UP JEECUP 2023 previous year paper practice · PYQ-pattern set

UP JEECUP 2023 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 · Introduction to Trigonometry (Class 10)

   If sin θ = 3/5 and θ is an acute angle, then the value of tan θ is:

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

   Answer: A

   Since sin θ = 3/5, opposite = 3 and hypotenuse = 5. Using Pythagoras: adjacent = √(25 - 9) = 4. So tan θ = opposite/adjacent = 3/4.

2. Q2 · Constructions (Class 10)

   To divide a line segment AB in the ratio 3:5, a ray AX is drawn making an acute angle with AB. What is the minimum number of equal arcs to be marked on AX?

   • A. 3
   • B. 5
   • C. 8
   • D. 15
   Answer and solution

   Answer: C

   To divide in ratio 3:5, we need 3 + 5 = 8 equal parts marked on the ray AX.

3. Q3 · Number Systems (Class 9)

   If (√5 + √3)/(√5 - √3) = a + b√15, then what is the value of a + b?

   • A. 4
   • B. 5
   • C. 6
   • D. 8
   Answer and solution

   Answer: B

   Rationalizing: [(√5 + √3)²]/[(5 - 3)] = (5 + 3 + 2√15)/2 = 4 + √15. So a = 4, b = 1, and a + b = 5.

4. Q4 · Coordinate Geometry — Basics (Class 9)

   The distance between the points A(4, 3) and B(8, 6) is:

   • A. 5 units
   • B. 6 units
   • C. 7 units
   • D. 25 units
   Answer and solution

   Answer: A

   Using the distance formula: d = √[(8−4)² + (6−3)²] = √[16 + 9] = √25 = 5 units.

5. Q5 · Heron's Formula (Class 9)

   The sides of a triangle are 13 cm, 14 cm, and 15 cm. Using Heron's formula, its area is:

   • A. 84 cm²
   • B. 90 cm²
   • C. 100 cm²
   • D. 120 cm²
   Answer and solution

   Answer: A

   Semi-perimeter s = (13 + 14 + 15)/2 = 21 cm. Area = √[21(21−13)(21−14)(21−15)] = √[21×8×7×6] = √7056 = 84 cm².

6. Q6 · Light — Reflection and Refraction (Class 10)

   A concave mirror has a focal length of 20 cm. An object is placed at 30 cm from the mirror. What is the image distance?

   • A. 60 cm
   • B. 40 cm
   • C. 50 cm
   • D. 45 cm
   Answer and solution

   Answer: A

   Using mirror formula 1/f = 1/v + 1/u: 1/20 = 1/v + 1/(−30) ⇒ 1/v = 1/20 + 1/30 = 5/60 = 1/12 ⇒ v = 60 cm (real image).

7. Q7 · Motion (Class 9)

   A car moving with a velocity of 72 km/h is brought to rest uniformly in 8 seconds. Calculate the retardation of the car.

   • A. 2.5 m/s²
   • B. 3.0 m/s²
   • C. 9.0 m/s²
   • D. 1.5 m/s²
   Answer and solution

   Answer: A

   Initial velocity u = 72 km/h = 20 m/s, final velocity v = 0. Using v = u + at: 0 = 20 + a×8 ⇒ a = −20/8 = −2.5 m/s². Retardation = 2.5 m/s².

8. Q8 · Work and Energy (Class 9)

   A force of 20 N displaces a body through 3 m in the direction of the force. How much work is done?

   • A. 40 J
   • B. 50 J
   • C. 60 J
   • D. 70 J
   Answer and solution

   Answer: C

   Work done W = F × d = 20 N × 3 m = 60 J.

9. Q9 · Carbon and its Compounds (Class 10)

   The functional group present in ethanol (C₂H₅OH) is:

   • A. Aldehyde
   • B. Ketone
   • C. Alcohol
   • D. Carboxylic acid
   Answer and solution

   Answer: C

   Ethanol contains the hydroxyl group (–OH) which is characteristic of the alcohol functional group.

10. Q10 · Is Matter Around Us Pure (Class 9)

    Which one of the following is a homogeneous mixture?

    • A. Sand and water
    • B. Sugar solution
    • C. Chalk powder in water
    • D. Oil and water
    Answer and solution

    Answer: B

    A sugar solution is a homogeneous mixture because sugar dissolves completely and uniformly in water, forming a single-phase system.