TOP NDST Question Paper PDF For Preparations
1. What is the value of x in the equation 3x + 5 = 20?
a) 3
b) 4
c) 5
d) 7
Explanation: Subtract 5 from both sides: 3x = 15. Divide by 3: x = 5.
2. If the polynomial x² – 5x + 6 factors as (x-2)(x-3), what are the roots?
a) 1 and 6
b) 2 and 3
c) 3 and 4
d) 4 and 5
Explanation: The roots are the values where each factor equals zero, so x = 2 and x = 3.
3. In a triangle with sides 5 cm, 12 cm, 13 cm, what type of triangle is it?
a) Right-angled
b) Acute
c) Obtuse
d) Isosceles
Explanation: Check Pythagoras: 5² + 12² = 25 + 144 = 169 = 13², so it is right-angled.
4. The point dividing the line segment joining (2, 3) and (8, 9) in the ratio 1:2 has coordinates:
a) (3, 4)
b) (4, 5)
c) (5, 6)
d) (6, 7)
Explanation: Section formula: x = (1·8 + 2·2)/(1+2) = 12/3 = 4; y = (1·9 + 2·3)/3 = 15/3 = 5.
5. What is the value of sin 30° + cos 60°?
a) 0.5
b) 0.75
c) 1
d) 1.5
Explanation: sin 30° = 1/2 = 0.5, cos 60° = 1/2 = 0.5, so 0.5 + 0.5 = 1.
6. What is the area of a circle with radius 7 cm? (Use π = 22/7)
a) 144 cm²
b) 154 cm²
c) 164 cm²
d) 174 cm²
Explanation: Area = πr² = (22/7) × 7 × 7 = 22 × 7 = 154 cm².
7. What is the mean of the numbers 2, 4, 6, 8, 10?
a) 4
b) 5
c) 6
d) 7
Explanation: Sum = 30, number of terms = 5, mean = 30/5 = 6.
8. What is the probability of getting heads when tossing a fair coin?
a) 0
b) 1/2
c) 1
d) 2
Explanation: There are 2 equally likely outcomes (heads or tails), so probability = 1/2.
9. An object starts from rest and covers 50 m in 5 s with uniform acceleration. What is the acceleration?
a) 2 m/s²
b) 4 m/s²
c) 6 m/s²
d) 8 m/s²
Explanation: Use s = ut + (1/2)at² → 50 = 0 + (1/2)a(25) → a = 4 m/s².
10. According to Newton’s second law, force equals:
a) mass × velocity
b) mass × acceleration
c) mass × displacement
d) mass × momentum
Explanation: F = m × a (Newton’s second law of motion).
11. When a force acts perpendicular to the direction of displacement, the work done is:
a) Zero
b) Maximum
c) Negative
d) Infinite
Explanation: Work = F × d × cos 90° = F × d × 0 = 0.
12. The approximate speed of sound in air at room temperature is:
a) 3 × 10⁸ m/s
b) 340 m/s
c) 1500 m/s
d) 3000 m/s
Explanation: Standard value is around 330–340 m/s in air.
13. The image formed by a plane mirror is always:
a) Real and inverted
b) Virtual and erect
c) Real and erect
d) Virtual and inverted
Explanation: Plane mirrors produce virtual, erect, and laterally inverted images.
14. What is the SI unit of electric current?
a) Volt
b) Ohm
c) Ampere
d) Watt
Explanation: Electric current is measured in amperes (A).
15. Magnetic field lines outside a bar magnet emerge from which pole?
a) South pole
b) North pole
c) Both poles equally
d) Center of magnet
Explanation: By convention, field lines emerge from the north pole and enter the south pole.
16. What is the value of the universal gravitational constant G?
a) 9.8 m/s²
b) 6.67 × 10⁻¹¹ Nm²/kg²
c) 3 × 10⁸ m/s
d) 1.6 × 10⁻¹⁹ C
Explanation: G is a fundamental constant with value 6.67 × 10⁻¹¹ Nm²/kg².
17. The three primary states of matter are solid, liquid, and:
a) Plasma
b) Gas
c) Bose-Einstein condensate
d) Fermionic condensate
Explanation: Basic everyday states are solid, liquid, and gas.
18. The atomic number of an element represents the number of:
a) Neutrons
b) Protons
c) Electrons in outer shell
d) Nucleons
Explanation: Atomic number = number of protons in the nucleus.
19. In the periodic table, vertical columns are called:
a) Periods
b) Groups
c) Blocks
d) Series
Explanation: Groups are vertical columns with similar properties.
20. The reaction 2H₂ + O₂ → 2H₂O is an example of:
a) Decomposition
b) Displacement
c) Combination
d) Double displacement
Explanation: Two reactants combine to form a single product.
21. The pH value of an acidic solution is generally:
a) Less than 7
b) Equal to 7
c) Greater than 7
d) Equal to 14
Explanation: Acids have pH below 7; neutral is 7.
22. Metals are good conductors of heat and electricity because:
a) They are brittle
b) They have free electrons
c) They are gases at room temperature
d) They are non-malleable
Explanation: Free electrons allow easy flow of current and heat.
23. Carbon typically forms how many covalent bonds?
a) 1
b) 2
c) 3
d) 4
Explanation: Carbon is tetravalent (has 4 valence electrons).
24. One mole of any substance contains:
a) 6.022 × 10²³ particles
b) 1 gram of substance
c) 22.4 liters at STP
d) 1 liter of volume
Explanation: Avogadro’s number defines one mole.
25. Complete the number series: 2, 5, 10, 17, ?
a) 24
b) 25
c) 26
d) 27
Explanation: Differences: +3, +5, +7 → next difference +9, so 17 + 9 = 26.
26. A is the brother of B, B is the sister of C, and C is the father of D. How is A related to D?
a) Father
b) Uncle
c) Brother
d) Grandfather
Explanation: A (male) is brother of B (female), who is sister of C (male, father of D), so A is D’s uncle.
27. If BOOK is coded as CPPL, how is PAGE coded?
a) QAHF
b) QBHF
c) PBHF
d) QCHF
Explanation: Each letter is shifted forward by +1 (B→C, O→P, O→P, K→L), so P→Q, A→B, G→H, E→F → QBHF.
28. In a row of people, you are 15th from the left and 20th from the right. How many people are there in total?
a) 33
b) 34
c) 35
d) 36
Explanation: Total = position from left + position from right – 1 = 15 + 20 – 1 = 34.
29. Which one is the odd one out: Circle, Square, Triangle, Rectangle?
a) Circle
b) Square
c) Triangle
d) Rectangle
Explanation: Circle has no straight sides or angles; others are polygons with straight sides.
30. All roses are flowers. Some flowers fade quickly. Which conclusion logically follows?
a) All roses fade quickly
b) No roses fade quickly
c) Some roses may fade quickly
d) Roses do not fade
Explanation: Since some flowers fade and roses are flowers, it is possible (but not definite) that some roses fade.
