A = {1, 2, 3} which of the following function f: A → A does not have an inverse function1.{(1, 1), (2, 2), (3, 3)}
2.{(1, 2), (2, 1), (3, 1)}
3. {(1, 3), (3, 2), (2, 1)}
4.{(1, 2), (2, 3), (3, 1)
A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings : a loves A} is-1.reflexive
2.symmetric and transitive
3.equivalence
4.None of the above
Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals
1.31
2.40
3.43
4.None of the above
Consider the non-empty set consisting of children is a family and a relation R defined as aRb If a is brother of b. Then R is
1.symmetric but not transitive
2.transitive but not symmetric
3.neither symmetric nor transitive
4.both symmetric and transitive
f(x) = log2(x+3)x2+3x+2 is the domain of
1.R – {-1, -2}
2.(- 2, ∞) .
3.R- {- 1,-2, -3}
4.(-3, + ∞) – {-1, -2}
f: A → B will be an into function if
1.range (f) ⊂ B
2.f(a) = B
3.B ⊂ f(a)
4.f(b) ⊂ A
For real numbers x and y, we write xRy ⇔ x – y + √2 is an irrational number. Then, the relational R is
1.Reflexive
2.Symmetric
3.Transitive
4.None of the above
he period of sin² θ is
1.π²
2.Ï€
3.2Ï€
4.Ï€2
If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f?
1.Many-one onto
2.Constant function
3.one-one onto
4.into
If A = [1, 2, 3}, B = {5, 6, 7} and f: A → B is a function such that f(x) = x + 4 then what type of function is f?1.into
2.one-one onto
3.many-onto
4.constant function
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is1.reflexive
2.transitive
3.symmetric
4.None of the above
If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then
1.A = B
2.A = C
3.B = C
4.A ∩ B = d
If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is
1.12
2.28
3.61
4.None of the above
If f : R → R such that f(x) = 3x then what type of a function is f?
1.one-one onto
2. many one onto
3.one-one into
4.many-one into
If F : R → R such that f(x) = 5x + 4 then which of the following is equal to f-1(x).
1.x−54
2.x−y5
3.x−45
4.x4 -5
If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =
1.x² – 2
2. 1
3.13 (x – 2)²
4.None of the above
If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is
1.one-one
2.one-one onto
3.onto
4.many one
If f: R → R defined by f(x) = 2x + 3 then f-1(x) =
1.2x – 3
2.x−32
3.x+32
4.None of the these
If f: R → R such that f(x) = 3x – 4 then which of the following is f-1(x)?
1.13 (x + 4)
2.13 (x – 4)
3.3x – 4
4.undefined
If the function f(x) = x³ + ex/2 and g (x) = fn(x), then the value of g'(1) is
1.1
2.2
3.3
4.4
If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is
1.720
2.120
3.0
4.None of the above
Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is1. reflexive but not symmetric
2.reflexive-but not transitive
3.symmetric and transitive
4.neither symmetric, nor transitive
Let A = {1, 2}, how many binary operations can be defined on this set?1.8
2.10
3.16
4.20
Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is1.14
2.16
3.12
4.8
Let f : R → R be defined by f (x) = 1x ∀ x ∈ R. Then f is
1.one-one
2.onto
3.bijective
4.f is not defined
Let f : R → R be given by f (,v) = tan x. Then f-1(1) is
1.Ï€/4
2.{nπ + π/4 : n ∈ Z}
3.does not exist
4. None of these
Let f: A → B and g : B → C be the bijective functions. Then (g o f)-1 is,
1. f-1 o g-1
2. f o g
3. g-1 o f-1
4.g o f
Let f: N → R be the function defined by f(x) = 2x−12 and g: Q → R be another function defined by g (x) = x + 2. Then (g 0 f) 32 is
1.1
2.0
3.7/2
4.None of the above
Let f: R – {35} → R be defined by f(x) = 3x+25x−3 then1.f-1(x) = f(x)
2. f-1(x) = -f(x)
3. (f o f)x = -x
4.f-1(x) = 119 f(x)
Let f: R → R be the function defined by f(x) = x³ + 5. Then f-1 (x) is
1. (x + 5)1/3
2. (x -5)1/3
3.(5 – x)1/3
4. 5 – x
Let f: [0, 1| → [0, 1| be defined by
1. Constant
2. 1 + x
3.x
4.None of the above
Let f: |2, ∞) → R be the function defined by f(x) – x² – 4x + 5, then the range of f is
1.R
2. [1, ∞)
3.[4, ∞)
4. [5, ∞)
Let function R → R is defined as f(x) = 2x³ – 1, then ‘f’ is
1.2x³ + 1
2.(2x)³ + 1
3.(1 – 2x)³
4.(1+x2)1/3
Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is1.Reflexive
2.Symmetric
3.Transitive
4.Anti-symmetric
Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is1.Reflexive
2.Symmetric
3.Transitive
4.None of the above
Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is
1. Reflexive and symmetric
2.Transitive and symmetric
3.Equivalence
4.Reflexive, transitive but not symmetric
Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is
1.Less than n
2.Greater than or equal to n
3.Less than or equal to n
4.None of the above
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a congruent to b ∀ a, b ∈ T. Then R is
1.eflexive but-not transitive
2.transitive but not symmetric
3.equivalence
4.None of the above
Let the functioin ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is
1.onto function
2.one-one, onto function
3.one-one, into function
4.many-one into function
Let us define a relation R in R as aRb if a ≥ b. Then R is
1.an equivalence relation
2.reflexive, transitive but not symmetric
3.neither transitive nor reflexive but symmetric
4.symmetric, transitive but not reflexive
The domain of sin-1 (log (x/3)] is. .
1.[1, 9]
2.[-1, 9]
3. [-9, 1]
4.[-9, -1]
The function f(x) = log (x² + x2+1−−−−−√ ) is
1.even function
2.odd function
3.Both of the above
4.None of the above
The identity element for the binary operation * defined on Q ~ {0} as
a * b = ab2 ∀ a, b ∈ Q ~ {0} is1.1
2.0
3.2
4.None of the above
The maximum number of equivalence relations on the set A = {1, 2, 3} are1.1
2.2
3.3
4.5
The range of the function f(x) = (x−1)(3−x)−−−−−−−−−−−√ is
1.[1, 3]
2.[0, 1]
3.[-2, 2]
4.None of the these
The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is1.Reflexive but not symmetric
2.Reflexive but not transitive
3.Symmetric and transitive
4.Neither symmetric nor transitive
The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is1.Reflexive but not symmetric
2.Reflexive but not transitive
3.Symmetric and transitive
4.Neither symmetric nor transitive
The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by1.{(2, 1), (4, 2), (6, 3),….}
2.{(1, 2), (2, 4), (3, 6),….}
3.R-1 is not defined
4.None of the above
The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by1.{(2, 1), (4, 2), (6, 3),….}
2.{(1, 2), (2, 4), (3, 6),….}
3.R-1 is not defined
4.None of the above
What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}1.Reflexive
2.Transitive
3.Symmetric
4.None of the above
What type of relation is ‘less than’ in the set of real numbers?
1.only symmetric
2.only transitive
3.only reflexive
4.equivalence
Which of the following functions from Z into Z are bijective?
1.f(x) = x³
2.f(x) = x + 2
3.f(x) = 2x + 1
4.f{x) = x² + 1
Which one of the following relations on R is an equivalence relation?
1.aR1b ⇔ |a| = |b|
2. aR2b ⇔ a ≥ b
3.aR3b ⇔ a divides b
4.aR4b ⇔ a < b