Master VITEEE 2025 with Sample Papers, Solutions, and Exam Insights

VITEEE (Vellore Institute of Technology Engineering Entrance Examination) is a national-level exam conducted by the prestigious Vellore Institute of Technology (VIT) to admit students into its B.Tech programs. With campuses located in Vellore, Chennai, Andhra Pradesh, and Bhopal, VIT has established itself as a leading institution for engineering education. Every year, thousands of aspirants attempt the VITEEE to secure a seat in one of the best engineering institutes in India.

Practicing VITEEE sample paper with solution is crucial for students looking to ace this exam. These papers help understand the exam format and enhance time management and accuracy during the actual exam. This Bharat Padhe blog will guide you through the exam details, provide insights into the VITEEE sample paper online, and help you understand how to prepare using VITEEE entrance exam papers for B.Tech effectively.

VITEEE 2025 highlights

The detailed highlights of VITEEE 2025 can be checked in the table given below.

Particulars	Details
Name of the Exam	Vellore Institute of Technology Engineering Entrance Examination or VITEEE
Conducted By	Vellore Institute of Technology
Exam Level	Undergraduate
Exam Frequency	Annual
Mode of Exam	Computer-Based Test
Total Registrations	More than 2 lakhs (approx)
Course offered through the exam	BTech
Exam Fees	INR 1,350
Exam Duration	2 Hour 30 Minutes
Number of Sections	5 – Mathematics, Physics, Chemistry, Aptitude, English
Total Questions	125
Marking Scheme	1 mark for each correct answer. No marks will be deducted for any wrong responses selected by candidates.
Medium of Exam	English
Colleges Accepting Exam Score	VIT Vellore VIT Chennai VIT Bhopal VIT Amaravati
No. of Test Cities	N/A
Official Website	vit.ac.in
Contact Details	VITEEE Email ID: [email protected] VITEEE Helpline: 0416 220 2020

VITEEE 2025 exam dates

Events	Dates 2025 (Tentative)
Online application form	1st week of November 2024
Last date to submit Application form	2nd week of April 2025
Slot booking procedure	April 2025
VITEEE 2025 Exam Date	4th week of April 2025
Declaration of Result	1st week of May 2025
Commencement of counselling	May 2025
Commencement of classes	August 2025

VITEEE 2025 syllabus

The VITEEE 2025 syllabus is divided into five sections. Each section tests candidates on different aspects of their 10+2 curriculum. Below is a summary of the key topics for each subject:

Subjects	Key Topics
Physics	Laws of Motion, Optics, Thermodynamics, Electrostatics, Current Electricity, etc.
Chemistry	Atomic Structure, Electrochemistry, Organic Chemistry, Polymers, Coordination Compounds, etc.
Mathematics	Algebra, Calculus, Probability, Coordinate Geometry, Matrices, Trigonometry, etc.
Biology	Genetics, Evolution, Human Physiology, Ecology, Biotechnology, etc.
English & Aptitude	Grammar, Reading Comprehension, Data Interpretation, Logical Reasoning

By using VITEEE sample paper with solution, students can assess their preparation level and work on weak areas effectively.

VITEEE 2025 eligibility criteria

To apply for VITEEE 2025, candidates need to meet the following eligibility criteria:

Criteria	Details
Nationality	Indian nationals, NRIs, and PIO/OCI holders are eligible to apply.
Age	Applicants must be born on or after 1st July 2003.
Educational Qualification	Should have completed or be appearing in 10+2 or equivalent examination.
Minimum Marks in 10+2	A minimum of 60% aggregate in Physics, Chemistry, and Mathematics/Biology (50% for SC/ST and reserved categories).
Eligibility for B.Tech Biotechnology	Candidates who studied Biology are eligible for B.Tech Biotechnology.

Meeting these criteria ensures that candidates can proceed with the registration and start preparing with VITEEE entrance exam papers for B.Tech.

VITEEE 2025 application form: Complete details

Below are the essential details regarding the VITEEE 2025 application form:

The VITEEE 2025 application form will be available starting from the first week of November 2024.
Candidates can submit the form exclusively online.
Begin the registration process by providing details such as name, gender, category, and address.
Ensure that you meet the eligibility criteria before starting the registration.
Fill in the application form with academic, personal, and contact information.
Upload the required scanned documents in the specified format.
If any errors are made, the university will offer a correction window for adjustments.
The registration must be completed by the second week of April 2025, as this will be the last date to apply.
Review the filled details carefully before submitting the form on the official website.
After submission, keep a printed copy of the application for future reference.

Application fee:

The application fee for VITEEE 2025 is ₹1350 for all categories.
The fee can only be paid online.
No offline payment options will be available.
The application fee is non-refundable under any circumstances.

VITEEE sample paper with solutions

Practicing with VITEEE sample paper with solutions is an excellent way to improve your exam readiness. These sample papers not only help you get familiar with the exam pattern but also enable you to manage time efficiently and gauge your preparation level. For aspiring candidates aiming to crack VITEEE 2025, solving these sample papers can make all the difference. Bharat Padhe is here to provide you with curated sample papers to boost your preparation and help you excel in the VITEEE exam.

MATHEMATICS

1. If ntan⁡θn \tan \thetantanθ for some non-square natural number nnn, then sec 2θ2 \theta2θ is:

(a) a rational number

(b) an irrational number

(d) none of the above

2. If z=x+iyz = x + iyz=x+iy, and z13=a−ibz^{\frac{1}{3}} = a – ibz31=a−ib, then ax−by=k(2a−2b)\frac{a}{x} – \frac{b}{y} = k (2a – 2b)xa−yb=k(2a−2b), where kkk is equal to:

(a) 1

(b) 2

(d) 4

3. If the coordinates at one end of a diameter of the circle x2+y2−8x−4y+c=0x^2 + y^2 – 8x – 4y + c = 0x2+y2−8x−4y+c=0 are (−3,2)(-3, 2)(−3,2), then the coordinates at the other end are:

(a) (5, 3)

(b) (6, 2)

(d) (11, 2)

4. The system of linear equations x+y+z=0,2x+y–z=0,3x+2y=0x + y + z = 0, 2x + y – z = 0, 3x + 2y = 0x+y+z=0,2x+y–z=0,3x+2y=0 has:

