CLASS-XI Mathematics ST MARGARET SR SEC. SCHOOL MID-TERM EXAMINATION 2025-26

ST MARGARET SR SEC. SCHOOL MID-TERM EXAMINATION 2025-26

Class:	XI
Subject:	Mathematics
Set:	SET – B
Time Duration:	03 Hours
Maximum Marks:	80

General Instructions:

1. This question paper contains five sections: A, B, C, D and E. Each section is compulsory.
2. Section A has 18 MCQs and 2 assertion-reason-based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA) questions of 2 marks each.
4. Section C has 6 Short Answer (SA) questions of 3 marks each.
5. Section D has 4 Long Answer (LA) questions of 5 marks each.
6. Section E has 3 source/case/passage-based integrated units of 4 marks each with sub-parts.

SECTION – A (20 questions of 1 mark each)

Q1. How many 4-digit even numbers are there when digits can be repeated?

a) 5040   b) 4500   c) 3024   d) 10000

Q2. If sinθ + cosθ = 1, then the value of sin2θ is equal to

a) 1   b) 0   c) −1   d) 2

Q3. Let V = {a, e, i, o, u}, V − B = {e, o, i} and B − V = {k}. Then the set B is

a) {a, i, u} b) {a, k, u}   c) {a, i, k, u}   d) {a, e, i, k, u}

Q4. Given sets A = {−2, 2} and B = {x ∈ Z : x² − 4 = 0}, then

a) A = B   b) A ≠ B   c) B ⊂ A   d) A and B are disjoint

Q5. Find the value of cos(−2220°).

a) 1   b) 1⁄2   c) −1   d) −1⁄2

Q6. The range of the greatest integer function f(x) = ⌊x⌋ is

a) R⁺   b) Z   c) W   d) {−1, 0, 1}

Q7. For two sets A and B, A ∪ B = A iff

a) B ⊂ A   b) A ⊂ B⁺   c) A ≠ B   d) A and B are disjoint

Q8. If a complex number lies in the fourth quadrant, where does its conjugate lie?

a) I quadrant   b) II quadrant   c) III quadrant   d) IV quadrant

Q9. If 15Cᵣ = 15Cᵣ₊₇, then the value of r is

a) 4   b) 6   c) 2   d) 8

Q10. Let (A) = m and (B) = n; then the total number of relations that can be defined from A to B is

a) mⁿ   b) 2ᵐⁿ   c) 2ᵐⁿ⁻¹   d) mⁿ − 1

Q11. The lines x + (k − 1)y + 1 = 0 and 2x + ky − 1 = 0 are at right angles if

a) k = 1   b) k = 2   c) k > 1   d) k = −1

Q12. The length of the perpendicular from origin to the line x cos θ + y θ = k is

a) k cosθ   b) k sinθ   c) k + 1   d) |k|

Q13. The number of terms in the expansion of (1 + x)⁴⁰ is

a) 21   b) 20   c) 41   d) 40

Q14. What is the inclination of a line parallel to the x-axis?

a) 0°   b) 10°   c) 45°   d) 90°

Q15. In an examination there are 3 MCQs and each has 4 choices. The number of ways in which a student can fail to get all answers correct is

a) 21   b) 12   c) 27   d) 63

Q16. The conjugate of the complex number (1+i)/(1−i) is

a) (1+i)/2   b) (i−1)/2   c) (−i+1)/2   d) (−i−1)/2

Q17. The value of tan(22.5°) is

a) √2 − 1   b) √2 + 1   c) −√2 − 1   d) √2

Q18. Evaluate (sin7x − sin5x)/(cos7x + cos5x)

a) tanx   b) secx   c) cotx   d) sinx

Q19. Assertion (A): The simplest form of i² is i.
Reason (R): The additive inverse of (1 − i) is (−1 + i).

Q20. Assertion (A): If (x−1, y−2) = (3,1), then x = 2, y = 3.
Reason (R): Two ordered pairs are equal if corresponding elements are equal.

SECTION – B (2 marks each)

Q21. Draw a Venn diagram showing one possible relationship among sets U, G, B and S.

Q22. Evaluate −8 sin(3π/12) + 6 sin(π/12).

Q23. Find the modulus of the complex number (1+i)/(1−i) and express it in a + ib form.

Q24. Show that 9ⁿ⁺¹ − 8ⁿ − 9 is divisible by 64 for every positive integer n.

Q25. Find the equation of a line through (2,2) perpendicular to the line joining (2,3) and (3,−1).

Q26. In a survey of 400 students… find how many take neither apple nor orange juice.

SECTION – C (3 marks each)

Q27. Find the domain and range of f(x) = 5/(5−x²).

Q28. If p and q are perpendicular distances from origin to two lines… Prove p² + 4q² = k².

Q29. If (x+iy)³ = u + iv, show that 1/x + 1/y = 4(x² − y²).

Q30. Find the number of words from “ARTICLE” under given conditions.

Q31. Find the number of arrangements of letters of “INDEPENDENCE” under given conditions.

Q32. Prove that sin20°·sin40°·sin60°·sin80° = 3/16.

SECTION – D (5 marks each)

Q33. Prove product of perpendicular distances from (√a²−b²,0) and (−√a²−b²,0)… is b²/a.

Q34. Find sin(x/2), cos(x/2), and tan(x/2) if tan x = −4/3 (x in quadrant II) OR evaluate the given expression.

Q35. If the different permutations of the word “EXAMINATION” are arranged as in a dictionary. How many words are there before the first word starting with E? Also find the rank of the word “ZENITH” according to the dictionary.

Q36. Q36. One triangular-shaped pond is there in a park. Three friends, Rani, Mansi, and Sneha, are sitting at the corners of the triangular park. Rani marked her position as (2, -2), Mansi marked as (1, 1), and Sneha marked her position as (-1, 0), as shown in the figure given below.

SECTION – E (Case Study)

Q37. Seema wants a mobile number having 10 digits. It is not just a group of numbers strung out at random. All mobile numbers have 3 things in common. a 2-digit access code (AC), a 3-digit provider code (PC), and a 5-digit subscriber code (SC). AC code and PC code are fixed, then:

(i) How many mobile numbers are possible if the number starts with 98173 and other digits can repeat? (1)

(ii) How many AC codes are possible if both digits in the AC code are different and must be greater than 5? (1)

(iii) How many mobile numbers ending with 5 are possible with AC code 97 and digits once used will not be used again? (2)

 

Q38. In a school at Chandigarh, students of class XI were discussing the relations and functions. Three students, Ankita, Babita and Kavita, form three sets: A={1,2,3,4,5}, B={2,4,6} and K={5,7}.

Based on the above information, answer the following:
(i) Find n(AxB) and n(KxB)
(ii) A correspondence of elements from A to B given as {(1,2),(2,2),(3,4),(3,6), (4,4), (5,6)}. Is it a function? Justify.
iii) If the function f: BA is such that (b,a) ∈ f and b < a, defined by f={(2,5),(x,4),(4,y),(2,3)}, then find x and y.