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

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.

Determine the area under the curve y = `sqrt("a"^2 - x^2)` included between the lines x = 0 and x = a.

tanx is periodic with period ____________.

The period of the function f(x) = tan3x is ____________.

The degree of the differential equation `(1 + "dy"/"dx")^3 = (("d"^2y)/("d"x^2))^2` is ______.

The degree of the differential equation `("d"^2y)/("d"x^2) + 3("dy"/"dx")^2 = x^2 log(("d"^2y)/("d"x^2))` is ______.

The order and degree of the differential equation `[1 + ("dy"/"dx")^2]^2 = ("d"^2y)/("d"x^2)` respectively, are ______.

The order of the differential equation of all circles of given radius a is ______.

Order of the differential equation representing the family of parabolas y² = 4ax is ______.

The degree of the differential equation `("dy"/"dx")^2 + (("d"^2y)/("d"x^2))^2` = 0 is ______.