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**

**Explaination / Solution: **

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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**

**Explaination / Solution: **

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If A = {(x, y) : y = e^{x}, x∈R} 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**

**Explaination / Solution: **

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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: **

No Explaination.

No Explaination.

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The relation R defined on a set A = {0,-1, 1, 2} by xRy if |x^{2} + y^{2}| ≤ 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**

**Explaination / Solution: **

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If {(x) = |x – 2| + |x + 2|, *x* ∊ R, then

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option A**

**Explaination / Solution: **

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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 }

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Let A and B be subsets of the universal set N,
the set of natural numbers. Then A’∪ [(A∩B)∪B’] is

**A. ** A

**B. ** A’

**C. ** B

**D. ** N

**Answer : ****Option D**

**Explaination / Solution: **

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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**

**Explaination / Solution: **

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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**

**Explaination / Solution: **

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