VITEEE 2025 25 April Shift 2 Question Paper (Available): Download Solutions with Answer Key

VITEEE 2025 25 April Shift 2 Question Paper is available here with solutions pdf. Vellore Institute of Technology is conducting VITEEE 2025 from April 20 to April 27. VITEEE 2025 Question Paper includes 40 questions from Mathematics/Biology, 35 questions from Physics, 35 questions from Chemistry, 5 questions from English, and 10 questions from Aptitude to be attempted in 150 minutes.

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VITEEE 2025 April 25 Shift 2 Question Paper with Solution PDF

Question 1:

The moment of inertia of a thin ring about its diameter is:

(A) \(MR^2\)
(B) \(\frac{1}{2}MR^2\)
(C) \(\frac{1}{4}MR^2\)
(D) \(2MR^2\)

Correct Answer: (B)

View Solution

For a ring, \(I_{diameter} = \frac{1}{2}MR^2\) using perpendicular axis theorem. Quick Tip: Ring: \(I_{center} = MR^2\), diameter = half of it.

Question 2:

A Carnot engine operates between 400 K and 300 K. Its efficiency is:

(A) 25%
(B) 30%
(C) 75%
(D) 100%

Correct Answer: (A)

View Solution

\[ \eta = 1-\frac{T_2}{T_1}=1-\frac{300}{400}=0.25 \] Quick Tip: Carnot efficiency depends only on temperatures.

Question 3:

In Young's double-slit experiment, the slits are 0.2 mm apart and the screen is 1 m away. The distance between the central bright fringe and the third bright fringe is 1.5 cm. The wavelength of light used is:

(A) 500 nm
(B) 600 nm
(C) 700 nm
(D) 400 nm

Correct Answer: (A)

View Solution

\[ y_n = n\frac{\lambda D}{d} \Rightarrow \lambda = \frac{yd}{nD} = \frac{0.015\times0.0002}{3\times1}=5\times10^{-7}\ m \] Quick Tip: Fringe distance is proportional to order number.

Question 4:

The binding energy per nucleon is maximum for:

(A) \(^2\mathrm{H}\)
(B) \(^4\mathrm{He}\)
(C) \(^56\mathrm{Fe}\)
(D) \(^238\mathrm{U}\)

Correct Answer: (C)

View Solution

Iron (\(^56\mathrm{Fe}\)) has the highest binding energy per nucleon. Quick Tip: Peak of binding energy curve is around iron.

Question 5:

The functional group in ethers is:

(A) –OH
(B) –CHO
(C) –O–
(D) –COOH

Correct Answer: (C)

View Solution

Ethers have an oxygen atom bonded to two alkyl/aryl groups. Quick Tip: Ether group = R–O–R.

Question 6:

Which of the following is not a buffer solution?

(A) CH\(_3\)COOH + CH\(_3\)COONa
(B) NH\(_4\)OH + NH\(_4\)Cl
(C) H\(_2\)SO\(_4\) + Na\(_2\)SO\(_4\)
(D) HCN + KCN

Correct Answer: (C)

View Solution

Strong acid + its salt does not form a buffer. Quick Tip: Buffers = weak acid/base + its salt.

Question 7:

The hybridization in SF\(_6\) molecule is:

(A) sp\(^3\)
(B) sp\(^3\)d
(C) sp\(^3\)d\(^2\)
(D) dsp\(^2\)

Correct Answer: (C)

View Solution

SF\(_6\) has six bond pairs → octahedral geometry → sp\(^3\)d\(^2\). Quick Tip: Six bond pairs → sp\(^3\)d\(^2\).

Question 8:

The heat of neutralization is maximum for:

(A) Weak acid and weak base
(B) Strong acid and strong base
(C) Strong acid and weak base
(D) Weak acid and strong base

Correct Answer: (B)

View Solution

Strong acid–strong base neutralization releases maximum heat (≈57 kJ/mol). Quick Tip: Complete ionization gives maximum heat.

Question 9:

If \(\cos\theta=-\frac{3}{5}\) and \(\theta\) lies in the second quadrant, then \(\sin\theta\) is:

(A) \(4/5\)
(B) \(-4/5\)
(C) \(3/5\)
(D) \(-3/5\)

Correct Answer: (A)

View Solution

In second quadrant, sine is positive: \[ \sin\theta=\sqrt{1-\cos^2\theta}=\frac{4}{5} \] Quick Tip: Remember signs of trigonometric ratios in quadrants.

Question 10:

The equation of the tangent to the curve \(y=x^3-2x+1\) at \((1,0)\) is:

(A) \(y=x-1\)
(B) \(y=x+1\)
(C) \(y=-x+1\)
(D) \(y=x\)

Correct Answer: (A)

View Solution

\[ \frac{dy}{dx}=3x^2-2 \Rightarrow m=1 \]
Equation: \(y-0=1(x-1)\Rightarrow y=x-1\) Quick Tip: Tangent slope = derivative at the point.

