State with reason whether following functions have inverse (i) `f:{1,2,3,4} -{10} w i t h f={(1, 10),(2, 10),(3, 10),(4, 10)}`(ii) `g:{5, 6, 7, 8}-{1,2,3,4} w i t h g={(5, 4),(6, 3),(7, 4),(8, 2)}

State with reason whether following functions have inverse (i) f:{1,2,3,4} ->{10} " with " f={(1, 10),(2, 10),(3, 10),(4, 10)} (ii) g:{5, 6, 7, 8}->{1,2,3,4}" with "g={(5, 4),(6, 3),(7, 4),(8, 2)} (iii) h : {2, 3, 4, 5} → {7, 9, 11, 13}" with "h = {(2, 7), (3, 9), (4, 11), (5, 13)}

Examine which of the following relations (defined on subsets of Z) are functions (i) f = {(2, 1), (2, 3), (4, 3), (1, 2)} (ii) g = {(2, 1), (4, 2), (6, 3), (8,4), (10, 5)}

Find the mode of (i) 7, 7, 8, 10, 10, 11,13, 14 (ii) 4, 5, 6, 7, 8, 7, 6, 5, 3, 4, 6, 7, 6

Show that the following points are collinear : (i) (0,7,-7), (1,4,-5), (-1, 10,-9) (ii) (3,-5,1), (-1,0,8), (7,-10,-6) (iii) (-2,3,5),(7,0,-1),(1,2,3)

Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not ? (i) R={(4,1),(5,1),(6,7)} (ii) R={(2,3),(2,5),(3,3),(6,6)} (iii) R={(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} (iv) R={(1,1),(2,1),(3,1),(4,1),(5,1)}

Wherever possible write each of the following as a single matrix. (i) [{:(,1,2),(,3,4):}]+[{:(,-1,-2),(,1,-7):}] (ii) [{:(,2,3,4),(,5,6,7):}]-[{:(,0,2,3),(,6,-1,0):}] (iii) [{:(,0,1,2),(,4,6,7):}]+[{:(,3,4),(,6,8):}]

Arrange the following data as an array (descending order): (i) 2,0,3,4, 1, 2, 3,5 (ii) 9.1, 3.7, 5.6, 8.3, 11.5, 10.6

If f and g two functions are defined as : f= {(1,2),(3,6),(4,5)} and g = {(2,3),(6,7),(5,8)}, then find gof.

Find the mean of the following frequency distribution: Variable (x_i) , 2, 4, 6, 8, 10, 12, 14, 16 Frequency (f_i) , 4, 4, 5, 15, 8, 5, 4, 5

If A={1,2,3} and B={2,3,4} , find which of the following are the functions from A to B? (i) f={(1,2),(2,3),(3,4)} (ii) g={(1,2),(1,3),(2,3),(3,4)} (iii) h={(1,3),(2,4)}