Maths Quiz on Sets Relations And Functions for IIT JEE & Engineering Exam

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Maths Quiz on Sets Relations And Functions
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JEE Maths Quiz on Sets Relations And Functions

JEE Maths Quiz on Sets Relations And Functions : In this article you will get to Online test for JEE Main, JEE Advanced, UPSEE, WBJEE and other engineering entrance examinations that will help the students in their preparation. The Quiz on Sets Relations And Functions is free of cost and will useful in performance and inculcating knowledge.

Quiz on Sets Relations And Functions

 

Q1. If f (x) = cos (log x), then find the value of f (x) * f (4) − [1 / 2] * [f (x / 4) + f (4x)].
a) 16
b) 4
c) 0
d) 5

View Answer

c) 0

Solution:

f (x) = cos (log x)

Now let y = f (x) * f (4) − [1 / 2] * [f (x / 4) + f (4x)]

y = cos (log x) * cos (log 4) − [1 / 2] * [cos log (x / 4) + cos (log 4x)]

y = cos (log x) cos (log 4) − [1 / 2] * [cos (log x −log 4) + cos (log x + log 4)]

y = cos (log x) cos (log 4) − [1 / 2] * [2 cos (log x) cos (log 4)]

y = 0

Q2. If A = [(x, y) : x2 + y2 = 25] and B = [(x, y) : x2 + 9y2 = 144], then A ∩ B contains _______ points.
a) Two
b) Three
c) Four
d) Six

View Answer

c) Four

Solution:

A = Set of all values (x, y) : x2 + y2 = 25 = 52

B = [x2 / 144] + [y2 / 16] = 1

i.e., [x/ (12)2] + [y2 / (4)2] = 1.

Clearly, A ∩ B consists of four points.

Q3. Let f : R → R be defined by f (x) = 2x + |x|, then f (2x) + f (−x) − f (x) = _______.
a) 4|x|
b) 8|x|
c) 16|x|
d) 2|x|

View Answer

d) 2|x|

Solution:

f (2x) = 2 (2x) + |2x| = 4x + 2 |x|,

y = x2 + 1,

f (x) = 2x + |x|

f (2x) + f (−x) − f (x) = 4x + 2 |x| + |x| −2x − 2x − |x|

= 2|x|

Q4. If f (x) = cos [π2] x + cos[−π2] x, then find the function of the angle.
a) −1
b) 0
c) 1
d) 2

View Answer

a) −1

Solution:

f (x) = cos [π2] x + cos[−π2] x

f (x) = cos (9x) + cos (−10x)

= cos (9x) + cos (10x)

= 2 cos (19x / 2) cos (x / 2)

f (π / 2) = 2 cos (19π / 4) cos (π / 4);

f (π / 2) = 2 * −1 / √2 * 1/ √2

= −1

Q5. In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is ________.
a) 25
b) 35
c) 30
d) 20

View Answer

a) 25

Solution:

Let the number of newspapers be x.

If every student reads one newspaper, the number of students would be x (60) = 60x

Since every student reads 5 newspapers, the number of students = [x * 60] / [5] = 300

x = 25

 

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