CTET Paper II (Mathematics and Science) Nov 2012 Solved Paper

Concept:The expression $2^{10} - 1$ simplifies to a number, and divisibility can be checked by direct calculation or by using the digit sum rule for 3.Explanation:First, compute $2^{10} = 1024$.Then, $2^{10} - 1 = 1024 - 1 = 1023$.Now check divisibility by each option:- 1023 is odd, so it is not divisible by 2 or 4 (both even).- 1023 is not divisible by 10 because it does not end in 0.- For 3: Sum of digits = $1+0+2+3 = 6$, and 6 is divisible by 3. Hence 1023 is divisible by 3.Thus, $2^{10} - 1$ is divisible by 3.Answer:Option B. 3