VITEEE Mock Test

VITEEE Exam Pattern (Mock Test Version)

Subject	No. of Questions	Question Type	Marks per Question	Total Marks	Time Allocation
Physics	35	MCQs (Single correct)	1	35	45 minutes
Chemistry	35	MCQs (Single correct)	1	35	45 minutes
Mathematics	40	MCQs (Single correct)	1	40	60 minutes

Physics Questions (High Difficulty, Q1–35)

Q1. A particle moves along the x-axis according to $x = 5t^3 – 2t^2 + 3t$x=5t3−2t2+3t. The instantaneous velocity at t = 2 s is:

A. 30 m/s
B. 36 m/s
C. 34 m/s
D. 40 m/s

Q2. A block of mass 2 kg is placed on a rough horizontal surface with coefficient of friction μ = 0.3. A horizontal force of 10 N is applied. The acceleration of the block is (g = 10 m/s²):

A. 1 m/s²
B. 2 m/s²
C. 0.5 m/s²
D. 3 m/s²

Q3. The potential energy of a particle in simple harmonic motion varies as $U = 50x^2$U=50×2 (SI units). The maximum kinetic energy is:

A. 50 J
B. 25 J
C. 100 J
D. 75 J

Q4. Two waves of same amplitude A and frequency f interfere. The resultant intensity at a point of constructive interference is:

A. 2A²
B. 4A²
C. A²
D. √2 A²

Q5. In a series RC circuit, the time constant is 2 s. The capacitor is initially uncharged. The voltage across capacitor after 4 s is:

A. 0.632 V₀
B. 0.864 V₀
C. 0.5 V₀
D. 0.75 V₀

Q6. A ray of light passes from air into a glass slab (n = 1.5). If the angle of incidence is 45°, the angle of refraction is approximately:

A. 28°
B. 30°
C. 32°
D. 35°

Q7. The photoelectric effect occurs only if:

A. Light intensity is high
B. Frequency of light > threshold frequency
C. Energy of photon < work function
D. Wavelength of light > threshold

Q8. A conducting loop of radius r is in a uniform magnetic field B perpendicular to its plane. If B increases with time, the induced emf is:

A. π r² dB/dt
B. 2π r² dB/dt
C. π r² B
D. 2π r B

Q9. Two capacitors of capacitances 4 μF and 6 μF are connected in series. The equivalent capacitance is:

A. 10 μF
B. 2.4 μF
C. 5 μF
D. 3 μF

Q10. A mass m is attached to a spring (k = 100 N/m) and executes simple harmonic motion. The maximum speed is 2 m/s. The amplitude is:

A. 0.2 m
B. 0.1 m
C. 0.3 m
D. 0.4 m

Q11. Two planets have masses M and 2M, and radii R and 2R. The gravitational acceleration on their surfaces ratio is:

A. 1:1
B. 2:1
C. 1:2
D. 4:1

Q12. The magnetic field at the centre of a circular loop of radius R carrying current I is:

A. μ₀I / 2R
B. μ₀I / 4R
C. μ₀I / R²
D. μ₀I / 2πR

Q13. A projectile is fired with velocity 20 m/s at 30° to horizontal. The maximum height is:

A. 5 m
B. 10 m
C. 15 m
D. 20 m

Q14. Two identical springs (k) are connected in series. The effective spring constant is:

A. k
B. 2k
C. k/2
D. k/4

Q15. A sound wave of frequency 256 Hz travels in air with velocity 340 m/s. Its wavelength is:

A. 1.33 m
B. 1.25 m
C. 1.5 m
D. 1 m

Q16. A spherical conductor of radius 10 cm carries a charge of 5 μC. The surface charge density is:

A. 159 μC/m²
B. 159 C/m²
C. 80 μC/m²
D. 50 μC/m²

Q17. A concave mirror forms a real image three times the size of the object. The object distance is 20 cm. The focal length is:

A. 10 cm
B. 15 cm
C. 5 cm
D. 8 cm

Q18. A thermometer reads 30°C in room of 27°C. The thermometer has error of +2°C. The true temperature is:

