UP JEECUP 2024 previous year paper practice · PYQ-pattern set

UP JEECUP 2024 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 · Polynomials (Class 10)

   If α and β are the zeroes of the polynomial 2x² + 5x + 3, then the value of (1/α + 1/β) is:

   • A. 5/3
   • B. -5/3
   • C. 3/5
   • D. -3/5
   Answer and solution

   Answer: B

   1/α + 1/β = (α + β)/(αβ). From the polynomial, α + β = -5/2 and αβ = 3/2. So (1/α + 1/β) = (-5/2)/(3/2) = -5/3.

2. Q2 · Coordinate Geometry (Class 10)

   The distance between the points A(3, 4) and B(7, 1) is:

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

   Answer: A

   Using distance formula: √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5 units.

3. Q3 · Circles (Class 10)

   A chord of length 16 cm is at a distance of 6 cm from the centre of a circle. What is the radius of the circle?

   • A. 8 cm
   • B. 10 cm
   • C. 12 cm
   • D. 14 cm
   Answer and solution

   Answer: B

   Half the chord = 8 cm. Using Pythagoras theorem: r² = 6² + 8² = 36 + 64 = 100, so r = 10 cm.

4. Q4 · Probability (Class 10)

   A bag contains 5 red balls, 4 blue balls, and 3 green balls. If one ball is drawn at random, what is the probability that it is NOT blue?

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

   Answer: C

   Total balls = 5 + 4 + 3 = 12. Non-blue balls = 5 + 3 = 8. Probability = 8/12 = 2/3.

5. Q5 · Linear Equations in Two Variables (Class 9)

   The pair of equations 2x + 3y = 7 and 4x + 6y = 18 represents:

   • A. Intersecting lines
   • B. Parallel lines
   • C. Coincident lines
   • D. Perpendicular lines
   Answer and solution

   Answer: B

   The ratios give a₁/a₂ = 2/4 = 1/2, b₁/b₂ = 3/6 = 1/2, c₁/c₂ = 7/18. Since a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel.

6. Q6 · Circles (Class 9)

   A chord of length 16 cm is at a distance of 6 cm from the centre of a circle. The radius of the circle is:

   • A. 8 cm
   • B. 10 cm
   • C. 12 cm
   • D. 14 cm
   Answer and solution

   Answer: B

   Perpendicular from centre bisects the chord. Using Pythagoras: r² = 6² + 8² = 36 + 64 = 100, so r = 10 cm.

7. Q7 · Statistics (Class 9)

   The mean of 8 numbers is 35. If one number 42 is excluded, what is the mean of the remaining numbers?

   • A. 34
   • B. 33
   • C. 36
   • D. 32
   Answer and solution

   Answer: A

   Sum of 8 numbers = 8 × 35 = 280. After excluding 42, sum = 280 − 42 = 238. Mean of remaining 7 numbers = 238/7 = 34.

8. Q8 · Sources of Energy (Class 10)

   Which of the following is a non-renewable source of energy?

   • A. Solar energy
   • B. Wind energy
   • C. Natural gas
   • D. Biomass
   Answer and solution

   Answer: C

   Natural gas is a fossil fuel and a non-renewable source of energy, whereas solar, wind, and biomass are renewable.

9. Q9 · Gravitation (Class 9)

   The mass of Earth is 6 × 10²⁴ kg and its radius is 6.4 × 10⁶ m. What is the acceleration due to gravity on the surface of Earth? (G = 6.67 × 10⁻¹¹ N m²/kg²)

   • A. 8.2 m/s²
   • B. 9.8 m/s²
   • C. 10.5 m/s²
   • D. 11.2 m/s²
   Answer and solution

   Answer: B

   Using g = GM/R², substituting values gives g = (6.67×10⁻¹¹ × 6×10²⁴)/(6.4×10⁶)² ≈ 9.8 m/s².

10. Q10 · Metals and Non-Metals (Class 10)

    Aluminium is extracted from its ore by:

    • A. Reduction with carbon
    • B. Electrolytic reduction
    • C. Roasting followed by reduction
    • D. Calcination followed by reduction
    Answer and solution

    Answer: B

    Aluminium is highly reactive and cannot be reduced by carbon; it is extracted from bauxite ore by electrolytic reduction.