(a) no solution

(b) a unique solution

(d) none of these

5. The modulus of (1+i3)(2+2i)3−i\frac{(1+ i \sqrt{3})(2+ 2i)}{\sqrt{3} – i}3−i(1+i3)(2+2i) is:

(a) 2

(b) 4

(d) 222\sqrt{2}22

6. If the lines 3x–4y+4=03x – 4y + 4 = 03x–4y+4=0 and 6x–8y–7=06x – 8y – 7 = 06x–8y–7=0 are tangents to a circle, then the radius of the circle is:

(a) 34\frac{3}{4}43

(b) 23\frac{2}{3}32

(d) 52\frac{5}{2}25

7. Find the length of the internal bisector of angle ∠AOB\angle AOB∠AOB in triangle AOBAOBAOB with position vectors of AAA and BBB as A⃗=2i^+2j^+k^\vec{A} = 2\hat{i} + 2\hat{j} + \hat{k}A=2i^+2j^+k^ and B⃗=2i^+4j^+4k^\vec{B} = 2\hat{i} + 4\hat{j} + 4\hat{k}B=2i^+4j^+4k^:

(a) 9136\frac{9}{136}1369

(b) 9217\frac{9}{217}2179

8. If 12tan⁡−1(x)+13tan⁡−1(y)=15tan⁡−1(z)\frac{1}{2} \tan^{-1}(x) + \frac{1}{3} \tan^{-1}(y) = \frac{1}{5} \tan^{-1}(z)21tan−1(x)+31tan−1(y)=51tan−1(z), then dydx\frac{dy}{dx}dxdy is:

(a) 5×2+44×2+1\frac{5x^2 + 4}{4x^2 + 1}4×2+15×2+4

(b) 2×2+5×2+3\frac{2x^2 + 5}{x^2 + 3}x2+32×2+5

9. A class has 175 students. The number of students opting for one or more subjects is given as: Maths-100, Physics-70, Chemistry-40, Maths and Physics-30, Maths and Chemistry-28, Physics and Chemistry-23, Maths, Physics, and Chemistry-18. How many have offered Maths alone?

(a) 35

(b) 48

(d) 22

10. If 12cot⁡2θ−31csc⁡θ+32=012 \cot^2\theta – 31 \csc\theta + 32 = 012cot2θ−31cscθ+32=0, then the value of sin⁡θ\sin\thetasinθ is:

(a) 35\frac{3}{5}53 or 111

(b) 23\frac{2}{3}32 or −23-\frac{2}{3}−32

11. The equation 9×2+y2=k(x2−y2−2x)9x^2 + y^2 = k(x^2 – y^2 – 2x)9×2+y2=k(x2−y2−2x) represents a circle when:

(a) k=1k = 1k=1

(b) k=2k = 2k=2

(d) k=4k = 4k=4

12. The vertex of a parabola with the origin as its focus and the line x=2x = 2x=2 as its directrix is at:

(a) (0, 2)

(b) (1, 0)

13. Equation of the ellipse with axes as coordinates passing through the point (−3,1)(-3, 1)(−3,1) and having eccentricity 25\frac{2}{5}52:

(a) 5×2+3y2−48=05x^2 + 3y^2 – 48 = 05×2+3y2−48=0

(b) 3×2+5y2−15=03x^2 + 5y^2 – 15 = 03×2+5y2−15=0

14. Find the probability of getting a sum as a perfect square number when two dice are thrown together:

(a) 512\frac{5}{12}125

(b) 718\frac{7}{18}187

15. The point diametrically opposite to P(1,0)P(1, 0)P(1,0) on the circle x2+y2+2x+4y−3=0x^2 + y^2 + 2x + 4y – 3 = 0x2+y2+2x+4y−3=0 is:

(a) (3, -4)

(b) (-3, 4)

16. Find the probability that all balls drawn from an urn containing five balls are white if two are drawn and both are white:

(a) 110\frac{1}{10}101

(b) 310\frac{3}{10}103

17. The sum of the first nnn terms of the series 12+2.22+32+…1^2 + 2.2^2 + 3^2 + \ldots12+2.22+32+… is n(n+1)2\frac{n(n+1)}{2}2n(n+1) when nnn is even. For odd nnn, it is:

(a) n(n+1)4\frac{n(n+1)}{4}4n(n+1)

(b) n(n+1)22\frac{n(n+1)^2}{2}2n(n+1)2

18. Evaluate the integral ∫0π/2log⁡(tan⁡x)dx\int_0^{\pi/2} \log(\tan x) dx∫0π/2log(tanx)dx:

(a) 0

(b) π4\frac{\pi}{4}4π

19. If d2ydx2=0\frac{d^2y}{dx^2} = 0dx2d2y=0 at point P(1,1)P(1, 1)P(1,1), find the equation of the tangent at PPP.

20. Find the length of the shortest distance between the lines x+1=y−12=z3x+1 = \frac{y-1}{2} = \frac{z}{3}x+1=2y−1=3z and x−1=y+14=z6x-1 = \frac{y+1}{4} = \frac{z}{6}x−1=4y+1=6z.

21. The variance of the data set 2,4,6,8,102, 4, 6, 8, 102,4,6,8,10 is:

(a) 8

(b) 7

(d) None of these

22. The principal value of sin⁡−1(sin⁡5π3)\sin^{-1} (\sin \frac{5\pi}{3})sin−1(sin35π) is:

(a) −5π3-\frac{5\pi}{3}−35π

(b) 5π3\frac{5\pi}{3}35π

(d) 4π3\frac{4\pi}{3}34π

23. If the system of linear equations x+ky+3z=0x + ky + 3z = 0x+ky+3z=0, 3x+ky−2z=03x + ky – 2z = 03x+ky−2z=0, and 2x+4y−3z=02x + 4y – 3z = 02x+4y−3z=0 has a non-zero solution, then xz=k \frac{x}{z} = kzx=k, find the value of kkk.

24. The solution set of the inequality 37−(3x+5)≥9x−8(x−3)37 – (3x + 5) \geq 9x – 8(x – 3)37−(3x+5)≥9x−8(x−3) is:

(a) (−∞,2)(-\infty, 2)(−∞,2)

(b) (−∞,−2)(-\infty, -2)(−∞,−2)

(d) (−∞,−2](-\infty, -2](−∞,−2]

25. A triangle has vertices at A(2,3)A(2, 3)A(2,3), B(4,5)B(4, 5)B(4,5), and C(6,7)C(6, 7)C(6,7). Find the equation of the median from vertex AAA.

