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JEE Questions for Maths Sets Relations And Functions Quiz 2 - MCQExams.com
JEE
Maths
Sets Relations And Functions
Quiz 2
If R is a relation defined as aRb, iff |a - b|> 0, then the relation is
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reflexive
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symmetric
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transitive
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symmetric and transitive
R is a relation on N given by R = { (x, y) : 4x + 3y = 20 }. Which of the following belongs to R?
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(- 4,
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(5, 0)
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(3, 4)
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(2, 4)
If A = {l, 2, 3} and B = {2, 3, 4}, then which of the following relations is a function from A to B?
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{(1, 2), (2, 3), (3, 4), (2, 2)}
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{(1, 2), (2, 3), (1, 3)}
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{(1, 3), (2, 3), (3, 3)}
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{(l, 1), (2, 3), (3, 4)}
If R is a relation from {11, 12,13} to {8, 10,12} defined by y = x - 3. Then, R
-1
is equal to
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{(8, 11), (10, 13)}
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{(11, 18), (13, 10)}
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{(10, 13), (8, 11)}
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None of these
On the set N of all natural numbers define the relation R by aRb, if and only if the GCD of a and b is 2, then R is
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reflexive but not symmetric
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only symmetric
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reflexive and transitive
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reflexive, symmetric and transitive
If R= {(1,3), (4, 2), (2, 4), (2, 3), (3, 1)1 is a relation on the set A = {1, 2, 3, 4}. Then, relation R is
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a function
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transitive
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not symmetric
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reflexive
If R = [(3,3), (6, 6), (9,9),(12, 12), (6,12),(3, 9), (3,(3, 6)} is a relation on the set A = {3, 6, 9,12}. Then, the relation is
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reflexive and symmetric
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an equivalence relation
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reflexive only
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reflexive and transitive
If R is an equivalence relation on a set A, then R
-1
is
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only reflexive
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symmetric but not transitive
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equivalence
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None of the above
The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3} is given by
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{(1, 4), (2, 5), (3, 6), ...1
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1(4, 1), (5, 2), (6, 3), ...1
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1(1, 3), (2, 61 (3, 9), ...1
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None of the above
Which of the following statements is not correct for the relation R defined by aRb, if and only if b lives within one kilometre from a?
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R is reflexive
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R is symmetric
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R is anti-symmetric
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None of the above
Explanation
R is not anti - symmetric.
If R is a relation on the set of integers given by aRb 4 => a = 2
k
.b for some integer k. Then, R is
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an equivalence relation
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reflexive but not symmetric
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reflexive and transitive but not symmetric
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reflexive and symmetric but not transitive
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symmetric and transitive but not reflexive
x
2
= xy is a relation which is
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0%
symmetric
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reflexive and transitive
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transitive
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None of the above
If A ={1, 3, 5, 7} and B = {1, 2, 3, 4, 5, 6, 7, 8}, then the number of one-one function from A into B is
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1340
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1860
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1430
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1880
0%
1680
The function f(x) = x
2
+ bx + c, where b and c are real constants, describes
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one-one mapping
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onto mapping
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not one-one but onto mapping
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neither one-one nor onto mapping
The total number of injections (one-one and into mappings) from{a
1
,a
2
,a
3
,a
4
} to {b
1
,b
2
,b
3
,b
4
,b
5
,b
6
,b
7
} is
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0%
400
0%
420
0%
800
0%
840
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one-one and onto
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one-one but not onto
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not one-one but onto
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neither one-one nor onto
A = {l, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6} are two sets and function f : A → B is defined by f(x) = x + 2, ∀ x ∈ A, then the function f is
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bijective
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onto
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one-one
0%
many-one
If f : R → C is defined by f(x) = e
2ix
for x ∈ R, then f is (where, C denotes the set of all complex numbers
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0%
one-one
0%
onto
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one-one and onto
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neither one-one nor onto
If A is a set containing 10 distinct elements, then the total number of distinct function from A to A is
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1010
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101
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210
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210-1
If f(x) is an odd periodic function with period 2, then f(is equal to
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-4
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4
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2
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0
The period of sin
2
θ is
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π2
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π
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2π
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π/2
If f : [2, 3] → R is defined by f(x) = x
3
+ 3x - 2 , then the range f(x) is contained in the interval
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[1, 12]
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[12, 34]
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[35, 50]
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[-12,12]
The period of the function f(x) = cosec
2
3x + cot 4x is
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0%
0%
2)
0%
0%
π
The function
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an even function
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an odd function
