Q-1) Attempt the following:                                                                                 (30)

a)    There are 260 persons with a skin disorder. If 150 had been exposed to the chemical A, 74 exposed to the chemical B, and 36 exposed to both chemicals A and B, find the number of persons exposed to

i)             Chemical A but not chemical B

ii)            Chemical B but not chemical A

iii)           Chemical A or chemical B

b)    If A,B and C are the sets of letters of the words, FLOWER, COMFORT and COMPUTER respectively, verify that

AU(B C) = (AUB) (AUC).

c)    If f(x) = (x - 2)(x - 3)(x + 5), -2 < x < 5, find f(-1), f(3) and f(6). d)    If f(x) = x2 + 5x + 7, find the value of x for which f(x) = f(x + 1).

e)    Show that fog(x) – gof(x) = 0.5:

f(x) = 1 + 2x and g(x) = f)    Express the following in the form of a + ib , where a,b R. g)   Find the value of x3 – 3x2 – 8x + 31, if x = 3 - .

h)     Simplify the following: i)     Show that (1 + 5w2+ w4)(1 + 5w + w2)(5 + w + w2) = 64

j)     If f(x) = x + 1 and g(x) = 2x – 3. Find

i)                    f + g    ii) f – g            iii) *************