How Cheenta works to ensure student success?

Explore the Back-StoryFind integers such that the sum of their cubes is equal to the square of their sum.

is an acute scalene triangle. The altitude and the bisector of meet at ( on and on ). is the altitude of triangle ; it meets at . The circumcircle of meets at other than . Prove that is an isosceles triangle.

Let are reals. The polynomial

can be factorized into linear factors where .

Find the possible values of .

There are (an even number) bags. Each bag contains at least one apple and at most apples. The total number of apples is . Prove that it is always possible to divide the bags into two parts such that the number of apples in each part is .

are positive reals satisfying

and . Find the maximum value of

The sum of the squares of four reals is 1 . Find the minimum value of the expression . Find also the values of and when this minimum occurs.

Let be a positive integer; and denote the sum of all digits in the decimal representation of . A positive integer obtained by removing one or several digits from the right hand end of the decimal representation of is called a truncation of . The sum of all truncations of is denoted as . Prove that .

is a cyclic quadrilateral. The midpoints of the diagonals and are respectively and . If bisects the , then prove that will bisect .

Find integers such that the sum of their cubes is equal to the square of their sum.

is an acute scalene triangle. The altitude and the bisector of meet at ( on and on ). is the altitude of triangle ; it meets at . The circumcircle of meets at other than . Prove that is an isosceles triangle.

Let are reals. The polynomial

can be factorized into linear factors where .

Find the possible values of .

There are (an even number) bags. Each bag contains at least one apple and at most apples. The total number of apples is . Prove that it is always possible to divide the bags into two parts such that the number of apples in each part is .

are positive reals satisfying

and . Find the maximum value of

The sum of the squares of four reals is 1 . Find the minimum value of the expression . Find also the values of and when this minimum occurs.

Let be a positive integer; and denote the sum of all digits in the decimal representation of . A positive integer obtained by removing one or several digits from the right hand end of the decimal representation of is called a truncation of . The sum of all truncations of is denoted as . Prove that .

is a cyclic quadrilateral. The midpoints of the diagonals and are respectively and . If bisects the , then prove that will bisect .

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