NAVIGATOR_THE STUDY POINT
TOPIC- TEST
Practise sheet
DIS. DATE- _/_/__ BY-SHIVANSH SUDHA SUB.DATE-_/_/__
SECTION – A [1 x 10 objectives]
1. The set (A ∩ B′)′ ∪ (B ∩ C) is equal to
(A) A′ ∪ B ∪ C (B) A′ ∪
(C) A′ ∪ C′ (D) A′ ∩ B
2. In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play
both the games. Then, the number of students who play neither is
(A) 0 (B) 25 (C) 35 (D) 45
3. If A and B are two sets, then A ∩ (A ∪ B) equals
(A) A (B) B (C) φ (D) A ∩ B
4. Let n (A) = m, and n (B) = n. Then the total number of non-empty relations that can be defined from
A to B is
(A) mn (B) nm– 1 (C) mn – 1 (D) 2mn – 1
5. If f (x) = ax + b, where a and b are integers, f (–1) = – 5 and f (3) = 3, then a and b are equal to
(A) a = – 3, b = –1 (B) a = 2, b = – 3
(C) a = 0, b = 2 (D) a = 2, b = 3
6.
(A) R – {3, – 2} (B) R – {–3, 2}
(C) R – [3, – 2] (D) R – (3, – 2).
7. If tan θ = 3 and θ lies in third quadrant, then the value of sin θ is
8.
9. The value of (z + 3) ( z + 3) is equivalent to
(A) 2z +3]2 (B) z −3 (C) z2 + 3 (D) None of these
10.
(A) x = 2n+1 (B) x = 4n (C) x = 2n (D) x = 4n + 1, where n ∈N
SECTION –B [2 x 9 18]
11. In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking
coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor
coffee?
12. Draw appropriate Venn diagram for each of the following :
(i) (A ∪ B)′, (iii) (A ∩ B)′
13. Let A ={1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5), (2,9), (3,1), (4,5), (2,11)} Are the following true?
(i) f is a relation from A to B (ii) f is a function from A to B.
Justify your answer in each case.
14. Find the domain and the range of the real function f defined by f (X)
15. Find the domain and the range of the real function f defined by
16.
17. Find the degree measures corresponding to the following radian measures (Use 22 π 7 = )
(ii) – 4
18. (1 – i) 4
19. Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2
1. z = – 1 – i √ 3
SECTION – C [4 x 9 =36]
20. Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X, show that A = B.
21. In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26
read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three
newspapers. Find: (i) the number of people who read at least one of the newspapers. (ii) the number
of people who read exactly one newspaper
22.
23. Let R be a relation from N to N defined by R = {(a, b) : a, b ∈N and a = b2 }. Are the following true?
(i) (a,a) ∈ R, for all a ∈ N (ii) (a,b) ∈ R, implies (b,a) ∈ R
(iii) (a,b) ∈ R, (b,c) ∈ R implies (a,c) ∈ R.
24.
25. sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x
26.
27.
28.
