PMC Forum: Maths

1)) Let z=x+iy be a complex nos where x and y are integers. then the area of the rectangle whose vertices are the roots of the equation z(zbar³⁾+ (zbar)z³= 350 is.............

i) 48 ii)32 iii)40 iv)80

2)) The solution set of f'(x)>g'(x) where f(x)= (1/2)5^2x+1 and g(x)=5^x+4xlog5 is.........

i) (1,infinity) ii) (0,1) iii) [0,infinity) iv) (0,infinity)

2))
f(x) = (1/2) 5^2x+1 f'(x) = 5^2x+1 log 5
g(x) = 5^x + 4xlog5
g'(x) = 5^x log5 + 4log5
According to the question f'(x) > g'(x)
therefore , 5^2x+1 log5 > 5^xlog5 + 4log5
log5 [ 5^2x+1 - 5^x - 4] >0
now, let 5^x = y
so we get,log5[5y² -y-4] > 0
(5y+4)(y-1) > 0
=> y < -4/5 , y > 1
=> 5^x > 1 or 5^x <-4/5 ( which is not possible)
therefore for 5^x > 1 , we get x>0
So the correct option is option iv)(0,infinty)

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