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can we actually make something out of wic i have calculated in my failed trial...

please give us hint..wic topic is applied here...

let f(x) = sinx ....g(x)= lnx...

the latter is monotinic incresing...

let any sign( <=> ) ..taking it as " o" exist between ...for some x...

f(1) o g(7) / g(9) ...

subtracting 1...

f(1) - 1 o g(7) - g(9) / g(9)

multiplying -1....

so sign in o is changed...

now dividing by 2 both sides...

1 - f(1) / 2 o* g(9) -g(7) / 2g(9)...

now rhs is g'(x) ..for some 7
1 - f(1) / 2 o* g'(c) / g(9)...

my trial over...damn..

being zero doesn't mean it have no dimensions...

it means magnitude is zero for flux in a closed loop....

nice methods...abv..

here i go with a general proof..( very unorthodox..bas aise hi aa gaya)..

let f(x) = ax^n + bx^n-1 .....+.z...(n be any natural no.)

now we know tht... f(10) mod 9 = 0...

=> f(9+1) mod 9 = 0...

now by binomial expansion ....

we get f(10) = a(9 + 1)^n. + b (9+1)^n-1...+..z ...

=>> 9m + a + b + c + d.....+z...

since l.hs is a multiple of 9...

so( a + b + c + ...+z) is also divisible by 9...

hence sum of digits or f(1) is also divisible by 9...

first calculate x^x ... it's nothing but ...1...

= >>

taking e power and then applying l.h..

now ques. reduces to 1^x - 1....

wic is nothing but zero...

here is another way...(though not tht touch of exellence)...

cancel (x-1)^3...u get x=1 as soln.

now u observe tht a^3 + b^3 -c^3 = 0...

also observe tht a+b+c=0...wic simply means tht a,b,c r 0..

providing us solns. -2 , -1 and -1/2 ..

my brother needs them

more replies please

that list given by him ..of branch cut-off is wrong..
i can teell u many cases ..like civil-roorkee ended at 2559..

it's good tht fiitjee module..wasn't a prob. as i had done TMH beforehand..

but i think for basics just go through TMH...

don't ever go through NCERT basics !!!!

two equations in three variables...

eliminate any one of them (not the one u have to minimize)...

u get a condition in two variables...and a task of minimizing one...

so the steps tht follow r of simple linear programming..

the instantaneous slope of line y=0.... is zero always...

so derivative of line y=0 ..exist..

best book combo is Adasgupta + TMH....tht's enuff jee ques. will be a free stuff...

where is the ques ??

iit1997 was the toughest as paper was leaked that year
then comes 2006
and then 2008