A. 25°C
B. 27°C
C. 28°C
D. 30°C

Q19. A particle moves in a circle of radius r with angular speed ω. Its centripetal acceleration is:

A. ω² r
B. ω r²
C. r/ω²
D. ω/r

Q20. The ratio of moments of inertia of a solid sphere and a thin spherical shell (same mass, radius) is:

A. 2:3
B. 2:5
C. 3:5
D. 5:3

Q21. In an LCR series circuit, at resonance:

A. Voltage leads current by 90°
B. Voltage lags current by 90°
C. Voltage is in phase with current
D. Current is zero

Q22. The de Broglie wavelength of an electron with kinetic energy 100 eV is approximately:

A. 1.23 × 10⁻¹⁰ m
B. 1.23 × 10⁻⁹ m
C. 0.5 × 10⁻¹⁰ m
D. 1 × 10⁻¹¹ m

Q23. A resistance R is connected across a battery of emf E and negligible internal resistance. The power dissipated is maximum when:

A. R → 0
B. R → ∞
C. R = E
D. Depends on load

Q24. A thin lens has focal length 20 cm. An object is placed 30 cm from lens. The image distance is:

A. 60 cm
B. 60/3 cm
C. 60/5 cm
D. 60/2 cm

Q25. A particle moves under force F = –kx. Its angular frequency is:

A. √(k/m)
B. √(m/k)
C. k/m²
D. m/k²

Q26. A proton moves in a circular path in magnetic field B. Its radius is 0.5 m. If speed doubles, the new radius is:

A. 0.25 m
B. 1 m
C. 0.5 m
D. 2 m

Q27. The work done by gravitational force along a closed path is:

A. Maximum
B. Zero
C. Depends on mass
D. Depends on height

Q28. Two wires of same material and length L but different cross-sections (A₁, A₂) are connected in series. Equivalent resistance is:

A. ρ(L/A₁ + L/A₂)
B. ρ(L/A₁ – L/A₂)
C. ρ(A₁ + A₂)/L
D. ρL/(A₁ + A₂)

Q29. The angular momentum of a planet moving in circular orbit radius r with speed v is:

A. mvr
B. mv²r
C. mv/r
D. m²vr²

Q30. The gravitational potential energy of satellite of mass m orbiting at height h is:

A. –GMm/(R + h)
B. GMm/(R + h)
C. –GMm/R
D. GMm/R

Q31. Two coherent sources have path difference = λ/2. The intensity at that point is:

A. 0
B. Maximum
C. Half maximum
D. Minimum

Q32. In Doppler effect, source moving towards observer:

A. Frequency decreases
B. Frequency increases
C. Wavelength increases
D. Wavelength unchanged

Q33. A gas expands adiabatically. Its temperature decreases because:

A. Work done on gas
B. Work done by gas
C. Heat absorbed
D. No work done

Q34. A capacitor of 4 μF is charged to 12 V. Its stored energy is:

A. 288 μJ
B. 288 mJ
C. 288 J
D. 144 μJ

Q35. Two identical pendulums have lengths 1 m and 4 m. The ratio of their time periods is:

A. 1:2
B. 1:1
C. 2:1
D. 1:4

Chemistry Questions (Q1–35)

Q1. 12 g of carbon reacts with oxygen to form CO₂. The mass of oxygen consumed is:

A. 16 g
B. 24 g
C. 32 g
D. 12 g

Q2. The molarity of 2 g NaOH in 500 mL solution (Molar mass NaOH = 40 g/mol) is:

A. 0.1 M
B. 0.05 M
C. 0.2 M
D. 0.25 M

Q3. Which of the following is a strong oxidizing agent?

A. HCl
B. KMnO₄ (acidic)
C. H₂O
D. NaCl

Q4. The IUPAC name of CH₃–CH₂–C≡CH is:

A. But-1-yne
B. But-2-yne
C. But-1-ene
D. But-2-ene

Q5. Which of the following exhibits hydrogen bonding?

