1.
If f(x + y) = f(x)f(y) and f (4) = 4096, then find f(10)
(A) 216 (B) 264 (C) 230 (D) 232
f(243) – f(81)
2. If f(xy) = f(x) + f(y) for all positive values of x and f(3) = 1, then =
f(27) – f(9)
1 2 3 199
3. If f(x) + f(2 – x) = 4, then the value of f(100) + f(100) + f(100) +……..+ f(100) =
4. If f (x) = ax + b where a and b are constants and f (f (f (x))) = 125x +217 then find the value of 7a
– 5b.
(A) 0 (B) 1 (C) 5 (D) –1
5. What is the maximum value of min(x + 2, 4 – 3x)?
6. If g(x) = 8x –9, h(x) = 9x + 8 and 2(goh (a)) = hog (a), then a =
−183 −72 −72 −167
(B) (C) (D)
72 167 183 72
7. If h(x –2) = 4(h(x))2 – 5, find h(x – 4).
(A) 64(h(x))4 – 120h(x))2 + 105 (B) 64 (h(x))4 – 200(h(x))2 + 125
(C) 64(h(x))4 – 140(h(x))2 + 95 (D) 64(h(x))4 – 160(h(x))2 + 95
8. If 3f(x) + 2f(1 - x) = x2 + 4, find f(3).
1 23 5 9
(A) 9 (B) 5
(C) 9 (D) 5
9. If f(x) = 3x + 4 and g(x) = 4x – 3; then fog (x) + gof (x) =
24x + 12 (B) 24x + 8 (C) 24x – 8 (D) 24x – 12
1 1 3
10. If 𝑥 f(x) - 3f(𝑥) = 2 for all x 0, then f (3) =
−8 8 −9 9
(A) 9
(B) 9 (C) 8
(D) 8
11. If f(x + y) = f(x)f(y) for all x, yR and f(a) = 3, then the value of f(20a) is
(A) (243)3 (B) 310 (C) 320 (D) 35
12. If f(x) = 8x4 and g (x) = 3√𝑓(𝑥), find the value of log 2(fog (64))
(A) 39 (B) 15 (C) 28 (D) 32
13. Let f(x) be a function satisfying f(x)f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value
1
of f(2)?
1 1
(B) 0 (B) 4 (C) 2 (D) 1
1
14. If 3f(x + 2) + 4f( ) = 4x, x -2,then f(4) =
x+2
52
(A) 7 (B) (C) 8 (D) None of these
7
0, when x 1
15. If f(x) = { – 1, when x 2
1, when x is an odd prime number
and f(xy) = f(x) + f(y), then find the value of f(1995) ?
(A) 3 (B) 4 (C) 5 (D) None of these
16. Given, g(x) is a function such that g(x + 1) + g(x – 1) = g(x), where x is a positive real number.
For what minimum value of p does the relation g(x + p) = –g(x) necessarily hold true?
(A) 2 (B) 3 (C) 5 (D) 6
17. f(x) = max (2x – 6, 4 – 3x).
(1) What is the value of f(x) at x = 10 ?
(2) What is the minimum value of f(x)
(3) What is the maximum value of f(x) if – 5 ≤ x ≤ 10
1 1
18. A ‘polynomial f(x) with real coefficients satisfies the functional equation f(x).f ( ) = f(x) + f( ).
𝑥 𝑥
If f(2) = 9, then f(4) is
(A) 82 (B) 17 (C) 65 (D) None of these
19. If [x] is the greatest integer less than or equal to x then find the value of the following series [√1 ]
+ [√2 ] + [√3 ] + [√4 ] + ... + [√361]
(A) 4408 (B) 4839 (C) 3498 (D) 3489
20. Find how many positive real values of x satisfy the equation 2[x]2 = 5x + 2, where [x] denotes
greatest integer less than or equal to x.
(A) 0 (B) 1 (C) 2 (D) 3
4x 1 2 1996
21. Let f(x) = x
4 +2
then f(1997) + f(1997) +………+ f(1997) is equal to
(A) 1 (B) 997 (C) 998 (D) 996
22. Suppose, a function f is defined over the set of natural numbers as follows: f(1) = 1, f(2) = 1, f(3)
= –1, and f(n) = f(n – 1) f(n – 3) for n > 3. Then the value of f(694) + f(695) is
(A) –2 (B) –1 (C) 1 (D) 2
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