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This mock test of Test Level 1: Relations And Functions- 2 for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE Test Level 1: Relations And Functions- 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If f (x) equals

Solution:

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

QUESTION: 2

If A = {(x,y):x^{2}+y^{2} = 25} and B = {(x,y) : x^{2}+9y^{2}+y^{2} = 144} then A∩B contains

Solution:

A is the set of all points on the circle x^{2} + y^{2} = 25 and B is the set of all points on the ellipse x^{2} + 9y^{2} = 144. These two intersect at four points P,Q,R and S.

Hence, A∩B contains four points.

QUESTION: 3

Solution:

QUESTION: 4

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

Solution:

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

Solution:

QUESTION: 6

The domain of the function

Solution:

QUESTION: 7

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

Solution:

A = {(x, y) : x^{2}+y^{2} = 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

QUESTION: 8

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

Solution:

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 ?

Solution:

QUESTION: 10

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

Solution:

sin(sinx/3)

As we know that {T : 2π}

T = (sinx/3)

2π = (sinx/3)

Period = 6π

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

Solution:

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)

QUESTION: 12

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

Solution:

QUESTION: 13

For all x ∈ (0, 1)

Solution:

QUESTION: 14

The domain of the function

Solution:

f(x) = (1-x)^{½} + (6-x)^{½}

x-1≥0 6-x≥0

x≥1 x≤6

= [1,6]

QUESTION: 15

Let f (x) = x^{2} and g (x) = √x, then

Solution:

QUESTION: 16

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

Solution:

QUESTION: 17

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

Solution:

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 2^{3} = 8

So, B = {{1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},{empty set}} and the number of elements are 8.

QUESTION: 18

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

Solution:

QUESTION: 19

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

Solution:

QUESTION: 20

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

then (gof)(e) + (fog)(π) =

Solution:

QUESTION: 21

Solution:

QUESTION: 22

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

Solution:

QUESTION: 23

Coefficient of x^{3} in the expansion of tan x is

Solution:

QUESTION: 24

then (fof) (2) is equal to

Solution:

QUESTION: 25

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

Solution:

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