Below are 50 sample multiple-choice questions based on the Class 10 syllabus, covering Class 9 topics and the first two chapters of Class 10.
1. Which of the following is an irrational number?
2. Simplify $(3^2 \times 3^3) \div 3^4$.
3. On the number line, where does $\sqrt{5}$ lie relative to 2 and 3?
4. What is the degree of the polynomial $4x^5 - 3x^2 + 2x + 1$?
5. If $(x + 2)$ is a factor of $x^2 + x - 2$, what is the other factor?
6. Using the identity $(a + b)^2$, simplify $(x + 3)^2$.
7. The solution to the system of equations $2x + y = 7$ and $x - y = 1$ is:
8. Which equation represents a line parallel to $y = 2x + 3$?
9. A boat’s speed in still water is 10 km/h, and the river flows at 2 km/h. If it takes 6 hours to travel upstream and back, what is the distance traveled upstream?
10. What is the distance between points $(3, 4)$ and $(7, 1)$?
11. The coordinates of the midpoint of the line segment joining $(2, 3)$ and $(4, 5)$ are:
12. In which quadrant does the point $(-2, 5)$ lie?
13. Which of the following is a postulate in Euclid’s Geometry?
14. An axiom is a statement that is:
15. According to Euclid, how many lines can be drawn through a point parallel to a given line?
16. If two parallel lines are cut by a transversal, the corresponding angles are:
17. The sum of angles in a triangle is:
18. If one angle of a triangle is $50^\circ$ and the other is $60^\circ$, what is the third angle?
19. Which criterion proves triangle congruence if two sides and the included angle are equal?
20. In a triangle, if two sides are equal, the angles opposite them are:
21. The longest side of a right-angled triangle is called:
22. In a parallelogram, the diagonals:
23. What is the sum of the interior angles of a quadrilateral?
24. The midpoint theorem states that the line joining midpoints of two sides of a triangle is:
25. Two triangles on the same base and between the same parallels have:
26. The area of a parallelogram with base 6 cm and height 4 cm is:
27. If a triangle and a parallelogram share the same base and height, the area of the triangle is:
28. The angle subtended by an arc at the center is $90^\circ$. What is the angle subtended at a point on the remaining arc?
29. A tangent to a circle is:
30. Chords equidistant from the center of a circle are:
31. A triangle has sides 3 cm, 4 cm, and 5 cm. Its area using Heron’s formula is:
32. The semi-perimeter of a triangle with sides 5 cm, 12 cm, and 13 cm is:
33. Heron’s formula is used to find the area of a triangle when its _____ are known.
34. The surface area of a cube with side 5 cm is:
35. The volume of a cylinder with radius 2 cm and height 5 cm is:
36. The curved surface area of a cone with radius 3 cm and height 4 cm is:
37. The mean of the numbers 4, 6, 8, 10, 12 is:
38. The median of the data set {2, 5, 3, 7, 1} is:
39. The mode of the data set {1, 2, 2, 3, 3, 3, 4} is:
40. The probability of getting an even number when rolling a fair die is:
41. A bag contains 4 red and 3 blue balls. The probability of picking a blue ball is:
42. If a coin is tossed, the probability of getting heads is:
43. Using Euclid’s Division Lemma, find the HCF of 56 and 88.
44. The LCM of 12 and 18 is:
45. The decimal expansion of $13/125$ is:
46. Which of the following numbers has a non-terminating repeating decimal expansion?
47. If the zeroes of the polynomial $x^2 - 5x + 6$ are 2 and 3, what is the sum of the zeroes?
48. The product of the zeroes of the polynomial $2x^2 + 3x - 5$ is:
49. Using the division algorithm, if $x^2 + 2x + 1$ is divided by $x + 1$, the remainder is:
50. If one zero of the polynomial $x^2 - 4x + k$ is 2, what is the value of $k$?