CBSE 11TH MATHEMATICS - Online Test

an=a+(n−1)d=8−6i+(n−1)2i=8+i(2n−8)

for real n, imaginary part = 0

so 2n - 8=0

which gives, n = 4

ρ=±bxy.byx−−−−−−√=±27.27−−−−√=±27

but sign of ρ$\rho$ is same as the sign of bxy,byx

therefore, ρ=27

Equation of a line passing through (x1,y1) and (x2,y2) 

 y−y1y2−y1=x−x1x2−x1

Substituting the given values we get,

y−b−b−b = x−a−a−a

That is y−b−2b = x−a−2a

On cross multiplying and reaaranging we get,

bx - ay = 0

If this passes through the given point (a2,ab) then

b(a2) - a(ab) = 0

when n = 2 ,  L H S  :  n ! = 2 ! = 2x1 = 2    RHS: (3/2)2=9/4

But if n = 1 , the inequation does not hold good.

The general equation of the circle is x2+y2-2gh-2fy+c = 0. Sice the given equations satisfies the general equation, it represents the equation of the circle.

No: of combinations of n different things taken r at at a time is given by nCr

No: of combinations of n different things taken r at a time and excluding m particular things is n - mCr = C(n-m,r)