Relations and Functions · Question 4

Let A=\2, 3, 4, 5, 6\. Let R be a relation on the set A A given by (x, y)R(z, w) if and only if x divides z and y w. Then the number of elements in R is .

If the domain of the function f(x) = (10x2 - 17x + 7) (18x2 - 11x + 1 ) is (- , a) (b, c) (d, ) - \e\, then 90(a + b + c + d + e) equals:

1. 170
2. 316
3. 177
4. 307

The sum of all the real solutions of the equation (x+3) (6x2 + 28x + 30 ) = 5 - 2 (6x+10) (x2 + 6x + 9 ) is equal to :

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

If the domain of the function f(x) = -1 ( 5 - x3 + 2x ) + 1 e(10 - x) is (- , ] [ , ) - \ \, then 6( + + + ) is equal to

1. 66
2. 68
3. 70
4. 67

Let f(x) = [x]2 - [x + 3] - 3, x R, where [.] is the greatest integer function. Then

1. f(x) = 0 for finitely many values of x
2. f(x) < 0 only for x [-1, 3)
3. 02 f(x) dx = -6
4. f(x) > 0 only for x [4, )

Let the domain of the function f(x) = 3 5 (7 - 2 (x2 - 10x + 85 ) ) + -1 ( | 3x - 717 - x | ) be ( , ]. Then + is equal to :

1. 12
2. 8
3. 10
4. 9

The number of elements in the relation R = \(x, y) : 4x2 + y2 < 52, x, y Z \ is

1. 86
2. 67
3. 89
4. 77

Let the domain of the function f(x) = -1 ( 4x + 53x - 7 ) be [ , ] and the domain of g(x) = 2 (2 - 6 27(2x + 5) ) be ( , ). Then |7( + ) + 4( + )| is equal to .

If the range of the function f(x) = 5-xx2-3x+2, x 1, 2, is (- , ] [ , ), then 2 + 2 is equal to :

1. 188
2. 192
3. 190
4. 194

Let the domains of the functions f(x) = 4 3 7 (8 - 2 (x2 + 4x + 5 ) ) and g(x) = -1 ( 7x + 10x - 2 ) be ( , ) and [ , ], respectively. Then 2 + 2 + 2 + 2 is equal to :

1. 15
2. 13
3. 16
4. 14