A.c 2

(a) If a^(2)+2bc,b^(2)+2ac,c^(2)+2ab are in A.P ., show that (1)/(b-c),(1)/(c-a),(1)/(a-b) are in A.P . (b) Prove that the sum to n terms of the series 11+103+1005+…. = (10)/(9)(10^(n)-1)+n^(2) .

Let a=hati - hatj, b=hati + hatj + hatk and c be a vector such that a xx c + b=0 and a.c =4, then |c|^(2) is equal to .

If Delta_n=|{:(a^(2)+n,ab,ac),(ab,b^(2)+n,bc),(ac,bc,c^(2)+n):}|,n in N and the equation x^(3)-lambdax^(2)+11x-6=0 has roots a,b,c where a,b,c are in AP. The value of sum_(r=1)^(30)((27Delta_(r)-Delta_(3r))/(27r^(2))) is

Distinguish between d.c. and a.c.

A : Wires of the transmission lines carrying A.C. are made of multiple stands. R : A.C. flows on surface of the conductor.

The capacitive reactance in an A.C. circuit is

State one advantage of a.c. over d.c.

Give two similarities between an A.C. generator and a D.C. motor.

Name one d.c. source and one a.c. source.

At what frequency is A.C. supplied to residential houses ?