CBSE Class 10 Pre-Board Exam 2024-25: Maths Most Important Questions with Answers – Free PDF Download

The CBSE Pre-board Exam is an important part of your preparation for the final board exams. To help you study better, we’ve created a list of the most important Maths questions with answers.

This collection of most important Maths questions with answers will guide you in practicing and mastering key topics across all subjects. This post covers focuses on the topics that are most likely to appear in your exams.

The CBSE Pre-board Exam Maths questions cover key topics. It includes objective, short/long answer, and competency-based questions, all matching the latest exam pattern.

CBSE 10 Pre-board Exam 2024-25 Maths Most Important Questions

1. LCM (850, 500) is:
(a) 850 × 50 (b) 17 x 500 (c) 17 x 5² x 2² (d) 17 × 5³ × 2

Answer. (b) 17 ´ 500

2. If the roots of quadratic equation 4x²-5x+k=0 are real and equal, then value of k is :

Answer. 

3. The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is :
(a) 27
(b) 22
(c) 17
(d) 23

Answer. (a) 27

4. The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone is :
(a) 24 cm
(b) 31 cm
(c) 26 cm
(d) 25 cm

Answer. (d) 25 cm

5. If one of the zeroes of the quadratic polynomial (a-1)x²+ax+1 is -3, then the value of a is:

Answer.

6. A card is drawn from a well shuffled deck of 52 playing cards. The probability that drawn card is a red queen, is :

Answer.

7. If a certain variable x divides a statistical data arranged in order into two equal parts, then the value of x is called the :
(a) mean
(b) median
(c) mode
(d) range of the data.

Answer. (b) median

8. Three coins are tossed together. The probability of getting exactly one tail, is :

Answer.

9.

Answer.

10. Outer surface area of a cylindrical juice glass with radius 7 cm and height 10 cm, is:

(a) 440 sq m
(b) 594 sq m
(c) 748 sq m
(d) 1540 sq m

Answer. (b) 594 sq cm

11. On a throw of a die, if getting 6 is considered success then probability of losing the game is:

Answer.

12. The distance between the points (2,-3) and (-2, 3) is:
(a) 2√13 units
(b) 5 units
(c) 13√2 units
(d) 10 units

Answer.

13. For what value of θ, sin²θ+ sine+cos²θ is equal to 2 ?
(a) 45°
(b) 0°
(c) 90°
(d) 30°

Answer. (c) 90°

14. The diameter of a circle is of length 6 cm. If one end of the diameter is (-4, 0), the other end on x-axis is at :
(a) (0,2)
(b) (6,0)
(c) (2,0)
(d) (4,0)

Answer. (c) (2,0)

15. The value of k for which the pair of linear equations 5x+2y-7=0 and 2x+ky+1=0 don't have a solution, is:

Answer.

16. For what value of k, the product of zeroes of the polynomial kx²-4x-7 is 2?

Answer.

17. In an A.P.; if a = 8 and a_₁0 =-19, then value of d is:

Answer. (d) – 3

18.

Answer.

Directions:
Assertion (A) is followed by a statement
of Reason (R). Select the correct option from the following options:
(a) Both, Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.
(b) Both, Assertion (A) and Reason (R) are true. Reason (R) does not explain Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

19. Assertion (A): If PA and PB are tangents drawn to a circle with centre O from an external point P, then the quadrilateral OAPB is a cyclic quadrilateral.

Reason (R): In cyclic quadrilateral opposite angles are equal.
Answer. (c) Assertion (A) is true but Reason (R) is false.

20. Assertion (A): Zeroes of a polynomial p(x) = x²-2x-3 are -1 and 3.
Reason (R): The graph of polynomial p(x) = x²-2x-3 intersects x-axis at (-1, 0) and (3, 0).

Answer. (a) Both Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.

21. (A) Prove that 6-4√5 is an irrational number, given that √5 is an irrational number.

Answer. (A) Let us assume 6 – 4 5 = x is a rational number

Now RHS is rational but LHS is irrational. 1
⸫ Our assumption is wrong
Hence 6 – 4 5 is irrational.

OR

(B) Show that 11 × 19 × 23 + 3 × 11 is not a prime number.

Answer. (B) 11 ´ 19 ´ 23 + 3 ´ 11 = 11 ´ (19 ´ 23 + 3)
Þ The given number has more than two factors
Hence it is not a prime number.

22. A bag contains 4 red, 5 white and some yellow balls. If probability of

yellow ball at random.

Answer. Let no. of yellow balls in the bag be n.
\ Total no. of balls = 9 + n

23. In a ∆ABC, <A = 90°. If tan C =√3, then find the value of sin B+ cos C-cos² B.

Answer.

24. In the given figure, AP ⊥ AB
and BQ ⊥AB. If OA = 15 cm,
BO = 12 cm and AP = 10 cm,
then find the length of BQ.

Answer. D OAP ~ D OBQ (AA)

25. (A) Solve the following pair of linear
equations for x and y algebraically:
x+2y=9 and y-2x=2

Answer. (A) x + 2y = 9, _________ (i)
y – 2x = 2 _________ (ii)
Solving to get x = 1, y = 4.

OR

(B) Check whether the point (− 4, 3) lies on both the lines represented by the linear equations x + y + 1 = 0 and x - y = 1.

Answer. (B) Substituting x = – 4 and y = 3 in equation x + y + 1 = 0,
(– 4, 3) satisfies the equation x + y + 1 = 0

So (– 4, 3) lies on it.
For x – y = 1, (– 4, 3) doesn’t satisfy the equation x – y = 1
therefore (– 4, 3) does not lie on x – y = 1

26.

Answer.

