EXERCISE 13.1 Q 1 AND Q2

Let S_n=1+q+q^2 +...+q^n and T_n =1+((q+1)/2)+((q+1)/2)^2+...((q+1)/2)^n If alpha T_100=^101C_1 +^101C_2 x S_1 ...+^101C_101 x S_100, then the value of alpha is equal to (A) 2^99 (B) 2^101 (C) 2^100 (D) -2^100

If adj B=A ,|P|=|Q|=1,t h e na d j(Q^(-1)B P^(-1)) is P Q b. Q A P c. P A Q d. P A^1Q

If adj B=A ,|P|=|Q|=1, then. adj(Q^(-1)B P^(-1)) is a. P Q b. Q A P c. P A Q d. P A^-1Q

If f(x) = px +q, where p and q are integers f (-1) = 1 and f (2) = 13, then p and q are

The common difference of the A.P. is 1/(2q),(1-2q)/(2q),(1-4q)/(2q),\ dot is (a)-1 (b) 1 (c) q (d) 2q

If 2p+q=11 and p+2q=13, then p+q=

Threee charges +Q_(1),+Q_(2) and q are placed on a straight line such that q is somewhere in between +Q_(1) and Q_(2) . If this system of charges is in equlibirium what should be the magnitude and sign of charge q?

In figure, the charges on C_(1),C_(2) , and C_(3) , are Q_(1), Q_(2) , and Q_(3) , respectively. .

(p^^~q) is logically equal to 1. p -> q 2. ~ p->q 3. p -> ~ q 4. ~(p ->q)

If O is the origin and if the coordinates of any two points Q_1 \ a n d \ Q_2 are (x_1,y_1) \ a n d \ (x_2,y_2), respectively, prove that O Q_1.O Q_2cos/_Q_1O Q_2=x_1x_2+y_1y_2 .