Long Answer TypeShow that the height of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is 
Also find the maximum volume.
Given, radius of the sphere is R.
Let r and h be the radius and the height of the inscribed cylinder respectively.
We have:
Let Volume of cylinder = V
Differentiating the above function w.r.t r, we have, 
For maxima or minima, 
Now, when 
When 
Hence, the volume of the cylinder is the maximum when the height of the cylinder is 
Find the equation of the normal at a point on the curve x2 = 4y which passes through the point (1, 2). Also, find the equation of the corresponding tangent.
Short Answer TypeFind the Cartesian equation of the line passes through the point (-2, 4, -5) and is parallel to the line 
The amount of pollution content added in air in city due to x-diesel vehicles is given by 
Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above questions.
Switch
and 
are two equal vectors, then write the value of x+y+z.
makes angle 
then find the value of 
.
