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 subparts of Section E.
9. Use π = 22/7 wherever required. Calculators are not allowed.
10. Show all necessary steps and draw neat figures wherever required.

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 α² + β² is: (A) 1/4 (B) 13/4 (C) 19/4 (D) 25/4
3. The pair of equations 3x + 2y = 7 and 6x + 4y = k has infinitely many solutions when k is: (A) 7 (B) 10 (C) 14 (D) 21
4. If one root of x² − 5x + k = 0 is 2, then k is: (A) 4 (B) 5 (C) 6 (D) 7
5. The 10th term of the AP 7, 13, 19, 25, … is: (A) 55 (B) 61 (C) 63 (D) 67
6. The distance between (−2, 3) and (4, −5) is: (A) 8 (B) 10 (C) 12 (D) 14
7. If the areas of two similar triangles are in the ratio 25:36, the ratio of their corresponding sides is: (A) 5:6 (B) 25:36 (C) 10:12 (D) 6:5
8. If tan θ = 5/12, where θ is acute, then sin θ is: (A) 5/12 (B) 12/13 (C) 5/13 (D) 13/5
9. The value of (1 − sin²A)/cos²A is: (A) 0 (B) 1 (C) tan²A (D) sec²A
10. If the angle between two tangents drawn from an external point is 60°, then the angle subtended by the chord of contact at the centre is: (A) 60° (B) 90° (C) 120° (D) 150°
11. The area of a sector of radius 14 cm and angle 90° is: (A) 44 cm² (B) 77 cm² (C) 154 cm² (D) 616 cm²
12. A cone has radius 3 cm and height 4 cm. Its curved surface area is: (A) 12π cm² (B) 15π cm² (C) 20π cm² (D) 24π cm²
13. If the mean of 2, 4, 6, 8, x is 6, then x is: (A) 8 (B) 10 (C) 12 (D) 14
14. Two dice are thrown simultaneously. The probability that the sum is 7 is: (A) 1/12 (B) 1/9 (C) 1/6 (D) 1/3
15. If the sum of the first n terms of an AP is Sₙ = 3n² + 2n, its common difference is: (A) 3 (B) 5 (C) 6 (D) 8
16. The roots of 2x² − 7x + 3 = 0 are: (A) 3, 1/2 (B) −3, −1/2 (C) 2, 3 (D) 1, 3/2
17. If a point P divides the line segment joining A(2, 3) and B(8, 9) internally in the ratio 1:2, then P is: (A) (4, 5) (B) (5, 4) (C) (6, 7) (D) (3, 4)
18. The volume of a sphere of radius 3 cm is: (A) 9π cm³ (B) 18π cm³ (C) 27π cm³ (D) 36π cm³

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 of a rational number has only the prime factors 2 and 5.
20. Assertion (A): The tangent at any point of a circle is perpendicular to the radius through the point of contact. Reason (R): The perpendicular from a point to a line is the shortest distance from the point to the line.