If R is the real line. Consider the following subsets of the plane R × R S = {(x, y) : y x + 1 and 0 T = {(x, y) : x - y is an integer} Which one of the following is correct?

T is an equivalence relation on R but S is not

Neither S nor T is an equivalence relation on R

Both S and T are an equivalence relations on R

S is an equivalence relation on R but T is not

neither injective nor surjective

neither injective or not surjective

A function f : A → B, where A = {x : -1 ≤ X ≤ 1} and B = {y : 1 ≤ y ≤ 2} is defined by the rule y= f (x)= 1+ x 2 . Which of the following statement is correct?

f is surjective but not injective

f is injective but not surjective

f is both injective and surjective

f is neither injective nor surjective

JEE Questions for Maths Sets Relations And Functions Quiz 3

Universal set, U = {x : x⁵ - 6x⁴ + 11x³ - 6x² = 0} , A ={x:x² - 5x+ 6= O} and B = {x:x² - 3x+ 2= 0}. Then, (A ∩ B)' is equal to

0%
{1, 3}
0%
{1, 2, 3}
0%
{0, 1, 3}
0%
{0, 1, 2, 3}

If A = {χ : χ is a multiple of 3} and B = {χ : χ is a multiple of 5}. Then, A ∩ B is given by

0%
{3,6,9,...}
0%
{5,10,15,20,...}
0%
{15,30,45,...}
0%
None of these

Maths-Sets Relations and Functions-49424.png

0%
A ∩ B =A
0%
A ∩ B = B
0%
A ∩ B = ϕ
0%
None of these

If R is the real line. Consider the following subsets of the plane R × R
S = {(x, y) : y x + 1 and 0 < x < 2 }
T = {(x, y) : x - y is an integer}
Which one of the following is correct?

0%
T is an equivalence relation on R but S is not
0%
Neither S nor T is an equivalence relation on R
0%
Both S and T are an equivalence relations on R
0%
S is an equivalence relation on R but T is not

If W denotes the words in the English dictionary define the relation R by R= {(x, y) ∈ W × W : the words x and y have atleast one letter in common} . Then, R is

0%
reflexive, symmetric and not transitive
0%
reflexive, symmetric and transitive
0%
reflexive, not symmetric and transitive
0%
not reflexive, symmetric and transitive

Maths-Sets Relations and Functions-49428.png

0%
onto but not one-one
0%
one-one and onto
0%
neither one-one nor onto
0%
one-one but not onto

The function f : [0, 3] →[1, 29], defined by f(x)= 2x³ -15x² + 36x + 1,is

0%
one-one and onto
0%
onto but not one-one
0%
one-one but not onto
0%
neither one-one nor onto

If f(x) = (x + 1)² -1, X ≥ -1.Then,
Statement I The set {x : f (x) = f^-1(x)} = {0, -1}.
Statement II f is a bijection.

0%
Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statement I
0%
Statement I is correct, Statement II is correct; Statement II is not a correct explanation for Statement I
0%
Statement I is correct, Statement II is incorrect
0%
Statement I is incorrect, Statement 11 is correct

Maths-Sets Relations and Functions-49432.png

0%
injective but not surjective
0%
neither injective nor surjective
0%
surjective but not injective
0%
bijective

If R and C denote the set of real numbers and complex numbers, respectively.Then, the function f : C →R defined by f(z)= |z| is

0%
one-one
0%
onto
0%
bijective
0%
neither one-one nor onto

If f : N —> N defined by f(x) = X²+ x + 1,x ∈ N, then f is

0%
one-one and onto
0%
many-one and onto
0%
one-one but not onto
0%
None of the above

Maths-Sets Relations and Functions-49437.png

0%
surjective but not injective
0%
injective but not surjective
0%
bijective
0%
neither injective or not surjective

The mapping f : N → N given by f(n) = 1 +n², n ∈ N, where N is the set of natural numbers, is

0%
one-one and onto
0%
onto but not one-one
0%
one-one but not onto
0%
neither one-one nor onto

A function f : A → B, where A = {x : -1 ≤ X ≤ 1} and B = {y : 1 ≤ y ≤ 2} is defined by the rule y= f (x)= 1+ x². Which of the following statement is correct?

0%
f is injective but not surjective
0%
f is surjective but not injective
0%
f is both injective and surjective
0%
f is neither injective nor surjective

The function f : R → R given by f(x)= x³-1is

0%
a one-one function
0%
an onto function
0%
a bijection
0%
neither one-one nor onto

If A = [-1, 1] and f : A → A is defined as f(x) = x|x|,∀ x ∈ A, then f(x) is

0%
many-one and into function
0%
one-one and into function
0%
many-one and onto function
0%
one-one and onto function

The function f : R → R defined by f(x) = (x -1)(x -2)(x - 3)is

0%
one-one but not onto
0%
onto but not one-one
0%
both one-one and onto
0%
neither one-one nor onto

The function f : X → Y defined by f(x) = sin x is one-one but not onto, if X and Y are respectively equal to

0%
R and R
0%
[0,π] and [0,1]
0%
0%

If R denotes the set of all real numbers, then the function f : R → R defined by f(x)= lxl is

0%
only one-one
0%
only onto
0%
both one-one and onto
0%
neither one-one nor onto

Maths-Sets Relations and Functions-49447.png

0%
one-one and into
0%
neither one-one nor onto
0%
many-one and onto
0%
one-one and onto

Which one of the following is not correct for the feature of exponential function given by f(x) = b²,where b > 1?

