# WeCP Sets and Function Quiz 1

Question 1

Time: 00:00:00
While preparing for GATE, Tom was unable to solve a problem. Can you please help him out to solve this problem. The question is as follows:
The function f: R→R is defined by f(x)= sin4x + 2 + cos2x  for all x ∈ R. Then the range of f(x) is

$\left (2\frac{3}{4}, 3 \right ]$

$\left (2\frac{3}{4}, 3 \right ]$

$\left [ 2\frac{3}{4}, 3 \right )$

$\left [ 2\frac{3}{4}, 3 \right )$

$\left [ 2\frac{3}{4}, 3 \right ]$

$\left [ 2\frac{3}{4}, 3 \right ]$

$\left ( 2\frac{3}{4}, 3 \right )$

$\left ( 2\frac{3}{4}, 3 \right )$

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Question 2

Time: 00:00:00
Let X = {1, 7, 5, 6}   Y = {3, 2, 9, 8}   Z = {5, 9, 7, 6}, find  YΔ Z.

{2, 3, 5, 6, 7, 8}

{2, 3, 5, 6, 7, 8}

{9, 5, 2, 6, 7, 8}

{9, 5, 2, 6, 7, 8}

{2, 3, 7, 9, 1, 8}

{2, 3, 7, 9, 1, 8}

{2, 3, 6, 8, 9, 7}

{2, 3, 6, 8, 9, 7}

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Question 3

Time: 00:00:00
Find the intersection of A = {x | x ∈ N, x is a factor of 15} and B = {x | x ∈ N, x is a multiple of 2, x < 10}.

{1}

{1}

{3, 6, 10}

{3, 6, 10}

{∅}

{∅}

{}

{}

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Question 4

Time: 00:00:00
Given two sets A and B where A = {x : x is a letter in the word TESSLA} and  B = {x : x is a letter in the word LEAST}. Determine whether set A and set B are:

Equal

Equal

Not equal

Not equal

A<B

A<B

Can’t determine

Can’t determine

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Question 5

Time: 00:00:00
In JEE Advanced 2015 mock examination the following question was given: Let R={(5,3),(4,2), (6,4), (2,3), (3,5)} be a relation on the set A={2, 3, 4, 5, 6}. The relation R is

A function

A function

Not symmetric

Not symmetric

Transitive

Transitive

Reflexive

Reflexive

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Question 6

Time: 00:00:00
In GRE mock test, the following question was asked. The range of $f(x)={cos}^{-1}\left( \frac{1+{{x}^{2}}}{2x} \right)+\sqrt{2-{{x}^{2}}}$ is given by:

$\{ 1,\ 1+\frac{\pi }{2} \}$

$\{ 1,\ 1+\frac{\pi }{2} \}$

$\{ 0,\ 1+\frac{\pi }{2} \}$

$\{ 0,\ 1+\frac{\pi }{2} \}$

$\{ 0,\ 1+\pi \}$

$\{ 0,\ 1+\pi \}$

$\{ 1,\ 1+\pi \}$

$\{ 1,\ 1+\pi \}$

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Question 7

Time: 00:00:00
If {.} and [.] denote the greatest integer function and fractional part of a function then calculate the range of $f(x)= \left[\frac{1}{\sin \left\{ x \right\}} -1 \right]$.

Set of all integers

Set of all integers

Set of all whole numbers

Set of all whole numbers

Set of all natural numbers

Set of all natural numbers

Set of all non-positive integers

Set of all non-positive integers

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Question 8

Time: 00:00:00
Which of the following is the example of equal sets ?

Set A= APPLE, and Set B= PALE

Set A= APPLE, and Set B= PALE

Set A= ALLOY, and Set B= LOYAL

Set A= ALLOY, and Set B= LOYAL

Both of them

Both of them

None of them

None of them

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Question 9

Time: 00:00:00
In the maths exam, it is given that P = {4, 7, 9, 11, 12, 16, 18}, A = {4, 5, 7, 9, 12} and B = {7, 11, 12, 16,19}. Cardinality of (AU(P-B))

5

5

4

4

7

7

6

6

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Question 10

Time: 00:00:00
Write the following set in set-builder form. A = {27, 64, 125, 216, 343 . . . }

A = {x : x is the square of a natural number}

A = {x : x is the square of a natural number}

A = {x : x is the cube of n ∀ n∈[0, ∞) and n is natural number}

A = {x : x is the cube of n ∀ n∈[0, ∞) and n is natural number}

A = {x : x is the cube of all natural number}

A = {x : x is the cube of all natural number}

A = {x : x is the cube of n ∀ n∈[3, ∞) and n is natural number}

A = {x : x is the cube of n ∀ n∈[3, ∞) and n is natural number}

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