10th Science Important Problem Questions

Application-based problems and numerical sets are the highest-scoring sections of your exam, but they require the right step-by-step approach. This comprehensive collection of Class 10 Science Important Problem Questions brings together the most frequently asked numerical exercises and chemical balancing problems from across the syllabus. From calculating circuit resistance and lens focal lengths to balancing complex chemical reactions, these handpicked questions help you understand the core formulas, perfect your calculation speed, and secure full marks in the analytical sections.

X - Physics Important Problems Question Paper - 2026

1. Calculate the velocity of a moving body of mass 5 kg whose linear momentum is 2.5 kg m/s

2. A door is pushed, at a point whose distance from the hinges is 90 cm, with a force of 40 N. Calculate the moment of the force about the hinges

3. At what height from the centre of the Earth the acceleration due to gravity will be 1/4th of its value as at the Earth.

4. Two bodies have a mass ratio of 3:4. The force applied on the bigger mass produces an acceleration of 12 ms^-2. What could be the acceleration of the other body, if the same force acts on it.

5. A ball of mass 1 kg moving with a speed of 10 ms^-1 rebounds after a perfect elastic collision with the floor. Calculate the change in linear momentum of the ball.

6. A mechanic unscrews a nut by applying a force of 140 N with a spanner of length 40 cm. What should be the length of the spanner if a force of 40 N is applied to unscrew the same nut?

7. The ratio of masses of two planets is 2:3 and the ratio of their radii is 4:7. Find the ratio of their accelerations due to gravity.

8. Two blocks of masses 8 kg and 2 kg respectively lie on a smooth horizontal surface in contact with one another. They are pushed by a horizontally applied force of 15 N. Calculate the force exerted on the 2 kg mass.

9. A heavy truck and bike are moving with the same kinetic energy. If the mass of the truck is four times that of the bike, then calculate the ratio of their momenta. (Ratio of momenta = 2:1)

10. "Wearing helmet and fastening the seat belt is highly recommended for safe journey" Justify your answer using Newton's laws of motion

11. While doing an experiment for the determination of focal length of a convex lens, Raja Suddenly dropped the lens. It got broken into two halves along the axis. If he continues his experiment with the same lens, (a) can he get the image? (b) Is there any change in the focal length?

12. The eyes of the nocturnal birds like owl are having a large cornea and a large pupil. How does it help them?

13. An object is placed at a distance 20cm from a convex lens of focal length 10cm. Find the image distance and nature of the image.

14. An object of height 3cm is placed at 10cm from a concave lens of focal length 15cm. Find the size of the image

15. Light rays travel from vacuum into a glass whose refractive index is 1.5. If the angle of incidence is 30°, calculate the angle of refraction inside the glass.

16. For a person with hypermetropia, the near point has moved to 1.5m. Calculate the focal length of the correction lens in order to make his eyes normal

17. A person with myopia can see objects placed at a distance of 4m. If he wants to see objects at a distance of 20m, what should be the focal length and power of the concave lens he must wear

18. A beam of light passing through a diverging lens of focal length 0.3m appear to be focused at a distance 0.2m behind the lens. Find the position of the object.

19. A container whose capacity is 70 ml is filled with a liquid up to 50 ml. Then, the liquid in the container is heated. Initially, the level of the liquid falls from 50 ml to 48.5 ml. Then we heat more, the level of the liquid rises to 51.2 ml. Find the apparent and real expansion.

20. Keeping the temperature as constant, a gas is compressed four times of its initial pressure. The volume of gas in the container changing from 20cc (V₁ cc) to V₂ cc. Find the final volume V₂.

21. Find the final temperature of a copper rod. Whose area of cross section changes from 10 m² to 11 m² due to heating. The copper rod is initially kept at 90 K. (Coefficient of superficial expansion is 0.0021 /K).

22. Calculate the coefficient of cubical expansion of a zinc bar. Whose volume is increased 0.25 m³ from 0.3 m³ due to the change in its temperature of 50 K

23. The work done in moving a charge of 10 C across two points in a circuit is 100 J. What is the potential difference between the points?

24. Calculate the resistance of a conductor through which a current of 2 A passes, when the potential difference between its ends is 30 V

25. The resistance of a wire of length 10 m is 2 ohm. If the area of cross section of the wire is 2 × 10^-7 m², determine its (i) resistivity (ii) conductance and (iii) conductivity

26. A charge of 12 coulomb flows through a bulb in 5 second. What is the current through the bulb

27. Three resistors of resistances 5 ohm, 3 ohm and 2 ohm are connected in series with 10 V battery. Calculate their effective resistance and the current flowing through the circuit

28. An electric heater of resistance 5 Ω is connected to an electric source. If a current of 6 A flows through the heater, then find the amount of heat produced in 5 minutes.

