11,3) put z = x+iy
2) use sinxcosx = (sinx+cosx)2 -12
then you get a quadratic in sinx + cosx i.e √2sin(x+pi4) solve this normally by setting x+pi/4 = θ
4) n(s) = 40C5 i.e just selection of 5 cards since there is only 1 way to arrange each selection.
n(E) = 23C2 * 16C2 i.e. selecting 2 cards each from the left and right of 24
=> 23C2 * 16C2 40C5
5) take general point on the curve as (3t34,t)
now differentiate the curve to get slope of normal and write equation of normal since you have a point and slope. (0,1) should satisfy it from this we get ,
27t5 + 16t -16 =0
differentiate it to get , (27*5) t^4 +16 which is always positive hence the curve is increasing so it has only 1 root .
hence the answer is 1.
11. I was wondering if there was any method without going to co ordinate systems
which gives answer in |z-c|=a form of circle
by the way the co ordinate system worked
2. i got
Sin (∂) = (1/√2)-1
Now For what Value of Sin ∂ it satisfies ?
acc to calculator:
-17.03124846...
how am i supposed to calculate it or solve it on the exam hall ?
5.I understood your Answer BUT
Your general point 3t34 and t Should satisfy the equation
of the curve
just like
Parabola , at2 , 2at Satisfies y2 = 4ax
SO if you ask my opinion , this Should be something else !
thanks for the rest of the answers !
1
rishabh
·2012-03-22 09:06:34
5) i dint get ur point? (3t3/4,t) does satisfy the eqn. of the curve
1
rishabh
·2012-03-22 09:20:57
2) you only need to find number of solutions not the solns. so just draw the graph of sinx and check at how many points the line y= 1/√2 -1 intersects it in the given domain.
1
Ironman [TDC]
·2012-03-23 07:09:02
Sory i was putting x in y and y in x
My Bad
