If `p,x_1 ,x_2 ,...`, and `q,y_1 ,y_2 ,...,y_i ,...` are in A.P.,with common difference `a` and `b` respectively, then locus of the center of mean position of the points `A_i (x_i ,y_i) ,i=1,2...n` is

If a, x_1, x_2, …, x_k and b, y_1, y_2, …, y_k from two A. Ps with common differences m and n respectively, the the locus of point (x, y) , where x= (sum_(i=1)^k x_i)/k and y= (sum_(i=1)^k yi)/k is: (A) (x-a) m = (y-b)n (B) (x-m) a= (y-n) b (C) (x-n) a= (y-m) b (D) (x-a) n= (y-b)m

p,x_(1), x_(2) ,. . . x_(n) and q, y_(1),y_(2), . . . ,y_(n) are two arithmetic progressions with common differences a and b respectively. If alpha and beta are the arithmetic means of x_(1), x_(2), . . . . x_(n), and y_(1), y_(2), . . . . y_(n) respectivley . then the locus of p(alpha, beta) is

The circle orthogonal to the three circles x^2+y^2+a_i x +b_i y+c=0 , (i=1,2,3) is

If x and y are complex numbers, then the system of equations (1+i)x+(1-i)y=1,2i x+2y=1+i has

If a, b, c are in G.P., x and y are the A.M.'s of a, b and b, c respectively, then prove that: (i)(a)/(x)+(c)/(y)=2" "(ii) (1)/(x)+(1)/(y)=(2)/(b)

Find the real values of x\ a n d\ y ,\ if:(x+i y)(2-3i)=4+i

Let x_1, x_2, ,x_n be x_n observations. Let y_i=a x_i+b for i=1,2,...,n where a and b are constants. If the mean of x_i's is 48 and their standard deviation is 12, the mean of y_i 's is 55 and standard deviation of y_i's is 15, the values of a and b are (a) a=1. 25 ,b=-5 (b) a=-1. 25 ,b=5 (c) a=2. 5 ,b=-5 (d) a=2. 5 ,b=5

Let x_1, x_2, ,x_n be x_n observations. Let y_i=a x_i+b for i=1,2,...,n where a and b are constants. If the mean of x_i's is 48 and their standard deviation is 12, the mean of y_i 's is 55 and standard deviation of y_i's is 15, the values of a and b are (a) a=1. 25 ,b=-5 (b) a=-1. 25 ,b=5 (c) a=2. 5 ,b=-5 (d) a=2. 5 ,b=5

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=?

Find the real values of x\ a n d\ y ,\ if:(1+i)(x+i y)=2-5i