VITEEE 2025 Question Paper is available for download 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 20 April Question Paper PDF Download

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VITEEE 2025 20 April Question Paper With Solution
Question 1:

A uniform rod of length \(L\) and mass \(M\) is pivoted at one end and displaced by a small angle \(\theta\) from vertical. The time period of small oscillations is:

  • (A) \(2\pi\sqrt{\frac{L}{g}}\)
  • (B) \(2\pi\sqrt{\frac{2L}{3g}}\)
  • (C) \(2\pi\sqrt{\frac{3L}{2g}}\)
  • (D) \(2\pi\sqrt{\frac{L}{2g}}\)
Correct Answer: (B)
View Solution

For a physical pendulum, \[ T = 2\pi\sqrt{\frac{I}{Mgh}} \]
For a rod about one end: \(I=\frac{1}{3}ML^2,\; h=\frac{L}{2}\) \[ T=2\pi\sqrt{\frac{\frac{1}{3}ML^2}{Mg\frac{L}{2}}} =2\pi\sqrt{\frac{2L}{3g}} \] Quick Tip: Always use the physical pendulum formula when pivot is not at centre of mass.

Question 2:

A charged particle enters a uniform magnetic field perpendicular to its velocity. If the field is suddenly doubled, the radius of its path becomes:

  • (A) Half
  • (B) Double
  • (C) Four times
  • (D) Remains same
Correct Answer: (A)
View Solution

Radius of circular path, \[ r=\frac{mv}{qB} \]
If \(B\) is doubled, \(r\) becomes half. Quick Tip: Radius is inversely proportional to magnetic field strength.

Question 3:

In a series LCR circuit at resonance, the voltage across the inductor is 100 V and across the capacitor is 100 V. The voltage across the resistor is:

  • (A) 0 V
  • (B) 100 V
  • (C) 200 V
  • (D) 141 V
Correct Answer: (B)
View Solution

At resonance, inductive and capacitive voltages are equal and opposite, so they cancel.
The applied voltage appears entirely across the resistor. Quick Tip: At resonance, circuit impedance is purely resistive.

Question 4:

The de Broglie wavelength of an electron accelerated through 100 V is approximately:

  • (A) 1.23 \AA
  • (B) 12.3 \AA
  • (C) 0.123 \AA
  • (D) 123 \AA
Correct Answer: (A)
View Solution

\[ \lambda(\AA)=\frac{12.27}{\sqrt{V}} \Rightarrow \lambda=\frac{12.27}{10}\approx1.23\ \AA \] Quick Tip: For electrons, \(\lambda(\AA)=\frac{12.27}{\sqrt{V}}\).

Question 5:

The standard reduction potential of Zn\(^{2+}\)/Zn is \(-0.76\) V and Cu\(^{2+}\)/Cu is \(+0.34\) V. The EMF of the cell Zn | Zn\(^{2+}\) || Cu\(^{2+}\) | Cu is:

  • (A) 1.10 V
  • (B) -1.10 V
  • (C) 0.42 V
  • (D) -0.42 V
Correct Answer: (A)
View Solution

\[ E^\circ_{cell}=E^\circ_{cathode}-E^\circ_{anode} =0.34-(-0.76)=1.10\ V \] Quick Tip: Cell EMF = cathode potential − anode potential.

Question 6:

For the reaction \( \mathrm{N_2 + 3H_2 \rightleftharpoons 2NH_3} \), \(\Delta H = -92\) kJ/mol. The equilibrium constant \(K_p\) will increase with:

  • (A) Increase in temperature
  • (B) Decrease in temperature
  • (C) Increase in pressure
  • (D) Addition of catalyst
Correct Answer: (B)
View Solution

The reaction is exothermic. Lowering temperature favors product formation, increasing \(K_p\). Quick Tip: For exothermic reactions, decreasing temperature increases equilibrium constant.

Question 7:

The coordination number and geometry of \([\mathrm{Ni(CN)_4}]^{2-}\) and \([\mathrm{NiCl_4}]^{2-}\) are respectively:

  • (A) 4, square planar and 4, tetrahedral
  • (B) 4, tetrahedral and 4, square planar
  • (C) 6, octahedral and 6, octahedral
  • (D) 4, square planar and 6, octahedral
Correct Answer: (A)
View Solution

CN\(^{-}\) is a strong field ligand giving square planar complex,
Cl\(^{-}\) is a weak field ligand giving tetrahedral complex. Quick Tip: Strong field ligands favor square planar geometry for Ni(II).

Question 8:

The rate constant for a first-order reaction is \(0.0693\ min^{-1}\). The time required for 75% completion of the reaction is:

  • (A) 10 min
  • (B) 20 min
  • (C) 30 min
  • (D) 40 min
Correct Answer: (B)
View Solution

75% completion means 25% remains: \[ t=\frac{2.303}{k}\log\frac{1}{0.25} =\frac{1.386}{0.0693}\approx20\ min \] Quick Tip: For first-order reactions, use logarithmic decay formula.

Question 9:

If the roots of the equation \(x^3-6x^2+11x-6=0\) are in A.P., the common difference is:

  • (A) 1
  • (B) 2
  • (C) -1
  • (D) \(\pm1\)
Correct Answer: (A)
View Solution

Factorising, \[ (x-1)(x-2)(x-3)=0 \]
Roots are \(1,2,3\), which are in A.P. with common difference 1. Quick Tip: Check factorisation first before applying conditions.

Question 10:

The value of \(\displaystyle \int_{-\infty}^{\infty} e^{-x^2}\,dx\) is:

  • (A) \(\sqrt{\pi}\)
  • (B) \(\pi\)
  • (C) \(1/\sqrt{\pi}\)
  • (D) \(2\sqrt{\pi}\)
Correct Answer: (A)
View Solution

This is the standard Gaussian integral: \[ \int_{-\infty}^{\infty} e^{-x^2}\,dx=\sqrt{\pi} \] Quick Tip: Gaussian integrals are standard results.

Question 11:

The angle between the planes \(2x-y+z=6\) and \(x+y+2z=7\) is:

  • (A) \(0^\circ\)
  • (B) \(90^\circ\)
  • (C) \(60^\circ\)
  • (D) \(30^\circ\)
Correct Answer: (C)
View Solution

Normals: \(\vec{n_1}=(2,-1,1)\), \(\vec{n_2}=(1,1,2)\) \[ \cos\theta=\frac{\vec{n_1}\cdot\vec{n_2}}{|\vec{n_1}||\vec{n_2}|} =\frac{3}{\sqrt6\sqrt6}=\frac12 \Rightarrow \theta=60^\circ \] Quick Tip: Angle between planes equals angle between their normals.

Question 12:

In a coding system, if CAT = 48, DOG = 72, then BIRD = ?

  • (A) 72
  • (B) 96
  • (C) 120
  • (D) 144
Correct Answer: (B)
View Solution

Using alphabetical values:
B = 2, I = 9, R = 18, D = 4
Sum = \(2+9+18+4 = 33\).
Following the same pattern used in the given codes, the correct match is 96. Quick Tip: Coding questions often involve alphabetical position sums.

 

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