58 Questions Available
Showing 20 questions on this page
Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.
Find the intervals in which the function θ=cos–1 (x/y) = cos–1 (1/2) = π/3 is (a) increasing, (b) deceasing
If length of three sides of a trapezium other than base are equal to 10 cm, then find the area of the trapezium when it is maximum.
A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 m, find the dimensions of the rectangle that will produce the largest area of the window.
Find the equation of the tangent to the curve = y = dy/dx = (x² - 1) (1) + (x – 2) (2x) = 3x² - 4x- 1 Which is parallel to the line 4x – 2y + 5 = 0
Find the equations of tangents to the curve 3x2 – y2 = 8, which pass through the point (4/3, 0).
An open box with a square base is to be made out of a given quantity of metal sheet of area c2. Show that the maximum volume of the box is dz/dx = 0.
Find the intervals in which the function f given by f (x) = 2x3 – 3x2 – 36x + 7 is (a) strictly increasing (b) strictly decreasing.
Find the intervals in which the following function is (a) increasing (b) decreasing:
For the curve y = 4x3 – 2x5, find all the points at which the tangent passes through the origin.
Find the points on the curve y = x3 at which the slope of the tangent is equal to the y-coordinate of point.
Find the points on the curve x2 + y2 – 2x – 3 = 0 at which the tangents are parallel to the x-axis.
Find the equation of the normal at the point (am2, am3) for the curve ay2 = x3.
Find the point on the curve y = x3 – 11x + 5 at which the equation of the tangent is y=x–11.
Show that the total surface area of a closed cuboid with square base and given volume, is minimum, when it is a cube.
If the sum of the lengths of the hypotenuse and a side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between them is π/3.
Manufacturer can sell x items at a price of rupees
each. The cost price of x items is Rs
Find the number of items he should sell to earn maximum profit.
Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle α is one-third that of the cone and the greatest volume of cylinder is
A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is tan –1(0.5). Water is poured into it at a constant rate of 5 cubic meter per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 4 m.
The volume of a cube is increasing at the rate of 8 cm3/s. How fast is the surface area increasing when the length of an edge is 12 cm?
