Test: Relations & Functions- 4 - JEE MCQ

# Test: Relations & Functions- 4 - JEE MCQ

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## 25 Questions MCQ Test Chapter-wise Tests for JEE Main & Advanced - Test: Relations & Functions- 4

Test: Relations & Functions- 4 for JEE 2024 is part of Chapter-wise Tests for JEE Main & Advanced preparation. The Test: Relations & Functions- 4 questions and answers have been prepared according to the JEE exam syllabus.The Test: Relations & Functions- 4 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Relations & Functions- 4 below.
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Test: Relations & Functions- 4 - Question 1

### If f (x)  equals

Detailed Solution for Test: Relations & Functions- 4 - Question 1

f(x) = (x−1)/(x+1)
1/f(x) = (x+1)/(x-1)
f(1/f(x)) = [(x+1)/(x-1) - 1]/[(x+1)/(x-1) + 1]
⇒ (x+1-x+1)/(x+1+x-1)
= 2/2x
= 1/x

Test: Relations & Functions- 4 - Question 2

### If A = {(x,y):x2+y2 = 25} and B = {(x,y) : x2+9y2+y2 = 144} then A∩B contains

Detailed Solution for Test: Relations & Functions- 4 - Question 2

A is the set of all points on the circle x2 + y2 = 25 and B is the set of all points on the ellipse x2 + 9y2 = 144. These two intersect at four points P,Q,R and S.
Hence, A∩B contains four points.

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Test: Relations & Functions- 4 - Question 3
Test: Relations & Functions- 4 - Question 4

The function f(x) = log (1+x/1-x) satisfies the equation

Test: Relations & Functions- 4 - Question 5

If f(x + y + z) = f(x) f(y) f(z) for all x , y z and if f(2) = 4, f’(0) = 5 and f(0) ≠ 0, then f’(2) is equal to

Detailed Solution for Test: Relations & Functions- 4 - Question 5

Test: Relations & Functions- 4 - Question 6

The domain of the function

Detailed Solution for Test: Relations & Functions- 4 - Question 6

Test: Relations & Functions- 4 - Question 7

If A = {(x, y) : x2+y2 = 5} and B = {(x, y) : 2x = 5y}, then A∩B contains

Detailed Solution for Test: Relations & Functions- 4 - Question 7

A = {(x, y) : x2+y2 = 5} B = {2x = 5y}
A is the set of all the points on a circle with centre (0, 0)
B is the set of all points on a line with slope 2/5 and passing through (0, 0)
So, the circle and the line intersect at two points.
So, A ∩ B contains two points

Test: Relations & Functions- 4 - Question 8

If f : R → R is given by f(x) = |x| and A = {x∈R:x<0}, then f-1 (A) equals

Test: Relations & Functions- 4 - Question 9

If f : N × N →N is such that f (m, n) = m + n where N is the set of natural number, then which of the following is true ?

Test: Relations & Functions- 4 - Question 10

The function (sin x/3) is periodic with period

Detailed Solution for Test: Relations & Functions- 4 - Question 10

sin(sinx/3)
As we know that {T : 2π}
T = (sinx/3)
2π = (sinx/3)
Period = 6π

Test: Relations & Functions- 4 - Question 11

If A = [a, b], B = [c,d], C = [d, e] then {(a, c), (a, d), (a,e), (b,c), (b, d), (b, e)} is equal to

Detailed Solution for Test: Relations & Functions- 4 - Question 11

Clearly, the set of first elements of ordered pairs in the given set is (a,b) and the set of second elements is {c, d, e}.
∴ {(a,c),(a,d),(a,e),(b,c),(b,d),(b,e)}
∴ {(a,c),(a,d),(a,e),(b,c),(b,d),(b,e)}
= {a,b}×{c,d,e}=A×(B∪C)

Test: Relations & Functions- 4 - Question 12

The function f(x) = 10x from R to [0, ∞) is

Test: Relations & Functions- 4 - Question 13

For all x ∈ (0, 1)

Test: Relations & Functions- 4 - Question 14

The domain of the function

Detailed Solution for Test: Relations & Functions- 4 - Question 14

f(x) = (1-x)½ + (6-x)½
x-1≥0   6-x≥0
x≥1        x≤6
= [1,6]

Test: Relations & Functions- 4 - Question 15

Let f (x) = x2 and g (x) = √x, then

Test: Relations & Functions- 4 - Question 16

Suppose that g (x) = 1+ √x and f(g(x)) = 3 + 2 √x + x, then f (x) is

Detailed Solution for Test: Relations & Functions- 4 - Question 16

Test: Relations & Functions- 4 - Question 17

The number of elements in the Power set P(S) of the set S = [[Φ], 1, [2, 3]] is

Detailed Solution for Test: Relations & Functions- 4 - Question 17

A = {1,2,3}
B : set of all subsets of A
List out all the subsets of A - {1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},{empty set}
Number of elements in A (n) = 3 so 23 = 8
So, B = {{1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},{empty set}} and the number of elements are 8.

Test: Relations & Functions- 4 - Question 18

The minimum value of (x - α) (x – β) is

Detailed Solution for Test: Relations & Functions- 4 - Question 18

Test: Relations & Functions- 4 - Question 19

If f(x) = (25 - x4)1/4 for 0 < x < √5, then f(f(1/2)) =

Detailed Solution for Test: Relations & Functions- 4 - Question 19

Test: Relations & Functions- 4 - Question 20

Two functions f:R→R g : R→Rare defined as follows :

then (gof)(e) + (fog)(π) =

Test: Relations & Functions- 4 - Question 21

Test: Relations & Functions- 4 - Question 22

Let function f : R → R be defined by f(x) = 2x + sin x for x ∈ R. Then f is

Test: Relations & Functions- 4 - Question 23

Coefficient of x3 in the expansion of tan x is

Test: Relations & Functions- 4 - Question 24

then (fof) (2) is equal to

Test: Relations & Functions- 4 - Question 25

If f(x) = log (1+x/1-x), then f(x) is

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