Short Answer TypeDivide a number 15 into two parts such that the square of one multiplied with the cube of the other is a maximum.
Long Answer TypeHow should we choose two numbers, each greater than or equal to -2 whose sum is 
so that the sum of the square of the first and cube of the second is the minimum?
The space s described in time t by a particle moving in a straight line is given by s = r5 – 40r + 30r2 + 80t – 250. Find the minimum value of its acceleration.
Short Answer TypeTwo sides of a triangle are given. Find the angle between them such that the area shall be maximum.
Show that of all the rectangles with a given perimeter, the square has the largest area.
Let x , y be the lengths of sides of rectangle and 2 k be the perimeter.
...(1)
Let 
∴ area of a rectangle of given perimeter is maximum when its sides are equal i.e., when it is a square.
Long Answer TypeShow that, of all the rectangles inscribed in a given fixed circle, the square has the maximum area.
Short Answer TypeFind the dimensions of the rectangle of greatest area that can be inscribed in a semi-circle of radius r.
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