COLUMN - I		COLUMN-II
A)	Number of terms in $(\mathrm{x}+\mathrm{y}-\mathrm{z}+\mathrm{w}{)}^6$ is	p)	67
B)	Last two digits in $7^{2011}$ is	q)	84
C)	Number of rational terms in $(\sqrt[3]{7}+\sqrt[5]{11}{)}^{1001}$ is	r)	4
D)	Remainder when $2^{2011}$ is divided by 127 is	s)	43

$(\mathrm{x}+\mathrm{y}-\mathrm{z}+\mathrm{w}{)}^6$

A) no. of terms ${=}^{\mathrm{n}+\mathrm{r}-1}{\mathrm{C}}_{\mathrm{r}-1}{=}^9{\mathrm{C}}_3=84$

$\begin{array}{l}\mathrm{B}) 7^{2011}=7[50-1{]}^{1005}\\ =7\left[{ }^{1005}{\mathrm{C}}_0{(50{)}^{1005}}^{1005}{\mathrm{C}}_1(50{)}^{1004}+\dots .{.}^{1005}{\mathrm{C}}_{1004}50-1\right]\end{array}$

2011 is two reminder is = 43

C) $(3\sqrt{7}+5\sqrt{11}{)}^{1001}=\left[\frac{1001}{15}\right]=66$

D) $2^{2011}127=2^2{\left(2^7\right)}^{287}\Rightarrow =2^2[127+1{]}^{287}$

Reminder is 4.