Class: XI Mathematics ST. MARGARET SR. SEC. SCHOOL PT-II EXAMINATION 2025-26

ST MARGARET SR SEC. SCHOOL

PT-2 EXAMINATION 2025-26

Subject:	Mathematics
Class:	XI
Set:	SET-B
Time:	1 Hour
Maximum Marks:	25

General Instructions:

1. This question paper contains four sections: A, B, C and D. Each section is compulsory.
2. Section A has 6 MCQs of 1 mark each.
3. Section B has 3 questions of 2 marks each.
4. Section C has 3 questions of 3 marks each.
5. Section D has 1 case study of 4 marks.

SECTION A (1 Mark Each)

Q1. If the parabola y² = 4ax passes through the point P(3, 2), then the length of its latus rectum is

• (a) 1⁄3
• (b) 2⁄3
• (c) 4⁄3
• (d) 5⁄3

Q2. IQ = (MA ÷ CA) × 100. If 40 ≤ IQ ≤ 120 for 10-year-olds, find the range of mental age.

• (a) (9, 16)
• (b) [9, 16]
• (c) (4, 12)
• (d) [4, 12]

Q3. M is the foot of the perpendicular from A(6, 7, 8) on the xy-plane. Coordinates of M are

• (a) (6, 0, 0)
• (b) (6, 7, 0)
• (c) (6, 0, 8)
• (d) (0, 7, 8)

Q4. Length of latus rectum of ellipse x²⁄25 + y²⁄49 = 1 is

• (a) 49⁄5
• (b) 50⁄7
• (c) 25⁄7
• (d) 49⁄7

Q5. Area of circle centred at (1, 2) passing through (4, 6) is

• (a) 5π
• (b) 10π
• (c) 25π
• (d) 36π

Q6. Which point satisfies 3x − y > 15?

• (a) (5, 1)
• (b) (1, 5)
• (c) (2, 0)
• (d) (5, −1)

SECTION B (2 Marks Each)

Q7. Find the equation of the circle of radius 5 whose centre lies on the x-axis and passes through (2, 3).

Q8. Find points on the y-axis at a distance of √21 from (1, 2, 3).

Q9. Find the eccentricity of an ellipse whose latus rectum = ½ of the major axis.

SECTION C (3 Marks Each)

Q10. Find the equation of the hyperbola whose foci are (±3√5, 0) and latus rectum length is 8.

Q11. Find the equation on the set of points P, such that PA + PB = 10, where A(4, 0, 0), B(−4, 0, 0).

Q12. Solve the inequalities (2x+1) ÷ (7x−1) ≥ 5 and (x+7) ÷ (x−8) > 2.

SECTION D (Case Study – 4 Marks)

Q13. A student has 600 L of 9% acid solution. A 30% solution is added so the final concentration is 15% to 20%.
Let x be the volume added.
(a) Form inequality for pure acid quantity
(b) Solve for x
(c) Show the solution on the number line.