CBSE Class 10 Maths Pre-Board Sample Paper 2025 With Solutions, Download PDF

GENERAL INSTRUCTIONS:

1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with subparts of the values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks questions of Section E.
8. Draw neat figures wherever Take π =22/7 wherever required if not stated.

SECTION A

SN

Section A consists of 20 questions of 1 mark each.

MARKS

1

Which of the following numbers is a rational number?
(A) 3+√5
(B) 3−√5
(C) (3+√5)(3−√5)
(D) 3√5

1

2

The product of a non-zero rational and an irrational number is

(A) always rational          (B) rational or irrational      (C) always irrational (D) zero

1

3

The number of zeroes, the polynomial p (x) = (x – 2)² - 4 can have, is

(A)1          (B) 2          (C) 3            (D) 0

1

4

If a pair of linear equations has a consistent solution, the lines will be:
(A) Parallel
(B) Coincident
(C) Intersecting or Coincident
(D) Intersecting only

1

5

(sec A + tan A) (1 – sin A) =

(A) sec A           (B) sin A        (C) cosec A      (D) cos A

1

6

The roots of the quadratic equation 2x²+x+4 are:
(A) Both positive
(B) Both negative
(C) One positive and one negative
(D) No real roots

1

7

The distance of the point P(–6, 8) from the origin is

(A) 10 units          (B) 2√7 units          (C) 8 units           (D) 6 units

1

8

The fourth vertex DDD of a parallelogram ABCD whose three vertices are A(3,2), B(7,6) and C(5,8)C(5, 8)C(5,8) is:
(A) (1,4)
(B) (3,5)
(C) (1,6)
(D) (5,4)

1

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

(A) 12 cm            (B) 13 cm              (C) 8.5 cm         (D) √119 cm

10

P and Q are the midpoints of sides XY and XZ of triangle XYZ, respectively, and YZ = 8 cm. If PQ || YZ, what is the length (in cm) of PQ?
(A) 3
(B) 4
(C) 5
(D) 8

1

11

If triangles XYZ and PQR are similar, and XY = 5 cm, PQ = 7.5 cm, QR = 10 cm, and RP = 15 cm, the perimeter of triangle XYZ is:
(A) 25 cm
(B) 20 cm
(C) 22.5 cm
(D) 24 cm

1

12

A girl calculates that the probability of her winning the first prize in a lottery is

0.08. If 6000 tickets are sold, how many tickets has she bought? (A) 40                 (B) 240             (C) 480       (D) 750

1

13

For a frequency distribution, mean, median and mode are connected by the relation

(a) mode = 3mean – 2median                  (b) mode = 2median – 3mean

(c) mode = 3median – 2mean              (d) mode = 3median + 2mean

1

14

The minute hand of a clock is 7 cm long. Find the area of the face of the clock described by minute hand in 15 minutes.

(a) 154 Sq cm          (b)38.5 Sq cm       (c)105 Sq cm      (d)77 Sq cm

1

15

If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

(A) 2 units    (B) π units (C) 4 units     (D) 7 units

1

16

Two identical solid cubes of side a are joined end to end. Then the total surface area of the resulting cuboid is

(A) 12a²          (B) 10a²          (C) 8a²     (D) 11a²

1

17

The pair of equations y = 0 and y = –7 has:

(A) one solution (B) two solutions (C) infinitely many solutions (D) no solution

1

18

If 3 sinθ-cosθ=0 and 0⁰<θ< 90⁰, then the value of θ is a)30⁰ b)60⁰                 c)90⁰      d)45⁰

1

19

DIRECTION: In the question number 19 and 20, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct option

Statement A (Assertion): sin 45⁰=cos 45⁰

Statement R( Reason) : sin θ = cos θ for all values of θ.

(a)  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

(b)  Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

(c)  Assertion (A) is true but reason(R) is false.

(d)  Assertion (A) is false but reason(R) is true.

1

Statement A (Assertion): For any two positive integers p and q, HCF (p, q) × LCM (p, q) = p × q

Statement R( Reason) : If the HCF of two numbers is 5 and their product is 150, then their LCM is 30.

• Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
• Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
• Assertion (A) is true but reason(R) is false.
• Assertion (A) is false but reason(R) is true.

1.(c)

2.(c)

3.(B)

4(c)

5(d)

6(d)

7(a)

8(a)

9(d)

10(b)

11(b)

12(c)

13 (c)

14 (b)

15(a)

16 (b)

17 (d)

18 (a)

19 (c)

20 (b)

Q21.

Correct value of x=-2, y=5 1 mark, correct value of m = -1

Or correct value of zeroes are -5, -2 (1 mark), verify the coefficient

1

1

Q22.

Fig. given, to prove, correct proof

½ 1+1/2

Q23.

Correct fig

mark and correct proof Or

Use of correct Bpt, correct proof

½ 1+1/2

1

1

Q24.

cos(B) = 12/13

tan(B) = 5/12

1+1

Q25.

Minor sector =205.33 cm², major sector =410.11 cm²

1+1

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