CBSE Class 12 Maths – MCQ and Online Tests – Unit 1 – Relations and Functions
Every year CBSE conducts board exams for 12th standard. These exams are very competitive to all the students. So our website provides online tests for all the 12th subjects. These tests are also very effective and useful for those who preparing for competitive exams like NEET, JEE, CA etc. It can boost their preparation level and confidence level by attempting these chapter wise online tests.
These online tests are based on latest CBSE Class 12 syllabus. While attempting these our students can identify the weak lessons and continuously practice those lessons for attaining high marks. It also helps to revise the NCERT textbooks thoroughly.
CBSE Class 12 Maths – MCQ and Online Tests – Unit 1 – Relations and Functions
Question 1.
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
Answer: (c) B = C
Question 2.
Let A = {1, 2}, how many binary operations can be defined on this set?
(a) 8
(b) 10
(c) 16
(d) 20
Answer
Answer: (c) 16
Question 3.
If f: R → R defined by f(x) = 2x + 3 then f-1(x) =
(a) 2x – 3
(b) \(\frac{x-3}{2}\)
(c) \(\frac{x+3}{2}\)
(d) None of these
Answer
Answer: (b) \(\frac{x-3}{2}\)
Question 4.
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
Answer: (c) 61
Question 5.
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
Answer: (c) one-one onto
Question 6.
The period of sin² θ is
(a) π²
(b) π
(c) 2π
(d) \(\frac{π}{2}\)
Answer
Answer: (b) π
Question 7.
f(x) = \(\frac{log_2(x+3)}{x^2+3x+2}\) is the domain of
(a) R – {-1, -2}
(b) (- 2, ∞) .
(c) R- {- 1,-2, -3}
(d) (-3, + ∞) – {-1, -2}
Answer
Answer: (d) (-3, + ∞) – {-1, -2}
Question 8.
Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is
(a) Reflexive
(b) Symmetric
(c) Transitive
(d) Anti-symmetric
Answer
Answer: (b) Symmetric
Question 9.
The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by
(a) {(2, 1), (4, 2), (6, 3),….}
(b) {(1, 2), (2, 4), (3, 6),….}
(c) R-1 is not defined
(d) None of these
Answer
Answer: (b) {(1, 2), (2, 4), (3, 6),….}
Question 10.
The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
(a) Reflexive but not symmetric
(b) Reflexive but not transitive
(c) Symmetric and transitive
(d) Neither symmetric nor transitive
Answer
Answer: (a) Reflexive but not symmetric
Question 11.
The identity element for the binary operation * defined on Q ~ {0} as
a * b = \(\frac{ab}{2}\) ∀ a, b ∈ Q ~ {0} is
(a) 1
(b) 0
(c) 2
(d) None of these
Answer
Answer: (c) 2
Question 12.
Let f : R → R be defined by f (x) = \(\frac{1}{x}\) ∀ x ∈ R. Then f is
(a) one-one
(b) onto
(c) bijective
(d) f is not defined
Answer
Answer: (d) f is not defined
Question 13.
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
(a) symmetric but not transitive
(b) transitive but not symmetric
(c) neither symmetric nor transitive
(d) both symmetric and transitive
Answer
Answer: (b) transitive but not symmetric
Question 14.
Let us define a relation R in R as aRb if a ≥ b. Then R is
(a) an equivalence relation
(b) reflexive, transitive but not symmetric
(c) neither transitive nor reflexive but symmetric
(d) symmetric, transitive but not reflexive
Answer
Answer: (b) reflexive, transitive but not symmetric
Question 15.
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
Answer: (a) f-1 o g-1
Question 16.
Let f: [0, 1| → [0, 1| be defined by
(a) Constant
(b) 1 + x
(c) x
(d) None of these
Answer
Answer: (c) x
Question 17.
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
(a) Reflexive and symmetric
(b) Transitive and symmetric
(c) Equivalence
(d) Reflexive, transitive but not symmetric
Answer
Answer: (d) Reflexive, transitive but not symmetric
Question 18.
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}
(a) Reflexive
(b) Transitive
(c) Symmetric
(d) None of these
Answer
Answer: (d) None of these
Question 19.
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
Answer: (a) 31
Question 20.
The range of the function f(x) = \(\sqrt{(x-1)(3-x)}\) is
(a) [1, 3]
(b) [0, 1]
(c) [-2, 2]
(d) None of these
Answer
Answer: (a) [1, 3]
Question 21.
Let A = {1, 2, 3, 4,…. n} How many bijective function f : A → B can be defined?
(a) \(\frac{1}{2}\)n
(d) n
Answer
Answer: (c) [n
Question 22.
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
Answer: (c) one-one onto
Question 23.
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
Answer: (b) only transitive
Question 24.
f: A → B will be an into function if
(a) range (f) ⊂ B
(b) f(a) = B
(c) B ⊂ f(a)
(d) f(b) ⊂ A
Answer
Answer: (a) range (f) ⊂ B
Question 25.
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
(a) reflexive but-not transitive
(b) transitive but not symmetric
(c) equivalence
(d) None of these
Answer
Answer: (c) equivalence
Question 26.
The maximum number of equivalence relations on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5
Answer
Answer: (d) 5
Question 27.
Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is
(a) Less than n
(b) Greater than or equal to n
(c) Less than or equal to n
(d) None of these
Answer
Answer: (b) Greater than or equal to n
Question 28.
Let f: R – {\(\frac{3}{5}\)} → R be defined by f(x) = \(\frac{3x+2}{5x-3}\) then
(a) f-1(x) = f(x)
(b) f-1(x) = -f(x)
(c ) (f o f)x = -x
(d ) f-1(x) = \(\frac{1}{19}\) f(x)
Answer
Answer: (a) f-1(x) = f(x)
Question 29.
Which of the following functions from Z into Z are bijective?
(a) f(x) = x³
(b) f(x) = x + 2
(c) f(x) = 2x + 1
(d) f{x) = x² + 1
Answer
Answer: (b) f(x) = x + 2
Question 30.
If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is
(a) one-one
(b) one-one onto
(c) onto
(d) many one
Answer
Answer: (a) one-one
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