Class X Mathematics (Basic) – Code 241

Preparatory Examination 1 | Academic Session 2026–27

General Instructions

1. This question paper contains 38 questions. All questions are compulsory.
2. The paper is divided into five sections: A, B, C, D and E.
3. Section A contains 18 MCQs and 2 Assertion–Reason questions of 1 mark each.
4. Section B contains 5 very short answer questions of 2 marks each.
5. Section C contains 6 short answer questions of 3 marks each.
6. Section D contains 4 long answer questions of 5 marks each.
7. Section E contains 3 case-study questions of 4 marks each.
8. Internal choices are provided in selected questions. Attempt only one alternative wherever an OR is given.
9. Use π = 22/7 wherever required, unless stated otherwise. Calculators are not allowed.
10. Draw neat figures wherever necessary and show all essential steps.

SECTION A – Multiple Choice Questions (20 × 1 = 20)

Choose the correct option. Each question carries 1 mark.

1. The HCF of 96 and 404 is: (A) 2 (B) 4 (C) 8 (D) 12
2. If the zeroes of p(x) = x² − 7x + 10 are α and β, then α + β is: (A) 10 (B) −10 (C) 7 (D) −7
3. For which value of k will the pair 2x + 3y = 7 and 4x + 6y = k have infinitely many solutions? (A) 7 (B) 12 (C) 14 (D) 21
4. The discriminant of x² − 6x + 9 = 0 is: (A) 36 (B) 0 (C) 9 (D) −9
5. The 8th term of the AP 5, 8, 11, 14, … is: (A) 23 (B) 24 (C) 26 (D) 29
6. The distance between (0, 0) and (6, 8) is: (A) 8 units (B) 9 units (C) 10 units (D) 14 units
7. If two triangles are similar, the ratio of their corresponding sides is 2:3. The ratio of their areas is: (A) 2:3 (B) 4:9 (C) 3:2 (D) 8:27
8. For an acute angle θ, if sin θ = 3/5, then cos θ is: (A) 3/4 (B) 4/5 (C) 5/4 (D) 2/5
9. The value of tan 45° + cos 60° is: (A) 1/2 (B) 1 (C) 3/2 (D) 2
10. The angle between a tangent and the radius through the point of contact is: (A) 0° (B) 45° (C) 90° (D) 180°
11. The circumference of a circle of radius 7 cm is: (A) 22 cm (B) 44 cm (C) 49 cm (D) 154 cm
12. The volume of a cylinder with radius 3 cm and height 7 cm is: (A) 66 cm³ (B) 99 cm³ (C) 198 cm³ (D) 396 cm³
13. If the mean of 4, 6, 8, 10 and x is 8, then x is: (A) 10 (B) 12 (C) 14 (D) 16
14. A die is thrown once. The probability of getting an even number is: (A) 1/6 (B) 1/3 (C) 1/2 (D) 2/3
15. If the sum of the first n terms of an AP is Sₙ = n² + 2n, its first term is: (A) 1 (B) 2 (C) 3 (D) 4
16. The pair of equations x + y = 5 and x − y = 1 has solution: (A) (2, 3) (B) (3, 2) (C) (4, 1) (D) (1, 4)
17. If the radius of a sphere is doubled, its volume becomes: (A) 2 times (B) 4 times (C) 6 times (D) 8 times
18. In a right triangle, if the perpendicular is 5 cm and the base is 12 cm, the hypotenuse is: (A) 10 cm (B) 11 cm (C) 13 cm (D) 17 cm

Assertion–Reason Questions

For Questions 19 and 20, choose: (A) Both A and R are true and R correctly explains A. (B) Both A and R are true but R does not correctly explain A. (C) A is true but R is false. (D) A is false but R is true.

19. Assertion (A): The probability of an impossible event is zero. Reason (R): The number of favourable outcomes for an impossible event is zero.
20. Assertion (A): The tangents drawn from an external point to a circle are equal in length. Reason (R): The perpendicular distance from the centre to every chord is equal.