NSTSE 2024 previous year paper practice · PYQ-pattern set

NSTSE 2024 PYQ-pattern questions

Showing 10 of the 18 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

   If α and β are the zeros of the polynomial p(x) = 3x² - 7x + 2, then the value of (1/α + 1/β) is:

   • A. 2/7
   • B. 7/2
   • C. 3/2
   • D. -7/3
   Answer and solution

   Answer: B

   Using sum and product of roots: α+β = 7/3 and αβ = 2/3. Therefore, 1/α + 1/β = (α+β)/(αβ) = (7/3)/(2/3) = 7/2.

2. Q2 · Triangles

   In △ABC, DE is parallel to BC, with D on AB and E on AC. If AD = 4 cm, DB = 6 cm, and AE = 3 cm, then EC equals:

   • A. 4.5 cm
   • B. 5 cm
   • C. 6 cm
   • D. 4 cm
   Answer and solution

   Answer: A

   By Basic Proportionality Theorem: AD/DB = AE/EC, so 4/6 = 3/EC. Cross-multiplying: 4×EC = 18, hence EC = 4.5 cm.

3. Q3 · Trigonometry

   If sin θ = 5/13 and θ is an acute angle, then what is the value of tan θ?

   • A. 5/12
   • B. 12/5
   • C. 13/12
   • D. 12/13
   Answer and solution

   Answer: A

   Using the Pythagorean identity, cos θ = 12/13. Therefore, tan θ = sin θ / cos θ = (5/13) / (12/13) = 5/12.

4. Q4 · Force and Laws of Motion

   A force of 20 N acts on a body of mass 5 kg which is at rest. What is the acceleration produced?

   • A. 2 m/s²
   • B. 3 m/s²
   • C. 4 m/s²
   • D. 5 m/s²
   Answer and solution

   Answer: C

   Using Newton's second law, F = ma, acceleration a = F/m = 20/5 = 4 m/s².

5. Q5 · Sound

   A sound wave travels through air at 340 m/s. If the frequency of the wave is 170 Hz, what is its wavelength?

   • A. 0.5 m
   • B. 1 m
   • C. 2 m
   • D. 4 m
   Answer and solution

   Answer: C

   Wavelength λ = velocity/frequency = 340/170 = 2 m.

6. Q6 · Matter

   Which of the following exhibits the Tyndall effect?

   • A. Sugar solution
   • B. Milk
   • C. Salt solution
   • D. Copper sulfate solution
   Answer and solution

   Answer: B

   Milk is a colloid and exhibits the Tyndall effect, where light is scattered by colloidal particles. True solutions do not show this effect.

7. Q7 · Cell — Fundamental Unit of Life

   Which organelle is known as the 'powerhouse of the cell' because it generates energy in the form of ATP?

   • A. Ribosome
   • B. Mitochondria
   • C. Chloroplast
   • D. Endoplasmic reticulum
   Answer and solution

   Answer: B

   Mitochondria are called the powerhouse of the cell as they produce ATP through cellular respiration.

8. Q8 · Life Processes

   In which part of the human digestive system does maximum absorption of digested nutrients occur?

   • A. Stomach
   • B. Large intestine
   • C. Small intestine
   • D. Esophagus
   Answer and solution

   Answer: C

   The small intestine, particularly the ileum, has a large surface area due to villi and microvilli, making it the primary site for nutrient absorption.

9. Q9 · Health and Disease

   Which of the following diseases is caused by a virus?

   • A. Tuberculosis
   • B. Malaria
   • C. Influenza
   • D. Typhoid
   Answer and solution

   Answer: C

   Influenza is caused by the influenza virus, while tuberculosis and typhoid are bacterial infections, and malaria is caused by a protozoan.

10. Q10 · Coding-Decoding

    If BOOK is coded as CPPL, then how is PAGE coded in the same pattern?

    • A. QBHF
    • B. QBGF
    • C. QCHF
    • D. PBHF
    Answer and solution

    Answer: A

    Each letter is shifted one position forward in the alphabet: P→Q, A→B, G→H, E→F, giving QBHF.