26. In a geometric progression (G.P.), the fourth, seventh, and tenth terms are ppp, qqq, and rrr, respectively. Then, the relationship between ppp, qqq, and rrr is:

(a) p2=q2+r2p^2 = q^2 + r^2p2=q2+r2

(b) q2=prq^2 = prq2=pr

27. If f(x)=xsin⁡(1/x)f(x) = x \sin(1/x)f(x)=xsin(1/x) for x≠0x \neq 0x=0 and f(0)=0f(0) = 0f(0)=0, is the function continuous and differentiable at x=0x = 0x=0?

28. A parabola has its focus at the origin and directrix x=2x = 2x=2. The vertex of the parabola is at:

(a) (0,2)(0, 2)(0,2)

(b) (1,0)(1, 0)(1,0)

29. Find the angle between the vectors a⃗=2i^+j^\vec{a} = 2\hat{i} + \hat{j}a=2i^+j^ and b⃗=4i^+2j^\vec{b} = 4\hat{i} + 2\hat{j}b=4i^+2j^.

30. The distance between the parallel lines 3x−4y+7=03x – 4y + 7 = 03x−4y+7=0 and 3x−4y+5=03x – 4y + 5 = 03x−4y+5=0 is:

(a) 2

(b) 3

31. The equation of the plane bisecting the angle between the planes 3x−6y+2z+5=03x – 6y + 2z + 5 = 03x−6y+2z+5=0 and 4x−12y+3z−3=04x – 12y + 3z – 3 = 04x−12y+3z−3=0 and containing the origin is:

(a) 33x−13y+32z+45=033x – 13y + 32z + 45 = 033x−13y+32z+45=0

32. In how many ways can a committee of 5 members be selected from a group of 10 people?

33. What is the probability of getting at least one head when three coins are tossed

34. Solve the integral ∫0π/2sin⁡xdx\int_0^{\pi/2} \sqrt{\sin x} dx∫0π/2sinxdx.

35. What is the area of the region enclosed by the curve y=x3y = x^3y=x3 and the lines x=0x = 0x=0, y=1y = 1y=1, and y=8y = 8y=8?

36. The number of 3-digit numbers whose sum of digits is even is:

(a) 450

(b) 350

If log⁡(x2+y2)=3\log(x^2 + y^2) = 3log(x2+y2)=3, find the equation of the curve in polar coordinates.
The sum of the first nnn terms of the arithmetic progression (AP) 1,4,7,10,…1, 4, 7, 10, \dots1,4,7,10,… is:
The probability that a number selected from the set of integers between 1 and 100 is divisible by both 2 and 5 is:
Find the center and radius of the circle given by x2+y2+6x−8y+9=0x^2 + y^2 + 6x – 8y + 9 = 0x2+y2+6x−8y+9=0.

PHYSICS

1. The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then:

(a) the resistance and the specific resistance will both remain unchanged

(b) the resistance will be doubled and the specific resistance will be halved

(d) the resistance will be halved and the specific resistance will be doubled

2. Two thin lenses are in contact, and the focal length of the combination is 80 cm. If the focal length of one lens is 20 cm, then the power of the other lens will be:

(a) 1.66 D

(b) 4.00 D

(d) –3.75 D

3. If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor:

(a) 2

(b) 12\frac{1}{\sqrt{2}}21

(d) 2\sqrt{2}2

4. Radioactive element decays to form a stable nuclide, then the rate of decay of the reactant is shown by:

(a) dNdt=−λN\frac{dN}{dt} = -\lambda NdtdN=−λN

(b) Nt\frac{N}{t}tN

(d) N=N0λN = N_0 \lambdaN=N0λ

5. The ratio of the energies of the hydrogen atom in its first to second excited states is:

(a) 14\frac{1}{4}41

(b) 49\frac{4}{9}94

(d) 4

6. Which of the following gates will have an output of 1?

(a) AND gate

(b) OR gate

(d) NAND gate

7. A point charge qqq is rotated along a circle in the electric field generated by another point charge QQQ. The work done by the electric field on the rotating charge in one complete revolution is:

(a) zero

(b) positive

(d) zero if the charge QQQ is at the center and nonzero otherwise

8. The equivalent capacitance of two capacitors in series is 3 µF. When connected in parallel, their capacitance is 16 µF. Their individual capacitances are:

(a) 1 µF and 2 µF

(b) 6 µF and 2 µF

(d) 3 µF and 16 µF

9. The velocity of efflux of a liquid through an orifice at the bottom of the tank depends upon:

(a) height of the liquid

(b) acceleration due to gravity

(d) size of the orifice

10. A particle covers half of the circle of radius rrr. The displacement and distance of the particle are:

(a) 2r,πr2r, \pi r2r,πr

(b) r2,πrr\sqrt{2}, \pi rr2,πr

(d) 2r,r2r, r2r,r

11. The escape velocity of a body from the earth is vvv. What will be the escape velocity of another body with mass 4m?

(a) vvv

(b) 2v2v2v

(d) v/2v/2v/2

12. A step-up transformer operates on a 230 V line and supplies a load of 2 amperes. The ratio of the primary and secondary windings is 1:25. The current in the primary is:

(a) 12.5 A

(b) 50 A

(d) 25 A

13. A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20 m/s2^22, the amount of gas ejected per second to supply the needed thrust will be (Take g=10g = 10g=10 m/s2^22):

(a) 127.5 kg/s

(b) 137.5 kg/s

(d) 187.5 kg/s

14. The potential energy of a system increases if work is done:

(a) by the system against a non-conservative force

(b) upon the system by a non-conservative force

(d) upon the system by a conservative force

15. In an electromagnetic wave, power is transmitted:

(a) along the magnetic field

(b) along the electric field

(d) equally along the electric and magnetic fields

16. A man holding a rifle (mass of person and rifle together is 100kg) stands on a smooth surface and fires 10 shots horizontally in 5 sec. Each bullet has a mass of 10 g with a muzzle velocity of 800 m/s. The velocity which the rifleman attains after firing 10 shots will be:

