JEE Questions for Maths Sets Relations And Functions Quiz 5 - MCQExams.com

if f : R → R is defined as f(x) = (1-x)1/3, then f-1(x) is equal to
  • (1-x)-1/3
  • (1-x)3
  • 1-x3
  • 1-x1/3
If f(x) = ex and g(x) = loge x, then which of the following is correct?
  • f{g(x)} ≠ { g{ f(x)}
  • f {g(x)} = g{ f(x)}
  • f{g(x)} + g{f(x)} = 0
  • f{g(x)} - g{f(x)} = 1
If f : R → R is defined by f(x) = x3 , then f-1(is equal to
  • {2}
  • {2, 2ω, 2ω2}
  • {2, -2}
  • {2, 2}

Maths-Sets Relations and Functions-49655.png
  • [f(x)]3
  • [f(x)]2
  • -f(x)
  • f(x)
  • 3f(x)
The function
Maths-Sets Relations and Functions-49657.png
  • f(x+- 2f(x++ f(x) = 0
  • f(x) + f(x+= f{x(x+1)}

  • Maths-Sets Relations and Functions-49658.png
  • f(x+y) = f(x) f(y)
If f(x) = [x - 2] , where [x] denotes the greatest integer less than or equal to x, then f(2.is equal to

  • Maths-Sets Relations and Functions-49660.png
  • 0
  • 1
  • does not exist
If f : R → R is defined by f(x) = |x| , then
  • f-1(x) = -x
  • 2)
    Maths-Sets Relations and Functions-49662.png
  • f-1(x) does not exit

  • Maths-Sets Relations and Functions-49663.png
Let [x] denotes the greatest integer ≤ x. If f(x) = [x] and g(x) = |x|, then the value of
Maths-Sets Relations and Functions-49665.png
  • 2
  • -2
  • 1
  • 0
  • -1
The inverse of the function
Maths-Sets Relations and Functions-49667.png

  • Maths-Sets Relations and Functions-49668.png
  • 2)
    Maths-Sets Relations and Functions-49669.png

  • Maths-Sets Relations and Functions-49670.png
  • None of these
If the functions f, g and h are defined from the set of real numbers R to R such that f(x) = x2 - 1, g(x) = √(x2 +and
Maths-Sets Relations and Functions-49672.png
  • x
  • x2
  • 0
  • None of these
If g(x) = 1 + x and
Maths-Sets Relations and Functions-49674.png
  • x
  • 1
  • f(x)
  • g(x)
If f(= 1, f(= 5 and f(= 11, then the equation of polynomial of degree two is
  • x2 + 1 =0
  • x2 + 3x + 1 = 0
  • x2 - 2x+ 1 = 0
  • None of these
If [x] denotes the greatest integer ≤ x, then
Maths-Sets Relations and Functions-49677.png
  • 99
  • 98
  • 66
  • 65
  • 33
If f(x) = cos(log x), then
Maths-Sets Relations and Functions-49679.png
  • -1
  • 2)
    Maths-Sets Relations and Functions-49680.png
  • -2
  • 0
If
Maths-Sets Relations and Functions-49682.png

  • Maths-Sets Relations and Functions-49683.png
  • 2)
    Maths-Sets Relations and Functions-49684.png

  • Maths-Sets Relations and Functions-49685.png

  • Maths-Sets Relations and Functions-49686.png
If
Maths-Sets Relations and Functions-49688.png

  • Maths-Sets Relations and Functions-49689.png
  • 2)
    Maths-Sets Relations and Functions-49690.png

  • Maths-Sets Relations and Functions-49691.png
  • x
If
Maths-Sets Relations and Functions-49693.png
  • x = f(y)
  • f(= 3
  • y increases with x for x < 1
  • f is a rational function of x
Which of the following functions is inverse of itself ?

  • Maths-Sets Relations and Functions-49695.png
  • f(x) = 3logx
  • f(x) = 3 x(x+1)
  • None of these

Maths-Sets Relations and Functions-49697.png
  • A=3, B=6, C=2, D=5
  • A=3, B=4, C=2, D=5
  • A=4, B=3, C=2, D=1
  • A=3, B=6, C=5, D=2
The second degree polynomial f(x), satisfying f(= 0, f(1)=1, f'(x) > 0, ∀ x ϵ (0,is
  • f(x) = ∅
  • f(x)= ax + (1- a)x2,V a ϵ (0,.)
  • f(x)= ax + (1- a)x2 , a ϵ (0,2)
  • no such polynomials
If X and Y are two non-empty sets, where f : X → Y is function is defined such that
f(C)= {f(x) : x ϵ C} for C ⊆ X
and f-1 (D).= {x : f(x) ϵ D} for D ⊆ Y,
for any A ⊆ X and B ⊆ Y, then
  • f-1 {f(A )} = A only if A c X
  • f-1 {f(A )} = A only if f(X ) = Y
  • f{f-1 (B)}=B only if B f(X ) ⊆ f(x)
  • f {f-1 (B )} = B
The function f satisfies the functional equation
Maths-Sets Relations and Functions-49701.png
  • 8
  • 4
  • -8
  • 11
  • 44

