HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius 10 cm

Prove that among all the rectangles of the given perimeter, the square has the maximum area

Find the dimensions of the largest rectangle that can be inscribed in a semi-circle of radius r cm

A manufacturer wants to design an open box having a square base and a surface area of 108 sq.cm. Determine the dimensions of the box for the maximum volume

The volume of a cylinder is given by the formula V = `pi"r"^2"h"`. Find the greatest and least values of V if r + h = 6

A hollow cone with a base radius of a cm and’ height of b cm is placed on a table. Show that) the volume of the largest cylinder that can be hidden underneath is `4/9` times the volume of the cone

Find the asymptotes of the following curves:

f(x) = `x^2/(x + 1)`

Find the asymptotes of the following curves:

f(x) = `(x^2 - 6x - 1)/(x + 3)`

Choose the correct alternative:

One of the closest points on the curve x² – y² = 4 to the point (6, 0) is

Find the area of the region bounded by 3x – 2y + 6 = 0, x = – 3, x = 1 and x-axis

Find the area of the region bounded by 2x – y + 1 = 0, y = – 1, y = 3 and y-axis

Find the area of the region bounded by the curve 2 + x – x² + y = 0, x axis, x = – 3 and x = 3

Find the area of the region bounded by the line y = 2x + 5 and the parabola y = x² – 2x

Find the area of the region bounded between the curves y = sin x and y = cos x and the lines x = 0 and x = π

Find the area of the region bounded by y = tan x, y = cot x and the lines x = 0, x = `pi/2`, y = 0

Find the area of the region bounded by the parabola y² = x and the line y = x – 2

Father of a family wishes to divide his square field bounded by x = 0, x = 4, y = 4 and y = 0 along the curve y² = 4x and x² = 4y into three equal parts for his wife, daughter and son. Is it possible to divide? If so, find the area to be divided among them

The curve y = (x – 2)² + 1 has a minimum point at P. A point Q on the curve is such that the slope of PQ is 2. Find the area bounded by the curve and the chord PQ

Find the area of the region common to the circle x² + y² = 16 and the parabola y² = 6x

Choose the correct alternative:

The area between y² = 4x and its latus rectum is