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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) = p(x)... 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) = √[(2/(x2-x+1)) -... 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 = {(n,1/n)| n∈ I} (d) t = {(n, n2) | n ∈ N} Solution:... 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 f(x) = √(x2 -5x+6) +... 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 and x < 3}. B = {x∈ N,... 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 the number of elements in set B... 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 of 3 and x ≤100} S = {x | x... 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 × B = {(1, 3), (1, 4), (2, 3), (2, 4)}... 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) {(a, 1), (b, 2), (c, 3)} Solution: {(a, 1), (a, 3)}... 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), (3, 2), (2, 3)} (c) {(1, 3), (2, 3), (3, 1), (3, 2), (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: Given R = {(x, y) : y = x + 6/x: x, y... 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 ,√11), (4√2,... 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 (a) and (b) (d) None of these Solution: The Cartesian... 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, 4, 5} n(A) = 3 n(B) = 5 Number of... 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, Silver fluoride [AgF] is... 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 are true. The reason is... 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)... 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 (B) n=2 to n=1 The n=2 to n=1 transitions in... 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 < sec alkyl... View Article

Which of the following elements produce H2 gas with sodium hydroxide?

(A) Zn (B) Al and Pb (C) Si and Sn (D) All of these. The Correct Answer is (D) All of These. Solution: In the above-given elements,... View Article

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