The domain of the function f(x) = √(x- √(1 – x2)) is
(a) [-1, -1/√2] ⋃ [1/√2, 1] (b) [-1,1] (c) (-∞, -½] ⋃ [1/√2, ∞) (d) [1/√2, 1] Solution: We have... View Article
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The domain of f(x) = (1/√(2x-1)) – √(1-x2) is
(a) ]½, 1[ (b) [-1, ∞[ (c) [1, ∞[ (d) none of these Solution: Given f(x) = (1/√(2x-1)) – √(1-x2)... View Article
Find the domain of the function f(x) = √[(2/(x2-x+1)) – 1/(x+1) – (2x-1)/(x3+1))].
(a) (-∞, 2] – {-1} (b) (-∞, 2) (c) ] -1, 2] (d) None of these Solution: Given f(x) =... View Article
Which of the following relation is NOT a function?
(a) f = {(x, x) | x ∈ R} (b) g = {(x, 3) | x ∈ R} (c) h... View Article
The domain of the function √(x2 -5x+6) + √(2x+8-x2) is
(a) [2, 3] (b) [-2, 4] (c) [-2, 2] ⋃ [3, 4] (d) [-2, 1] ⋃ [2, 4] Solution: Given... View Article
Let A = {x ∈ W, the set of whole numbers and x < 3}, B = {x∈ N, the set of natural numbers and 2 ≤ x < 4} and C = {3, 4}, then how many elements will (A⋃B)×C contain?
(a) 6 (b) 8 (c) 10 (d) 12 Solution: Given A = {x ∈ W, the set of whole numbers... View Article
Suppose that the number of elements in set A is p, the number of elements in set B is q and the number of elements in A × B is 7. Then p2 + q2 =
(a) 42 (b) 49 (c) 50 (d) 51 Solution: Given that number of elements in set A is p and... View Article
Let R = {x | x∈ N, x is a multiple of 3 and x ≤100}, S = {x | x ∈ N, x is a multiple of 5 and x ≤ 100}. What is the number of elements in (R × S) ⋂ (S × R)?
(a) 36 (b) 33 (c) 20 (d) 6 Solution: Given R = {x | x∈ N, x is a multiple... View Article
Let A = {1, 2}, B = {3, 4}. Then, number of subsets of A × B is
(a) 4 (b) 8 (c) 18 (d) 16 Solution: Given A = {1, 2}, B = {3, 4} A ×... View Article
If A = {a, b, c, d}, B = {1, 2, 3}, which of the following sets of ordered pairs are not relations from A to B?
(a) {(a, 1), (a, 3)} (b) {(b, 1), (c, 2), (d, 1)} (c) {(a, 2), (b, 3), (3, b)} (d)... View Article
If A = {1, 2}, B = {1, 3}, then (A × B) ⋃ (B × A) is equal to
(a) {(1, 3), (2, 3), (3, 1), (3, 2), (1, 1), (2, 1), (1, 2)} (b) {(1, 3), (3, 1),... View Article
The domain and range of the relation R given by R = {(x, y) : y = x + 6/x, where x, y ∈ N and x < 6} is
(a) {1, 2, 3}, {7, 5} (b) {1, 2}, {7, 5} (c) {2, 3}, {5} (d) None of these Solution:... View Article
A relation R is defined over the set of non-negative integers as xRy => x2+y2=36. What is R?
(a) {(0, 6)} (b) {(6,0) (√11, 5), (3, 3√3) (c) {(6, 0), (0, 6)} (d) (√11, 5), (2, 4√2), (5... View Article
The Cartesian product of two sets P and Q, i.e.,P × Q = Ø, if
(a) either P or Q is the null set (b) neither P nor Q is the null set (c) Both... View Article
If A = {8, 9, 10} and B = {1, 2, 3, 4, 5}, then the number of elements in A × A × B are
(a) 15 (b) 30 (c) 45 (d) 75 Solution: Given A = {8, 9, 10} B = {1, 2, 3,... View Article
Which of the following is most soluble in water?
(A) AgI (B) AgF (C) AgCl (D) AgBr The Correct Answer is (B) AgF Solution: Among the given silver halides,... View Article
Assertion: Phenolphthalein is an acid-base indicator. Reason: In an acid-base titration, this indicator is used.
(A) Both Assertion and Reason are false. (B) Assertion is false, but Reason is true. (C) Both Assertion and Reason... View Article
Phenol with CCl4 and KOH gives salicylic acid. This reaction is known as_______.
(A) Siemlet reaction. (B) Rosenmund’s reaction. (C) Friedel-Craft reaction. (D) Reimer – Tiemann reaction. The Correct Answer is (D) Reimer... View Article
Which of the following transitions in hydrogen atoms emit photons of highest frequency?
(A) n=1 to n=2 (B) n=2 to n=1 (C) n=2 to n=6 (D) n=6 to n=2 The Correct Answer is... View Article
Which one of the following compounds most readily undergoes substitution by SN2 mechanism?
The Correct Answer is (B) Solution: The increasing order of the nucleophilic substitution by SN2 mechanism is: alkyl halide <... View Article
