If `p,x_1,x_2,x_3....` and `q,y_1,y_2,y_3,...` from two infinite AP's with common difference `a` and `b` respectively. Then locus of `p(alpha,beta)` where `alpha=(1/n)[x_1+x_2+x_3+...+x_n]` and `beta=(1/n)[y_1+y_2+y_3+...y_n]` is

If a,x_1,x_2,.... and b,y_1,y_2... form two infinite G.P's with same common ratio 'r' then the locus of P(h,k) when h= (x_1x_2x_3...x_n)^(1/n) and k=(y_1y_2y_3.....y_n)^(1/n) is

If a,x_(1),x_(2),x_(3),... .and b,y_(1),y_(2)...... form two infinite geometric prograssions with same common ratio 'r' then the locus of p(h,k) when h=root(n)(x_(1)x_(2)...x_(n)) and k=root(n)(y_(1)y_(2)..... y_(n)) is.

If x_(1),x_(2),x_(3), are in A.P.and y_(1),y_(2),y_(3), are also in A.P.with same common difference then the points (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) form

The geometric mean of (x _(1) , x _(2), x _(3), ... X _(n)) is X and the geometric mean of (y _(1), y _(2), y _(3),... Y _(n)) is Y. Which of the following is/are correct ? 1. The geometric mean of (x _(1) y _(1), x _(2) y _(2) . x _(3) y _(3), ... x _(n) y _(n)) is XY. 2. The geometric mean of ((x _(1))/( y _(1)) , ( x _(2))/( y _(2)), (x _(3))/( y _(3)) , ... (x _(n))/( y _(n))) is (X)/(Y). Select the correct answer using the code given below:

The lines x cos alpha+y sin alpha=P_(1) and x cos beta+y sin beta=P_(2) will be perpendicular,if :

If [[x-y,2x-x_1],[2x-y,3x+y_1]], =[[-1,5],[0,13]] and coordinats of points P and Q be (x,y) and (x_1,y_1) respectively then P,Q=?