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a periodic function
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neither an even nor an odd function
The domain of the function
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[0, 2]
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[0,
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[1,
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[1. 2]
If f : R → R is defined by f (x)= x - [x] - 1/2 for x ∈ R, where [x] is the greatest integer not exceeding x, then
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Z, the set of all integers
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N, the set of all natural numbers
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0, the empty set
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R, the set of all rational numbers
Range of the function
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(-1, 0)
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(-1, 1)
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[0,
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(1, 1)
The domain of the function f(x) = loge (x - [x]) is
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R
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R - Z
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(0, +∞ )
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Z
The range of the function f(x) = x
2
- 6x + 7 is
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(-∞,0)
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(-2,∞)
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(-∞,∞)
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(-∞,-2)
If R is the set of real numbers and the functions f : R → R and g : R → R be defined by f(x) = x
2
+ 2x -- 3 and g(x) = x + 1. Then, the value of x for which f(g(x)) = g( f(x)) is
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0%
-1
0%
0
0%
1
0%
2
If f : R → R and g : R → R are defined by f(x) = x - 3 and g(x ) = x
2
+ 1, then the values of x for which g {f(x)} = 10 are
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0.-6
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2,-2
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1,-1
0%
0,6
0%
0,2
If f : [-6, 6] → R is defined by f(x) = x
2
- 3 for x ϵ R, then (fofof )(-1)+ (fofof)(+ ( fofof)(is equal to
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f(4√2)
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f(3√2)
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f(2√2)
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f(√2)
If
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d = - a
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d = a
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a = b = c = d = 1
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a = b = 1
If the graph of the function of y = f(x) is symmetrical about the line x = 2, then
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f(x += f(x -
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f(2 + x) = f(2 - x)
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f(x) = f(-x)
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f(x) = - f(-x)
If f(x)• f(1/x) = f(x) + f(1/ x) and f(= 65,then f(is equal to
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65
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217
0%
215
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64
If f(x) = ax + b, g(x) = cx + d, then f{g(x)} = g {f(x)} is equivalent to
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f(a) = g(c)
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f(b) = g(b)
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f(d) = g(b)
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f(c) = g(a)
If Q denotes the set of all rational numbers and f (p/q) = √p
2
- √q
2
for any p/q ϵ Q, then observe the following statements. I. f(p/q) is real for each p/q ϵ Q II. f(p/q) is a complex number for each p/q ϵ Q
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Both I and II are correct
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I is correct, II is incorrect
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I is incorrect, II is correct
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Both I and II are incorrect
If f : R → R and g : R → R are defined by f(x) = x -[x] and g(x) = [x] for x ϵ R, where [x] is the greatest integer not exceeding x, then for every x ϵ R, f (g(x)) is equal to
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x
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0
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f(x)
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g(x)
If f : R → R is given by
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1
0%
-1
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√3
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0
If f(x) = (a-x
n
)
1/n
, where a > 0 and n ϵ N, then fof(x) is equal to
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a
0%
x
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xn
0%
an
If f : (2,→ (0,is defined by f(x) = x - [x] , then f
-1
(x) is equal to
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x - 2
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x + 1
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x - 1
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x + 2
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(1, 4)
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[1, 4)
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(1, 4]
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[1, 4]
If X = {4
n
- 3n - 1: n ∈ N} and Y = {9(n - 1): n ∈ N}, where N is the set of natural numbers, then X ∪ Y is equal to
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N
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Y - X
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X
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Y
The set A = {x : |2x + 3| < 7} is equal to the set
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D = { x : 0 < x+5 < 7 }
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B = { x : -3 < x < 7 }
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E = { x : -7 < x < 7 }
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C = { x : -13 < 2x < 4 }
If the number of elements of the sets A and B are p and q, respectively. Then, the number of relations from the set A to the set B is
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2p+q
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2pq
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p+q
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pq
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a singleton set
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not a finite set
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an empty set
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a finite set with more than one element
If A = {(x,y) : y = e
-x
} and B = {(x,y) : y = -x}. Then,
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A ∩ B = ϕ
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A ⊂ B
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B ⊂ A
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A ∩ B = {(0,1),(0,0)}
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R - {0}
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R - {0,1,3}
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R - {0,-1,-3}
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If A = {a, b, c}, B = {b, c, d} and C = {a, d , c}, then (A - B) x (B ∩ C) is equal to
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{(a, c), (a, d)}
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{(a,b),(c,d)}
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{(c, a), (d, a)}
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{(a, c), (a, d), (b, d)}
If Z denotes the set of all integers and A = {(a,b):a
2
+ 3b
2
= 28, a, b ∈ Z} and B = {(a, b): a> b, a, b ∈ Z}. Then, the number of elements in A ∩ B is
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2
0%
3
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4
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5
0%
6
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