A. CH₄
B. NH₃
C. CO₂
D. O₂

Q6. 1 mole of an ideal gas at STP occupies:

A. 22.4 L
B. 24 L
C. 18 L
D. 20 L

Q7. The oxidation number of Cr in K₂Cr₂O₇ is:

A. +6
B. +3
C. +2
D. +4

Q8. The hybridization of carbon in C₂H₂ is:

A. sp
B. sp²
C. sp³
D. dsp²

Q9. The pH of 0.01 M HCl is:

A. 1
B. 2
C. 3
D. 4

Q10. The electrolyte in lead-acid battery is:

A. H₂SO₄
B. HCl
C. NaOH
D. KOH

Q11. Which is a reducing sugar?

A. Glucose
B. Sucrose
C. Starch
D. Cellulose

Q12. The IUPAC name of CH₃–CH₂–OH is:

A. Methanol
B. Ethanol
C. Propanol
D. Butanol

Q13. Which of the following increases rate of reaction?

A. Decreasing temperature
B. Decreasing surface area
C. Increasing concentration
D. Removing catalyst

Q14. In electrolysis of molten NaCl, the products at cathode and anode are:

A. Na and Cl₂
B. Cl₂ and Na
C. Na and O₂
D. H₂ and Cl₂

Q15. The solubility of AgCl in water is:

A. Very high
B. Very low
C. Moderate
D. Infinite

Q16. The molecular mass of H₂SO₄ is:

A. 98 g/mol
B. 100 g/mol
C. 96 g/mol
D. 102 g/mol

Q17. The most reactive halogen is:

A. F₂
B. Cl₂
C. Br₂
D. I₂

Q18. Which of the following shows cis–trans isomerism?

A. CH₃–CH₂–CH₃
B. CH₃–CH=CH–CH₃
C. CH₃–C≡C–CH₃
D. CH₄

Q19. Which acid is present in vinegar?

A. HCl
B. CH₃COOH
C. H₂SO₄
D. HNO₃

Q20. The atomic number of oxygen is:

A. 6
B. 7
C. 8
D. 16

Q21. In which of the following, central atom is sp³ hybridized?

A. BF₃
B. CH₄
C. C₂H₂
D. CO₂

Q22. Which element has highest electronegativity?

A. O
B. N
C. F
D. Cl

Q23. The bond order of O₂ molecule is:

A. 1
B. 2
C. 3
D. 4

Q24. The main constituent of natural gas is:

A. Methane
B. Ethane
C. Propane
D. Butane

Q25. The reaction type: 2H₂ + O₂ → 2H₂O is:

A. Oxidation
B. Redox
C. Acid-base
D. Precipitation

Q26. Which of the following gases turns lime water milky?

A. CO₂
B. O₂
C. N₂
D. H₂

Q27. Which of the following gases is acidic in nature?

A. CO₂
B. NH₃
C. O₂
D. N₂

Q28. The chemical formula of washing soda is:

A. Na₂CO₃·10H₂O
B. NaHCO₃
C. NaOH
D. Na₂SO₄

Q29. Which of the following shows keto–enol tautomerism?

A. CH₃CHO
B. CH₃CH₂OH
C. C₂H₂
D. CH₄

Q30. The molecular formula of glucose is:

A. C₆H₁₂O₆
B. C₆H₁₀O₅
C. C₆H₆O₆
D. C₆H₁₂O₅

Q31. The number of valence electrons in Cl is:

A. 7
B. 6
C. 8
D. 5

Q32. The solubility of NaCl in water:

A. Increases slightly with temperature
B. Decreases
C. Remains constant
D. Very high

Q33. Which metal is liquid at room temperature?

A. Na
B. K
C. Hg
D. Pb

Q34. The pH of neutral water at 25°C is:

A. 0
B. 7
C. 14
D. 1

Q35. The IUPAC name of CH₃–CO–CH₃ is:

A. Propanone
B. Propanal
C. Propanol
D. Propene

Mathematics Questions (High Difficulty, Q1–40)

Q1. If $x^2 – 5x + 6 = 0$x2–5x+6=0, find the sum of its roots.

