TCS Company Logical Reasoning Letter Arrangement

the letters of the word REGAIN when arranged as per a dictionary, find the 32nd word
a)aegirn
b)aegrin
c)aeigrn
d)none of these

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TCS Other Question

a cow and a horse are brought for 200000. the cow is sold at a profit of 20% and the horse at a loss of 10%. the overall gain is 4000. the cost price of cow is
a)130000
b)80000
c)70000
d)120000
e)none of these
p(x)=(x^999+x^998+.......x+1)^2-x^999
q(x)=x^998+x^997+.....x+1
the reminder when p(x) is divided by q(x) is
a)x+1
b)0
c)1
d)x-1