0%
For very large negative values of x, the function is very close to 0
0%
The domain of the function is R, the set of real numbers
0%
The point (1, 0)is always on the graph of the function
0%
The range of the function is the set of all positive real numbers

If f(x) = |x - 2|, where x is a real number. Then, which one of the following is correct ?

0%
f is periodic
0%
f(x+y) = f(x) + f(y)
0%
f is an odd function
0%
f is not one- one function
0%
f is an even function

The range of the function f(x) = x²+ 2x + 2 is

0%
(1,∞ )
0%
(2,∞)
0%
(0,∞)
0%
[1,∞)
0%
(-∞,∞)

Maths-Sets Relations and Functions-49452.png

0%
0%
[0,1]
0%
0%
[0, ∞ )

If A = {1, 2, 3, 4} and R be the relation on A defined by {(a, b) : a, b ∈ A, a x b is an even number}, then find the range of R.

0%
{1,2,3,4}
0%
{2,4}
0%
{2,3,4}
0%
{1,2,4}

Find the domain of the function f (x) = (x²+1)/ (x²- 3x + 3).

0%
R - {1,2}
0%
R - {1,4}
0%
R
0%
R - {1}

Find the range of the function f : [0,1] → R, f(x)= x³-x²+ 4x + 2 sin^-1 x.

0%
[-(π+2), 0]
0%
[0,4+π]
0%
[2,3]
0%
(0,2+π]

If A = {1, 2, 3, 4, 5}, then find the domain in the relation from A to A by R = {(x, y) : y = 2x - 1}.

0%
{1, 2, 3}
0%
{1, 2}
0%
{1, 3, 5}
0%
{2, 4}

If f(x) = cos ax + sin x is periodic, then a must be

0%
irrational
0%
rational
0%
positive real number
0%
None of these

If f(x)= sin √x, then period of f(x) is

0%
π
0%
π/2
0%
2π
0%
None of these

The period of the function f(x)=|sin 2x|+ |cos 8x|is

0%
2π
0%
π
0%
2π/3
0%
π/2
0%
π/4

The even function is

0%
0%
2)
0%
0%

The period of the function f(θ ) = 4 + 4 sin³ θ - 3sinθ is

0%
0%
2)
0%
0%
π

Maths-Sets Relations and Functions-49472.png

0%
odd
0%
even
0%
neither odd nor even
0%
constant

Maths-Sets Relations and Functions-49474.png

0%
[2,12]
0%
[- 1,1]
0%
0%
0%
[6, 24]

Maths-Sets Relations and Functions-49478.png

0%
(-3,
0%
[-3, 3]
0%
(-∞,-∪ (3,∝)
0%
(-∞,-3] ∪ [3,∝)

Maths-Sets Relations and Functions-49480.png

0%
(-∞,-∞)
0%
[-1,1]
0%
0%
[-√2, √2]

if f is a function with domain [- 3, 5] and g(x) = |3x + 4|. Then, the domain of (fog) (x) is

0%
0%
2)
0%
0%

The domain of the function f(x) = log 2 [log 3 (log4 x)] is

0%
(-∞,4)
0%
(4,∝)
0%
(0,4)
0%
(1,∝)
0%
(-∞,1)

The domain of definition of the function
Maths-Sets Relations and Functions-49489.png

0%
-∞ < x ≤ 0
0%
2)
0%
-∞ < x ≤ 1
0%
x ≥ 1 -e

Maths-Sets Relations and Functions-49492.png

0%
(-∞,0)
0%
(-∞,2)
0%
(-∞,∞)
0%
None of these

The domain of the real function
Maths-Sets Relations and Functions-49494.png

0%
the set of all real numbers
0%
the set of all positive real numbers
0%
(- 2, 2)
0%
[- 2, 2]

The domain of
Maths-Sets Relations and Functions-49496.png

0%
[1, 9]
0%
[-1, 9]
0%
[- 9, 1]
0%
[- 9, -1]

If f : R → R and g : R → R are defined by f(x)= Ix I and g(x)=-[x - 3] for x ℇ R, then
Maths-Sets Relations and Functions-49498.png

0%
{0, 1}
0%
{1, 2}
0%
{-3, -2}
0%
{2, 3}

The Period of the function
Maths-Sets Relations and Functions-49500.png

0%
π
0%
2π
0%
0%
None of these

The range of the function
Maths-Sets Relations and Functions-49503.png

0%
[1,∝)
0%
[2,∝)
0%
0%
None of these

If f(x) is an even function and f ' (x) exists, then f ' (e) + f ' (-e) is

0%
> 0
0%
= 0
0%
≥ 0
0%
< 0

If n is the natural number. Then, the range of the function f(n) = ^{8 - n} p_{n - 4}, 4 ≤ n ≤ 6, is

0%
{1, 2, 3, 4}
0%
{1, 2, 3, 4, 5, 6}
0%
{1, 2, 3}
0%
{1, 2, 3, 4, 5}
0%
∅

The domain of the function
Maths-Sets Relations and Functions-49508.png

0%
(1,∝)
0%
2)
0%
(0,∝)
0%
None of these

Maths-Sets Relations and Functions-49511.png

0%
0%
2)
0%
0%

JEE Questions for Maths Sets Relations And Functions Quiz 3 - MCQExams.com

0:0:1

Practice Maths Quiz Questions and Answers

JEE Questions for Maths Sets Relations And Functions Quiz 3 - MCQExams.com

0:0:1

Practice Maths Quiz Questions and Answers

Support mcqexams.com by disabling your adblocker.