Remainder when N is divided by A

	COLUMN - I		COLUMN - II
A)	$\mathrm{N}={99}^{100}\text{ and }\mathrm{A}=10$	p)	7
B)	$\mathrm{N}=2^{2007}+2008\text{ and }\mathrm{A}=9$	q)	0
C)	$\mathrm{N}=9^{2009}-8\left(2008\right)-9\text{ and }\mathrm{A}=64$	r)	1
D)	$\mathrm{N}=7^{100}\text{ and }\mathrm{A}=1000$	s)	19

$\mathrm{N}={99}^{100}=(100-1{)}^{100}$

A) $={{100}^{100}}^{100}{\mathrm{C}}_1(100{)}^{99}+\dots {.}^{100}{\mathrm{C}}_{99}(100)+1\Rightarrow 10\mathrm{m}+1\mathrm{m}\in \mathrm{N}$

B) $2^3=(9-1{)}^{669}=9\mathrm{m}-{12}^{2007}+2008\text{ is divisiable by }9$

C) $(1+8{)}^{2009}-8(2008)-9=1{+}^{2009}{\mathrm{C}}_{1}8{+}^{2009}{\mathrm{C}}_2(8{)}^2+\dots \dots ..{+}^{2009}{\mathrm{C}}_{2009}$

      $8^{2009}-8\times 2008-9\text{ is divisible by }64\text{ reminder }=0$

D) $\mathrm{N}=7^{100}={\left(7^2\right)}^{50}=1+1000\mathrm{k}\text{ reminder }1$