The product of the last two digits of (1919) 1919 is
Step-by-Step Solution
Key Concept: Use the general term of the binomial expansion for last two digits using modular binomial pattern and impose the required coefficient or exponent condition.
(1919)$1919 = (1920 - 1)$1919 1919 1919 1919 1918 (63) =$C_{0}$(1920) -$C_{1}$(1920) +$\ldots$. 1919 1$1919 + C1918$$(1920) - C1919 = 10$0$\lambda$+ 1919 $\times$$1920 - 1 = 10$0$\lambda$+$3684480 - 1 = 10$0$\lambda$+$\ldots$$\ldots$$\ldots$. .79 (last two digit) $\Rightarrow$ Number having last two digit 79 ∴ Product of last two digit 63$1016-r$r
Correct Answer: 63