JEE Questions for Maths Sets Relations And Functions Quiz 6 - MCQExams.com

Let R be the relation over the set N × N and is defined by (a,b) R (c,d) ⇒ a + d = b + c Then R is
  • Reflexive only
  • Symmetric only
  • Transitive only
  • An equivalence relation
R = {(x, y) / x, y ϵ I, x2 + y2 ≤ 4} is a relation in I then domain of R is
  • {0,1,2}
  • {-2,-1,0}
  • {-2,-1,0,1,2}
  • {-2,-1}
An integer m is said to be related to another integer n if m is a multiple of n then the relation is
  • Reflexive and symmetric
  • Reflexive and transitive
  • Symmetric and transitive
  • Equivalence relation
If S is defined on R by (x,y) ϵ S ⇔ xy ≥ 0. Then S is......
  • an equivalence relation
  • reflexive only
  • symmetric only
  • transitive only
If A = {1,2,3}, then the number of equivalence relation containing (1,is
  • 1
  • 2
  • 3
  • 8
For n, m ϵ N n/m means that n is a factor of m, the relation / is
  • reflexive and symmetric
  • transitive and symmetric
  • reflexive transitive and symmetric
  • reflexive transitive and not symmetric
Let R be a relation on N defind by R = {(x, y) / x + 2y = 8} The domain of R is
  • {2,4,8}
  • {2,4,6,8}
  • {2,4,6}
  • {1,2,3,4}
A real valued function f(x) satisfies the functional equation f(x - y) = f(x) f(y) - f(3 - x) f (3 + y) where f(= 1, f(6 - x) is equal to
  • f(x)
  • f(3)
  • f(+ f(3 - x)
  • -f(x)
If f(2x + 3y, 2x - 3y) = 24xy then f(x, y) is
  • 2xy
  • 2(x2 - y2 )
  • x2 - y2
  • none of these

Maths-Sets Relations and Functions-49756.png

  • Maths-Sets Relations and Functions-49757.png
  • 2)
    Maths-Sets Relations and Functions-49758.png

  • Maths-Sets Relations and Functions-49759.png

  • Maths-Sets Relations and Functions-49760.png

Maths-Sets Relations and Functions-49762.png
  • tan2θ
  • sec2θ
  • cos2θ
  • cot2θ

Maths-Sets Relations and Functions-49764.png
  • {1,2}
  • {1,2,3}
  • {1,2,3,4,5}
  • {1}

Maths-Sets Relations and Functions-49766.png
  • [0,3]
  • [-1,1]
  • [0,1]
  • [-1,3]
Two finite sets have m and n elements respectively The total number of subsets of first set is 48 more than the total number of subsets of the second set and f = IN then f(m+n) is
  • 9
  • 10
  • 48
  • 15
If f: R → R defined by f(x) = x4 + 2 then the value of f -1(and f -1(-respectively are.
  • ϕ, {3,-3}
  • {3,-3}, ϕ
  • {4,-4}, ϕ
  • {4,-4}, {2,-2}
The domain of the definition of the function f(x) given by the equation ax + ay = a is ...... (a > 1)
  • 0 ≤ x ≤ 2
  • 0 ≤ x ≤ 1
  • - ∞ < x ≤ 0
  • - ∞ < x < 1
The domain of f(x) = log5 [log6 [log8 x]] is
  • x > 4
  • x > 8
  • x < 8
  • x < 4
If f(x) = 2x and g is identity function, then
  • (fog) (x) = g(x)
  • (gog) (x) = g(x)
  • (fog) (x) = (g + g) (x)
  • (fog) (x) = (f + f) (x)

Maths-Sets Relations and Functions-49773.png

  • Maths-Sets Relations and Functions-49774.png
  • 2)
    Maths-Sets Relations and Functions-49775.png

  • Maths-Sets Relations and Functions-49776.png

  • Maths-Sets Relations and Functions-49777.png
The range of f(x) = 6x + 3x + 6-x + 3x + 2 is subset of.....

  • Maths-Sets Relations and Functions-49778.png
  • 2)
    Maths-Sets Relations and Functions-49779.png

  • Maths-Sets Relations and Functions-49780.png

  • Maths-Sets Relations and Functions-49781.png
If f is satisfied the condition 2 f(x) + f(1 - x) = x2 , x ∈ R then f(x) = .....

  • Maths-Sets Relations and Functions-49783.png
  • 2)
    Maths-Sets Relations and Functions-49784.png

  • Maths-Sets Relations and Functions-49785.png

  • Maths-Sets Relations and Functions-49786.png
If f : R → R, f(x) = x2 + 1 then f -1(-∪ f -1(17)......
  • { ± 4}
  • { ± 1, ± 4}
  • {4}
  • {1,4}
For real x, if f (x)= x3 + 5x + 1, then
  • f is one-one but not onto R
  • f is onto R but not one-one
  • f is one-one and onto R
  • f is neither one-one nor onto R
The domain of the function F(x) = √cosx is

  • Maths-Sets Relations and Functions-49790.png
  • 2)
    Maths-Sets Relations and Functions-49791.png

  • Maths-Sets Relations and Functions-49792.png

  • Maths-Sets Relations and Functions-49793.png
If f(x) = 3 - x, where - 4 ≤ x ≤ 4, then the domain of loge [ f(x)] is
  • [- 4, 4]
  • (-∞,3]
  • (-∞,3)
  • [-4,3)

Maths-Sets Relations and Functions-49796.png
  • [0,π]
  • 2)
    Maths-Sets Relations and Functions-49797.png

