Mathematics - Online Test

The slope of the first line is -(a/b) and slope of the second line is a+ba−b

Angle between the lines is tanθ  = |m2−m1|1+m1m2

Let m1 =-(a/b) and m2 = a+ba−b

Hence tanθ =[ (−a/b)−(a+b)/a−b)1+(−a/b)(a+b)/(a−b)

On simplifying we get, 

tanθ = 1

This implies θ = 450

ddx(f(x))=f(x)

It implies that the function remains same after integrating or differentiating it. So the function must be ex

(x−1)2+(y−2)2=10

comparing the above equation with (x−h)2+(y−k)2=r2we get center as (1,2)

putting (1,2) in L.H.S of above line ,we get 1+2=3=R.H.S

=> it satisfies center satisfies the equation of line or the line passes through center

and the line passing through the centre is normal.

Total ways of getting 6 heads out of 8 toss of coins is 28.

Total number of outcome is 28 = 256

Therefore probability is  28256=764