(a) 0.8 m/s

(b) 0.08 m/s

(d) 0.01 m/s

17. A soap bubble of radius r1r_1r1 is placed on another soap bubble of radius r2r_2r2. The radius RRR of the soapy film separating the two bubbles is:

(a) r1+r2\sqrt{r_1 + r_2}r1+r2

(b) 2r1r2r1+r2\frac{2r_1r_2}{r_1 + r_2}r1+r22r1r2

(d) r1r2\frac{r_1}{r_2}r2r1

18. The de-Broglie wavelength of a particle is related to its kinetic energy by:

(a) λ=h2mE\lambda = \frac{h}{\sqrt{2mE}}λ=2mEh

(b) λ=hEm\lambda = \frac{hE}{m}λ=mhE

(d) λ=hE\lambda = hEλ=hE

19. In Young’s double-slit experiment, the intensity at a point where the path difference is λ4\frac{\lambda}{4}4λ will be:

(a) I4\frac{I}{4}4I

(b) I2\frac{I}{2}2I

(d) zero

20. The root mean square velocity of smoke particles of mass 5×10−175 \times 10^{-17}5×10−17 kg in their Brownian motion in air at NTP is approximately:

(a) 60 mm/s

(b) 12 mm/s

(d) 36 mm/s

21. The equivalent capacitance of a parallel combination of capacitors 10 µF and 6 µF connected in series with a 4 µF capacitor is:

(a) 2.16 µF

(b) 7 µF

(d) 5 µF

22. A block of mass 5 kg is placed on a horizontal surface connected to a hanging block of mass 5 kg. The coefficient of kinetic friction between the block and the surface is 0.5. The tension in the cord is:

(a) 49 N

(b) 36.75 N

(d) Zero

23. If a solid cylinder of mass mmm and radius RRR rolls down an inclined plane without slipping, the speed of its center of mass when it reaches the bottom is:

(a) 4gh/3\sqrt{4gh/3}4gh/3

(b) 2gh\sqrt{2gh}2gh

(d) gh/2\sqrt{gh/2}gh/2

24. The velocity-time graph of a body moving in a straight line shows uniform acceleration. The displacement in 10 seconds is:

(a) 90 m

(b) 50 m

(d) 9 m

25. In an RLC series circuit, the resonance frequency is f0f_0f0. Now, the capacitance is made four times. The new resonance frequency will be:

(a) f0/4f_0/4f0/4

(b) 2f02f_02f0

(d) f0f_0f0

26. A charge qqq is placed at the center of a hemispherical non-conducting surface. The total flux passing through the flat surface would be:

(a) zero

(b) q4ϵ0\frac{q}{4 \epsilon_0}4ϵ0q

(d) q2πϵ0\frac{q}{2 \pi \epsilon_0}2πϵ0q

27. A conducting circular loop of radius rrr carries a constant current iii. It is placed in a uniform magnetic field B0B_0B0 such that B0B_0B0 is perpendicular to the plane of the loop. The magnetic force acting on the loop is:

(a) irB0i r B_0irB0

(b) 2πirB02 \pi i r B_02πirB0

(d) πirB0 \pi i r B_0πirB0

28. The force acting on a charge moving parallel to a magnetic field is:

(a) qvBq v BqvB

(b) zero

(d) Bv/qB v/qBv/q

29. A 0.5 kg mass moving with a speed of 1.5 m/s on a horizontal surface collides with a spring of force constant k=50k = 50k=50 N/m. The maximum compression of the spring would be:

(a) 0.5 m

(b) 0.15 m

(d) 1.5 m

30. The velocity of sound is maximum in:

(a) Air

(b) Water

(d) Vacuum

31. Which of the following is not an electromagnetic wave?

(a) X-rays

(b) Gamma rays

(d) Beta rays

32. In Young’s double-slit experiment, if the separation between the slits is increased, the fringe width will:

(a) increase

(b) decrease

(d) become zero

33. When a current of 2 A flows through a resistor of 6 ohms for 3 seconds, the energy dissipated is:

(a) 36 J

(b) 72 J

(d) 18 J

34. A light ray undergoes total internal reflection if:

(a) the angle of incidence is equal to the critical angle

(b) the angle of incidence is less than the critical angle

(d) the angle of refraction is greater than the critical angle

35. The temperature of a body is 27°C. Its temperature in Kelvin is:

(a) 300 K

(b) 273 K

(d) 298 K

CHEMISTRY

1. Consider the following reactions:

NaCl + K₂Cr₂O₇ + H₂SO₄ (Conc.) → (A) + Side products
(A) + NaOH → (B) + Side products
(B) + H₂SO₄ (dilute) + H₂O₂ → (C) + Side products
The sum of the total number of atoms in one molecule each of (A), (B), and (C) is:

(a) 18

(b) 15

(d) 20

2. Xenon hexafluoride on partial hydrolysis produces compounds ‘X’ and ‘Y’. Compounds ‘X’, ‘Y’, and the oxidation state of Xe are respectively:

(a) XeOF₄ (+6) and XeO₃ (+6)

(b) XeO₂ (+4) and XeO₃ (+6)

(d) XeO₂F₂ (+6) and XeO₂ (+4)

3. The edge length of the unit cell of a metal having a molecular weight of 75 g/mol is 5Å, which crystallizes in a cubic lattice. If the density is 2g/cm³, find the radius of the metal atom:

(a) 217 pm

(b) 210 pm

(d) 205 pm

4. Which of the following is not an intermediate in the acid-catalyzed reaction of benzaldehyde with two equivalents of methanol to give acetal?

(a) HOCH₃

(b) HO₂CH₃

(d) CH₂OHCH₃

5. The substance C₄H₁₀O yields on oxidation a compound C₄H₈O which gives an oxime and a positive iodoform test. The original substance on treatment with conc. H₂SO₄ gives C₄H₈. The structure of the compound is:

(a) CH₃CH₂CH₂CH₂OH

(b) CH₃CHOHCH₂CH₃

(d) CH₃CH₂–O–CH₂CH₃

6. What is the product of the following reaction?

Hex-3-ynal + NaBH₄, PBr₃, Mg/ether, CO₂/H₂O → ?

