Fahaheel Al-Watanieh Indian Private School, Ahmadi-Kuwait
First Term Weekly Test, 2023-24 (14-May-2023)
Mathematics – (Answer Key)
Class XI
Time:1 hour. Max. Marks: 30
General Instructions: Page Nos.: 4
1. All questions are compulsory
2. The question paper consists of 14 questions divided in to 5 sections A, B, C, D & E
3. Section A contains 6 MCQ of 1 mark each. Section B contains 3 questions of 2
marks each. Section C contains 3 questions of 3 marks each. Section D has 1 question on
case study. The case study has 4 case-based sub-parts of 1 mark each. Section E contains
one question of 5 mark.
Section A (1 mark each)
(Choose correct answers from the options given below)
1. If the number of non-empty proper subsets of a set is 255, the number of elements of the
set is
a) 10 b) 9 c) 8 d) none of these.
2. If A = {(x, y): x2 + y2 = 25} and B = {(x, y): x2 + 9y2 = 144} where x and y are integers,
the number of elements in A Ս B is
a) 8 b) 16 c) 12 d) none of these.
3. For any two sets A and B, A∩ (B ∩ A)ꞌ is
a) A b) B c) d) A – B
4. If A = {1, 2, 3, 4, 5}, the number of elements in the power set of A is
a) 5 b) 25 c) 32 d) none of these
DIRECTION: In question numbers 5 and 6, a statement of assertion (A) is followed by a
statement of reason (R)
Choose the correct option:
5. Assertion (A): If A = {1,2} and B = {3,5,7}, then number of all possible relations from A
to B is 32
Reason (R): If n(A) = p and n(B) = q, then number of all possible relations from A
to B = 2pq.
a) Both (A) and (R) are individually true and (R) is the correct explanation of (A)
b) Both (A) and (R) are individually 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
Page 1 of 4
6. Assertion (A): If the ordered pairs (p + 2, 4) and (5, 2p + q) are equal,
then p = 3 and q = – 2
Reason (R): Two ordered pairs are equal if their corresponding elements are equal.
a) Both (A) and (R) are individually true and (R) is the correct explanation of (A)
b) Both (A) and (R) are individually 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
Section-B (2 Marks each) (3 x 2 = 6)
7. If A = {x : x N and 1< x < 5} and B = {x : x N and 3 ≤ x ≤ 6}
Find (A∩B) U (B-A)
(A∩B) U (B-A) = {3,4} U {5, 6} = {3,4,5,6}.
OR
If A = {x : x = 2n, n N, n ≤ 6}, B = {x : x = 5n, n N, n ≤ 4}and
C = {x : x = 10n, n N, n ≤ 3}, find A ∩ (B Ս C)
A = {2,4,6,8,10,12}, B = {5,10,15,20}, C = {10,20,30}
A ∩ (B Ս C) = {2,4,6,8,10,12} ∩ {5,10,15,20,30} = {10}
8. If A and B are two sets such that A ⊂ B, draw a Venn diagram representing B – A.
9. A function f(x) = ax + b. Find the values of a and b if f (-1) = 1 and f (2) = 7
-a + b = 1
2a + b = 7
a = 2, b = 3
Section-C (3 Marks each) (3 x 3 = 9)
10. If A = {3, 4, 5, 6, 7}, B = {6, 7, 8} and the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Prove that: a) (A ∩B)ꞌ = Aꞌ U Bꞌ and b) (A U B)ꞌ = Aꞌ ∩ Bꞌ.
Aꞌ = {1,2,8,9,10}, Bꞌ = {1,2,3,4,5,9,10}, A ∩B = {6,7}, A U B = {3, 4, 5, 6, 7, 8, 9, 10}
a) (A ∩B)ꞌ = Aꞌ U Bꞌ = {1, 2, 3, 4, 5, 8, 9, 10}
b) (A U B)ꞌ = Aꞌ ∩ Bꞌ = {1,2}
11. Let R = {(x, y): x, y N and 2x + y = 9}, N being the set of all natural numbers.
Write R in Roster form. Also find the domain and range.
Page 2 of 4
Ans: R = {(1, 7), (2, 5), (3, 3), (4, 1)}
Domain = {1, 2, 3, 4} and Range = {1, 3, 5, 7}
𝑥 2 +3 𝑓(0)−𝑓(−1)
12. If f(x) = 2𝑥+1, find the value of 𝑓(1)+𝑓(−2)
𝑓(0)−𝑓(−1) 3+4
Ans: = 4 7 = −7
𝑓(1)+𝑓(−2) ( − )
3 3
OR
If A = {a, b}, find A × A× A
A × A× A = { (a,a,a), (,a,a,b), (a,b,a), (a,b,b), (b,a,a), (b,a,b), (b,b,a), (b,b,b)}
Section D (Case Study Based Question) (2 x 2 = 4)
13. Math teacher of class 11 writes three sets A, B and C such that
𝑛
A = {𝑥: 𝑥 = 𝑛2 +1
, 𝑛𝑁 𝑎𝑛𝑑 𝑛 ≤ 4 }
𝑛
B = {𝑥: 𝑥 = , 𝑛𝑊 𝑎𝑛𝑑 𝑛 < 4 } and
𝑛+1
C = {x: x is a solution of 2x2 – x = 0}
Based on the information answer the following questions:
(a) Write sets A, B and C in roaster form (2 mark)
𝟏 𝟐 𝟑 𝟒 𝟏 𝟐 𝟑 𝟏
A = {𝟐 , 𝟓 , 𝟏𝟎 , 𝟏𝟕}, B = {𝟎, 𝟐 , 𝟑 , 𝟒} and C = {𝟎, 𝟐}
𝟐 𝟑 𝟒 𝟐 𝟑 𝟐 𝟑 𝟒 𝟐 𝟑
(b) Find (A – C) Ս (B – C) = { 𝟓 , 𝟏𝟎 , 𝟏𝟕} Ս {𝟑 , 𝟒 } = = { 𝟓 , 𝟏𝟎 , 𝟏𝟕 , 𝟑 , 𝟒} (2 mark)
Page 3 of 4
Section E (5 Mark) (3+2 = 5)
14. (a) Draw the graph of the function f(x) = [x], where [x] is the greatest integer not
greater than x. Also write down the domain and its range. (3 mark)
Ans: Domain = R and Range = Z
(b) Also find the domain and range of the following functions. (2 mark)
(i) 𝑓(𝑥) = √𝑥 2 − 9, Ans: Domain = R – {3} and Range = [0, ∞)
|𝑥−3|
(ii) 𝑓(𝑥) = , Ans: Domain = R – {3} and Range = {-1, 1}
𝑥−3
Page 4 of 4
