NCERT Solutions for class 12 Maths | Chapter 1 - Relations and Functions
Questions
2
Let the functioin ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is
Answer:many-one into function
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3
Let A = {1, 2}, how many binary operations can be defined on this set?
Answer:16
is
5
A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings : a loves A} is-
Answer:equivalence
6
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?
Answer:one-one onto
7
If the function f(x) = x³ + ex/2 and g (x) = fn(x), then the value of g'(1) is
Answer:2
8
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?
Answer:one-one onto
9
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
Answer:transitive
10
Let A = {1, 2,3,…. n} and B = { a, b}. Then the number of surjections from A into B is
Answer:2n – 2
11
Let f: R → R be the function defined by f(x) = x³ + 5. Then f-1 (x) is
Answer:(x -5)1/3
12
Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals
Answer:31
13
If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is
Answer:one-one
14
What type of relation is ‘less than’ in the set of real numbers?
Answer:only transitive
15
A = {1, 2, 3} which of the following function f: A → A does not have an inverse function
Answer:{(1, 2), (2, 1), (3, 1)}
16
Let f: |2, ∞) → R be the function defined by f(x) – x² – 4x + 5, then the range of f is
Answer:[1, ∞)
17
Let f: A → B and g : B → C be the bijective functions. Then (g o f)-1 is,
Answer:f-1 o g-1
18
Which one of the following relations on R is an equivalence relation?
Answer:aR1b ⇔ |a| = |b|
19
If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then
Answer:B = C
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