Top 20 Maths Question Answer Practice Sets – Defence Exam

If you are preparing for Defence Exam, then here you can practice Best Top 20 Maths Question Answer which can help you in improvement.

Question 1: 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

Question 2: Let f : R → R be the functions defined by f(x) = x³ + 5. Then f^-1(x) is

(a) (x+5)13
(b) (x−5)13
(c) (5−x)13
(d) 5 – x

Question 3: Let f : R – {35} → R be defined by f(x) = 3x+25x−3. Then

(a) f^-1(x) = f(x)
(b) f^-1(x) = -f(x)
(c) (fof) x = -x
(d) f^-1(x) = 119 f(x)

Question 4: Let f : R → R be given by f(x) = tan x. Then f^-1(1) is

(a) π4
(b) {nπ + π4; n ∈ Z}
(c) Does not exist
(d) None of these

Question 5: 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

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Question 6: Let S = {1, 2, 3, 4, 5} and let A = S × S. Define the relation R on A as follows:
(a, b) R (c, d) iff ad = cb. Then, R is

(a) reflexive only
(b) Symmetric only
(c) Transitive only
(d) Equivalence relation

Question 7: Let R be the relation “is congruent to” on the set of all triangles in a plane is

(a) reflexive
(b) symmetric
(c) symmetric and reflexive
(d) equivalence

Question 8: Total number of equivalence relations defined in the set S = {a, b, c} is

(a) 5
(b) 3!
(c) 23
(d) 33

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 defiend
(d) None of these

Question 10: Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x⁴, is

(a) one-one onto
(b) one-one into
(c) many-one onto
(d) many-one into

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Question 11: Let f : R → R be a function defined by f(x)=e|x|−e−xex+e−x then f(x) is

(a) one-one onto
(b) one-one but not onto
(c) onto but not one-one
(d) None of these

Question 12: Let g(x) = x² – 4x – 5, then

(a) g is one-one on R
(b) g is not one-one on R
(c) g is bijective on R
(d) None of these

Question 13: Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x)=x−2x−3. Then,

(a) f is bijective
(b) f is one-one but not onto
(c) f is onto but not one-one
(d) None of these

Question 14: The mapping f : N → N is given by f(n) = 1 + n², n ∈ N when N is the set of natural numbers is

(a) one-one and onto
(b) onto but not one-one
(c) one-one but not onto
(d) neither one-one nor onto

Question 15: The function f : R → R given by f(x) = x³ – 1 is

(a) a one-one function
(b) an onto function
(c) a bijection
(d) neither one-one nor onto

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Question 16: Let f : [0, ∞) → [0, 2] be defined by f(x)=2×1+x, then f is

(a) one-one but not onto
(b) onto but not one-one
(c) both one-one and onto
(d) neither one-one nor onto

Question 17: If N be the set of all-natural numbers, consider f : N → N such that f(x) = 2x, ∀ x ∈ N, then f is

(a) one-one onto
(b) one-one into
(c) many-one onto
(d) None of these

Question 18: Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is

(a) a bijection
(b) injection but not surjection
(c) surjection but not injection
(d) neither injection nor surjection

Question 19: Let f : R → R be a function defined by f(x) = x³ + 4, then f is

(a) injective
(b) surjective
(c) bijective
(d) none of these

Question 20: If f(x) = (ax² – b)³, then the function g such that f{g(x)} = g{f(x)} is given by

(a) g(x)=(b−x1/3a)1/2
(b) g(x)=1(ax2+b)3
(c) g(x)=(ax2+b)1/3
(d) g(x)=(x1/3+ba)1/2

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