Chapter 2
sin-1 1/2 − 2. cos-1 3/2 3. cosec-1 (2)
If / 2 5 113 3 3 3 x ,y - , + = , find the values of x and y.
The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
The Cartesian product A × A has 9 elements among which are found (-1, 0) and (0,1). Find the set A and the remaining elements of A × A.
If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).
If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.
tan-1 ( 3)− 5. cos-1 1/2 − 6. tan-1 (-1) 7. sec-1 2/3 8. cot-1 ( 3) 9. cos-1 1/2 − 10. cosec-1 ( 2− ) Find the values of the following: 11. tan-1(1) + cos -1 1/2 − + sin-1 1 − 12. cos-1 1/2 + 2 sin -1 1 13. If sin-1 x = y, then (A) 0 ≤ y ≤ π (B) 2 2 yπ π− ≤ ≤ (C) 0 < y < π (D) 2 2 yπ π− < < 14. tan-1 ( )13 sec 2−− − is equal to (A) π (B) 3 / π− (C) 3 / π (D) 2 π
State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If P = {m, n} and Q = { n, m}, then P × Q = {(m, n),(n, m)}. (ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B. (iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ φ) = φ.
If A = {-1, 1}, find A × A × A.
If A × B = {( a, x),(a , y), (b, x), (b, y)}. Find A and B.
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that (i) A × (B ∩ C) = (A × B) ∩ (A × C). (ii) A × C is a subset of B × D.
Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.
Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.