Maths-Sets Relations and Functions-49703.png
  • √2
  • -√2
  • 1
  • 2
  • -1
If f(x + y, x - y) = xy, then the arithmetic mean of f(x, y) and f(y, x) is
  • x
  • y
  • 0
  • None of these
The function f : C → C defined by
Maths-Sets Relations and Functions-49706.png
  • a = c
  • b = d
  • ad = bc
  • ab = cd
The values of b and c for which the identity f(x +- f(x) = 8x + 3 is satisfied, where f(x) = bx2 + cx + d , are
  • b = 2, c = 1
  • b = 4, c = -1
  • b= -1, c = 4
  • b= -1, c =1
If f(2x += sin x+2x , then ,f(4m- 2 n + 3)is equal to
  • sin (m - 2 n) + 22m-n
  • sin (2m- n) + 2(m-n)2
  • sin (m- 2 n) + 2(m+n)2
  • sin (2m- n) + 2m-n
If f(χ) is a polynomial function of the second degree such that, f(-= 6, f(= 6 and f(= 11, then the graph of the function, f(χ) cuts the ordinate χ = 1at the point
  • (1, 8)
  • (1,4)
  • (1,-2)
  • None of these

Maths-Sets Relations and Functions-49711.png

  • Maths-Sets Relations and Functions-49712.png
  • 2)
    Maths-Sets Relations and Functions-49713.png

  • Maths-Sets Relations and Functions-49714.png
  • None of these

Maths-Sets Relations and Functions-49716.png

  • Maths-Sets Relations and Functions-49717.png
  • 2)
    Maths-Sets Relations and Functions-49718.png

  • Maths-Sets Relations and Functions-49719.png

  • Maths-Sets Relations and Functions-49720.png

Maths-Sets Relations and Functions-49722.png

  • Maths-Sets Relations and Functions-49723.png
  • 2)
    Maths-Sets Relations and Functions-49724.png

  • Maths-Sets Relations and Functions-49725.png

  • Maths-Sets Relations and Functions-49726.png

  • Maths-Sets Relations and Functions-49727.png

Maths-Sets Relations and Functions-49729.png
  • (-3,2)
  • [-3,2)
  • (-3,2]
  • [-3,2]

Maths-Sets Relations and Functions-49731.png
  • d + a = 0
  • d – a = 0
  • a = b = c
  • a = b = 1

Maths-Sets Relations and Functions-49733.png
  • 2
  • 1
  • 3
  • None of these

Maths-Sets Relations and Functions-49735.png
  • (− ∞, −
  • [0, ∞ )
  • (− ∞, −∪ [0, ∞)
  • None of these
If aN = {ax/x∈N} and bN ∩ cN = dN Where b,c ∈ N are relatively prime then
  • d = bc
  • c = bd
  • b = cd
  • a = bd

Maths-Sets Relations and Functions-49737.png
  • {(2,3,5)}
  • {(1,4,5)}
  • {(5,1,4)}
  • {(2,3,5), (1,4,5)}
If set A is empty set then n [P[P[P(A) ] ] ] = ⋯
  • 6
  • 16
  • 2
  • 4
A and B are two sets n(A - B) = 8 + 2x, n(B - A) = 6x and n(A ∩ B) = x. If n(A) = n(B) then n(A ∩ B) = ...
  • 26
  • 50
  • 24
  • none of these
A={(a,b) / b = 2a - 5} If (m,and (6,n) are the member of set A then m and n are respectively
  • 5,7
  • 7,5
  • 2,3
  • 5,3
In a collage of 400 students every students read 5 newspapers and every news paper is read by 80 students. The number of news paper is
  • 25
  • at the most 20
  • at the most 25
  • at least 25

Maths-Sets Relations and Functions-49740.png
  • {-1,1,i,-i}
  • {-1,1}
  • {i, -i}
  • {-1,1,i}
If A={n3 + (n+1)3 + (n+z)3 ; n ϵN} and B = {9n, n ϵ N} then
  • A ⊂ B
  • B ⊂ A
  • A = B
  • A' = B
If n(A) = 6 and n (B) = 4 then minimum value of n(A - B) is
  • 2
  • 7
  • 6
  • 4
If n(A) = 3, n(B) = 5 and n(A ∩ B) = 2 then n [(A × B) ∩ (B × A)] = ..........
  • 5
  • 3
  • 4
  • 6
If A = {1,3,5,7,9,11,13,15,17}, B = {2,4,...18} and N is the universal set then A\'∪ (A ∪ (B ∩ B\')) is
  • A
  • B
  • A ∪ B
  • N
Taking U = [1,5], A = {x / x ϵ N, x2 - 6x + 5 = 0} A\' = ....
  • {1,5}
  • (1,5)
  • [1,5]
  • [-1, -5]
Let R be a reflexive relation of a finite set A having n elements and let there be m ordered pairs in R. Then
  • m ≥ n
  • m ≤ n
  • m = n
  • None of these
If A is the set of even natural numbers less then 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is
  • 29
  • 92
  • 32
  • 29 - 1
Given the relation on R = {(a, b), (b, c)} in the set A = {a, b, c} Then the minimum number of ordered pairs which added to R make it an equivalence relation is
  • 5
  • 6
  • 7
  • 8
0:0:1


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