A curve `g(x)=intx^(27)(1+x+x^2)^6(6x^2+5x+4)dx` is passing through origin. Then (a)`g(1)=(3^7)/7` (b) `g(1)=(2^7)/7` (c)`g(-1)=1/7` (d)`g(-1)=(3^7)/(14)`

I = int 1/((x+a)^(8/7)(x - b)^(6/7)) dx =

Evaluate: int(dx)/(x^2(1+x^7)^(6/7))

Find the image of the point (1, 2, 3) in the line (x-6)/(3)=(y-7)/(2)=(z-7)/(-2) .

Let g(x) be a function defined on [-1,1]dot If the area of the equilateral triangle with two of its vertices at (0,0) a n d (x ,g(x)) is (a) (sqrt(3))/4 , then the function g(x) is (b) g(x)=+-sqrt(1-x^2) (c) g(x)=sqrt(1-x^2) (d) g(x)=-sqrt(1-x^2) g(x)=sqrt(1+x^2)

If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0) , and f(0) = 0, then the value of f(1) is

If sin^(-1)(5/x)+sin^(-1)((12)/x)=pi/2, then x is equal to 7/(13) (b) 4/3 (c) 13 (d) (13)/7

The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing through the origin and touching the line y=x always passes through the point. (a) (-1/2,1/2) (b) (1, 1) (c) (1/2,1/2) (d) none of these

If g(x-2)=x^(2)-4x+5 , the determine - (a) g (x) and (b) g(x + 1).

If x = sqrt7 + sqrt6 , then find the simpliest value of (a) x - (1)/(x) , (b) x + (1)/(x) , (c) x^(2) + (1)/(x^(2)) , (d) x^(3) + (1)/(x^(3))

If f(x)=-6+10x-7x^(2) , then f(-1) =