[" 4."(1)/(2x)+(1)/(3y)=2],[(1)/(3x)+(1)/(2y)=(13)/(6)]

Solve : (1)/(2x)+(1)/(4y)-(1)/(3z)=(1)/(4),(1)/(x)=(1)/(3y),(1)/(x)-(1)/(5y)+(4)/(z)=2 (2)/(15)

(1)/(2(3x+4y))=(1)/(5(2x-3y))=(1)/(4),

[" The solution of "(dy)/(dx)=(1)/(2x-y^(2))" is given by "],[[" (A) "y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)],[" (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)]]

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

The solution of (dy)/(dx)=(1)/(2x-y^(2)) is given by , (A) y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," 4"(1)/(2)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)," (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)

Solve the following simultaneous equations. (1)/(2(3x+4y))+(1)/(5(2x-3y))=(1)/(4) , (5)/((3x+4y)) - (2)/((2x-3y))=(3)/(2)

((1)/(2)x^(2)-(1)/(2)y^(2)+(1)/(4)z^(2))-((1)/(3)x^2+(1)/(4)y^(2)+(1)/(2)z^(2))+((1)/(4)x^(2)+(1)/(3)y^(2)+(1)/(3)z^(2))

Find the angle between the following pairs of lines (i) veci=3hati+2hatj-4hatk+lambda(hati-2hatj+2hatk) and vecr=5hatj+hatk+mu(3hati+2hatj+6jhatk) (ii) vecr=hati+hatj+lambda(hati+2hatj+hatk) and vecr=mu(3hati+6hatj+4hatk) (iii) (x-1)/(2)=(y-2)/(3)-(z-1)/(-3) and (x+3)/(-1)=(y-5)/(8) = (z-1)/(4) (iv) (5-x)/(-2)=(y+3)/(-2)=(z-5)/(1) and (x+1)/(2) =(2y-3)/(4) = (z-2)/(1) (v) (x+3)/(1) = (y-1)/(2), z= 3 and (x-1)/(-2)=(y+3)/(3) = (z+5)/(4)