Question 11:

The value of \(\int e^x(\sin x+\cos x)\,dx\) is:

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

Correct Answer: (A)

View Solution

Differentiate \(e^x\sin x\) to verify. Quick Tip: Check by differentiation when in doubt.

Question 12:

If the coefficient of correlation between \(x\) and \(y\) is 0.8, then the regression coefficient of \(y\) on \(x\) is:

(A) Always 0.8
(B) Always greater than 0.8
(C) Depends on standard deviations
(D) Always less than 0.8

Correct Answer: (C)

View Solution

\[ b_{yx}=r\frac{\sigma_y}{\sigma_x} \]
Hence it depends on standard deviations. Quick Tip: Regression coefficient ≠ correlation coefficient.

Question 13:

The number of ways to arrange the letters of the word ``MISSISSIPPI'' is:

(A) 34650
(B) 12600
(C) 9450
(D) 69300

Correct Answer: (A)

View Solution

\[ \frac{11!}{4!4!2!}=34650 \] Quick Tip: Use factorial formula for repeated letters.

Question 14:

A boat takes 4 hours to travel 40 km downstream and 6 hours to return. The speed of the stream is:

(A) 2 km/h
(B) 4 km/h
(C) 6 km/h
(D) 8 km/h

Correct Answer: (A)

View Solution

Downstream speed = 10 km/h, upstream = 6.67 km/h \[ Stream speed=\frac{10-6.67}{2}=2\ km/h \] Quick Tip: Stream speed = half of speed difference.

Question 15:

If the 5th term of a G.P. is 81 and the 8th term is 6561, the first term is:

(A) 3
(B) 9
(C) 1
(D) 27

Correct Answer: (B)

View Solution

\[ \frac{T_8}{T_5}=r^3=\frac{6561}{81}=81 \Rightarrow r=3 \] \[ a=\frac{81}{3^4}=9 \] Quick Tip: Divide terms to eliminate first term.

Question 16:

Find the odd one out: 16, 25, 36, 49, 64, 81, 100

(A) 16
(B) 36
(C) 81
(D) 100

Correct Answer: (C)

View Solution

All are squares of even numbers except 81. Quick Tip: Look for hidden patterns like parity.

Question 17:

If `PEN' is coded as `371' and `INK' is coded as `946', then `PIN' is coded as:

(A) 391
(B) 379
(C) 739
(D) 937

Correct Answer: (D)

View Solution

Using the same letter–digit mapping gives PIN = 937. Quick Tip: Preserve letter order in coding.

Question 18:

Choose the antonym of ``Benevolent'':

(A) Kind
(B) Generous
(C) Malevolent
(D) Friendly

Correct Answer: (C)

View Solution

Benevolent means kind; its opposite is malevolent. Quick Tip: Prefix male- indicates bad or evil.

Question 19:

Fill in the blank: The committee ____ divided on the issue.

(A) is
(B) are
(C) were
(D) have

Correct Answer: (B)

View Solution

Collective noun takes plural verb when members act individually. Quick Tip: Collective noun + divided → plural verb.

Question 20:

Find the next number in the series: \(1,\,4,\,13,\,40,\,121,\,?\)

(A) 244
(B) 364
(C) 484
(D) 363

Correct Answer: (D)

View Solution

Pattern: \(\times3+1\) \[ 121\times3+1=364 \] Quick Tip: Check multiplication-based patterns.

VITEEE 2025 Expected Difficulty Level

According to the exam pattern, candidates must attempt 125 questions in 150 minutes across 5 major sections: Mathematics/Biology, Physics, Chemistry, English, and Aptitude.

As per the past year's trends, this is the expected difficulty level of VITEEE 2025:

Section	No. of Questions	Expected Difficulty Level	Remarks
Mathematics / Biology	40	Moderate to Difficult	Maths will have more application-based questions, and biology will have more NCERT-based questions.
Physics	35	Moderate	It will be conceptual and related to formulas with few calculations.
Chemistry	35	Easy to Moderate	Questions will be direct theory-based, with a focus on NCERT and a few tricky numerical problems
English	5	Easy	This section will focus on Grammar and comprehension-based questions.
Aptitude	10	Moderate	Basic logical reasoning and pattern questions

VITEEE 2025: Expected Section-Wise Weightage

Below is the expected section-wise topic weightage for VITEEE 2025:

Mathematics (40 Questions) – For PCM Candidates

Important Topics	Expected No. of Questions
Calculus	8–10
Coordinate Geometry	5–6
Algebra (Quadratic, Complex No.)	6–7
Trigonometry	4–5
Probability & Statistics	4–5
Matrices and Determinants	3–4
Vectors and 3D Geometry	4–5

Physics (35 Questions)

Important Topics	Expected No. of Questions
Mechanics	6–8
Electrostatics & Current Electricity	5–6
Optics	4–5
Thermodynamics & Heat Transfer	4–5
Modern Physics	4–5
Waves & Oscillations	3–4
Magnetism & EMI	4–5

Chemistry (35 Questions)

