11th Class CBSE Board Mathematics Mid Term Examination (2025-26)

St. Margaret Sr. Sec. School, Prashant Vihar, Sector 14, Rohini, Delhi-85, India

School Name:	St. Margaret Sr. Sec. School, D-BLOCK, Prashant Vihar, Sector 14, Rohini, Delhi-110085
Class:	11th Standard (CBSE)
Subject:	Mathematics
Time Duration:	01 Hour
Maximum Marks:	25
Set:	SET – B

General Instructions: 11th Class Mathematics Exam 2025-26

• This Question Paper contains four sections: A, B, C and D. Each section is compulsory.
• Section A has 6 MCQ questions of 1 mark each.
• Section B has 3 Very Short Answer (VSA) questions of 2 marks each.
• Section C has 3 Short Answer (SA) questions of 3 marks each.
• Section D has 1 Case Study of 4 marks.

SECTION – A (Each question carries 1 mark)

Question 01: 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

Question 02: IQ of a person is given by the formula IQ = (MA ÷ CA) × 100. If 40 ≤ IQ ≤ 120 for a group of 10-year-old children, find the range of their mental age.

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

Question 03: M is the foot of the perpendicular drawn from the point A(6, 7, 8) on the xy-plane. What are the coordinates of point M?

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

Question 04: Length of latus rectum of the ellipse x²⁄25 + y²⁄49 = 1 is

• a) 98⁄5
• b) 50⁄7
• c) 25⁄7
• d) 49⁄5

Question 05: The area of the circle centred at (1, 2) and passing through (4, 6) is

• a) 5π sq. units
• b) 10π sq. units
• c) 25π sq. units
• d) 36π sq. units

Question 06: Which of the following points lies in the solution region of inequality 3x − y > 15?

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

SECTION – B (Each question carries 2 marks)

Question 07: Find the equation of the circle with radius 5 whose centre lies on the x-axis and passes through the point (2, 3).

Question 08: Find the points on the y-axis which are at a distance of √21 from the point (1, 2, 3).

Question 09: Find the eccentricity of the ellipse if its latus rectum is equal to one-half of its major axis.

SECTION – C (Each question carries 3 marks)

Question 10: Find the equation of the hyperbola whose foci are (±3√5, 0) and whose latus rectum is of length 8.

Question 11: Find the equation of the set of points P such that the sum of its distances from A(4, 0, 0) and B(−4, 0, 0) is equal to 10.

Question 12: Solve the system of inequalities:
(2x + 1) ÷ (7x − 1) ≥ 5,    (x + 7) ÷ (x − 8) > 2
Represent the solution on the number line.

SECTION – D (Case Study – 4 Marks)

Question 13: A chemistry student has 600 litres of hydrochloric acid solution of 9% concentration. The student adds a 30% acid solution so that the final concentration is greater than 15% and less than 20%. Let x be the volume (in litres) of the 30% solution added.

a) Write an expression for the total volume of pure acid in the final mixture in terms of x and frame the compound inequality.

b) Solve the inequality and find the minimum and maximum volume of the 30% solution required.

c) Represent the solution on a number line.