NCERT Solutions for class 12 Maths | Chapter 1 - Relations and Functions

Advertisement
Questions
1 The period of sin² θ is
A π²
B π
C 2π
D π/2

Answer:π
2 Let the functioin ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is
A onto function
B one-one, onto function
C one-one, into function
D many-one into function

Answer:many-one into function
Advertisement
Article and Schedule Quiz Start Test!

DOWNLOAD CURRENT AFFAIRS PDF FROM APP

3 Let A = {1, 2}, how many binary operations can be defined on this set?
A 8
B 10
C 16
D 20

Answer:16
4 The range of the function f(x) = Relations and Functions is
A [-2, 2]
B [0, 1]
C [1, 3]
D None of these

Answer:[1, 3]
5 A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings : a loves A} is-
A reflexive
B symmetric and transitive
C equivalence
D None of these

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?
A Many-one onto
B Constant function
C one-one onto
D into

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
A 1
B 2
C 3
D 4

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?
A into
B one-one onto
C many-onto
D constant function

Answer:one-one onto
9 If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
A reflexive
B transitive
C symmetric
D None of these

Answer:transitive
10 Let A = {1, 2,3,…. n} and B = { a, b}. Then the number of surjections from A into B is
A nP2
B 2n – 2
C 2n – 1
D None of these

Answer:2n – 2
11 Let f: R → R be the function defined by f(x) = x³ + 5. Then f-1 (x) is
A (x + 5)1/3
B (x -5)1/3
C (5 – x)1/3
D 5 – x

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
A 31
B 40
C 43
D None of these

Answer:31
13 If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is
A many one
B one-one onto
C onto
D one-one

Answer:one-one
14 What type of relation is ‘less than’ in the set of real numbers?
A only symmetric
B only transitive
C only reflexive
D equivalence

Answer:only transitive
15 A = {1, 2, 3} which of the following function f: A → A does not have an inverse function
A {(1, 1), (2, 2), (3, 3)}
B {(1, 2), (2, 1), (3, 1)}
C {(1, 3), (3, 2), (2, 1)}
D {(1, 2), (2, 3), (3, 1)

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
A R
B [1, ∞)
C [4, ∞)
D [5, ∞)

Answer:[1, ∞)
17 Let f: A → B and g : B → C be the bijective functions. Then (g o f)-1 is,
A f-1 o g-1
B f o g
C g-1 o f-1
D g o f

Answer:f-1 o g-1
18 Which one of the following relations on R is an equivalence relation?
A aR1b ⇔ |a| = |b|
B aR2b ⇔ a ≥ b
C aR3b ⇔ a divides b
D aR4b ⇔ a < b

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
A A = B
B A = C
C B = C
D A ∩ B = d

Answer:B = C
20 If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is
A 12
B 28
C 61
D None of these

Answer:61

ADRE 2.0 FULL LENGTH MOCK TEST

Take Mock Tests

Missiles Mock Test Start Test!
SSC MTS Mock Test Start Test
IBPS CLERK MOCK TEST Start Test
SSC MTS 2022 JULY 26 Shift 1 (ENGLISH) Start Test!
SSC GD Previous Year Paper 2021 Nov 17 Shift - I (Hindi) Start Test!
SSC CGL Tier - 1 PYP 2022 April 21 Shift- 1 (ENGLISH) Start Test!
MPSC PAPER I MOCK TEST 1 (ENGLISH) Start Test!
IB Security Assistant Mock test 1 (english) Start Test!
UP POLICE CONSTABLE MOCK TEST 1 Start Test!
DELHI POLICE CONSTABLE MOCK TEST 1 (HINDI) Start Test!

Chapters

Advertisement
Assam Direct Recruitment Test Series