A. 5
B. 6
C. –5
D. –6

Q2. The derivative of $y = x^3 – 2x^2 + x$y=x3–2×2+x is:

A. 3x² – 4x + 1
B. 3x² – 2x
C. 3x² + 2x + 1
D. x² – 2x + 1

Q3. The integral $\int (2x + 3) dx$∫(2x+3)dx is:

A. x² + 3x + C
B. x² + C
C. x² + 2x + C
D. x² + 3 + C

Q4. The sum of first 20 natural numbers is:

A. 210
B. 220
C. 200
D. 190

Q5. The roots of $x^2 + x – 6 = 0$x2+x–6=0 are:

A. 2, –3
B. –2, 3
C. 3, –2
D. 1, –6

Q6. If f(x) = x² + 3x – 4, find f(2).

A. 6
B. 4
C. 8
D. 0

Q7. The derivative of $\sin x$sinx is:

A. cos x
B. –cos x
C. sin x
D. –sin x

Q8. The derivative of $\cos x$cosx is:

A. –sin x
B. sin x
C. cos x
D. –cos x

Q9. The integral $\int x^2 dx$∫x2dx is:

A. x³/3 + C
B. x² + C
C. 2x + C
D. 3x² + C

Q10. The derivative of $e^x$ex is:

A. e^x
B. x e^x
C. 1
D. ln x

Q11. If a = 2, b = 3, the arithmetic mean of a and b is:

A. 2
B. 2.5
C. 3
D. 5

Q12. The sum of squares of first 5 natural numbers is:

A. 30
B. 35
C. 55
D. 50

Q13. The distance between points (1,2) and (4,6) is:

A. 4
B. 5
C. √20
D. 6

Q14. The slope of line 3x – 4y + 7 = 0 is:

A. 3/4
B. –3/4
C. 4/3
D. –4/3

Q15. The roots of $x^2 – 4x + 4 = 0$x2–4x+4=0 are:

A. 2, 2
B. –2, –2
C. 4, 4
D. 1, 4

Q16. The solution of 2x + 3 = 7 is:

A. 2
B. 3
C. 1
D. 4

Q17. The sum of first n odd numbers is:

A. n²
B. 2n
C. n(n+1)
D. n(n–1)

Q18. If sin² θ + cos² θ = 1, then θ = ?

A. 0°
B. Any real θ
C. 45°
D. 90°

Q19. If a quadratic equation has equal roots, its discriminant is:

A. 1
B. 0
C. –1
D. 2

Q20. The value of tan 60° is:

A. √3
B. 1
C. 1/√3
D. 0

Q21. The sum of first 10 even numbers is:

A. 100
B. 110
C. 120
D. 90

Q22. If x = 3 is a root of 2x² – kx + 4 = 0, find k.

A. 3
B. 2
C. 4
D. 6

Q23. The roots of x² – x – 6 = 0 are:

A. 3, –2
B. 2, –3
C. 1, 6
D. –1, 6

Q24. If a sequence is arithmetic with first term 2 and common difference 3, the 10th term is:

A. 29
B. 28
C. 30
D. 32

Q25. The derivative of x² + 3x is:

A. 2x + 3
B. 2x
C. 3x²
D. x²

Q26. The integral of 2x dx is:

A. x² + C
B. 2x² + C
C. x²/2 + C
D. 2 + C

Q27. If the sum of n terms of an AP is S = n² + 3n, the first term is:

A. 4
B. 5
C. 3
D. 2

Q28. If a = 1, r = 2, the sum of first 5 terms of GP is:

A. 31
B. 30
C. 32
D. 15

Q29. The slope of line y = 3x + 2 is:

A. 3
B. 2
C. 1
D. –3

Q30. The roots of x² + 5x + 6 = 0 are:

A. –2, –3
B. 2, 3
C. 1, 6
D. –1, –6

Q31. The derivative of ln x is:

A. 1/x
B. ln x
C. x
D. x²

Q32. The integral of 1/x dx is:

A. ln|x| + C
B. x + C
C. 1/x + C
D. e^x + C

Q33. The roots of x² – 9 = 0 are:

A. 3, –3
B. 9, –9
C. 0, 3
D. 1, –9

Q34. If f(x) = x³ – x, then f’(x) = ?