29. Two bulbs are having the ratings as 60 W, 220 V and 40 W, 220 V respectively. Which one has a greater resistance?

30. Calculate the current and the resistance of a 100 W, 200 V electric bulb in an electric circuit

31. In the circuit diagram given below, three resistors R₁, R₂ and R₃ of 5 Ω, 10 Ω and 20 Ω respectively are connected as shown. Calculate:

Parallel Resistors: 5 Ω • 10 Ω • 20 Ω

Battery Voltage: 10 V

A) Current through each resistor
B) Total current in the circuit
C) Total resistance in the circuit

32. Three resistors of 1 Ω, 2 Ω and 4 Ω are connected in parallel in a circuit. If a 1 Ω resistor draws a current of 1 A, find the current through the other two resistors

33. Two resistors when connected in parallel give the resultant resistance of 2 ohm; but when connected in series the effective resistance becomes 9 ohm. Calculate the value of each resistance

34. How many electrons are passing per second in a circuit in which there is a current of 5 A?

35. A piece of wire of resistance 10 ohm is drawn out so that its length is increased to three times its original length. Calculate the new resistance.

36. At what temperature will the velocity of sound in air be double the velocity of sound in air at 0°C?

37. A source producing a sound of frequency 90 Hz is approaching a stationary listener with a speed equal to (1/10) of the speed of sound. What will be the frequency heard by the listener

38. A source producing a sound of frequency 500 Hz is moving towards a listener with a velocity of 30 ms^-1. The speed of the sound is 330 ms^-1. What will be the frequency heard by listener?

39. A source of sound is moving with a velocity of 50 ms^-1 towards a stationary listener. The listener measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the listener after crossing him? (velocity of sound in the medium is 330 ms^-1)

40. A source and listener are both moving towards each other with a speed v/10 where v is the speed of sound. If the frequency of the note emitted by the source is f, what will be the frequency heard by the listener?

41. At what speed should a source of sound move away from a stationary observer so that observer finds the apparent frequency equal to half of the original frequency?

42. A sound wave has a frequency of 200 Hz and a speed of 400 ms^-1 in a medium. Find the wavelength of the sound wave.

43. The thunder of cloud is heard 9.8 seconds later than the flash of lightning. If the speed of sound in air is 330 ms^-1, what will be the height of the cloud?

44. A person who is sitting at a distance of 400 m from a source of sound is listening to a sound of 600 Hz. Find the time period between successive compressions from the source?

45. An ultrasonic wave is sent from a ship towards the bottom of the sea. It is found that the time interval between the transmission and reception of the wave is 1.6 seconds. What is the depth of the sea, if the velocity of sound in the seawater is 1400 ms^-1?

46. A man is standing between two vertical walls 680 m apart. He claps his hands and hears two distinct echoes after 0.9 seconds and 1.1 second respectively. What is the speed of sound in the air?

47. Two observers are stationed in two boats 4.5 km apart. A sound signal sent by one, under water, reaches the other after 3 seconds. What is the speed of sound in the water?

48. A strong sound signal is sent from a ship towards the bottom of the sea. It is received back after 1s. What is the depth of sea given that the speed of sound in water 1450 ms^-1?

49. Suppose that a sound wave and a light wave have the same frequency, then which one has a longer wavelength? a) Sound b) Light c) both a and b d) data not sufficient

50. When sound is reflected from a distant object, an echo is produced. Let the distance between the reflecting surface and the source of sound remain the same. Do you hear an echo sound on a hotter day? Justify your answer.

51. ₉₂U²³⁵ experiences one α decay and one β decay. Find number of neutrons in the final daughter nucleus that is formed.

52. Identify A, B, C, and D from the following nuclear reactions:
(i) ₁₃Al²⁷ + A → ₁₅P³⁰ + B
(ii) ₁₂Mg²⁴ + B → ₁₁Na²⁴ + C
(iii) ₉₂U²³⁸ + B → ₉₃Np²³⁹ + D

53. A radon specimen emits radiation of 3.7 × 10³ GBq per second. Convert this disintegration in terms of curie. (one curie = 3.7 × 10¹⁰ disintegration per second)

54. ₈₈Ra²²⁶ experiences three α decay. Find the number of neutrons in the daughter element

55. A cobalt specimen emits induced radiation of 75.6 millicurie per second. Convert this disintegration into becquerel (one curie = 3.7 × 10¹⁰ Bq)

56. Mass number of a radioactive element is 232 and its atomic number is 90. When this element undergoes certain nuclear reactions, it transforms into an isotope of lead with a mass number 208 and an atomic number 82. Determine the number of alpha and beta decay that can occur

57. 'X-rays should not be taken often'. Give the reason

58. Cell phone towers should be placed far away from the residential area — why

59. Mr. Ramu is working as an X-ray technician in a hospital. But, he does not wear the lead aprons. What suggestion will you give to Mr. Ramu

60. If A is a radioactive element which emits an α particle and produces ₁₀₄Rf²⁵⁹. Write the atomic number and mass number of the element A.