Maths Quiz (NTSE)

A palindrome is a sequence that reads the same forwards and backwards. A single digit number like 1 satisfies this condition.

To find the unit digit of the product, multiply the unit digits: 4 * 8 * 7 * 3. 4 * 8 = 32 (unit digit 2), 2 * 7 = 14 (unit digit 4), 4 * 3 = 12 (unit digit 2).

The sum of the first n natural numbers is given by n(n+1)/2. For n=45, the sum is 45 * 46 / 2 = 45 * 23 = 1035.

A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of digits of 5x311 is 5+x+3+1+1 = 10+x. For 10+x to be divisible by 9, x must be 8 (18 is divisible by 9).

Multiples of 10 between 150 and 450 inclusive are 150, 160, ..., 450. This is an arithmetic progression where a=150, l=450, d=10. n = (450-150)/10 + 1 = 30 + 1 = 31.

The power cycle of 7 is 4 (7^1=7, 7^2=49, 7^3=343, 7^4=2401). The unit digits repeat in the sequence 7, 9, 3, 1.

Area = length * breadth. New Area = (2 * length) * (0.5 * breadth) = 1 * length * breadth. The area remains unchanged, so the percentage change is 0%.

If the side increases by 20%, the new side is 1.2 * s. The new area is (1.2 * s)^2 = 1.44 * s^2. This represents a 44% increase.

10% of 87.5% of 880 = 0.10 * 0.875 * 880. 0.875 * 880 = 770. 0.10 * 770 = 77.