Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201922 Apr 2019Morning ShiftMathematicsComplex NumberActual

Let ( ) be a root of (x^2+x+ I =0 ) and suppose that a fair die is thrown 3 times. If (a, b ) and (c ) are the numbers shown on the die, then the probability that ( ^a+ ^b+ ^c=0 ), is

Options

  1. A( 2 36 )
  2. B( 1 27 )
  3. C( 1 72 )
  4. D( 2 9 )

Correct answer

D. ( 2 9 )

Step-by-step solution

Total numbers of ways for ((a, b, c)=6 6 6 ) Here, ( aligned & , ^2 & ^3=1, & ^4= , & ^5= ^2, aligned ) and ( ^6=1 ) Since, ( ^2 ), ( ) are roots of (x^2+x+1=0 ). ( ^a+ ^b+ ^c=0 ) Now, suitable values for ((a, b, c)=6 4 2 ) ( ) Required probability (= 6 4 2 6 6 6 = 8 36 = 2 9 )

Practice Complex Number on Quantrex Academy →

More from Complex Number

If z and are two non-zero complex numbers such that |z |=1 and Arg z- Arg = 2 then z = 2025Let z satisfy |z|=1, z=1- z and Im (z)>0 Statement-I : z is a real number Statement-II : Principal argument of z is 3 . Then 2025If ₁ and ₂ are two non-zero complex numbers and a , b are non zero real numbers such that | a ₁+ b ₂ |= | a ₁- b ₂ | , then ₁ ₂ is 2025If a complex number z=x+i y represents a point P on the Argand plane and Arg ( z-3+2 i z+2-3 i )= 4 , then the locus of P is a 2025By taking a i b =x i y, x>0 , if we get 21+12 2 i 21-12 2 i =a+i b , then b a = 2025Two values of (-8-8 3 i)^ 1 / 4 are 2025If x=3-2 3 i , then x^4-12 x^3+54 x^2-108 x-54= 2025z ₁, z ₂, z ₃ represent the vertices A , B , C of a triangle ABC respectively in the Argand plane. If |z₁-z₂ |= 25-12 3 , | z₁-z₃ z₂-z₃ |= 3 4 and ACB =30^ , then the area (in sq. 2025 Full Complex Number list All AP EAMCET PYQs