Relations and Functions

Let S = N \0\. Define a relation R from S to R by : R = \(x, y) : e y = x e ( 25 ), x S, y R \. Then, the sum of all the elements in the range of R is equal to :

1. 32
2. 109
3. 52
4. 53

If the domain of the function 5(18x - x2 - 77) is ( , ) and the domain of the function (x-1) ( 2x2 + 3x - 2x2 - 3x - 4 ) is ( , ), then 2 + 2 + 2 is equal to:

1. 186
2. 179
3. 195
4. 174

Let f : R R be a function defined by f(x) = (2 + 3a)x2 + ( a+2a-1 )x + b, a 1. If f(x + y) = f(x) + f(y) + 1 - 27xy, then the value of 28 i=15|f(i)| is

1. 735
2. 675
3. 715
4. 545

The number of real solution(s) of the equation x2+3x+2= \|x-3|,|x+2|\ is :

1. 2
2. 3
3. 1
4. 0

Let f(x)= e x and g(x)= x4-2x3+3x2-2x+22x2-2x+1. Then the domain of f g is

1. (0, )
2. [1, )
3. R
4. [0, )

The product of all solutions of the equation e5( ex)2+3=x8, x>0, is :

1. e2
2. e
3. e6/5
4. e8/5

Let f(x) = 17 - 5x be a function defined on R. Then the range of the function f(x) is equal to :

1. [ 18, 15 ]
2. [ 17, 16 ]
3. [ 17, 15 ]
4. [ 18, 16 ]

If S = \a R : |2a - 1| = 3[a] + 2\a\\, where [t] denotes the greatest integer less than or equal to t and \t\ represents the fractional part of t, then 72 a S a is equal to .

If the domain of the function -1 ( 3x-222x-19 )+ e ( 3x2-8x+5x2-3x-10 ) is ( , ], then 3 +10 is equal to:

1. 95
2. 100
3. 97
4. 98

Let the sum of the maximum and the minimum values of the function f(x)= 2x2-3x+82x2+3x+8 be mn, where (m, n)=1. Then m+n is equal to :

1. 217
2. 182
3. 201
4. 195