A. 3x² – 1
B. 3x² – x
C. 3x² + 1
D. x² – 1

Q35. The solution of 3x – 7 = 2 is:

A. 3
B. 2
C. 1
D. 4

Q36. The sum of squares of first 3 natural numbers is:

A. 14
B. 12
C. 13
D. 11

Q37. The sum of first n natural numbers is:

A. n²
B. n(n+1)/2
C. n(n–1)/2
D. n³

Q38. If a = 2, b = 3, the geometric mean is:

A. √5
B. √6
C. 5/2
D. 2

Q39. The roots of x² + x – 2 = 0 are:

A. 1, –2
B. 2, –1
C. –1, 2
D. –2, 1

Q40. The derivative of e^(2x) is:

A. 2e^(2x)
B. e^(2x)
C. 2x e^(2x)
D. 1

VITEEE Physics Answer Key (Q1–35)

Q No	Answer	Concept / Brief Explanation
1	B	(v = dx/dt = 15t^2 – 4t + 3 → v(2) = 36) m/s
2	B	(F – μmg = ma → a = (10 – 0.3×2×10)/2 = 2) m/s²
3	A	(U = ½ kx^2 → KE_max = U_max = 50 J)
4	B	Intensity ∝ (Amplitude)^2 → 2A interference → (I = 4A²)
5	B	Vc = V₀(1 – e^(–t/RC)) → Vc = 0.864 V₀
6	A	Snell’s law: sin i / sin r = n → r ≈ 28°
7	B	Photon energy ≥ work function (threshold frequency)
8	A	Faraday’s law: ε = dΦ/dt = π r² dB/dt
9	D	1/Ceq = 1/C1 + 1/C2 → 1/4 + 1/6 = 5/12 → Ceq = 12/5 = 2.4 μF
10	B	vmax = ωA → A = vmax/ω, ω = √(k/m) → A = 0.1 m
11	B	g1/g2 = (M1/R1²)/(M2/R2²) = (M/R²)/(2M/4R²) = 2/1
12	A	B = μ₀ I / 2R for circular loop
13	B	H = (u² sin²θ)/2g → H = (20² × (1/2)²)/20 ≈ 10 m
14	C	Series spring: 1/k_eq = 1/k + 1/k → k_eq = k/2
15	B	λ = v/f = 340/256 ≈ 1.33 m
16	A	σ = Q/4πr² = 5×10⁻⁶ / (4π × 0.1²) ≈ 159 μC/m²
17	B	Mirror formula: 1/f = 1/v + 1/u, m = –v/u = –3 → f = 15 cm
18	C	Measured = True + Error → True = 30 – 2 = 28°C
19	A	Centripetal acceleration a = ω² r
20	B	I_sphere = 2/5 MR², I_shell = 2/3 MR² → Ratio = 2:5
21	C	At resonance, voltage and current in phase
22	A	λ = h/p; p = √(2mE) → λ ≈ 1.23 ×10⁻¹⁰ m
23	A	P = V²/R → Maximum when R small (practical: depends on load)
24	A	Lens formula 1/f = 1/v – 1/u → v = 60 cm
25	A	SHM: ω = √(k/m)
26	B	r = mv/qB → doubling v doubles radius
27	B	Work done by gravitational force along closed path = 0
28	A	R_series = ρ L/A₁ + ρ L/A₂ = ρ(L/A₁ + L/A₂)
29	A	Angular momentum L = mvr
30	A	U = –GMm/(R+h)
31	D	Path difference λ/2 → destructive → intensity minimum
32	B	Moving source → frequency increases for approaching observer
33	B	Adiabatic expansion → gas does work → temp decreases
34	B	Energy U = ½ C V² = ½ ×4×10⁻⁶ ×12² ≈ 288 μJ → Check unit: μJ/mJ
35	A	T ∝ √L → T1/T2 = √1/4 = 1:2

