NSTSE 2021 previous year paper practice · PYQ-pattern set

NSTSE 2021 PYQ-pattern questions

Showing 10 of the 17 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 · Arithmetic Progression

   The 15th term of an arithmetic progression is 47 and the common difference is 3. What is the first term?

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

   Answer: A

   Using the formula a_n = a + (n-1)d: 47 = a + (15-1)(3) = a + 42, hence a = 47 - 42 = 5.

2. Q2 · Polynomials

   If the sum of the zeros of the polynomial f(x) = kx² - 5x + 9 is 5/3, then the value of k is:

   • A. 1
   • B. 2
   • C. 3
   • D. 5
   Answer and solution

   Answer: C

   Sum of zeros = -b/a = -(-5)/k = 5/k. Given this equals 5/3, we have 5/k = 5/3, so k = 3.

3. Q3 · Probability

   A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability that it is red?

   • A. 3/8
   • B. 5/8
   • C. 1/2
   • D. 2/3
   Answer and solution

   Answer: B

   Total balls = 5 + 3 = 8. Probability of drawing a red ball = 5/8.

4. Q4 · Mensuration

   The radius of a cylinder is 7 cm and its height is 10 cm. What is the curved surface area of the cylinder? (Use π = 22/7)

   • A. 420 cm²
   • B. 440 cm²
   • C. 460 cm²
   • D. 480 cm²
   Answer and solution

   Answer: B

   Curved surface area = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².

5. Q5 · Electricity

   Three resistors of 3Ω, 6Ω, and 9Ω are connected in parallel. What is the equivalent resistance of the combination?

   • A. 1.64 Ω
   • B. 2.0 Ω
   • C. 3.0 Ω
   • D. 6.0 Ω
   Answer and solution

   Answer: A

   For parallel: 1/R = 1/3 + 1/6 + 1/9 = (6+3+2)/18 = 11/18, so R = 18/11 ≈ 1.64 Ω.

6. Q6 · Light — Reflection and Refraction

   Light travels from air into glass. If the angle of incidence is 30° and the angle of refraction is 20°, which statement is correct?

   • A. Light bends away from the normal
   • B. Light bends towards the normal
   • C. Light travels in a straight line
   • D. Total internal reflection occurs
   Answer and solution

   Answer: B

   When light travels from rarer (air) to denser (glass) medium, it bends towards the normal, so the angle of refraction (20°) is less than the angle of incidence (30°).

7. Q7 · Carbon and its Compounds

   An organic compound has the molecular formula C₃H₆. It decolorizes bromine water. Which type of compound is it most likely to be?

   • A. Saturated hydrocarbon
   • B. Unsaturated hydrocarbon
   • C. Alcohol
   • D. Carboxylic acid
   Answer and solution

   Answer: B

   The compound decolorizes bromine water, which is a characteristic test for unsaturated hydrocarbons (alkenes) containing C=C double bonds.

8. Q8 · Structure of the Atom

   An ion of element Y carries a charge of +2 and has 10 electrons. What is the atomic number of element Y?

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

   Answer: C

   The ion has 10 electrons and a +2 charge, meaning it lost 2 electrons. Originally, the neutral atom had 12 electrons, so the atomic number is 12.

9. Q9 · Heredity and Evolution

   A pea plant with genotype Tt (tall) is crossed with a pea plant with genotype tt (dwarf). What is the probability of obtaining a tall offspring?

   • A. 25%
   • B. 50%
   • C. 75%
   • D. 100%
   Answer and solution

   Answer: B

   The cross Tt × tt produces offspring with genotypes Tt (tall) and tt (dwarf) in a 1:1 ratio, giving a 50% probability of tall plants.

10. Q10 · Number and Letter Series

    Complete the letter series: A, C, F, J, O, ?

    • A. S
    • B. T
    • C. U
    • D. V
    Answer and solution

    Answer: C

    The pattern adds consecutive integers: +2, +3, +4, +5, so the next step is +6, making the answer U.