Class X Mathematics (Standard) – Code 041

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: Questions 1–18 are MCQs and Questions 19–20 are Assertion–Reason questions, 1 mark each.
4. Section B: Questions 21–25 are very short answer questions, 2 marks each.
5. Section C: Questions 26–31 are short answer questions, 3 marks each.
6. Section D: Questions 32–35 are long answer questions, 5 marks each.
7. Section E: Questions 36–38 are case-study questions, 4 marks each.
8. Internal choices are provided in two questions each in Sections B, C and D, and in the 2-mark subpart of each case study.
9. Use π = 22/7 wherever required. Calculators are not allowed. Draw neat figures wherever necessary.

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

1. The greatest number which divides 134 and 188 leaving remainders 4 and 6 respectively is: (A) 13 (B) 26 (C) 39 (D) 65
2. If α and β are the zeroes of 2x² − 5x + 3, then α + β is: (A) 3/2 (B) 5/2 (C) −5/2 (D) 3
3. The pair x − y = 6 and 2x − 3y = 13 has solution: (A) (5,−1) (B) (−1,5) (C) (6,0) (D) (4,−2)
4. If one root of x² + px + 1 − p = 0 is 1 − p, the other root is: (A) 0 (B) 1 (C) −1 (D) p
5. The 10th term of the AP 7, 11, 15, … is: (A) 39 (B) 41 (C) 43 (D) 47
6. The distance between (−2, 3) and (4, 11) is: (A) 8 (B) 10 (C) 12 (D) 14
7. If the areas of two similar triangles are in the ratio 25:49, the ratio of their corresponding sides is: (A) 5:7 (B) 25:49 (C) 7:5 (D) 10:14
8. If tan θ = 3/4 for an acute angle θ, then sin θ is: (A) 3/5 (B) 4/5 (C) 5/3 (D) 4/3
9. The value of (1 − sin²A)/cos²A, where cos A ≠ 0, is: (A) 0 (B) 1 (C) tan²A (D) sec²A
10. The angle between a tangent and the radius through the point of contact is: (A) 30° (B) 45° (C) 60° (D) 90°
11. The area of a sector of angle 90° in a circle of radius 14 cm is: (A) 77 cm² (B) 154 cm² (C) 308 cm² (D) 616 cm²
12. The volume of a cone of radius 3 cm and height 4 cm is: (A) 12π cm³ (B) 18π cm³ (C) 24π cm³ (D) 36π cm³
13. If the mean of 2, 4, 6, 8 and x is 6, then x is: (A) 8 (B) 10 (C) 12 (D) 14
14. A number is selected at random from 1 to 30. The probability that it is a prime number is: (A) 1/3 (B) 2/5 (C) 1/2 (D) 3/5
15. If the discriminant of ax² + bx + c = 0 is positive, its roots are: (A) real and equal (B) real and distinct (C) not real (D) always irrational
16. The midpoint of the line segment joining (−2, 5) and (6, −3) is: (A) (2,1) (B) (4,2) (C) (2,−1) (D) (−2,1)
17. If the radius of a sphere is tripled, its volume becomes: (A) 3 times (B) 6 times (C) 9 times (D) 27 times
18. In ΔABC, DE ∥ BC. If AD/DB = 2/3 and AC = 15 cm, then AE is: (A) 5 cm (B) 6 cm (C) 9 cm (D) 10 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 decimal expansion of 13/125 is terminating. Reason (R): In lowest terms, the denominator 125 has only the prime factor 5.
20. Assertion (A): The lengths of tangents drawn from an external point to a circle are equal. Reason (R): The radii drawn to the points of contact are perpendicular to the tangents.