due to paucity of time I'll just give u the hints.
4)
draw of the graph of the quadratic equation. note that the mod of it will bring the negative part of the graph above x axis (mirror image). i.e the part in between its roots -3,1.
draw the graph of 1.5lnx (fairly simple). note that it also passes through 1,0
note that at which value of x will its summation become max. once graph drawn it can be seen that at x=4 it becomes max. similarly minimum at x=1. (note that f(x) wont become negative in between [1/2,1] )
5)
i'll write alpha as a and beta as b
a^n+1 + b^n+1 = a^n * a + b^n *b
= (a^n + b^n)(a+b) -b^n *a - a^n *b
= x_n(a+b) -ab*( b^(n-1) + a^(n-1) )
=option A
7)
x2>x1
ln is an increasing function just like y=x
x > lnx
also the value of lnx declines much more rapidly than that of y=x
lnx1 >1 as x1>e
use these properties. and get option A
u can also verify it by putting x1=6 & x2=36
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"You don't have to believe in God, but you should believe in The Book." -Paul Erdős
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