MATH

NDA MATHS QUESTIONS WITH SOLUTION Here are the best Top 20 NDA Maths questions with solution type which can help to improve your preparation. Answer Key is also attached in the end.   Question 1. The function f : A → B defined by f(x) = 4x + 7, x ∈ R is (a) one-one (b) Many-one (c) Odd (d) Even   Question 2. The smallest integer function f(x) = [x] is (a) One-one (b) Many-one (c) Both (a) & (b) (d) None of these Question 3. The function f : R → R defined by f(x) = 3 – 4x is (a) Onto (b) Not onto (c) None one-one (d) None of these Question 4. The number of bijective functions from set A to itself when A contains 106 elements is (a) 106 (b) (106)2 (c) 106! (d) 2106 Question 5. 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) (b) g(x)=1(ax2+b)3 (c) g(x)=(ax2+b)1/3 (d) g(x)=(x1/3−ba)1/2 NDA MATHS QUESTIONS WITH SOLUTION Question 6. If f : R → R, g : R → R and h : R → R is such that f(x) = x2, g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = π√2 will be (a) 0 (b) 1 (c) -1 (d) 10 Question 7. If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the value of x for which f(g(x)) = 25 is (a) ±1 (b) ±2 (c) ±3 (d) ±4 Question 8. Let f : N → R : f(x) = (2x−1)2 and g : Q → R : g(x) = x + 2 be two functions. Then, (gof) (32) is (a) 3 (b) 1 (c) 72 (d) None of these Question 9. Let f(x)=x−1x+1, then f(f(x)) is (a) 1x (b) −1x (c) 1x+1 (d) 1x−1 Question 10. If f(x) = 1−1x, then f(f(1x)) (a) 1x (b) 11+x (c) xx−1 (d) 1x−1 NDA MATHS QUESTIONS WITH SOLUTION Question 11. If f : R → R, g : R → R and h : R → R are such that f(x) = x2, g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be (a) 0 (b) 1 (c) -1 (d) π Question 12. If f(x) = 3x+25x−3 then (fof)(x) is (a) x (b) -x (c) f(x) (d) -f(x) Question 13. If the binary operation * is defind on the set Q+ of all positive rational numbers by a * b = ab4. Then, 3∗(15∗12) is equal to (a) 3160 (b) 5160 (c) 310 (d) 340 Question 14. The number of binary operations that can be defined on a set of 2 elements is (a) 8 (b) 4 (c) 16 (d) 64 NDA MATHS QUESTIONS WITH SOLUTION Question 15. Let * be a binary operation on Q, defined by a * b = 3ab5 is (a) Commutative (b) Associative (c) Both (a) and (b) (d) None of these NDA MATHS QUESTIONS WITH SOLUTION Question 16. Let * be a binary operation on set Q of rational numbers defined as a * b = ab5. Write the identity for *. (a) 5 (b) 3 (c) 1 (d) 6 Question 17. For binary operation * defind on R – {1} such that a * b = ab+1 is (a) not associative (b) not commutative (c) commutative (d) both (a) and (b) Question 18. The binary operation * defind on set R, given by a * b = a+b2 for all a,b ∈ R is (a) commutative (b) associative (c) Both (a) and (b) (d) None of these Question 19. Let A = N × N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Then * is (a) commutative (b) associative (c) Both (a) and (b) (d) None of these Question 20. Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+. (a) 1 (b) 2 (c) 3 (d) 0 NDA MATHS QUESTIONS WITH SOLUTION TOP 20 NDA MATHS QUESTIONS WITH SOLUTION ANSWER KEY: –   Question No. Answer Question No. Answer Question 1 A Question 11 A Question 2 B Question 12 A Question 3  A Question 13 A Question 4 C Question 14 C Question 5 D Question 15 C Question 6 A Question 16 A Question 7 B Question 17 D Question 8 A Question 18 A Question 9 B Question 19 C Question 10 C Question 20 D NDA MATHS QUESTIONS WITH SOLUTION

Here is the best top 20 NDA Maths questions Objective type which can help to improve in your preparation. Answer Key is also attached in the end.   Question 1. Let * be a binary operation on set Q – {1} defind by a * b = a + b – ab : a, b ∈ Q – {1}. Then * is (a) Commutative(b) Associative(c) Both (a) and (b)(d) None of these Question 2. The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is (a) commutative only(b) associative only(c) both commutative and associative(d) none of these Question 3. The number of commutative binary operation that can be defined on a set of 2 elements is (a) 8(b) 6(c) 4(d) 2 Question 4. 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 is 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 Question 5. The maximum number of equivalence relations on the set A = {1, 2, 3} are (a) 1(b) 2(c) 3 (d) 5 Question 6. 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) symmetric, transitive but not reflexive(d) neither transitive nor reflexive but symmetric Question 7. 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 (a) reflexive but not symmetric(b) reflexive but not transitive(c) symmetric and transitive(d) neither symmetric, nor transitive Question 8. The identity element for the binary operation * defined on Q – {0} as a * b = ab2 ∀ a, b ∈ Q – {0) is (a) 1(b) 0(c) 2(d) None of these Question 9. 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 Question 10. Let f : R → R be defind by f(x) = 1x ∀ x ∈ R. Then f is (a) one-one(b) onto(c) bijective(d) f is not defined Question 11. 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 12. 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 13. 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 14. 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 15. 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 Question 16. 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 17. 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 18. Total number of equivalence relations defined in the set S = {a, b, c} is (a) 5(b) 3!(c) 23(d) 33 Question 19. 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 20. Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2×4, is (a) one-one onto(b) one-one into(c) many-one onto(d) many-one into   TOP 20 NDA MATHS QUESTIONS  Answer Key: – Question No. Answer Question No. Answer Question 1 C Question 11 B Question 2 C Question 12 B Question 3 D Question 13 A Question 4 C Question 14 B Question 5 D Question 15 D Question 6 B Question 16 D Question 7 A Question 17 D Question 8 C Question 18 A Question 9 B Question 19 B Question 10 D Question 20 C