Question

1) A committee of 12 members is to be formed from 9 women and 8 men. Find the number of committees in which the women are in majority.

2) If 2nd term of a G.P. is 24 and 5th term is 81. Find the first term.

ANSWER THESE QUESTIONS FAST PLZ!!!!!!!!

Answer 1

1) ans is in pic

2) I am taking2nd term 81 and 5th term 24

5th term = 81 = ar5-1 = ar4

2nd term = 24 = ar2-1 = ar

.

(ar4 / ar) = (81 / 24)

r3 = (27 / 8) = (3/2)3

r = (3/2)

,

Hence, first term a= (2nd term / r) = 24 / (3/2) = (24*2)/3 = 16.

.

Sum of n terms of a GP = a[(r)n - 1] / [(r-1)]

Sum of first 8 terms = 16 [(3/2)8 - 1] / [(3/2) - 1]

= 16 [(3/2)8 - 1] / [(3-2)/3]

= 16 [(3/2)8- 1] / (1/3)

= (16*3) [(3/2)8- 1]

= 48 (6561 / 256) - 48

= [3(6561) / 16] - 48

= {19683 - 768) / 16

= (18915) / (16)