(a) CH₃COOH

(b) C₂H₅COOH

(d) COOHCH₂CH₃

7. A compound is soluble in conc. H₂SO₄. It does not decolorize bromine in carbon tetrachloride but is oxidized by chromic anhydride in aqueous sulfuric acid within two seconds, turning orange solution to blue, green, and then opaque. The original compound is:

(a) a primary alcohol

(b) a tertiary alcohol

(d) an ether

8. The limiting equivalent conductivities of NaCl, KCl, and KBr are 126.5, 150.0, and 151.5 S cm² eq⁻¹, respectively. The limiting equivalent ionic conductivity for Br⁻ is 78 S cm² eq⁻¹. The limiting equivalent ionic conductivity for Na⁺ ions would be:

(a) 128

(b) 125

(d) 50

9. The form of iron obtained from a blast furnace is:

(a) Steel

(b) Cast iron

(d) Wrought iron

10. In the following sequence of reactions, what is the product D?

OCH₃ → NaBH₄ → A → HBr → B → OCH₃ → H₂O/heat → C → PCC → D

(a) CHO

(b) COOH

(d) OHCH₃

11. Which of the following statements is incorrect regarding the chemistry of lanthanoids?

(a) The ionic size of Ln³⁺ decreases with increasing atomic number.

(b) Ln³⁺ compounds are generally colorless.

(d) Because of the large size of Ln³⁺ ions, the bonding in its compounds is predominantly ionic.

12. Saponification of coconut oil yields glycerol and:

(a) Palmitic acid

(b) Sodium palmitate

(d) Stearic acid

13. Bragg’s law is given by which of the following equations?

(a) nλ = 2d sinθ

(b) λ = 2d sinθ

(d) 2nλ = d sinθ

14. The half-life of the first-order reaction CH₃OCH₃ → CO₂ + CH₄ + other products, if the initial pressure of CH₃OCH₃ is 80 mm Hg and the total pressure at the end of 20 minutes is 120 mm Hg, is:

(a) 80 min

(b) 120 min

(d) 40 min

15. The exothermic formation of ClF₃ is represented by the equation:

Cl₂(g) + 3F₂(g) → 2ClF₃(g), ΔH = –329 kJ
Which of the following will increase the quantity of ClF₃ in the equilibrium mixture?**

(a) Adding F₂

(b) Increasing the volume of the container

(d) Increasing the temperature

16. In a chemical reaction, which of the following is not a factor that influences the rate of the reaction?

(a) Temperature

(b) Concentration of reactants

(d) Color of the reactants

17. Which of the following has the highest electronegativity?

(a) Oxygen

(b) Sulfur

(d) Nitrogen

18. When potassium nitrate is heated, the product is:

(a) K₂O + O₂

(b) KNO₂ + O₂

(d) K₂O + NO₂

19. Which type of isomerism is exhibited by the compound [Cr(NH₃)₄Cl₂]⁺?

(a) Structural isomerism

(b) Geometrical isomerism

(d) Linkage isomerism

20. What is the major product of the reaction between bromine and ethene in the presence of sunlight?

(a) Bromoethane

(b) 1,2-Dibromoethane

(d) Polybromoethene

21. Which reagent is used in the detection of reducing sugars?

(a) Tollen’s reagent

(b) Fehling’s solution

(d) All of the above

22. In a reversible chemical reaction, the equilibrium constant is dependent on:

(a) Pressure

(b) Volume

(d) Concentration of reactants

23. Which of the following is an example of homogeneous catalysis?

(a) Decomposition of H₂O₂ in the presence of MnO₂

(b) Sulfuric acid-catalyzed esterification

(d) Cracking of hydrocarbons in the presence of zeolites

24. Which of the following exhibits Schottky defects?

(a) NaCl

(b) KCl

(d) CaF₂

25. Which of the following is a nucleophilic substitution reaction?

(a) Hydrolysis of ethyl acetate

(b) Chlorination of methane

(d) Oxidation of ethanol

26. Which gas is produced when NaOH reacts with Cl₂ gas?

(a) NaClO₃

(b) Cl₂

(d) HCl

27. Which compound is known as Quick Lime?

(a) CaCO₃

(b) CaO

(d) CaSO₄

28. Which of the following is a reducing agent?

(a) Na₂O₂

(b) H₂O₂

(d) SO₃

29. The oxidation number of sulfur in SO₄²⁻ is:

(a) +2

(b) +4

(d) +8

30. The hybridization of the central atom in SF₆ is:

(a) sp³d²

(b) sp²

(d) sp³d

31. What is the molecular formula of sodium thiosulfate?

(a) Na₂SO₃

(b) Na₂SO₄

(d) Na₂SO₄·10H₂O

32. Which is the weakest acid among the following?

(a) HF

(b) HCl

(d) HI

33. Which of the following is a d-block element?

(a) Magnesium

(b) Calcium

(d) Sodium

34. The bond order in N₂ is:

(a) 2

(b) 3

(d) 4

35. Which of the following is not a Lewis base?

(a) NH₃

(b) H₂O

(d) Cl⁻

APTITUDE

1. What is the total marks obtained by Meera in all the subjects?

(a) 448

(b) 580

(d) 74.67

2. What is the average marks obtained by these seven students in History (rounded off to two digits)?

(a) 72.86

(b) 27.32

(d) 29.14

3. How many students have got 60% or more marks in all the subjects?

(a) One

(b) Two

(d) Four

4. A series is given with one term missing. Choose the correct alternative from the given ones to complete the series: 5, 11, 24, 51, 106, _?

(a) 122

(b) 217

(d) 153

5. In a certain code, BANKER is written as LFSCBO. How will CONFER be written in that code?

(a) GFSDPO

(b) GFSEPO

(d) FHSDPO

6. Kailash faces north. After turning right and walking 25 meters, he turns left and walks 30 meters. He turns right again and walks 25 meters, then turns right once more and walks 55 meters. In which direction is he now from his starting point?

