Let `barx` be the mean of `x_1,x_2,……,x_n` and `bary` the mean of `y_1,y_2……,y_n` `barz` is the mean of `x_1,x_2,…. ,x_n, y_1, y_2` is equal to :

If barx is the mean of x1,x2,x3, ………..xn , then for a ne 0, the mean of ax_1,ax_2,…..,ax_n,(x_2)/a, (x_2)/a ,……., (x_n)/a is :

If barx is the mean of x1, x2,x2,x3, ………..xn , then the mean of x1+a,x2+a, x3+a...xn+a

If barx represents the mean of n observations x_1, x_2,…….,x_n , then value of sum_(i=1)^n (x_1-barx) is :

Given that bar x is the mean and sigma^2 is the variance of n observations x_1, x_2, ... x_n . Prove that the mean and variance of the observations ax_1, ax_2, ... ,ax_n , are a bar x and a^2 sigma^2 respectively (a ne 0) .

Given that bar x is the mean and sigma^2 is the variance of n observations x_1 , x_2 ,.... x_n . Prove that the mean and variance of the observations ax_1, ax_2, ax_3 ,......, ax_n are a bar x and a^2 sigma^2 , respectively, (a ne 0) .

Let N^m be the set of al ordered m-tuples of natral numbers. If x = (x_1.x_2……x_m) y = ( y_1,y_2…..y_m) where x_i,y_i, in N, I = 1, 2 ….m and an operation '+' is defined on N^m by x+y = (x_1 + y_1.x_2+y_2,……x_m + y_m) then prove that given operation is commutative as well as associative.

Normals at two points (x_1y_1)a n d(x_2, y_2) of the parabola y^2=4x meet again on the parabola, where x_1+x_2=4. Then |y_1+y_2| is equal to

If the points (x_1,y_1), (x_2,y_2) and (x_1 + x_2, y_1+y_2) are collinear, prove that x_1y_2 = x_2y_1

Area of the triangle with vertices (a, b), (x_1,y_1) and (x_2, y_2) where a, x_1,x_2 are in G.P. with common ratio r and b, y_1, y_2 , are in G.P with common ratio s, is