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Functions

01. If  f(x)=| x – 2 |,  then which of the following is always true ? 
(a) f(x) = (f(x))2 (b) f(x) = f(-x) (c) f(x) = x – 2 (d) None of these
02. Which of the following functions will have a minimum value at x = -3 ?
(a)f(x) = 2x- 4x + 3 (b)  f(x)=4x4- 3x+5 (c)  f(x) = x- 2x – 6 (d) None of these
03. Find the maximum value of the functions 1/(x- 3x + 2) ?
(a) 11/4 (b) 1/4 (c) 0 (d) None of these
04. Find the minimum value off function f(x)= log(x- 2x + 5) (base 2) ?
(a) -4 (b) 2 (c) 4 (d) -2
05. A function f(x) satisfies f(1)=3600  and f(1) + f(2) +……f(n) =n2f(n), for all positive integers n>1. What is the value of f(9) ?
(a) 200 (b) 100 (c) 120 (d) 80
06. Let f(x)= max( 2x + 1, 3 – 4x), where x is any real number. Then, the minimum possible value of f(x) is 
(a) 4/3 (b) 1/2 (c) 2/3 (d) 5/3
07. Let g(x) be a function such that g(x + 1) + g(x – 1) = g(x) for every real x. Then, for what value of p is the relation g(x + p)= g(x) necessarily true for every real x ?
(a) 5 (b) 3 (c) 2 (d) 6
08. If f(x)=x3- 4x + p  and f(0) and f(1) are of opposite signs, then which of the following is necessarily true ?
(a) -1 < p < 2 (b) 0 < p < 3 (c)  -2 < p < 1 (d) -3 < p < 0 
09. Let g(x) =  max ( 5 – x , x + 2 ). The smallest possible value of g(x) is ?
(a) 4.0 (b) 4.5 (c) 1.5 (d) None of these
10. Let f(x)= |x – 2| + |2.5 – x| + |3.6 – x|, where x is a real number, attains a minimum at ?
(a) x = 2.3 (b) x = 2.5 (c) x = 2.7  (d) None of these
11. Largest value of min ( 2 + x, 6 – 3x), when x > 0 is  
(a) 1 (b) 2 (c) 3 (d) 4

Answers :

1.  D 2.  D
3.  D 4.  B
5.  D 6.  D
7.  D 8.  B
9.  D 10.  B    
11.  C

Detailed Solution

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7 comments

  1. Rajat Tripathi

    f(1) = 3600
    3600 + f(2)= 4f(2)–>f(2)= 1200
    4800 + f(3)= 9f(3)–>f(3)= 600
    5400 + f(4)= 16f(4)–>f(4)= 360
    5760 + f(5)= 25f(5)–>f(5)= 240
    6000 + f(6)= 36f(6)–>f(6)= 171.428
    6171.428 + f(7)= 49f(7)–> f(7)=128.571
    6300 + f(8)=64f(8)–>f(8)= 100
    6400 + f(9)= 81f(9)–>f(9)= 80

  2. Jasvinder Singh

    answer for Q.3 should be d.
    to get max. value denominator should be min. and min. value can be calculated by putting x=-b/2a

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