NSTSE 2022 previous year paper practice · PYQ-pattern set

NSTSE 2022 PYQ-pattern questions

Showing 10 of the 20 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

   For what value of k does the quadratic equation x² - 4x + k = 0 have equal roots?

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

   Answer: B

   For equal roots, discriminant must be zero: b² - 4ac = 0. Here, (-4)² - 4(1)(k) = 0, so 16 - 4k = 0, giving k = 4.

2. Q2 · Real Numbers

   The HCF and LCM of two numbers are 12 and 180 respectively. If one of the numbers is 36, the other number is:

   • A. 48
   • B. 60
   • C. 72
   • D. 90
   Answer and solution

   Answer: B

   Using the relation: HCF × LCM = Product of two numbers. So 12 × 180 = 36 × x, giving x = 2160/36 = 60.

3. Q3 · Statistics

   The mean of five numbers is 18. If one number is excluded, the mean of the remaining four numbers becomes 16. What is the excluded number?

   • A. 22
   • B. 24
   • C. 26
   • D. 28
   Answer and solution

   Answer: C

   Sum of five numbers = 18 × 5 = 90. Sum of four numbers = 16 × 4 = 64. Excluded number = 90 − 64 = 26.

4. Q4 · Trigonometry

   What is the value of sin²30° + cos²60°?

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

   Answer: B

   sin 30° = 1/2, so sin²30° = 1/4. cos 60° = 1/2, so cos²60° = 1/4. Therefore, sin²30° + cos²60° = 1/4 + 1/4 = 1/2.

5. Q5 · Human Eye and Colourful World

   A person cannot see distant objects clearly but can see nearby objects well. Which type of lens should be used to correct this defect?

   • A. Convex lens
   • B. Concave lens
   • C. Bifocal lens
   • D. Cylindrical lens
   Answer and solution

   Answer: B

   The defect is myopia (nearsightedness), which is corrected using a concave lens to diverge light rays before they enter the eye.

6. Q6 · Work, Energy and Power

   A ball of mass 0.5 kg is dropped from a height of 20 m. Just before hitting the ground, what is its kinetic energy? (Take g = 10 m/s²)

   • A. 50 J
   • B. 75 J
   • C. 100 J
   • D. 200 J
   Answer and solution

   Answer: C

   By conservation of energy, KE at ground = PE at height = mgh = 0.5 × 10 × 20 = 100 J.

7. Q7 · Metals and Non-Metals

   Which of the following metals can displace hydrogen from dilute hydrochloric acid?

   • A. Copper
   • B. Silver
   • C. Zinc
   • D. Gold
   Answer and solution

   Answer: C

   Zinc is more reactive than hydrogen and can displace it from dilute HCl, whereas copper, silver, and gold are less reactive than hydrogen.

8. Q8 · Cell — Fundamental Unit of Life

   A cell is placed in a hypertonic solution. What will happen to the cell?

   • A. It will swell and may burst
   • B. It will shrink due to water loss
   • C. It will remain unchanged
   • D. It will divide into two cells
   Answer and solution

   Answer: B

   In a hypertonic solution, the concentration of solutes outside is higher than inside the cell, so water moves out by osmosis causing the cell to shrink.

9. Q9 · Reproduction

   Binary fission in Amoeba is a form of:

   • A. Sexual reproduction
   • B. Asexual reproduction
   • C. Budding
   • D. Fragmentation
   Answer and solution

   Answer: B

   Binary fission is an asexual mode of reproduction where a single organism divides into two identical daughter organisms without gamete formation.

10. Q10 · Number and Letter Series

    Find the missing number in the series: 3, 7, 15, 31, ?, 127

    • A. 56
    • B. 63
    • C. 72
    • D. 48
    Answer and solution

    Answer: B

    Each term is obtained by multiplying the previous term by 2 and adding 1: (31 × 2) + 1 = 63.