COLUMN - I		COLUMN - II
A)	The remainder, when $\left({15}^{23}+{23}^{23}\right)$ is divided by 19, is	p)	0
B)	If $(11{)}^{27}+(21{)}^{27}$ when divided by 16 leaves the remainder	q)	01
C)	Last Two digits of the number $\mathrm{N}=7^{100}-3^{100}$ are	r)	15
D)	The last two digits of the number $3^{400}$ are	s)	10

A) ${15}^{23}+{23}^{23}\Rightarrow {\mathrm{a}}^{\mathrm{n}}+{\mathrm{b}}^{\mathrm{n}}$ is divisible $\mathrm{a}+\mathrm{b}\Rightarrow {15}^{23}+{23}^{23}$ is divisible by 38 $\Rightarrow {15}^{23}+{23}^{23}$ is divisible by 19

B) ${11}^{27}+{21}^{27}$ is divisible by 32 i.e., 16 $\Rightarrow$

C) $\mathrm{N}=7^{100}-3^{100}={\left(7^4\right)}^{25}-{\left(3^4\right)}^{100}\Rightarrow \text{ units }\mathrm{y} 7^4\text{ is }1$

     $\Rightarrow 3^4\text{ is }1\Rightarrow \therefore \text{ two digits are }\mathrm{N}=00$

      $\Rightarrow 7^{100}-3^{100}=(5+2{)}^{100}-(5-2{)}^{100}2\left[{ }^{100}{\mathrm{C}}_1{52}^{99}{+}^{100}{\mathrm{C}}_3{5}^{97}{2}^3+\dots \dots {.}^{100}{\mathrm{C}}_{99}{52}^{99}\right]=$last two plane are 00

D) The last two digits $3^{400}=(81{)}^{100}=(1+80{)}^{100}=80\mathrm{K}+1 \Rightarrow$ The last two place an 01