d integral terms in d expansion of (3^1/2+2^1/2)⁵⁰⁰ is

if S=n=1to infinity  [ nc₀+nc₁+....................+nc_n]/np_n den S=

sin{x³}/xsinxis equal to {but x->0}

if T=8 ,k₁=2 k₂=4 & sigma r->0to n r³g(x+8r) = 225 g(x) den n is

x+y+z=xyz den sigma 2x/1-x² =

 d set of values of a fr which 1 lies in between d roots of x²-ax +3=0 is

if  d expression can resolved into factors

ax²+by²+ cz²+2ayz+2bzx+czy   can be resolved into a rational factor den a³+b³+c³ is  

1)(rt3+rt2)⁵⁰⁰=500c_r(rt3)^500-r(rt2)^r

500c_r is always an integer,for the remaining two terms to be integers,r shud be a multiple of 2,so,r=0,2,4,...,500.Thus,the no. of integral terms are 251.

2) =(2/1!+2²/2!+.....)=(1+2/1!+2²/2!+....)-1=e²-1.

Since we know that nc₀+....+nc_n=2ⁿ and np_n=n!

6)Since 1 lies between the roots,D>0 and f(1)<0

So,a²-12>0 and 1-a+3<0a²>12 and a>4

The intersection of above two is a>4

Is the ans for fifth question 8xyz/(1-x²)(1-y²)(1-z²)

Also 3,4 questions are not clear.Please post them clearly.Where is a in 3rd question and what are T,k₁,k₂ in fourth question.Post them clearly plz.