Topic: Chapter 1: Sets, Relations and Functions (Test 2)



Topic: Chapter 1: Sets, Relations and Functions
Q.1
The function f : R → R is defined by f(x) = sin x + cos x is
A. an odd function
B. neither an odd function nor an even function
C. an even function
D. both odd function and even function.
Answer : Option B
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Q.2
The function f : R → R is defined by f(x) =  is
A. an odd function
B. neither an odd function nor an even function
C. an even function
D. both odd function and even function.
Answer : Option B
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Q.3
If A = {(x, y) : y = ex, xR} and B = {(x, y) : y = e-x, x R} then n(A B) is
A. Infinity
B. 0
C. 1
D. 2
Answer : Option C
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Q.4
If A = {(x, y) : y = sin x, x R} and B = {(x, y) : y = cos x, x R} then A B contains
A. no element
B. infinitely many elements
C. only one element
D. cannot be determined
Answer : Option B
Explaination / Solution:
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Q.5
The relation R defined on a set A = {0,-1, 1, 2} by xRy if |x2 + y2| ≤  2, then which one of the following is true?
A. R = {(0, 0), (0,-1), (0, 1), (-1, 0), (-1, 1), (1, 2), (1, 0)}
B. R-1 = {(0, 0), (0,-1), (0, 1), (-1, 0), (1, 0)}
C. Domain of R is {0,-1, 1, 2}
D. Range of R is {0,-1, 1}
Answer : Option D
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Q.6
If {(x) = |x 2| + |x + 2|, x R, then
A.
B.
C.
D.
Answer : Option A
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Q.7

Let R be the set of all real numbers. Consider the following subsets of the plane R x  R:

S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x - y is an integer }

Then which of the following is true?
A. T is an equivalence relation but S is not an equivalence relation
B. Neither S nor T is an equivalence relation
C. Both S and T are equivalence relation
D. S is an equivalence relation but T is not an equivalence relation
Answer : Option A
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Q.8
Let A and B be subsets of the universal set N, the set of natural numbers. Then A’ [(AB)B’] is
A. A
B. A’
C. B
D. N
Answer : Option D
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Q.9
The number of students who take both the subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. The number of students take at least one of these two subjects, is
A. 1120
B. 1130
C. 1100
D. insufficient data
Answer : Option B
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Q.10
If n((A x B) (A x C)) = 8 and n(B C) = 2, then n(A) is
A. 6
B. 4
C. 8
D. 16
Answer : Option B
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