PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.

The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.

Find the sum of the following arithmetic progression :

50, 46, 42, ... to 10 terms

Find the sum of the following arithmetic progression :

1, 3, 5, 7, ... to 12 terms

Find the sum of the following arithmetic progression :

3, 9/2, 6, 15/2, ... to 25 terms

Find the sum of the following arithmetic progression :

41, 36, 31, ... to 12 terms

Find the sum of the following arithmetic progression :

a + b, a − b, a − 3b, ... to 22 terms

Find the sum of the following arithmetic progression :

 (x − y)², (x² + y²), (x + y)², ... to n terms

Find the sum of the following arithmetic progression :

\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.

Find the sum of the following serie:

 2 + 5 + 8 + ... + 182

Find the sum of the following serie:

101 + 99 + 97 + ... + 47

Find the sum of the following serie:

(a − b)² + (a² + b²) + (a + b)² + ... + [(a + b)² + 6ab]

Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.

Find the sum of all integers between 50 and 500 which are divisible by 7.