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| Section | Qs | Each | Marks | Types |
|---|---|---|---|---|
| SECTION A | 5 | 1 | 5 | 5 MCQ |
| SECTION B | 3 | 2 | 6 | 3 Short answer |
| SECTION C | 3 | 3 | 9 | 3 Short answer |
| SECTION D | 2 | 5 | 10 | 2 Long answer |
| SECTION E | 1 | 4 | 4 | 1 Case study |
| Total | 14 | 34 | of 80 |
- ! Questions add up to 34; 46 marks still to allocate out of 80.
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Examination & school
General instructions
Sections (5)
5 marks
Q.1
(a)
(b)
(c)
(d)
Q.2
(a)
(b)
(c)
(d)
Q.3
(a)
(b)
(c)
(d)
Q.4
(a)
(b)
(c)
(d)
Q.5
(a)
(b)
(c)
(d)
Paste several questions at once
Separate questions with a blank line. Lines starting (a), a) or A. become MCQ options. End a question with [3] or (3 marks) to set its marks. Numbers such as “1.” at the start are removed.
6 marks
9 marks
10 marks
4 marks
Series / Set: ARoll No.: [ ______________________ ]
DELHI PUBLIC ACADEMY
Vasant Vihar, New Delhi — 110057 | Affiliated to CBSE (Affiliation No: 2130045)
PRE-BOARD EXAMINATION (2025-2026)
SUBJECT: MATHEMATICS (STANDARD) (Code: 041)CLASS X
Time Allowed: 3 HoursMaximum Marks: 80
General Instructions:
- This question paper contains 38 questions divided into 5 Sections: A, B, C, D and E.
- Section A comprises 20 Multiple Choice Questions (MCQs) of 1 mark each.
- Section B comprises 5 Short Answer Questions (SA-I) of 2 marks each.
- Section C comprises 6 Short Answer Questions (SA-II) of 3 marks each.
- Section D comprises 4 Long Answer Questions (LA) of 5 marks each.
- Section E comprises 3 Case-Based integrated units of assessment of 4 marks each with sub-parts.
- All questions are compulsory. However, an internal choice in 2 questions of Section B, 2 questions of Section C and 2 questions of Section D has been provided.
- Use of calculators is strictly prohibited. Draw neat figures wherever required.
SECTION A
Questions 1 to 5 carry 1 mark each (Multiple Choice Questions)
Q.1.If two positive integers a and b are written as a = x³y² and b = xy³, where x, y are prime numbers, then HCF(a, b) is:
[1](a) xy
(b) xy²
(c) x³y³
(d) x²y²
Q.2.The LCM of the smallest two-digit composite number and the smallest composite number is:
[1](a) 12
(b) 4
(c) 20
(d) 44
Q.3.If the quadratic equation x² + 4x + k = 0 has real and equal roots, then the value of k is:
[1](a) k < 4
(b) k > 4
(c) k = 4
(d) k ≥ 4
Q.4.The distance of the point P(-6, 8) from the origin (0, 0) is:
[1](a) 8 units
(b) 2√7 units
(c) 10 units
(d) 6 units
Q.5.If sin θ + cos θ = √2 cos θ, then the value of tan θ is equal to:
[1](a) √2 - 1
(b) √2 + 1
(c) 1 / √2
(d) √3
SECTION B
Questions 6 to 8 carry 2 marks each (Short Answer Type I)
Q.6.Prove that √5 is an irrational number by contradiction method.
[2]Q.7.Find the coordinates of the point which divides the line segment joining the points A(4, -3) and B(8, 5) in the ratio 3:1 internally.
[2]Q.8.Evaluate without using trigonometric tables: (5 cos² 60° + 4 sec² 30° - tan² 45°) / (sin² 30° + cos² 30°).
[2]— OR —
If tan(A + B) = √3 and tan(A - B) = 1/√3, where 0° < A + B ≤ 90° and A > B, find the measures of angles A and B.
SECTION C
Questions 9 to 11 carry 3 marks each (Short Answer Type II)
Q.9.Find the zeroes of the quadratic polynomial 6x² - 3 - 7x and verify the relationship between the zeroes and the coefficients.
[3]Q.10.The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the original number.
[3]Q.11.Prove that the lengths of two tangents drawn from an external point to a circle are equal.
[3]— OR —
In a triangle ABC, if AD ⊥ BC and AD² = BD × CD, prove that triangle ABC is a right-angled triangle at A.
SECTION D
Questions 12 to 13 carry 5 marks each (Long Answer Type)
Q.12.A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Determine the speed of the stream.
[5]— OR —
Two water taps together can fill a tank in 9⅜ hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Q.13.From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the cable tower (Take √3 = 1.732).
[5]SECTION E
Question 14 carries 4 marks (Case Study Based / Integrated Unit of Assessment)
Q.14.CASE STUDY: A manufacturer of electric scooters produces 600 units in the 3rd year and 700 units in the 7th year. Assuming that production increases uniformly by a fixed number every year:
(i) Find the fixed increase in production each year. [1 Mark]
(ii) Find the production in the 1st year. [1 Mark]
(iii) Calculate the total production in the first 10 years. [2 Marks]
[4]* * * END OF QUESTION PAPER * * *