UP JEECUP 2025 previous year paper practice · PYQ-pattern set

UP JEECUP 2025 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 · Real Numbers (Class 10)

   The HCF of two numbers is 18 and their LCM is 360. If one of the numbers is 72, what is the other number?

   • A. 90
   • B. 108
   • C. 72
   • D. 54
   Answer and solution

   Answer: A

   Using the formula: Product of two numbers = HCF × LCM. So, 72 × other number = 18 × 360 = 6480. Other number = 6480 ÷ 72 = 90.

2. Q2 · Triangles (Class 10)

   In triangle ABC, DE is parallel to BC where D and E lie on AB and AC respectively. If AD = 4 cm, DB = 6 cm, and BC = 15 cm, then the length of DE is:

   • A. 6 cm
   • B. 9 cm
   • C. 10 cm
   • D. 8 cm
   Answer and solution

   Answer: A

   By Basic Proportionality Theorem, AD/AB = DE/BC. AD = 4, AB = 4 + 6 = 10. So 4/10 = DE/15. Therefore, DE = (4 × 15)/10 = 6 cm.

3. Q3 · Applications of Trigonometry (Class 10)

   A tower stands vertically on level ground. From a point on the ground at a distance of 50 m from the foot of the tower, the angle of elevation of the top is 60°. What is the height of the tower?

   • A. 25√3 m
   • B. 50√3 m
   • C. 100 m
   • D. 50 m
   Answer and solution

   Answer: B

   Using tan 60° = height/distance, we get √3 = h/50, so h = 50√3 m.

4. Q4 · Statistics (Class 10)

   The mean of 5 observations is 15. If one observation 20 is replaced by 30, what is the new mean?

   • A. 15
   • B. 17
   • C. 18
   • D. 20
   Answer and solution

   Answer: B

   Sum of 5 observations = 15 × 5 = 75. New sum = 75 - 20 + 30 = 85. New mean = 85/5 = 17.

5. Q5 · Polynomials (Class 9)

   If p(x) = 3x² + 5x − 2, then the value of p(−1) is:

   • A. −4
   • B. 0
   • C. 6
   • D. −10
   Answer and solution

   Answer: A

   Substitute x = −1 into p(x): p(−1) = 3(−1)² + 5(−1) − 2 = 3 − 5 − 2 = −4.

6. Q6 · Areas of Parallelograms and Triangles (Class 9)

   A parallelogram and a rectangle stand on the same base and between the same parallels. If the area of the rectangle is 96 cm², then the area of the parallelogram is:

   • A. 48 cm²
   • B. 72 cm²
   • C. 96 cm²
   • D. 192 cm²
   Answer and solution

   Answer: C

   Parallelograms and rectangles on the same base and between the same parallels have equal areas. Hence, area of parallelogram = 96 cm².

7. Q7 · Surface Areas and Volumes (Class 9)

   A cylindrical tank has a radius of 3.5 m and a height of 6 m. What is the total surface area of the tank? (Use π = 22/7)

   • A. 220 m²
   • B. 209 m²
   • C. 231 m²
   • D. 198 m²
   Answer and solution

   Answer: B

   Total surface area = 2πr(r + h) = 2 × (22/7) × 3.5 × (3.5 + 6) = 2 × (22/7) × 3.5 × 9.5 = 209 m².

8. Q8 · Magnetic Effects of Electric Current (Class 10)

   A straight conductor carrying a current of 5 A is placed in a uniform magnetic field of 0.8 T perpendicular to the conductor. If the length of the conductor in the field is 25 cm, what is the force experienced by the conductor?

   • A. 1.0 N
   • B. 0.5 N
   • C. 2.0 N
   • D. 1.5 N
   Answer and solution

   Answer: A

   Force F = BIL = 0.8 × 5 × 0.25 = 1.0 N (using SI units with L = 0.25 m).

9. Q9 · Force and Laws of Motion (Class 9)

   A body of mass 5 kg is moving with a velocity of 8 m/s. What is the force required to bring it to rest in 4 seconds?

   • A. 8 N
   • B. 10 N
   • C. 12 N
   • D. 15 N
   Answer and solution

   Answer: B

   Using F = ma, where a = (v - u)/t = (0 - 8)/4 = -2 m/s². Force = 5 × 2 = 10 N.

10. Q10 · Acids, Bases and Salts (Class 10)

    Which of the following solutions will turn red litmus blue?

    • A. Lemon juice
    • B. Vinegar
    • C. Baking soda solution
    • D. Hydrochloric acid
    Answer and solution

    Answer: C

    Baking soda (sodium bicarbonate) is a base and turns red litmus blue, while lemon juice, vinegar, and HCl are acids.