" 2."4sqrt(4)10^(2y)=25," " "10^(-y)" arrar "(1)/(6)-

Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)) , (b) (2)/(sqrt5 + sqrt3 + sqrt2) , (c) (x^(2))/(sqrt(x^(2) + y^(2)) - y) , (d) (1)/(sqrt6 + sqrt5 - sqrt11) (e) (sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y)) , (f) (sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)

If sqrt(1-x^(4))+sqrt(1-y^(4))=k(x^(2)-y^(2)), prove that (dy)/(dx)=(x sqrt(1-y^(4)))/(y sqrt(1-x^(4)))

sqrt(125)y^(2)+sqrt(25y^(4))by5y^(2)

The area bounded between the parabolas x^(2)=(y)/(4) and x^(2)=9y and the straight line y=2 is (1)20sqrt(2)(2)(10sqrt(2))/(3) (3) (20sqrt(2))/(3) (4) 10sqrt(2)

The area bounded between the parabolas x^2=y/4"and"x^2=9y and the straight line y""=""2 is (1) 20sqrt(2) (2) (10sqrt(2))/3 (3) (20sqrt(2))/3 (4) 10sqrt(2)

lim_(y->oo)(sqrt(1+sqrt(1+y^(4)))-sqrt(2))/(y^(4))= (a) (1)/(4sqrt(2)) (b) (1)/(2sqrt(2)) (c) (1)/(2sqrt(2)(1+sqrt(2))) (d) does not exist

lim_(y->o)(sqrt(1+sqrt(1+y^(4)))-sqrt(2))/(y^(4))= (a) (1)/(4sqrt(2)) (b) (1)/(2sqrt(2)) (c) (1)/(2sqrt(2)(1+sqrt(2))) (d) does not exist

Distance between the lines represented by 9x^2-6x y+y^2+18 x-6y+8=0 , is 1. 1/(sqrt(10)) 2. 2/(sqrt(10)) 3. 4/(sqrt(10)) 4. sqrt(10) 5. 2/(sqrt(5))

Distance between the lines represented by 9x^2-6x y+y^2+18 x-6y+8=0 , is 1/(sqrt(10)) 2. 2/(sqrt(10)) 3. 4/(sqrt(10)) 4. sqrt(10) 5. 2/(sqrt(5))