Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

x and y are the sides of two squares such that y = x – x². Find the rate of change of the area of second square with respect to the area of first square.

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when side is 10 cm is ______.

A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is ______.

Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?

Let R be the relation on N defined as by x + 2 y = 8 The domain of R is ____________.

Which of the following is not an equivalence relation on I, the set of integers: x, y

Find the area enclosed by the curve x = 3 cost, y = 2 sint.

Find the area of the region included between the parabola y = `(3x^2)/4` and the line 3x – 2y + 12 = 0.

R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A, then R is ____________.

Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A?

Find the area of the region bounded by the curves x = at² and y = 2at between the ordinate corresponding to t = 1 and t = 2.

Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ____________.

Let A = {1, 2, 3}, then the relation R = {(1, 1), (1, 2), (2, 1)} on A is ____________.

Find the area of a minor segment of the circle x² + y² = a² cut off by the line x = `"a"/2`

If A is a finite set containing n distinct elements, then the number of relations on A is equal to ____________.

Let A = {1, 2, 3}, then the domain of the relation R = {(1, 1), (2, 3), (2, 1)} defined on A is ____________.

Let A = {1, 2, 3, 4, 5, 6} Which of the following partitions of A correspond to an equivalence relation on A?

A relation R on a non – empty set A is an equivalence relation if it is ____________.

Calcualte the area under the curve y = `2sqrt(x)` included between the lines x = 0 and x = 1

Draw a rough sketch of the curve y = `sqrt(x - 1)` in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.