(a) South-West

(b) North-West

(d) South-East

7. An accurate clock shows 8 O’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 20 O’clock in the afternoon?

(a) 144°

(b) 150°

(d) 180°

8. The variance of the data set 2, 4, 6, 8, 10 is:

(a) 8

(b) 7

(d) None of these

9. Find the probability of getting the sum as a perfect square number when two dice are thrown together:

(a) 5/12

(b) 7/18

(d) None of these

10. The middle term in the expansion of (x + 1/x)^10 is:

(a) 10C5

(b) 10C6

(d) 10C5 x^10

ENGLISH

1. The character of a nation is the result of its:

(a) gross ignorance

(b) cultural heritage

(d) mentality

2. According to the author, the mentality of a nation is mainly a product of its:

(a) present character

(b) international position

(d) history

3. Find the synonym of the word “impeccable”:

(a) Remarkable

(b) Unbelievable

(d) Displeasing

4. Find the antonym of the word “ameliorate”:

(a) Improve

(b) Depend

(d) Worsen

5. Find the meaning of the idiom “A bolt from the blue”:

(a) An unpleasant event

(b) An inexplicable event

(d) An unexpected event

SOLUTIONS

MATHEMATICS

1. Solution:

The expression for sec 2θ2\theta2θ does not directly relate to a rational or irrational number based on the given condition without further information about nnn. Therefore, the answer is:

(d) None of the above

2. Solution:

For z1/3=a−ibz^{1/3} = a – ibz1/3=a−ib, expanding in polar form and simplifying leads to:

(a) 1

3. Solution:

The center of the circle is found by completing the square, and using the midpoint formula for diameters gives the other end:

(d) (11, 2)

4. Solution:

The determinant of the coefficient matrix is zero, indicating an infinite number of solutions.

5. Solution:

Multiplying and simplifying the complex numbers, the modulus is found to be:

(d) 222\sqrt{2}22

6. Solution:

The shortest distance between two parallel lines gives the radius:

(a) 34\frac{3}{4}43

7. Solution:

Using the vector geometry formula for internal bisectors, the result is:

(b) 9217\frac{9}{217}2179

8. Solution:

Differentiating the given equation using implicit differentiation leads to:

(a) 5×2+44×2+1\frac{5x^2 + 4}{4x^2 + 1}4×2+15×2+4

9 Solution:

Using the principle of inclusion and exclusion to count those who only chose Maths:

10. Solution:

Solving the quadratic equation yields:

(b) 23\frac{2}{3}32 or −23-\frac{2}{3}−32

11. Solution:

For the given condition to represent a circle, solving gives:

(d) k=4k = 4k=4

12. Solution:

The vertex of the parabola is equidistant from the focus and directrix:

(b) (1, 0)

13. Solution:

Substituting the point into the general equation of the ellipse and solving yields:

(d) 3×2+5y2−32=03x^2 + 5y^2 – 32 = 03×2+5y2−32=0

14. Solution:

The perfect square sums are 4, 9, and 16, so the probability is:

15. Solution:

Finding the center and using the formula for the diametrically opposite point gives:

16. Solution:

Using conditional probability, the required value is:

(d) 12\frac{1}{2}21

17. Solution:

Using the formula for the sum of an arithmetic-geometric progression for odd values of nnn:

(b) n(n+1)22\frac{n(n+1)^2}{2}2n(n+1)2

18. Solution:

This standard integral evaluates to:

(a) 0

19. Solution:

Setting the second derivative to zero at point P(1,1)P(1, 1)P(1,1), the equation of the tangent is:

y=2x−1y = 2x – 1y=2x−1

20. Solution:

Using the formula for the shortest distance between two lines:

Answer: 295\frac{\sqrt{29}}{5}529

21. Solution:

Variance formula σ2=1N∑(xi−xˉ)2\sigma^2 = \frac{1}{N} \sum (x_i – \bar{x})^2σ2=N1∑(xi−xˉ)2 gives:

(a) 8

22. Solution:

The principal value of sin⁡−1(sin⁡5π3)\sin^{-1} (\sin \frac{5\pi}{3})sin−1(sin35π) is:

23. Solution:

Using Cramer’s rule, solve the system of equations to find k=2k = 2k=2:

xz=30\frac{x}{z} = 30zx=30

24. Solution:

Solving the inequality gives the solution set:

25. Solution:

The equation of the median from AAA is the line passing through AAA and the midpoint of BCBCBC.

Answer: y=32x−1y = \frac{3}{2}x – 1y=23x−1

26. Solution:

Using the relationship in a G.P. for three terms:

(b) q2=prq^2 = prq2=pr

27. Solution:

The function is continuous at x=0x = 0x=0, but not differentiable at x=0x = 0x=0.

28. Solution:

The vertex of the parabola is halfway between the focus and directrix:

(b) (1, 0)

29. Solution:

The angle between the vectors is given by:

cos⁡−1(1020⋅16)\cos^{-1} \left( \frac{10}{\sqrt{20} \cdot \sqrt{16}} \right)cos−1(20⋅1610)

30. Solution:

The distance between the two parallel lines is:

(a) 2

31. Solution:

Using the angle bisector formula, the equation is:

33x−13y+32z+45=033x – 13y + 32z + 45 = 0 33x−13y+32z+45=0

32. Solution:

The number of ways to choose 5 members from 10 people is:

(105)=252\binom{10}{5} = 252(510)=252

33. Solution:

The probability of getting at least one head is:

1−18=781 – \frac{1}{8} = \frac{7}{8}1−81=87

34. Solution:

This standard integral evaluates to:

π4\frac{\pi}{4}4π

35. Solution:

The area between the curve and the lines is found by integrating x3x^3×3 from 0 to 2:

454\frac{45}{4}445

36. Solution:

There are 450 three-digit numbers with an even sum of digits:

(a) 450

37. Solution:

In polar coordinates, r=x2+y2r = \sqrt{x^2 + y^2}r=x2+y2, so the equation becomes:

r2=e3r^2 = e^3r2=e3

38. Solution:

The sum of the first nnn terms of the AP is given by:

Sn=n2⋅(2a+(n−1)d)S_n = \frac{n}{2} \cdot (2a + (n-1)d)Sn=2n⋅(2a+(n−1)d)

39. Solution:

The probability of selecting a number divisible by both 2 and 5 is 10100=0.1\frac{10}{100} = 0.110010=0.1.

Answer: 0.1

40. Solution:

Complete the square for the given equation to find the center and radius:

Center: (-3, 4), Radius: 2

PHYSICS

1. Solution:

The resistance RRR is proportional to length and inversely proportional to the square of the radius. If both are doubled, the resistance is halved while specific resistance remains unchanged.

2. Solution:

The combined focal length formula for two lenses in contact is 1f=1f1+1f2\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}f1=f11+f21. Using f=80f = 80f=80 cm and f1=20f_1 = 20f1=20 cm, we find f2=−25f_2 = -25f2=−25 cm.

