Find the G.M. of the following numbers :
(i) `(1)/(3)" and "(1)/(27)` (ii) `x^(2)" and "y^(2)`

Find the sum to infinity of the following G.P. (i) 1, (1)/(3) , (1)/(9) . (1)/(27),… (ii) 2 , (-2)/(3) , (2)/(9) , (-2)/(27),… .

Find the centre and radius of each of the following circles : (i) (x - 3)^(2) + (y- 1) ^(2) = 9 (ii) (x - (1)/(2) ) ^(2) + ( y + (1)/(3) ) ^(2) = (1)/(16) (iii) (x + 5) ^(2) + ( y- 3 ) ^(2) = 20 (iv) x ^(2) + (y- 1 ) ^(2) = 2

Find the number of terms in the following G.P. (1)/(3), (1)/(9), (1)/(27), …, (1)/(2187)

If x be real then find the range of the following rational expressions (i) y=(x^(2)+x+1)/(x^(2)+1) (ii) y=(x^(2)-2x+9)/(x^(2)+2x+9)

Find the angle between the following pairs of lines : (i) y=sqrt(3)x+1 and y=(1)/(sqrt(3))x+2 (ii) y=x and y=1-x (iii) 2x+3y=2 and 3x-2y=1 .

Find the angle between the following pairs of lines : (i) y=sqrt(3)x+1 and y=(1)/(sqrt(3))x+2 (ii) y=x and y=1-x (iii) 2x+3y=2 and 3x-2y=1 .

Find the value of each of the following : (i) p(x)=3x+7 " at" x=1 " " (ii) q(y)=y^(3)-3y^(2)+sqrt(3) " at" y=1 (iii) p(a)=a^(4)+6a^(2)-6a+3 at a=m

Find the value of each of the following : (i) p(x)=3x+7 " at" x=1 " " (ii) q(y)=y^(3)-3y^(2)+sqrt(3) " at" y=1 (iii) p(a)=a^(4)+6a^(2)-6a+3 at a=m

Find the cube of each of the following binomial expressions: (1)/(x)+(y)/(3)( ii) (3)/(x)-(2)/(x^(2))