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- If f : R → R defined by f(x) = \(\frac{3 x+5}{2}\) is an invertible function, then find f-1. (a) 2 x-5/3 1
- Let f : R → R, g : R → R be two functions such that f(x) = 2x – 3, g(x) = x3 + 5. The function (fog)-1 (x) is (d) (x-7/2)^(1 / 3) 1
- If * is a binary operation on set of integers I defined by a * b = 3a + 4b – 2, then find the value of 4 * 5. answer b) 30 1
- Let * be the binary operation on N given by a * b = HCF (a, b) where, a, b ∈ N. Find the value of 22 * 4 correct option is b) 2 2
- Consider the binary operation * on Q defind by a * b = a + 12b + ab for a, b ∈ Q. Find 2 * \(\frac{1}{3}\) ( (a) 20/3 1
- The domain of the function \(f(x)=\frac{1}{\sqrt{\{\sin x\}+\{\sin (\pi+x)\}}}\) where {.} (d) None of these 2
- Range of \(f(x)=\sqrt{(1-\cos x) \sqrt{(1-\cos x) \sqrt{(1-\cos x) \ldots \ldots \infty}}}\) Correct option is c) [0, 2] 2
- Let * be a binary operation on set Q of rational numbers defined as answer is a) 5 2
- The number of binary operations that can be defined on a set of 2 elements is (a) 8 (b) 4 (c) 16 (d) 64 answer is c) 16 2
- If the binary operation * is defind on the set Q+ of all positive rational numbers by a * b (a) 3/160 1
- 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, Answer is a)0 2
- If f(x) = \(1-\frac{1}{x}\), then f(f(\(\frac{1}{x}\))) (a) \(\frac{1}{x}\) (b) \(\frac{1}{1+x}\) Answer is (c) x/x-1 1
- Let \(f(x)=\frac{x-1}{x+1}\), then f(f(x)) is (a) \(\frac{1}{x}\) (b) \(-\frac{1}{x}\) Answer is (b) -1/x 1
- Let f : N → R : f(x) = \(\frac{(2 x-1)}{2}\) and g : Q → R : g(x) = x + 2 be two functions. Answer is (a) 3 2
- 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 Answer is (b) ±2 2
- If f : R → R, g : R → R and h : R → R is such that f(x) = x2, g(x) = tanx and h(x) = logx Answer is a) 0 2
- If f(x) = (ax2 + b)3, then the function g such that f(g(x)) = g(f(x)) is given by Correct option is d) g(x)=(fracx^(1 / 3)-ba)^(1 / 2) 1
- The number of bijective functions from set A to itself when A contains 106 elements is Correct option is c) 106! 2
- 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 Correct option is a) onto 2
- The smallest integer function f(x) = [x] is (a) One-one (b) Many-one (c) Both (a) & (b) (d) None of these Correct option is (b) Many-one 2
- The function f : A → B defined by f(x) = 4x + 7, x ∈ R is (a) one-one (b) Many-one (c) Odd (d) Even correct option is (a) one-one 2
- Digital signals (i) do not provide a continuous set of values, (ii) represent values as discrete steps, (Hi) (c) is correct because the decimal system is concerned with continuous values (i) to (iii). 1