How Cheenta works to ensure student success?

Explore the Back-Storyis a right angled triangle with as hypotenuse. The medians drawn to and are perpendicular to each other. If has length , find the area of triangle .

(a) Find the smallest positive integer such that it has exactly different positive integer divisors including and the number itself.

(b) A rectangle can be divided into ' ' equal squares. The same rectangle can also be divided into equal squares. Find .

Prove that is divisible by for all odd .

Is it possible to have lines in a plane such that (1) no three lines have a common point and (2) they have exactly points of intersection. Validate.

In a trapezium with parallel to , the diagonals intersect at . The area of is area of is . Find the area of the trapezium.

Let be three positive integers. Prove that among any consecutive positive integers there exists three different numbers such that divides .

(a) Let be positive integers. If is the square of an integer, then prove that is not a product of two different prime numbers.

(b) are real numbers such that, . Prove .

is a quadrilateral in a circle whose diagonals intersect at right angles. Through the centre of the circle, and are drawn parallel to respectively, meeting in and , produced in . Prove are parallel to and respectively.

is a right angled triangle with as hypotenuse. The medians drawn to and are perpendicular to each other. If has length , find the area of triangle .

(a) Find the smallest positive integer such that it has exactly different positive integer divisors including and the number itself.

(b) A rectangle can be divided into ' ' equal squares. The same rectangle can also be divided into equal squares. Find .

Prove that is divisible by for all odd .

Is it possible to have lines in a plane such that (1) no three lines have a common point and (2) they have exactly points of intersection. Validate.

In a trapezium with parallel to , the diagonals intersect at . The area of is area of is . Find the area of the trapezium.

Let be three positive integers. Prove that among any consecutive positive integers there exists three different numbers such that divides .

(a) Let be positive integers. If is the square of an integer, then prove that is not a product of two different prime numbers.

(b) are real numbers such that, . Prove .

is a quadrilateral in a circle whose diagonals intersect at right angles. Through the centre of the circle, and are drawn parallel to respectively, meeting in and , produced in . Prove are parallel to and respectively.

Cheenta is a knowledge partner of Aditya Birla Education Academy

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

JOIN TRIALAcademic Programs

Free Resources

Why Cheenta?

Online Live Classroom Programs

Online Self Paced Programs [*New]

Past Papers

More