Question

Let
Statement 1:(2002)2023 - (1919)2002 is divisible by 8.
Statement 2: 13.13n - 12n - 13 is divisible by 144 n$\varepsilon$N, then

• A. Statement-1 and statement-2 both are true
• B. Only statement-1 is true
• C. Only statement-2 is true
• D. Neither statement-1 nor statement-2 are true

Answer 1

Answer: (B)

Only statement-1 is true

Answer 2

The correct option is (B): Only statement-1 is true
∵ (2002)2023 = 8 m
∵ (2002)2023 is divisible by 8 and (1919)2002 is not divisible by 8
∴ (2002)2023 - (1919)2002 is not divisible by 8.
Also, 13.(13)n - 12n - 13
= 13(1+12)n - 12n - 13
= 13 [1+12n + nC2 122 + --] - 12n - 13
= 144n + 144nC2 + --
= 144 [n + nC2 + --]
= 144K
∴, the option (B) is the correct option.