Question

If ω ≠ 1 is a cube root of unity and (ω + x)n = 1 + 12ω + 69ω +…. Then values of n and x are respectively.

Solution

Correct option is

24, 1/2

As ωn = 1, n must be a multiple of 3. Let n = 3m. Then

                         

Thus, n = 24 and x = 1/2

SIMILAR QUESTIONS

Q1

The expression [x + (x3 - 1)1/2]5 + [x – (x3 – 1)1/2]5 is a polynomial of degree

Q2

The degree of the polynomial

              is equal to

Q3

 where {x} = Fractional part of x then the value of sec –1 (8θ) is

Q4

The remainder left out when 82n – (62)2n+1 is divided by 9 is

Q5
Q7

Sum of the last 30 coefficients in the expansion of (1 + x)59 when expanded in ascending powers of x is

Q8

 then k is equal to:

Q9

 is maximum when m is

Q10

If ω ≠ 1, is nth root of unity, and  then value of x is