Question 1: Let A and B be two finite sets having m and n elements respectively. Then the total number of mapping from A to B is

(a) mn                      (b) mⁿ                          (c) 2^mn                      (d) n^m

Question 2: Two sets A and B are as under:

A = {(a, b) ϵ R × R : |a − 5| < 1 and |b − 5| < 1};

B = {a, b) ϵ R × R : 4 (a − 6)² + 9(b−5) ² ≤ 36}. Then,

(a) A is subset of B

(b) A n B = φ (null set)

(c) neither A subset of B nor B is subset of A

(d) B is subset of A

Question 3: Let A and B be two sets containing 4 and 2 elements respectively. Then the number of subsets of the set AxB, each having at least 3 elements is

(a) 256                    (b) 275                       (c) 510                        (d) 219

Question 4: If A, B and C are three sets such that A ∩ B = A ∩ C and A U B = A U C then

(a) B = C

(b) A = B

(c) A = C

(d) A n B = 0 (empty set)

Question 5: Let S = {x Є R : x ≥ 0 and 2|√x − 3|+ √x (√x − 6) + 6 = 0}. Then S :

(a) is an empty set

(b) contains exactly one element

(c) contains exactly two elements

(d) contains exactly four elements

Question 6: Let S be the set of all functions f:[0,1] -> R, which are continuous on [0, 1] and differentiable on (0, 1). Then for every f in S, there exists a C Є (0, 1), depending on f, such that:

(a) |f(1) − f(C)| = (1- C)|f′(C)|

(b) |f(C) + f(1)| < (1 + c)|f′(C)|

(c) |f(C) − f(1)| < (1 − C)|f′(C)|

(d) None of these

Question 7: If f(x) + 2 f(1/x) = 3x, x not equal to 0 and S = {x Є R : f(x) = f(- x)}; then S

(a) is an empty set

(b) contains exactly one element

(c) contains more than two elements

(d) contains exactly two elements

Question 8: The general solution of sin x − 3 sin2x + sin3x = cos x − 3 cos2x + cos3x is _________.

Question 9: If sec 4θ − sec 2θ = 2, then the general value of θ is __________.

Question 10: If tan (cot x) = cot (tan x), then sin 2x = ___________.