UP JEECUP 2022 previous year paper practice · PYQ-pattern set

UP JEECUP 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 · Quadratic Equations (Class 10)

   The roots of the quadratic equation x² – 7x + 12 = 0 are:

   • A. 3 and 4
   • B. 2 and 6
   • C. -3 and -4
   • D. 1 and 12
   Answer and solution

   Answer: A

   Factorizing x² – 7x + 12 = 0, we get (x – 3)(x – 4) = 0. Therefore, the roots are x = 3 and x = 4.

2. Q2 · Arithmetic Progressions (Class 10)

   The sum of the first 20 terms of an A.P. whose first term is 5 and common difference is 3 is:

   • A. 670
   • B. 650
   • C. 660
   • D. 640
   Answer and solution

   Answer: A

   Using Sₙ = n/2[2a + (n-1)d]. S₂₀ = 20/2[2(5) + 19(3)] = 10[10 + 57] = 10 × 67 = 670.

3. Q3 · Areas Related to Circles (Class 10)

   The area of a sector of a circle of radius 14 cm is 102.67 cm². What is the central angle of the sector? (Use π = 22/7)

   • A. 60°
   • B. 90°
   • C. 120°
   • D. 135°
   Answer and solution

   Answer: A

   Full circle area = (22/7)·14² = 616 cm². Sector area 102.67 = 616·(θ/360). Testing 60°: 616/6 = 102.67 cm², which matches exactly.

4. Q4 · Applications of Trigonometry (Class 10)

   From the top of a building 80 m high, the angles of depression of two cars on the same side of the building are 30° and 45°. What is the distance between the two cars?

   • A. 40(√3 - 1) m
   • B. 80(√3 - 1) m
   • C. 80√3 m
   • D. 40√3 m
   Answer and solution

   Answer: B

   Distance of nearer car = 80/tan 45° = 80 m. Distance of farther car = 80/tan 30° = 80√3 m. Difference = 80√3 - 80 = 80(√3 - 1) m.

5. Q5 · Lines and Angles (Class 9)

   Two complementary angles are in the ratio 2:3. The smaller angle is:

   • A. 30°
   • B. 36°
   • C. 45°
   • D. 54°
   Answer and solution

   Answer: B

   Let the angles be 2x and 3x. Since they are complementary: 2x + 3x = 90°, so 5x = 90°, giving x = 18°. The smaller angle is 2x = 36°.

6. Q6 · Polynomials (Class 9)

   If the zeroes of the polynomial x² − kx + 6 are in the ratio 2:3, then the value of k is:

   • A. 4
   • B. 5
   • C. 6
   • D. 7
   Answer and solution

   Answer: B

   Let the zeroes be 2m and 3m. Product of zeroes = 2m × 3m = 6m² = 6, so m² = 1, m = 1. Sum of zeroes = 2m + 3m = 5m = 5 = k.

7. Q7 · Human Eye and Colourful World (Class 10)

   A person suffering from myopia can see clearly only up to a distance of 1.5 m. What power of lens is required to correct this defect so that the person can see distant objects clearly?

   • A. −0.67 D
   • B. +0.67 D
   • C. −1.5 D
   • D. +1.5 D
   Answer and solution

   Answer: A

   For myopia, a concave lens is used. Far point is 1.5 m, so focal length f = −1.5 m. Power P = 1/f = 1/(−1.5) = −0.67 D.

8. Q8 · Surface Areas and Volumes (Class 9)

   A solid sphere of radius 7 cm is melted and recast into smaller spheres each of radius 3.5 cm. How many smaller spheres can be formed?

   • A. 6
   • B. 8
   • C. 4
   • D. 12
   Answer and solution

   Answer: B

   Volume of large sphere = (4/3)πR³ = (4/3)π(7)³. Volume of each small sphere = (4/3)πr³ = (4/3)π(3.5)³. Number = (7³)/(3.5³) = 343/42.875 = 8.

9. Q9 · Sound (Class 9)

   A sound wave has a frequency of 500 Hz and travels with a speed of 350 m/s in air. What is its wavelength?

   • A. 0.5 m
   • B. 0.7 m
   • C. 0.9 m
   • D. 1.2 m
   Answer and solution

   Answer: B

   Using v = fλ, wavelength λ = v/f = 350/500 = 0.7 m.

10. Q10 · Force and Laws of Motion (Class 9)

    A car moving with a velocity of 15 m/s comes to rest after applying brakes in 5 seconds. What is the retardation?

    • A. 2 m/s²
    • B. 3 m/s²
    • C. 4 m/s²
    • D. 5 m/s²
    Answer and solution

    Answer: B

    Using a = (v - u)/t = (0 - 15)/5 = -3 m/s². The retardation is 3 m/s².