v = √(gr) = √(10 × 1) = √10 m/s.

Question 37Engineering (UGET Engineering – 2026)

A convex lens of focal length 20 cm forms an image of an object placed 30 cm from it. The image distance is:

  1. 60 cm Correct answer.
  2. 12 cm
  3. 30 cm
  4. 50 cm

Explanation

The lens formula 1/v − 1/u = 1/f with u = −30 cm and f = +20 cm gives 1/v = 1/20 − 1/30 = 1/60, so v = 60 cm. The image is real and inverted.

Question 38Engineering (UGET Engineering – 2026)

The number of σ and π bonds respectively in a molecule of ethyne (C₂H₂) is:

  1. 2 and 3
  2. 3 and 2 Correct answer.
  3. 5 and 0
  4. 4 and 2

Explanation

Each C–H single bond contributes one σ bond, and the C≡C triple bond contributes one σ and two π bonds. This gives three σ bonds and two π bonds in total.

Question 39Engineering (UGET Engineering – 2026)

Which of the following reactions is an example of an electrophilic substitution reaction?

  1. Addition of HBr to ethene
  2. Hydrolysis of ethyl ethanoate with aqueous NaOH
  3. Bromination of benzene in the presence of FeBr₃ Correct answer.
  4. Oxidation of ethanol with acidified K₂Cr₂O₇

Explanation

In bromination of benzene, Br⁺ generated by FeBr₃ attacks the aromatic ring and replaces a hydrogen, which is electrophilic substitution. The other reactions are addition, nucleophilic acyl substitution and oxidation respectively.

Question 40Engineering (UGET Engineering – 2026)

The number of moles of oxygen gas produced when 2 moles of KClO₃ decompose completely as 2KClO₃ → 2KCl + 3O₂ is:

  1. 1.5
  2. 2
  3. 4
  4. 3 Correct answer.

Explanation

The balanced equation shows that 2 moles of KClO₃ yield 3 moles of O₂. Since 2 moles of KClO₃ are given, exactly 3 moles of oxygen are produced.

Question 41Engineering (UGET Engineering – 2026)

The standard enthalpy of formation of an element in its most stable standard state is:

  1. Always positive
  2. Equal to its atomic mass
  3. Always negative
  4. Zero by convention Correct answer.

Explanation

By convention, the standard enthalpy of formation of an element in its most stable state at 1 bar and 298 K is taken as zero. This provides the reference baseline for all formation enthalpies.

Question 42Engineering (UGET Engineering – 2026)

If A is a 2 × 2 matrix with |A| = 3, then |2A| equals:

  1. 6
  2. 3
  3. 12 Correct answer.
  4. 9

Explanation

For an n × n matrix, |kA| = kⁿ|A|. Here n = 2 and k = 2, so |2A| = 2² × 3 = 12.

Question 43Engineering (UGET Engineering – 2026)

The sum of the infinite geometric series 1 + 1/3 + 1/9 + … is:

  1. 1/3
  2. 2/3
  3. 3
  4. 3/2 Correct answer.

Explanation

The first term is a = 1 and the common ratio is r = 1/3, so the sum is a/(1 − r) = 1/(2/3) = 3/2.

Question 44Engineering (UGET Engineering – 2026)

A particle moves along a curve whose position vector is r = t²i + 3tj. Its velocity at t = 2 s is:

  1. 2i + 6j
  2. 4i + 3j Correct answer.
  3. 2i + 3j
  4. 4i + 6j

Explanation

Velocity is dr/dt = 2ti + 3j. At t = 2 s this becomes 4i + 3j.

Question 45Engineering (UGET Engineering – 2026)

A charged particle of charge q and mass m moves with speed v perpendicular to a uniform magnetic field B. The radius of its circular path is:

  1. qB/(mv)
  2. q/(mvB)
  3. mvB/q
  4. mv/(qB) Correct answer.

Explanation

The magnetic force qvB provides the centripetal force mv²/r, so r = mv/(qB). The radius grows with momentum and shrinks with field strength.

Question 46Engineering (UGET Engineering – 2026)

An ideal gas undergoes an isothermal expansion at temperature T. For one mole of the gas, the work done by the gas when its volume doubles is:

  1. RT ln 2 Correct answer.
  2. 2RT
  3. Zero
  4. RT/2

Explanation

For an isothermal reversible expansion of an ideal gas, W = nRT ln(V₂/V₁). With n = 1 and V₂/V₁ = 2, the work is RT ln 2.

Question 47Engineering (UGET Engineering – 2026)

A solid sphere of radius R rolls without slipping down an incline. Its acceleration is:

  1. g sin θ
  2. (5/7)g sin θ Correct answer.
  3. (1/2)g sin θ
  4. (2/3)g sin θ

Explanation

For a solid sphere, I = (2/5)mR². Using a = g sin θ/(1 + I/mR²) gives a = g sin θ/(1 + 2/5) = (5/7)g sin θ.

Question 48Engineering (UGET Engineering – 2026)

Two coherent sources of light of wavelength 600 nm produce an interference pattern on a screen 2 m away. If the slit separation is 0.3 mm, the fringe width is:

  1. 40 mm
  2. 0.04 mm
  3. 0.4 mm
  4. 4 mm Correct answer.

Explanation

Fringe width β = λD/d = (600 × 10⁻⁹ × 2)/(0.3 × 10⁻³) = 4 × 10⁻³ m = 4 mm.

Question 49Engineering (UGET Engineering – 2026)

The area bounded by the parabola y = x² and the line y = 4 is:

  1. 8/3
  2. 32/3 Correct answer.
  3. 16/3
  4. 64/3

Explanation

The curves intersect at x = ±2. Integrating (4 − x²) from −2 to 2 gives [4x − x³/3] from −2 to 2 = (8 − 8/3) − (−8 + 8/3) = 32/3.

Question 50Engineering (UGET Engineering – 2026)

A particle executes SHM with amplitude A. At what displacement from equilibrium is its potential energy equal to one-third of its total energy?

  1. A/√3 Correct answer.
  2. 2A/3
  3. A/√2
  4. A/3

Explanation

Potential energy is ½kx² and total energy is ½kA². Setting ½kx² = (1/3)(½kA²) gives x² = A²/3, so x = A/√3.