Application of ...

The curve given by the equation $$y-e^{xy}+x=0$$ has a vertical tangent at the point

The sum of the intercepts made on the axes of coordinates by any tangent to the curve $$\sqrt{x}+\sqrt{y}=2$$ is equal to

lf $$\alpha = \cos 10^{\circ} - \sin 10^{\circ}, \beta = \cos 45^{\circ} - \sin 45^{\circ}, \gamma = \cos 70^{\circ} - \sin 70^{\circ}$$ then the descending order of $$\alpha, \beta, \gamma$$ is

lf the curve $$y=px^{2}+qx+r$$ passes through the point (1, 2) and the line $$y=x$$ touches it at the origin, then the values of $$p,\ q$$ and $$r$$ are

If there is an error of $$k%$$ in measuring the edge of a cube, then the percent error in estimating its volume is

At what points of curve $$y= \displaystyle \frac {2}{3} x^3 + \displaystyle \frac{1}{2} x^2 $$, the tangent makes equal angle with the axis

If the circle $$x^{2}+y^{2}+2gx+2fy+c=0$$ is touched by $$y=x$$ at $$P$$ such that 
$$OP=6\sqrt{2},$$ then the value of $$c$$ is

The number of tangents to the curve $$x^{3/2} + y^{3/2}= 2a^{3/2}$$, $$a>0$$, which are equally inclined to the axes, is

If $$m$$ is the slope of a tangent to the curve $$e^y= 1+x^2$$, then 

If at each point of the curve $$y=x^3-ax^2 +x+1$$, the tangent is inclined at an acute angle with the positive direction of the $$x$$-axis, then