The point of intersection of straight lines represented by 6x² + xy - 40y² – 35x - 83y + 11 = 0 is:

The radius of the base and depth of a conical funnel are 20 cm and 40 cm respectively. Water flows from the funnel at the rate 2.25 cc/sec. the rate at which the water level decreases when altitude is 30 cm is

The equation of the tangent to the curve y=x+9/x+5 so that is passes through the origin is

The maximum value of the area of the triangle with vertices (a, 0), (a cos θ, b sin θ), (a cos θ, -b sin θ) is

The values of x for which 2x³-3x²-36x+10 has extreme values are

The curve y=a²+bx has minimum at (2, -1) on it. Then (a, b)=

A stone thrown upwards, has its equation of motion s=490t-4.9t². Then the maximum height reached by it is

The equation of the normal to the curve y=3x²+4x-6 at (1, 1) is

The equation of the tangent to the curve y=x³-2x+7 at (1, 6) is

The values of ‘a’ for which the function (a+2)x³-3ax²+9ax-1 decreases monotically throughout for all real x are