ARMY PUBLIC SCHOOL MIRAN SAHIB
UT 1 (2024-25)
SET II
CLASS- XI MAXIMUM MARKS- 40
SUBJECT-MATHEMATICS TIME- 1 HOUR 30 MINUTES
GENERAL INSTRUCTIONS-
1. This Question paper contains - five sections A, B, C, D and E.
2. Section A has 10 multiple choice questions and 1 Assertion-Reason based question of 1
mark each.
3. Section B has 3 Very Short Answer (VSA)-type questions of 2 mark each.
4. Section C has 2 Short Answer (SA)-type questions of 3 mark each.
5. Section D has 2 Long Answer (LA)-type questions of 5 mark each.
6. Section E has 2 case based questions (4 marks each) with sub parts.
S.NO. SECTION A MARKS
Q1 The value of – (−1) , n ∈ N is 1
(a)i (b) – 𝑖 (c) 1 (d) – 1
Q2 Let 𝑧 = 𝑖99 + 𝑖118 then z lies in 1
(a) 1st quadrant (b) 2nd quadrant (c) 3rd quadrant (d) 4th quadrant
Q3 The modulus of the complex number (1 − i) + (1 + i) is equal to 1
(a) 1 (b) 2 (c) 3 (d) 0
Q4 If f (x) = ax + b, where a and b are integers, f (–1) = – 5 and f (3) = 3, then a and 1
b are equal to
(a) a = – 3, b = –1 (b) a = 2, b = – 3 (c) a = 0, b = 2 (d) a = 2, b = 3
Q5 If R is a relation on set A = {1, 2, 3, 4, 5, 6, 7, 8} given by xRy ↔ y = 3x, then 1
R=?
(a) {(3,1), (6,2), (8,2), (9,3)} (b) {(3,1), (6,2), (9,3)}
(c) {(3,1), (2,6), (3,9)} (d) None of these
Q6 If f(x) = [2.9], where [ ]is a greatest integer function, then f(x) = 1
(a)3 (b) 2 (c)2.9 (d) None of these
Q7 If A and B are two given sets, then A∩ (𝐴 ∩ 𝐵)′ is equals to 1
(a)A (b) B′ (c) ∅ (d) A–B
Q8 If A = {1, 2, 3, 4, 5}, then the number of proper subsets of A is 1
(a)120 (b) 30 (c)31 (d) 32
Q9 In set builder method the null set is represented by 1
(a){ } (b) ∅ (c){x: x ≠ 𝑥} (d) {x: x = 𝑥}
Q10 In the following questions, a statement of assertion (A) is followed by a 1
statement of Reason (R). Choose the correct answer out of the following choices.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Assertion (A): Let A = {1, 2} and B = {3, 4}. Then, number of relations from A
to B is 16.
Reason (R): If n(A) = p and n(B ) = q, then number of relations is 2pq.
SECTION B
Q11 (i)Write the [–23, 5) interval in set-builder form and represent it on number line. 1+1
(ii) Draw appropriate Venn diagram for (A ∪ B)′
Q 12 Draw graph of signum function. Also write its domain and range. 2
Q13 Let P = {9, 4, 25} and Q = {–5, –3, –2, –1, 1, 2, 3, 5}. Define a relation R from P 1+1
to Q by R = {(x, y): x is the square of y, x ∈ P, y ∈ Q}
(i) Depict this relation using an arrow diagram.
(ii) Write down the domain and range of R.
SECTION C
Q14 For any sets A and B show that 3
(i) (A ∩ B) ∪ (A − B) = A (ii)A ∪ (B − A) = A ∪ B
Q15 Let R be a relation from N to N defined by R = {(a, b) : a, b ∈N and a = b2}. 3
Check if R is Reflexive, Symmetric and transitive.
SECTION D
Q16 Let A and B be sets. If A ∩ X = B ∩ X = ∅ and A ∪ X = B ∪ X for some set X, 5
show that A = B.
Q17 If (x + iy) = a + ib prove + = 4(a − b ). 5
SECTION E
This section comprises of three case study questions
Q18 While solving a typical problem a Rohit finds that one of the root of the equation
( )
is a complex number z = , help him to find.
(i) The standard form of Z. 1
(ii) Find the multiplicative inverse of Z. 1
(iii) Modulus of Z. 1
(iv) In which quadrant Z lies. 1
Q19 A is the anthills of an ant, at B some sweets are there and ant wants to reach at B.
The path traced by an ant is shown in the following graph:
On the basis of the above graph find the following:
(i) When ordinate is 6 then find abscissa. 1
(ii) Which axis is line of symmetry for the graph? 1
(iii) Write the function for the graph along with domain and range. 2
