Relations and Functions

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

If the domain of the function f(x)= x2-25 (4-x2 )+ 10 (x2+2x-15 ) is (- , ) [ , ), then 2+ 3 is equal to :

1. 140
2. 175
3. 125
4. 150

If the domain of the function f(x)= -1 ( 2-|x|4 )+ \ e(3-x) \-1 is [- , )-\ \, then + + is equal to :

1. 11
2. 12
3. 9
4. 8

If the domain of the function f(x)= e ( 2 x+34 x2+x-3 )+ -1 ( 2 x-1x+2 ) is ( , ], then the value of 5 -4 is equal to

1. 9
2. 12
3. 11
4. 10