13) put z=cosθ+isinθ
then u hav to find max value of 2sin(3θ/2)cos(θ/2)
i guess i m getting 1.76 something
Q1. The value of
^{100}C_{0}\; ^{200}C_{100} - ^{100}C_{1}\; ^{199}C_{100} + ^{100}C_{2}\; ^{198}C_{100}-^{100}C_{3}\; ^{197}C_{100}+.......+^{100}C_{100}\; ^{100}C_{100}
Q2. If \left|az+b\bar{z}+c \right| = \alpha \left|a \right|\left|z-z_{1} \right|
a≠0, a=b,c ε R, where z1 is a given non-zero complex number and α ε R+, then locus of z may be
(a) Parabola (b) Ellipse (c) Hyperbola (d) Circle
Q3. If z lies on the unit circle with centre at origin then the maximum value of I_{m}(1-\bar{z}+z^2) is
-
UP 0 DOWN 0 0 7
7 Answers
12)
parabola
ellipse
hyperbola ??
since here a=b
so \left|a \right|=\left|b \right|=\left|\bar{b} \right|=\left|\bar{a} \right|
and since
the given eq is
2\left(\frac{\left|\bar{b}z+b\bar{z} +c\right|}{2\left|b \right|} \right)=\alpha \left|z-z_{1} \right|
\left(\frac{\left|\bar{b}z+b\bar{z} +c\right|}{2\left|b \right|} \right)=distance of z from line \bar{b}z+b\bar{z} +c
and \left|z-z_{1} \right| is distance of point z from z1
hence we can clearly see here \frac{2}{\alpha } is the eccentricity of conic
and z1 is teh focus and \bar{b}z+b\bar{z}+c=0 is the directrix
now e=\frac{2}{\alpha }
wen \alpha =2 it is a parabola
wen \alpha >2 it is an ellipse
wen \alpha <2 it is a hyperbola
1
341Where are these qns from? BTW, I've just seen a beautiful soln to #1 on Mathlinks - http://www.mathlinks.ro/viewtopic.php?t=329319
Do read it.
Someone's posted Q3 is disguised form asking what is max of sin θ + sin 2θ
1check this for another way
for 1st q
http://www.mathlinks.ro/viewtopic.php?p=1762870#1762870
it turns out to be Vandermonde's Convulution identity
got to know abt it today only [3]
btw this aint related to jee by miles
106thanks a lot prophet sir and che..
these were the unit test questions at aakash for another batch....(1 yr course)
1708can someone solve sin\theta +sin2\theta with the help of Trigonometry