If `y=x-x^2,` then the derivative of `y^2` with respect to `x^2` is (a)`1-2x` (b) `2-4x` (c)`3x-2x^2` (d) `1-3x+2x^2`

Integrate the following with respect to x : (i) (2x-3)/(x^2+4x-12) (ii) (5x-2)/(2+2x+x^2) (iii) (3x+1)/(2x^2-2x+3)

The first derivative of the function [cos^(-1)(sinsqrt((1+x)/2))+x^x] with respect to x at x=1 is (a) 3//4 (b) 0 (c) 1//2 (d) -1//2

Differentiate cosec^(-1)((1 + x^(2))/(2x)) with respect to cot^(-1)((1 - 3x^(2))/(3x - x^(3))).

Integrate the following with respect to x. (1)/((2x+1)^(3))+(3)/(5-2x)+(1)/(sqrt(1-4x^(2)))

The lines 2x-3y=5 and 3x-4y=7 are the diameters of a circle of area 154 sq. units. Then the equation of the circle is (a) x^2+y^2+2x-2y=62 (b) x^2+y^2+2x-2y=47 (c) x^2+y^2-2x+2y=47 (d) x^2+y^2-2x+2y=62

If points Aa n dB are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

Draw the graph of y=x^(2)+3x+2 and use it to solve x^(2)+2x+1=0 .