  • Maths-Sets Relations and Functions-49798.png

  • Maths-Sets Relations and Functions-49799.png
If f : (-1,→ B is a function defined by
Maths-Sets Relations and Functions-49801.png

  • Maths-Sets Relations and Functions-49802.png
  • 2)
    Maths-Sets Relations and Functions-49803.png

  • Maths-Sets Relations and Functions-49804.png

  • Maths-Sets Relations and Functions-49805.png
If fk(x)= 1/k (sink x + cosk x), where X ∈ R and k ≥ 1, then f4 (x) - f6 (x) is equal to

  • Maths-Sets Relations and Functions-49807.png
  • 2)
    Maths-Sets Relations and Functions-49808.png

  • Maths-Sets Relations and Functions-49809.png

  • Maths-Sets Relations and Functions-49810.png
If f : N → Y is a function defined as f(x)= 4x + 3, where Y = {∀ ϵ N : y= 4x + 3 for some x ϵ N}. Then, inverse of f is

  • Maths-Sets Relations and Functions-49812.png
  • 2)
    Maths-Sets Relations and Functions-49813.png

  • Maths-Sets Relations and Functions-49814.png

  • Maths-Sets Relations and Functions-49815.png
The function f(x) which satisfies
Maths-Sets Relations and Functions-49817.png

  • Maths-Sets Relations and Functions-49818.png
  • 2)
    Maths-Sets Relations and Functions-49819.png

  • Maths-Sets Relations and Functions-49820.png

  • Maths-Sets Relations and Functions-49821.png

Maths-Sets Relations and Functions-49823.png

  • Maths-Sets Relations and Functions-49824.png
  • 2)
    Maths-Sets Relations and Functions-49825.png

  • Maths-Sets Relations and Functions-49826.png

  • Maths-Sets Relations and Functions-49827.png
Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is
  • 144
  • 12
  • 24
  • 64

Maths-Sets Relations and Functions-49830.png

  • Maths-Sets Relations and Functions-49831.png
  • 2)
    Maths-Sets Relations and Functions-49832.png

  • Maths-Sets Relations and Functions-49833.png

  • Maths-Sets Relations and Functions-49834.png

Maths-Sets Relations and Functions-49836.png

  • Maths-Sets Relations and Functions-49837.png
  • 2)
    Maths-Sets Relations and Functions-49838.png

  • Maths-Sets Relations and Functions-49839.png
  • None of these

Maths-Sets Relations and Functions-49841.png
  • 3
  • 6
  • 12
  • 9
Let A = {x : x is a multiple of 3}
B = {x : x is a multiple of 5}
Then A ∩ B is given by
  • {3, 6, 9, ….}
  • {5, 10, 15, 20,….}
  • {15, 30, 45, ….}
  • none of these

Maths-Sets Relations and Functions-49843.png
  • f is both one − one and onto
  • f is one − one but not onto
  • f is onto but not one − one
  • f is neither one − one nor onto
Let A = {a, b, d, e }
B = {c, d, f, m}
C = {a, l, m, o}
Then C ∩ (A ∪ B) will be given by
  • {a, d, l, m}
  • {b, c, l, o}
  • {a, l, m}
  • {a, b, c, d, f, l, m, o}
If sets A and B are defined as
A = {(x, y) : y = ex, x ∈ R}
B = {(x, y) : y = x, x ∈ R}. Then
  • B ⊆ A
  • A ⊆ B
  • A ∩ B = φ
  • A ∪ B = R
Let A be a set of containing 10 distinct elements. Then the total number of distinct functions from A to A is
  • 10!
  • 1010
  • 210
  • 210 – 1
A set contains n elements. The power set of A contains
  • n elements
  • 2n elements
  • n2 elements
  • none of these
Let S be a set containing n elements. Then the total number of binary operations on S is
  • nn
  • 2)
    Maths-Sets Relations and Functions-49845.png

  • Maths-Sets Relations and Functions-49846.png

  • Maths-Sets Relations and Functions-49847.png
The number of surjections from A = {1, 2, ….n}, n ≥ 2 onto B = {a, b} is

  • Maths-Sets Relations and Functions-49848.png
  • 2)
    Maths-Sets Relations and Functions-49849.png

  • Maths-Sets Relations and Functions-49850.png
  • None of these

Maths-Sets Relations and Functions-49851.png

  • Maths-Sets Relations and Functions-49852.png
  • 2)
    Maths-Sets Relations and Functions-49853.png

  • Maths-Sets Relations and Functions-49854.png
  • Not defined

Maths-Sets Relations and Functions-49856.png
  • [0] U [1, 3)
  • (–3, –1)
  • [1, 3)
  • (–3, 3)

Maths-Sets Relations and Functions-49858.png

  • Maths-Sets Relations and Functions-49859.png
  • 2)
    Maths-Sets Relations and Functions-49860.png

  • Maths-Sets Relations and Functions-49861.png

  • Maths-Sets Relations and Functions-49862.png

Maths-Sets Relations and Functions-49864.png
  • 1
  • 0
  • 2
  • 3

Maths-Sets Relations and Functions-49866.png
  • 63
  • 64
  • 65
  • 66

Maths-Sets Relations and Functions-49868.png

  • Maths-Sets Relations and Functions-49869.png
  • 2)
    Maths-Sets Relations and Functions-49870.png

  • Maths-Sets Relations and Functions-49871.png
  • None of these
If the function f : R → R be such that f(x) = x − [x], where [x] denotes the greatest integer less than or equal to x, then f−1(x) is

  • Maths-Sets Relations and Functions-49873.png
  • 2)
    Maths-Sets Relations and Functions-49874.png
  • not defined

  • Maths-Sets Relations and Functions-49875.png
0:0:1


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