Important Topics	Expected No. of Questions
Organic Chemistry (Reactions, Mechanisms)	10–12
Physical Chemistry (Thermo, Equilibrium)	10–12
Inorganic Chemistry (p/d/f block, Coordination)	8–10
Environmental Chemistry, Biomolecules	2–3

English (5 Questions)

Type of Questions	Expected questions
Reading Comprehension	1–2
Grammar (Tense, Voice, Error Spotting)	2–3
Vocabulary (Synonyms/Antonyms)	1

Aptitude (10 Questions)

Important Topics	Expected No. of Questions
Number Series & Coding-Decoding	2–3
Data Interpretation	2–3
Syllogism & Logical Reasoning	2–3
Basic Arithmetic	2

VITEEE 2025 25 April Shift 2 Question Paper (Available): Download Solutions with Answer Key

VITEEE 2025 April 25 Shift 2 Question Paper PDF Download

VITEEE 2025 Expected Difficulty Level

VITEEE 2025: Expected Section-Wise Weightage

Mathematics (40 Questions) – For PCM Candidates

Physics (35 Questions)

Chemistry (35 Questions)

English (5 Questions)

Aptitude (10 Questions)

VITEEE Questions

1.
A block of mass \(2\, \text{kg}\) is placed on a smooth horizontal surface. A force of \(10\, \text{N}\) is applied horizontally on the block. What is the acceleration of the block?

2.
A car is moving along a straight road with a constant velocity of 20 m/s. The driver applies the brakes, and the car decelerates at a constant rate of \(4 \, \text{m/s}^2\). How much time will it take for the car to come to rest?

3.
The displacement of a particle executing $SHM$ is given by $y=5 \sin \left(4 t+\frac{\pi}{3}\right)$ If $T$ is the time period and the mass of the particle is $2\, g$, the kinetic energy of the particle when $t = T / 4$ is given by

4.
The centre of a wheel rolling on a plane surface moves with a speed $v_{ 0}$. A particle on the rim of the wheel at the same level as the centre will be moving at speed

5.
A projectile is fired at an angle of \( 30^\circ \) with an initial velocity of \( 40 \, \text{m/s} \). What is the range of the projectile? Assume \( g = 9.8 \, \text{m/s}^2 \).

6.
A body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at time $t_{1}$ and $t_{2}$ second during its flight. The maximum height attained is ( $g$ is acceleration due to gravity)

Comments

SUBSCRIBE TO OUR NEWS LETTER

VITEEE 2025 April 25 Shift 2 Question Paper PDF Download

VITEEE 2025 Expected Difficulty Level

VITEEE 2025: Expected Section-Wise Weightage

Mathematics (40 Questions) – For PCM Candidates

Physics (35 Questions)

Chemistry (35 Questions)

English (5 Questions)

Aptitude (10 Questions)

VITEEE Questions

1.A block of mass \(2\, \text{kg}\) is placed on a smooth horizontal surface. A force of \(10\, \text{N}\) is applied horizontally on the block. What is the acceleration of the block?

2.A car is moving along a straight road with a constant velocity of 20 m/s. The driver applies the brakes, and the car decelerates at a constant rate of \(4 \, \text{m/s}^2\). How much time will it take for the car to come to rest?

3.The displacement of a particle executing $SHM$ is given by $y=5 \sin \left(4 t+\frac{\pi}{3}\right)$ If $T$ is the time period and the mass of the particle is $2\, g$, the kinetic energy of the particle when $t = T / 4$ is given by

4.The centre of a wheel rolling on a plane surface moves with a speed $v_{ 0}$. A particle on the rim of the wheel at the same level as the centre will be moving at speed

5.A projectile is fired at an angle of \( 30^\circ \) with an initial velocity of \( 40 \, \text{m/s} \). What is the range of the projectile? Assume \( g = 9.8 \, \text{m/s}^2 \).

6.A body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at time $t_{1}$ and $t_{2}$ second during its flight. The maximum height attained is ( $g$ is acceleration due to gravity)

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A block of mass \(2\, \text{kg}\) is placed on a smooth horizontal surface. A force of \(10\, \text{N}\) is applied horizontally on the block. What is the acceleration of the block?

2.
A car is moving along a straight road with a constant velocity of 20 m/s. The driver applies the brakes, and the car decelerates at a constant rate of \(4 \, \text{m/s}^2\). How much time will it take for the car to come to rest?

3.
The displacement of a particle executing $SHM$ is given by $y=5 \sin \left(4 t+\frac{\pi}{3}\right)$ If $T$ is the time period and the mass of the particle is $2\, g$, the kinetic energy of the particle when $t = T / 4$ is given by

4.
The centre of a wheel rolling on a plane surface moves with a speed $v_{ 0}$. A particle on the rim of the wheel at the same level as the centre will be moving at speed

5.
A projectile is fired at an angle of \( 30^\circ \) with an initial velocity of \( 40 \, \text{m/s} \). What is the range of the projectile? Assume \( g = 9.8 \, \text{m/s}^2 \).

6.
A body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at time $t_{1}$ and $t_{2}$ second during its flight. The maximum height attained is ( $g$ is acceleration due to gravity)