27. (A) In two concentric circles, the radii are OA = r cm and OQ = 6 cm, as shown in the figure. Chord CD of larger circle is a tangent to smaller circle at Q. PA is tangent to larger circle. If PA = 16 cm and OP 20 cm, find the length CD.

 

Answer. (A)Since PA ⊥ OA therefore OA² = 20² – 16² = 144
Þ OA = r = 12 cm

In D OQD, QD² = 12² – 6² = 108
Þ QD = 6 3 cm
Now OQ bisects CD

OR

(B) In given figure, two tangents PT and QT are drawn to a circle with centre O from an external point T. Prove that <PTQ = 2 <OPQ.

Answer. (B) Let <PTQ = θ

28. (A) A solid is in the form of a cylinder with hemi-spherical ends of same radii. The total height of the solid is 20 cm and the diameter of the cylinder is 14 cm. Find the surface area of the solid.

Answer. (A) Height of cylinder = 20 – (2 ´ 7) = 6 cm
radius of cylinder = radius of hemisphere = 7 cm

OR

(B) A juice glass is cylindrical in shape with hemi-spherical raised up portion at the bottom. The inner diameter of glass is 10 cm and its height is 14 cm. Find the capacity of the glass. (use л = 3.14)

Answer. (B) radius of glass = 5 cm
Capacity of glass = volume of cylinder – volume of hemisphere

29. Two alarm clocks ring their alarms at regular intervals of 20 minutes and 25 minutes respectively. If they first beep together at 12 noon, at what time will they beep again together next time?

Answer. LCM (20, 25) = 100
\ After 100 minutes from 12:00 noon
Þ They will beep again together at 1:40 pm

30. The line AB intersects x-axis at A and y-axis at B. The point P(2, 3) lies on AB such that AP: PB = 3:1. Find the co-ordinates of A and B.

Answer. Let co-ordinates of point A be (x, 0) and B(0, y)

31. The greater of two supplementary angles exceeds the smaller by 18°. Find measures of these two angles.

Answer. Let the measure of two angles be x° and y° (x > y)
Given x + y = 180 and x – y = 18
solving equations to get y = 81 and x = 99

32. O is the centre of the circle. If AC = 28 cm, BC= 21 cm, <BOD = 90° and <BOC = 30°, then find the area of the shaded region given in the figure.

Answer. Assuming AOB to be a straight line and hence the diameter of the

33. (A) The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it was 60°. Find the height of the tower and the length of original shadow. (use √3 = 1.73)

Answer. (A) Let AB be the tower and AC and AD are shadows.

OR

(B) The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45° respectively. Find the height of the multi-storeyed building and the distance between the two buildings. (use √3 = 1.73)

Answer. Let CD and AB are buildings

 

34. (A) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that other two sides are divided in the same ratio.

Answer. (A)

OR

(B) Sides AB and BC and median AD of a AABC are respectively proportional to sides PQ and PR and median PM of APQR. Show that
AABC - APQR.

Answer. (B)Produce AD to E and PM to N such that AD = DE, PM = MN.

35. In an A.P. if S,, = 4n² - n, then
(i) find the first term and common difference.

Answer. (i) Sn = 4n2 – n
S1 = 4 – 1 = 3 = a 1
S2 = 2a + d = 14 Þ d = 14 – 6 = 8

(ii) write the A.P.

Answer. A.P. is 3, 11, 19, 27, .....

(iii) which term of the A.P. is 107?

Answer. 107 = 3 + (n – 1)8 Þ n = 14

36. Gurpreet is very fond of doing research on plants. She collected some leaves from different plants and measured their lengths in mm.

The data obtained is represented in the following table:

Based on the above information, answer the following questions:

(i) Write the median class of the data.

Answer. (i) Median class : 100 – 110 1

(ii) How many leaves are of length equal to or more than 10 cm ?

Answer. (ii) No. of leaves equal to or more than 10cm(100 mm) = 23 1

(iii) (a) Find median of the data.
(iii) (a)

OR

(b) Write the modal class and find the mode of the data.

Answer. Modal class is 100 – 110

OR

(b) Write the modal class and find the mode of the data.

Answer. Modal class is 100 – 110

37. The picture given below shows a circular mirror hanging on the wall with a cord. The diagram represents the mirror as a circle with centre O. AP and AQ are tangents to the circle at P and Q respectively such that AP = 30 cm and <PAQ = 60°.

Based on the above information, answer the following questions:
(i) Find the length <PQ.

Answer.

\ PQ = AP = 30 cm.

(ii) Find m <POQ.

Answer. Ð POQ = 180° – 60° = 120°

(iii) (a) Find the length OA.

Answer. (a) Ð PAO = 30°

OR

(b) Find the radius of the mirror.

Answer. (b) Ð PAO = 30

38. To keep the lawn green and cool, Sadhna uses water sprinklers which rotate in circular shape and cover a particular area.
The diagram below shows the circular areas covered by two sprinklers:

 

Two circles touch externally. The sum of their areas is 130 π sq m and the
distance between their centres is 14 m.
Based on above information, answer the following questions:

(i) Obtain a quadratic equation involving R and r from above.

Answer. R² + r² = 130

(ii) Write a quadratic equation involving only r.

Answer. r² – 14r + 33 = 0

(iii) (a) Find the radius r and the corresponding area irrigated.

Answer. (a) r² – 14r + 33 = 0 Þ (r – 11) (r – 3) = 0
Þ r = 3 m, r ¹ 11 m (As r < R)

Corresponding area irrigated = 9p m²

OR

(b) Find the radius R and the corresponding area irrigated.

Answer. (b) R² – 14R + 33 = 0 Þ (R – 11) (R – 3) = 0
Þ R = 11 m, R ¹ 3 (As R>r)

Corresponding area irrigated = 121p m²