Relations and Functions (Class 12)

Let f be a function such that 3f(x) + 2f ( m19x ) = 5x, x 0, where m = i=19 (i)2. Then f(5) - f(2) is equal to

1. 36
2. 9
3. -9
4. 18

Let A = \-2, -1, 0, 1, 2, 3, 4\. Let R be a relation on A defined by xRy if and only if 2x + y 2. Let l be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then l + m + n is equal to :

1. 34
2. 32
3. 33
4. 35

Consider two sets A = \x Z : |(|x - 3| - 3)| 1\ and B = \x R - \1, 2\ : (x - 2)(x - 4)x - 1 e(|x - 2|) = 0 \. Then the number of onto functions f : A B is equal to :

1. 32
2. 81
3. 79
4. 62

Let A = \0, 1, 2, , 9\. Let R be a relation on A defined by (x, y) R if and only if |x - y| is a multiple of 3. Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Statement I is correct but Statement II is incorrect
2. Both Statement I and Statement II are correct
3. Both Statement I and Statement II are incorrect
4. Statement I is incorrect but Statement II is correct

Let the relation R on the set M = \1, 2, 3, , 16\ be given by R = \(x, y) : 4y = 5x - 3, x, y M\. Then the minimum number of elements required to be added in R, in order to make the relation symmetric, is equal to

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

Let f and g be functions satisfying f(x + y) = f(x)f(y), f(1) = 7 and g(x + y) = g(xy), g(1) = 1, for all x, y N. If x = 1n ( f(x)g(x) ) = 19607, then n is equal to :

1. 6
2. 7
3. 4
4. 5

The number of strictly increasing functions f from the set \1, 2, 3, 4, 5, 6\ to the set \1, 2, 3, , 9\ such that f(i) i for 1 i 6, is equal to :

1. 21
2. 28
3. 27
4. 22

The number of relations, defined on the set \a, b, c, d\, which are both reflexive and symmetric, is equal to:

1. 16
2. 64
3. 256
4. 1024

Let A = \2, 3, 5, 7, 9\. Let R be the relation on A defined by xRy if and only if 2x 3y. Let l be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then l + m is equal to:

1. 21
2. 25
3. 23
4. 27

Let A = \0, 1, 2, 3, 4, 5\. Let R be a relation on A defined by (x, y) R if and only if \x, y\ \3, 4\. Then among the statements (S1): The number of elements in R is 18, and (S2): The relation R is symmetric but neither reflexive nor transitive

1. both are false
2. only (S1) is true
3. only (S2) is true
4. both are true