A = {1, 2, 3} which of the following function f: A → A does not have an inverse function
1.{(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)
Posted Date:-2021-12-15 12:15:22
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
Posted Date:-2021-12-15 12:05:40
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
Posted Date:-2021-12-15 11:52:45
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
Posted Date:-2021-12-15 12:16:55
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}
Posted Date:-2021-12-15 12:09:24
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
Posted Date:-2021-12-15 12:12:36
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
Posted Date:-2021-12-15 12:42:31
he period of sin² θ is
1.π²
2.Ï€
3.2Ï€
4.Ï€2
Posted Date:-2021-12-15 12:07:19
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
Posted Date:-2021-12-15 12:01:25
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
Posted Date:-2021-12-15 12:11:19
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
1.reflexive
2.transitive
3.symmetric
4.None of the above
Posted Date:-2021-12-15 12:18:08
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
Posted Date:-2021-12-15 11:57:58
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
Posted Date:-2021-12-15 11:48:39
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
Posted Date:-2021-12-15 12:13:38
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
Posted Date:-2021-12-15 11:48:01
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
Posted Date:-2021-12-15 12:06:38
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
Posted Date:-2021-12-15 11:44:59
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
Posted Date:-2021-12-15 11:55:27
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
Posted Date:-2021-12-15 12:14:32
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
Posted Date:-2021-12-15 12:09:47
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
Posted Date:-2021-12-15 12:22:20
Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
1. reflexive but not symmetric
2.reflexive-but not transitive
3.symmetric and transitive
4.neither symmetric, nor transitive
Posted Date:-2021-12-15 12:21:03
Let A = {1, 2}, how many binary operations can be defined on this set?
1.8
2.10
3.16
4.20
Posted Date:-2021-12-15 11:58:32
Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is
1.14
2.16
3.12
4.8
Posted Date:-2021-12-15 11:57:03
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
Posted Date:-2021-12-15 12:23:29
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
Posted Date:-2021-12-15 12:38:25
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
Posted Date:-2021-12-15 12:27:22
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
Posted Date:-2021-12-15 12:31:19
Let f: R – {35} → R be defined by f(x) = 3x+25x−3 then
1.f-1(x) = f(x)
2. f-1(x) = -f(x)
3. (f o f)x = -x
4.f-1(x) = 119 f(x)
Posted Date:-2021-12-15 12:28:17
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
Posted Date:-2021-12-15 12:26:34
Let f: [0, 1| → [0, 1| be defined by
1. Constant
2. 1 + x
3.x
4.None of the above
Posted Date:-2021-12-15 12:29:24
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, ∞)
Posted Date:-2021-12-15 12:30:18
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
Posted Date:-2021-12-15 12:02:15
Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is
1.Reflexive
2.Symmetric
3.Transitive
4.Anti-symmetric
Posted Date:-2021-12-15 12:41:07
Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is
1.Reflexive
2.Symmetric
3.Transitive
4.None of the above
Posted Date:-2021-12-15 12:43:45
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
Posted Date:-2021-12-15 12:45:35
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
Posted Date:-2021-12-15 12:41:47
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
Posted Date:-2021-12-15 12:16:08
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
Posted Date:-2021-12-15 12:04:49
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
Posted Date:-2021-12-15 12:20:19
The domain of sin-1 (log (x/3)] is. .
1.[1, 9]
2.[-1, 9]
3. [-9, 1]
4.[-9, -1]
Posted Date:-2021-12-15 12:08:11
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
Posted Date:-2021-12-15 11:56:18
The identity element for the binary operation * defined on Q ~ {0} as a * b = ab2 ∀ a, b ∈ Q ~ {0} is
1.1
2.0
3.2
4.None of the above
Posted Date:-2021-12-15 12:21:35
The maximum number of equivalence relations on the set A = {1, 2, 3} are
1.1
2.2
3.3
4.5
Posted Date:-2021-12-15 12:17:21
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
Posted Date:-2021-12-15 11:54:17
The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
1.Reflexive but not symmetric
2.Reflexive but not transitive
3.Symmetric and transitive
4.Neither symmetric nor transitive
Posted Date:-2021-12-15 12:40:20
The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
1.Reflexive but not symmetric
2.Reflexive but not transitive
3.Symmetric and transitive
4.Neither symmetric nor transitive
Posted Date:-2021-12-15 12:40:33
The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by
1.{(2, 1), (4, 2), (6, 3),….}
2.{(1, 2), (2, 4), (3, 6),….}
3.R-1 is not defined
4.None of the above
Posted Date:-2021-12-15 12:39:17
The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by
1.{(2, 1), (4, 2), (6, 3),….}
2.{(1, 2), (2, 4), (3, 6),….}
3.R-1 is not defined
4.None of the above
Posted Date:-2021-12-15 12:39:27
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
Posted Date:-2021-12-15 11:47:22
What type of relation is ‘less than’ in the set of real numbers?
1.only symmetric
2.only transitive
3.only reflexive
4.equivalence
Posted Date:-2021-12-15 12:10:31
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
Posted Date:-2021-12-15 12:24:51
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
Posted Date:-2021-12-15 12:44:42