Answer Any 5 Question.docx

Answer any 5 question. 1.

The sum of integers lying between 1 and 100 which are divisible by either 3 or 7.

2.

If a be the first term of an A.P and the sum of its first p terms is equal to zero show that the sum of the next q terms is 

a  p  q q. p 1

a  bx b  cx c  dx , then prove that a, b, c, d are in G.P   a  bx b  cx c  dx

3.

If

4.

If a and b are the roots of x 2  3x  p  0 and c, d are the roots of x 2  12 x  q  0 , where a, b, c, d form a G.P. Prove that  q  p  :  q  p   17 :15 .

5.

Find the sum of the series

13 13  23 13  23  33    ...  n terms. 1 1 3 1 3  5

6.

Find the value of n so that

a n+1 + b n+1 may be the geometric mean between a and b. a n + bn