(d) –3.75 D

3. Solution:

The de-Broglie wavelength λ\lambdaλ is inversely proportional to the square root of kinetic energy. If kinetic energy doubles, the wavelength is reduced by 12\frac{1}{\sqrt{2}}21.

(b) 12\frac{1}{\sqrt{2}}21

4. Solution:

The decay law is expressed by N=N0e−λtN = N_0 e^{-\lambda t}N=N0e−λt, where NNN is the number of undecayed nuclei at time ttt.

5. Solution:

The energy levels in a hydrogen atom are proportional to 1n2\frac{1}{n^2}n21, where nnn is the principal quantum number. For the first and second excited states, the ratio of energies is 49\frac{4}{9}94.

(b) 49\frac{4}{9}94

6. Solution:

The output of an OR gate will be 1 if any input is 1.

(b) OR gate

7. Solution:

The work done by the electric field on a point charge in a complete revolution around another point charge is zero.

(a) Zero

8. Solution:

For capacitors in series: 1Cs=1C1+1C2\frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2}Cs1=C11+C21, and in parallel Cp=C1+C2C_p = C_1 + C_2Cp=C1+C2. Solving these equations gives the individual capacitances as:

9. Solution:

The velocity of efflux is given by Torricelli’s law: v=2ghv = \sqrt{2gh}v=2gh, so it depends on the height of the liquid and gravity.

(a) Height of the liquid

10. Solution:

The displacement is the straight-line distance between the initial and final points, and the distance is half the circumference of the circle:

(a) 2r,πr2r, \pi r2r,πr

11. Solution:

Escape velocity does not depend on the mass of the body. Hence, for another body with mass 4m, the escape velocity remains the same.

(a) vvv

12. Solution:

Using the relation P1I1=P2I2P_1 I_1 = P_2 I_2P1I1=P2I2, and substituting the values for primary and secondary voltages, the current in the primary winding is:

(a) 12.5 A

13. Solution:

The force needed for the upward acceleration is F=ma+mgF = ma + mgF=ma+mg, and the required gas ejection rate is Fv\frac{F}{v}vF, yielding:

(b) 137.5 kg/s

14. Solution:

Potential energy increases when work is done by a non-conservative force on the system.

(b) Upon the system by a non-conservative force

15. Solution:

In an electromagnetic wave, power is transmitted in a direction perpendicular to both electric and magnetic fields.

16. Solution:

Using conservation of momentum: mbulletvbullet=mriflemanvriflemanm_{\text{bullet}} v_{\text{bullet}} = m_{\text{rifleman}} v_{\text{rifleman}}mbulletvbullet=mriflemanvrifleman, the velocity of the rifleman is:

(b) 0.08 m/s

17. Solution:

The radius of the soapy film separating the two bubbles is given by R=r12+r22R = \sqrt{r_1^2 + r_2^2}R=r12+r22.

(b) 2r1r2r1+r2\frac{2r_1r_2}{r_1 + r_2}r1+r22r1r2

18. Solution:

The de-Broglie wavelength λ=h2mE\lambda = \frac{h}{\sqrt{2mE}}λ=2mEh, where EEE is the kinetic energy of the particle.

(a) λ=h2mE\lambda = \frac{h}{\sqrt{2mE}}λ=2mEh

19. Solution:

The intensity at a point where the path difference is λ4\frac{\lambda}{4}4λ is half the maximum intensity.

(b) I2\frac{I}{2}2I

20. Solution:

The root mean square velocity is calculated using the kinetic theory of gases. For smoke particles of mass 5×10−175 \times 10^{-17}5×10−17 kg, the velocity is:

(b) 12 mm/s

21. Solution:

For capacitors in series and parallel combination, the equivalent capacitance is:

(a) 2.16 µF

22. Solution:

Using Newton’s second law and friction, the tension in the cord is:

(b) 36.75 N

23. Solution:

For a rolling object, the speed of the center of mass is v=4gh/3v = \sqrt{4gh/3}v=4gh/3.

(a) 4gh/3\sqrt{4gh/3}4gh/3

24. Solution:

The displacement is given by the area under the velocity-time graph. For uniform acceleration, the displacement in 10 seconds is:

(a) 90 m

25. Solution:

The resonance frequency f0f_0f0 is inversely proportional to the square root of the capacitance. If the capacitance is quadrupled, the new frequency becomes f0/2f_0/2f0/2.

26. Solution:

The flux through the flat surface of a hemispherical surface with a charge at the center is zero because the charge is symmetrically enclosed.

(a) Zero

27. Solution:

The magnetic force on a current-carrying loop in a uniform magnetic field is zero because the forces on opposite sides of the loop cancel each other out.

28. Solution:

If the charge moves parallel to the magnetic field, the force on it is zero because v⃗∥B⃗\vec{v} \parallel \vec{B}v∥B.

(b) Zero

29. Solution:

Using conservation of energy, the compression of the spring is given by 12kx2=12mv2\frac{1}{2} k x^2 = \frac{1}{2} m v^221kx2=21mv2, solving for xxx gives:

(b) 0.15 m

30. Solution:

The velocity of sound is maximum in solids, so it is highest in steel.

31. Solution:

Beta rays are not electromagnetic waves; they are streams of charged particles (electrons).

(d) Beta rays

32. Solution:

Fringe width w=λDdw = \frac{\lambda D}{d}w=dλD, so if the separation ddd increases, the fringe width decreases.

(b) Decrease

33. Solution:

The energy dissipated E=I2RtE = I^2 R tE=I2Rt, substituting the values gives:

34. Solution:

Total internal reflection occurs when the angle of incidence exceeds the critical angle.

35. Solution:

Converting Celsius to Kelvin, T(K)=T(°C)+273T(K) = T(°C) + 273T(K)=T(°C)+273, so 27°C27°C27°C becomes:

(a) 300 K

CHEMISTRY

1. Solution:

By analyzing the products and applying basic knowledge of the reactions involved, the sum of atoms in one molecule each of (A), (B), and (C) is:

2. Solution:

Partial hydrolysis of xenon hexafluoride gives XeOF₄ and XeO₃. Therefore, the oxidation state of xenon in both compounds is +6.

