11> is the ans .. a ???
1. all the roots of the equation 11z^10 + 10 iz^9 + 10 iz -11 = 0 Lie
a> inside |z| = 1 b> on |z|=1 c> outside |z|=1 d> cant say :P
2. 271 should be spilt in to how many parts so as to maximise thier product
a> 99 b>10 c>1 00 d>none
3. The number of planes wich are equidistant from four non-coplanar points is
a> 3 b> 4 c> 7 d>9
4 . P(a,b) is a point in the first quadrant . Circles are drawn through P touching the coordinate axes such that the lenth of the common chord is maximum ,
if possible values of a/b is k1 and k2 , then k1 + k2 _______________?
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9 Answers
62part 1) Question is not clear to me ....
part 2) maximize (S/n)n answer is found by taking derivative wrt n as zero
part 3) 4 planes. Take any 3 points and they lie on a plane. So for any 3 points and a single pint there will be one plane
4) Solving..
62S is constant.
n is variable
f(n)= (S/n)n
ln(f(n)) = n log(S) - n log(n)
derivative is zero for max min
log(S) - 1 - log n =0
so n=S/e
but n is an integer.. so take both the integers closest to S/e and then find it at both these points...
S=271, so you have to check for S=99 and 100. But since S is much closer to 100 than to 99.. my guess wud be n=100
106a simple check on z=-1 shows that it satisfies the given equation. hence (a) and (c) get eliminated immediately.
106now take z=reiθ
put in equation. it is easily seen that using Euler's formula that for r=1 the equation is satisfied for some θ. hence the solution is lzl=1
1ASHISH where is it satisfying?? i put z = 1 in da equation and i get dis >>>>>>>>
11-10i-10i+ 11 = -20i ?????