1. Express the following in the form a+ib:-

2. Find the roots of the equation
x²-2(5+2m)x+3(7+10m)=0 so that the equation has equal roots.

3. Find three numbers a,b,c between 2 and 18 such that (i) their sum is 25 (ii) the numbers 2,a,b are consecutive terms of an Arithmetic Progression (iii) the numbers b,c,18 are consecutive terms of a Geometric Progression.

4. If a,b,c are in Geometric Progression and

,
prove that x, y, z are in Harmonic Progression.

5. Find the toal number of 9 digit numbers which have all different digits.

6, Find the number of triangles which can be formed by joining 10 points, 6 of which are in the same straight line.

7. Given

for a fixed positive integer n≥2, prove that

8. Prove that

is divisible by 32.