(a) XeOF₄ (+6) and XeO₃ (+6)

3. Solution:

Using the density formula for cubic lattice and solving for the radius of the atom:

(a) 217 pm

4. Solution:

Among the given intermediates, HO₂CH₃ is not involved in the formation of an acetal.

(b) HO₂CH₃

5. Solution:

The compound that fits the described reactions (positive iodoform test, formation of alkene) is:

(b) CH₃CHOHCH₂CH₃

6. Solution:

The reaction leads to the formation of a carboxylic acid:

7. Solution:

The reaction describes oxidation typical of a primary alcohol.

(a) A primary alcohol

8. Solution:

Using the law of ionic conductance, the limiting equivalent conductivity of Na⁺ ions is calculated to be:

(b) 125

9. Solution:

The form of iron obtained from a blast furnace is called pig iron.

10. Solution:

The sequence of reactions ultimately leads to the formation of an aldehyde:

(a) CHO

11. Solution:

Lanthanoid compounds are generally colored, not colorless. Hence, the incorrect statement is:

(b) Ln³⁺ compounds are generally colorless

12. Solution:

Saponification of coconut oil yields glycerol and sodium palmitate.

(b) Sodium palmitate

13. Solution:

Bragg’s law is expressed as nλ=2dsin⁡θn\lambda = 2d\sin\thetanλ=2dsinθ.

(a) nλ=2dsin⁡θn\lambda = 2d\sin\thetanλ=2dsinθ

14. Solution:

The pressure data indicates that the reaction follows first-order kinetics with a half-life of 40 minutes.

(d) 40 min

15. Solution:

According to Le Chatelier’s principle, adding more F₂ will shift the equilibrium towards the production of ClF₃.

(a) Adding F₂

16. Solution:

The color of the reactants does not influence the rate of a chemical reaction.

(d) Color of the reactants

17. Solution:

Among the given elements, oxygen has the highest electronegativity.

(a) Oxygen

18. Solution:

When potassium nitrate is heated, it decomposes to form potassium nitrite and oxygen.

(b) KNO₂ + O₂

19. Solution:

The compound [Cr(NH₃)₄Cl₂]⁺ exhibits geometrical isomerism.

(b) Geometrical isomerism

20. Solution:

In the presence of sunlight, ethene reacts with bromine to form 1,2-dibromoethane.

(b) 1,2-Dibromoethane

21. Solution:

Reducing sugars can be detected using Tollen’s reagent, Fehling’s solution, or Benedict’s solution.

(d) All of the above

22. Solution:

The equilibrium constant of a reversible reaction depends only on the temperature.

23. Solution:

Sulfuric acid-catalyzed esterification is an example of homogeneous catalysis.

(b) Sulfuric acid-catalyzed esterification

24. Solution:

Schottky defects are exhibited by ionic compounds like NaCl, KCl, and AgBr.

(a) NaCl

25. Solution:

Nucleophilic substitution reactions involve the replacement of a leaving group by a nucleophile. Hydrolysis of ethyl acetate is a classic example.

(a) Hydrolysis of ethyl acetate

26. Solution:

When NaOH reacts with Cl₂ gas, it forms NaCl and NaClO, which are collectively called bleach.

(a) NaClO₃

27. Solution:

Quick lime is the common name for calcium oxide (CaO).

(b) CaO

28. Solution:

Carbon monoxide (CO) is a well-known reducing agent.

29. Solution:

In the sulfate ion (SO₄²⁻), the oxidation state of sulfur is +6.

30. Solution:

The central atom in SF₆ exhibits sp3d2sp³d²sp3d2 hybridization.

(a) sp³d²

31. Solution:

Sodium thiosulfate has the molecular formula Na₂S₂O₃.

32. Solution:

Hydrofluoric acid (HF) is the weakest acid among the halogen acids.

(a) HF

33. Solution:

Chromium (Cr) is a transition element and belongs to the d-block of the periodic table.

34. Solution:

The bond order in molecular nitrogen (N₂) is 3.

(b) 3

35. Solution:

BF₃ is an electron-deficient compound and acts as a Lewis acid, not a Lewis base.

Aptitude

1. What is the total marks obtained by Meera in all the subjects?

The correct total is calculated as (b) 580.

2. What is the average marks obtained by these seven students in History (rounded off to two digits)?

The average marks are calculated as (a) 72.86.

3. How many students have got 60% or more marks in all the subjects?

The correct answer is (b) Two.

4. A series is given with one term missing: 5, 11, 24, 51, 106, _?

The next number in the series is (b) 217.

5. In a certain code, BANKER is written as LFSCBO. How will CONFER be written in that code?

The correct code is (a) GFSDPO.

6. Kailash faces north. After walking 25m right, left 30m, right 25m, and right 55m, where is he?

The correct answer is (d) South-East.

7. An accurate clock shows 8 O’clock in the morning. How many degrees will the hour hand rotate when the clock shows 20 O’clock in the afternoon?

The hour hand rotates (d) 180°.

8. The variance of the data set 2, 4, 6, 8, 10 is:

The variance is (a) 8.

9. Find the probability of getting a sum as a perfect square number when two dice are thrown:

The correct probability is (c) 7/36.

10. The middle term in the expansion of (x+1/x)10(x + 1/x)^{10}(x+1/x)10 is:

The middle term is (b) 10C5.

English

1. The character of a nation is the result of its:

The correct answer is (b) cultural heritage.

2. According to the author, the mentality of a nation is mainly a product of its:

The correct answer is (d) history.

3. Find the synonym of the word “impeccable”:

The correct synonym is (c) Flawless.

4. Find the antonym of the word “ameliorate”:

The correct antonym is (d) Worsen.

5. Find the meaning of the idiom “A bolt from the blue”:

The correct meaning is (d) An unexpected event.

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FAQ

When will the VITEEE 2025 application form be released?
The VITEEE 2025 application form will be available from the first week of November 2024.
How can I submit the VITEEE 2025 application form?
The application form can be submitted online through the official VIT website. There is no offline submission option.
What is the application fee for VITEEE 2025, and how can I pay it?
The application fee is ₹1350 for all categories, and it can be paid only through online modes such as credit/debit card or net banking.
Can I make corrections to the application form after submission?
Yes, the university will provide a correction window for candidates to make changes to the submitted application form.
What is the last date to submit the VITEEE 2025 application form?
The last date to submit the application form is in the second week of April 2025. Make sure to complete the registration before the deadline.