IPMAT MASTER QUEST 3.0 2025 Quant Functions - II PDF

IPMAT MASTER QUEST 3.0 2025 (QUANT) Functions – II Lecture – 08 Q. Let f(x) be a function such that f(x + y) = f(x) + f(y) for all real numbers x and y. If f(1) = 2, find the value of f(5). (A) 11 (B) 10 (C) 1 (D) 0 Q. Let f(x) be a...

IPMAT MASTER QUEST 3.0 2025 (QUANT) Functions – II Lecture – 08 Q. Let f(x) be a function such that f(x + y) = f(x) + f(y) for all real numbers x and y. If f(1) = 2, find the value of f(5). (A) 11 (B) 10 (C) 1 (D) 0 Q. Let f(x) be a function such that f(2x) = 4f(x) for all real numbers x, and f(1) = 3. Find the value of f(8). (A) 192 (B) 191 (C) 193 (D) 190 Q. Let f(x) be a function such that f(x + 2) = f(x) + 6 for all real x, and f(1) = 4. Find the value of f(9). (A) 27 (B) 29 (C) 28 (D) 30 Q. Let f(x) be a function such that f(x + y) = f(x).f(y) for all real numbers x and y, and f(0) = 1. If f(2) = 4, find the value of f(4). (A) 4 (B) 32 (C) 8 (D) 16 Q. Let f(x) be a function such that f(2x) = 2f(x) + 3 for all real numbers x, and f(1) = 5. Find the value of f(2) + 7. (A) 20 (B) 13 (C) 17 (D) 10  b Q. If f a = a + 2 and 3f(b) = 18. What is the possible value of f ? 4 (A) 0 (B) 2 (C) 4 (D) –4 Q. For the modulus function 2m + 8 = |m + 10|. How many different values of m satisfies ? (A) 1 (B) 2 (C) 6 (D) 4 Q. The function f(x) is a product of all even integers from 1 to x inclusive, where x > 1. What is the value of f(81) – f(80) ? (A) 0 (B) 2 (C) 3 (D) 4  2 Q. If |a| = 2 and |b| = 5, how many possible values of a × b exist ? (A) 4 (B) 6 (C) 1 (D) 2  (a − m) Q. If f a = and g(a) = 7 + 5a. What is the value of m, if f(g(a)) = g(f(a)) ? 5 (A) 7 (B) 9 (C) 6 (D) 5  b Q. What is the minimum possible value of a, if |a – 8| = 18 and |3b – 18| = 12 ? (A) –0.4 (B) –1 (C) –2 (D) 5 Q. For the given modulus function ||a – 4| – 5| = 5, how many integer values of "a" satisfies it ? (A) 4 (B) 3 (C) 2 (D) 1  1 1 Q. What is the possible value of g(f(2)), if f = a−1 2 and g = 2a + 1 ? a a (A) 8 (B) 9 (C) 7 (D) 0 Q. For the given modulus function 2|a| + 3b = 27. How many positive integral values of (a, b) are possible such that b < 10 ? (A) 6 (B) 8 (C) 4 (D) 5 Q. Solve for x : |2x – 3| + | x + 1| = 7. 5 (A) x = −3, 3 5 (B) x = 3, 3 5 (C) x = −3, − 3 5 (D) x = 3, − 3 Q. If |x – 3| + |x – 10| > 24, then find the values of x. 11 37 (A) −∞, − ∪ , ∞ 2 2 11 37 (B) −∞, ∪ , ∞ 2 2 11 37 (C) −∞, − ∪ , ∞ 4 2 11 37 (D) −∞, ∪ , ∞ 4 2 Q. Find the range of x when ||x – 8| – 12| > 8. (A) (–∞, –12) ∪ (4, 12) ∪ (28, ∞) (B) (–∞, –12) ∪ (4, 12) ∪ (24, ∞) (C) (–∞, –12) ∪ (1, 12) ∪ (24, ∞) (D) (–∞, –12) ∪ (–4, 12) ∪ (28, ∞) Q. Find the minimum value of |x – 5| + |x – 15| + |x – 25| + |x – 50|. (A) 75 (B) 55 (C) 65 (D) 45 Q. Let f : R → R be a function satisfying the equation f(x + y) = f(x) + f(y) ∀ x, y ∈ R. Additionally, it is given that f(0) = 1. Which of the following could be f(x) ? (A) ax (B) x2 (C) 1+x (D) None of the above Q. Let f : R → R be a function satisfying the functional equation f(x + y).f(x – y) = f(x)2 – f(y)2, ∀ x, y ∈ R. If f(0) = 0, which of the following functions satisfied the equation ? (A) x2 (B) x (C) x3 (D) sin(x) Thank you