CUET UG 2022 previous year paper practice · PYQ-pattern set

CUET UG 2022 PYQ-pattern questions

Showing 10 of the 19 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · General Polity

   Which article of the Indian Constitution deals with the formation of new states and alteration of areas, boundaries, or names of existing states?

   • A. Article 2
   • B. Article 3
   • C. Article 4
   • D. Article 5
   Answer and solution

   Answer: B

   Article 3 empowers Parliament to form new states, alter boundaries or names of existing states by law, requiring only a simple majority and presidential recommendation.

2. Q2 · General Knowledge

   Who was the first Indian woman to win an Olympic medal?

   • A. P.T. Usha
   • B. Mary Kom
   • C. Karnam Malleswari
   • D. Saina Nehwal
   Answer and solution

   Answer: C

   Karnam Malleswari won a bronze medal in weightlifting at the 2000 Sydney Olympics, becoming the first Indian woman to win an Olympic medal.

3. Q3 · Basic Grammar & Vocabulary

   Choose the pair that has the same relationship as 'Teacher : Classroom'.

   • A. Doctor : Hospital
   • B. Student : Book
   • C. Farmer : Tractor
   • D. Pilot : Passenger
   Answer and solution

   Answer: A

   Teacher works in Classroom; similarly, Doctor works in Hospital, making A the correct analogy.

4. Q4 · General Mental Ability

   Which number does NOT belong in the group: 5, 10, 15, 22, 25?

   • A. 5
   • B. 10
   • C. 22
   • D. 25
   Answer and solution

   Answer: C

   All numbers except 22 are multiples of 5. Hence 22 does not belong to the group.

5. Q5 · Applications of the Integrals

   The area bounded by the curve y² = 8x and the line x = 2 is:

   • A. 32/3 square units
   • B. 16/3 square units
   • C. 8/3 square units
   • D. 64/3 square units
   Answer and solution

   Answer: A

   The parabola y² = 8x can be written as y = ±√(8x). Area = 2∫₀² √(8x) dx = 2 × 2√2 × (2/3)x^(3/2)|₀² = (8√2/3) × 2√2 = 32/3 square units.

6. Q6 · Continuity & Differentiability

   If f(x) = (e^(3x) - e^(-3x))/(x) for x ≠ 0 and f(0) = k for continuity at x = 0, then k equals:

   • A. 0
   • B. 3
   • C. 6
   • D. 1
   Answer and solution

   Answer: C

   For continuity at x = 0, k = lim(x→0) (e^(3x) - e^(-3x))/x. Using L'Hospital's rule or series expansion, this equals 3e^0 - (-3)e^0 = 3 + 3 = 6.

7. Q7 · Magnetic Effects of Current & Magnetism

   A circular coil of 100 turns and radius 5 cm carries a current of 2 A. What is the magnetic field at the center of the coil? (Take μ₀ = 4π × 10⁻⁷ T·m/A)

   • A. 2.5 × 10⁻³ T
   • B. 5.0 × 10⁻⁴ T
   • C. 1.26 × 10⁻³ T
   • D. 6.28 × 10⁻⁴ T
   Answer and solution

   Answer: A

   Magnetic field at center B = (μ₀nI)/(2r) = (4π × 10⁻⁷ × 100 × 2)/(2 × 0.05) = (8π × 10⁻⁵)/(0.1) = 8π × 10⁻⁴ ≈ 2.5 × 10⁻³ T.

8. Q8 · Probability

   Three unbiased coins are tossed simultaneously. What is the probability of getting at least two heads?

   • A. 1/2
   • B. 3/8
   • C. 5/8
   • D. 1/4
   Answer and solution

   Answer: A

   At least two heads means 2 heads or 3 heads. P(2H) = ³C₂(1/2)³ = 3/8. P(3H) = ³C₃(1/2)³ = 1/8. Total = 3/8 + 1/8 = 4/8 = 1/2.

9. Q9 · Atoms & Nuclei

   Two nuclei have mass numbers in the ratio 1:8. What is the ratio of their nuclear radii?

   • A. 1:2
   • B. 1:4
   • C. 1:8
   • D. 1:16
   Answer and solution

   Answer: A

   Nuclear radius R = R₀A^(1/3), where A is mass number. If A₁/A₂ = 1/8, then R₁/R₂ = (A₁/A₂)^(1/3) = (1/8)^(1/3) = 1/2.

10. Q10 · Chemical Kinetics

    For a first-order reaction, the time required for 75% completion is related to the half-life (t₁/₂) by:

    • A. t = t₁/₂
    • B. t = 2t₁/₂
    • C. t = 3t₁/₂
    • D. t = 4t₁/₂
    Answer and solution

    Answer: B

    For a first-order reaction, after one half-life 50% remains, after two half-lives 25% remains (i.e., 75% is complete). Therefore, t₇₅% = 2t₁/₂.