1 
m(21 + n/100) = 63.63 
2100 m + mn = 6363 = 6300 + 63 
m = 3 and n = 21 

2 
1, 5, 7, 4, 8 
11, 15, 17, 14, 18 

3 
If N is prime then it has 2 divisors. (Prime number is having 2 divisors) 
N + 1 is having 3 divisors means it is a square number (Square number is having odd number of divisors) 
N = 3 
divisors 1, 3 
N + 1 = 4 
divisors 1, 2, 4 
N + 2 = 5 is prime having 2 divisors. 

4 
Biggest 10 digit palindrome is 9999999999 
smallest 8 digit palindrome number is 11111111 
find difference. 

5 
P/9 + q/10 = r 
p/9 + p/10 = r 
19p = 90r 
p = 90 and r = 19 
Maximum value of r = 95 
when p = 450 

6 p, q , (p – q), (p + q) are prime 
sum = 3p + q 
p and q are odd so 3p is odd 
3p + q is even divisible by 2 

7 
a(b + c) = 32 
b(c + a) = 65 
c(a + b) = 32 
ab + ac + bc + ab + ac + bc = 174 
ab + bc + ac = 85 
bc = 87 – 32 = 55 
b = 11 or 5 and c = 5 or 11 

ac = 85 – 65 = 20 = 5 × 4 
so a = 5 or 4 and c = 4 or 5 

from above conclusion a = 4, b = 11 and c = 5 
abc = 220 

8 
Let full volume = x 
0.6x = 80 + 0.2x 
0.4x = 80 
x = 20 

10 
sum of all 5 angles = 540 
sum of remaining 3 angles = 540 – 180 = 360 
each angle = 120°