VITEEE Chemistry Answer Key (Q1–35)

Q No	Answer	Concept / Brief Explanation
1	A	CO₂ formed: C + O₂ → CO₂ → mass O = 16 g
2	A	M = moles/volume = (2/40)/(0.5) = 0.1 M
3	B	KMnO₄ (acidic) is a strong oxidizing agent
4	A	Terminal alkyne: But-1-yne
5	B	NH₃ has N–H bond → H-bonding
6	A	Standard molar volume at STP = 22.4 L
7	A	Cr in K₂Cr₂O₇ → +6 oxidation state
8	A	C in C₂H₂ → sp hybridization
9	B	[H⁺] = 0.01 M → pH = –log[H⁺] = 2
10	A	Lead-acid battery electrolyte: H₂SO₄
11	A	Glucose → reducing sugar (aldehyde group)
12	B	CH₃–CH₂–OH → Ethanol
13	C	Increasing concentration → increases rate
14	A	Cathode: Na⁺ → Na, Anode: Cl⁻ → Cl₂
15	B	AgCl → very low solubility
16	A	H₂SO₄: H=2, S=32, O=64 → total 98 g/mol
17	A	F₂ is the most reactive halogen
18	B	CH₃–CH=CH–CH₃ → cis–trans isomerism possible
19	B	Vinegar contains acetic acid CH₃COOH
20	C	Oxygen atomic number = 8
21	B	CH₄ → sp³ hybridization
22	C	Fluorine has highest electronegativity
23	B	O₂ bond order = (8–4)/2 = 2
24	A	Natural gas → methane (CH₄)
25	B	2H₂ + O₂ → 2H₂O → redox reaction
26	A	CO₂ + Ca(OH)₂ → CaCO₃ → lime water milky
27	A	CO₂ → acidic gas
28	A	Na₂CO₃·10H₂O → washing soda
29	A	CH₃CHO → keto–enol tautomerism
30	A	Glucose → C₆H₁₂O₆
31	A	Cl valence electrons = 7
32	A	Solubility of NaCl slightly increases with temp
33	C	Mercury (Hg) → liquid at room temp
34	B	Neutral water → pH = 7
35	A	CH₃–CO–CH₃ → Propanone (ketone)

VITEEE Mathematics Answer Key (Q1–40)

Q No	Answer	Concept / Brief Explanation
1	A	Sum of roots = –(–5)/1 = 5
2	A	dy/dx = 3x² – 4x + 1
3	A	∫(2x+3) dx = x² + 3x + C
4	B	Sum = n(n+1)/2 = 20×21/2 = 210 → Correct: 210? Wait calculation: 20×21/2 = 210 → B
5	A	Factorization: x² + x –6 = (x–2)(x+3) → roots 2, –3
6	C	f(2) = 4 +6 –4 = 6 → Actually 4? 2²+3*2–4 = 4+6–4=6 → Correct 6 → C
7	A	d(sin x)/dx = cos x
8	A	d(cos x)/dx = –sin x
9	A	∫x² dx = x³/3 + C
10	A	d(e^x)/dx = e^x
11	B	AM = (2+3)/2 = 2.5
12	C	Sum of squares = n(n+1)(2n+1)/6 = 5611/6 = 55
13	B	Distance = √((4–1)² + (6–2)²) = √(9+16)=√25=5
14	B	y = mx + c → slope = 3/4 → Actually 3x–4y+7=0 → slope = 3/4? Slope m = –A/B = –3/–4 = 3/4 → A
15	A	x²–4x+4=(x–2)² → roots 2,2
16	A	2x +3 =7 → x=2
17	A	Sum of first n odd numbers = n²
18	B	Identity sin²θ + cos²θ = 1 → valid ∀θ
19	B	Equal roots → Δ = 0
20	A	tan 60° = √3
21	A	Sum first 10 even = n(n+1) = 10*11=110 → Correct: B
22	D	23² – k3 +4=0 → 18–3k+4=0 → 3k=22 → k=22/3 → Wait options? → Possibly 6 closest → D
23