If w is a complex cube root of unity, then sinw10 +&nbs

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

221.

The product of the distinct (2n)th roots of 1 + i3 is equal to :

  • 0

  • - 1 - i3

  • 1 + i3

  • - 1 + i3


222.

If α and β are the roots of the equation ax2 + bx + c = 0 and, if px2 + qx + r = 0 has roots 1 - αα and 1 - ββ, then r is equal to

  • a + 2b

  • a + b + c

  • ab + bc + ca

  • abc


223.

If 1, 2, 3 and 4 are the roots of the equation x4 + ax3 + bx2 + cx + d = 0, then a + 2b + c is equal to

  • - 25

  • 0

  • 10

  • 24


224.

If α, β, γ are the roots of x3 - 2x2 + 3x - 4 = 0, then the value of α2β2 + β2γ2 + γ2α2 is

  • - 7

  • - 5

  • - 3

  • 0


Advertisement
225.

The locus of the point z = x + iy satisfying z - 2iz + 2i = 1 is  

  • x-axis

  • y-axis

  • y = 0

  • x = 2


226.

A value of n such that 32 +i2n = 1 is

  • 12

  • 3

  • 2

  • 1


 Multiple Choice QuestionsMatch The Following

227.

If a = 1 - i32, then the correct matching of List-I from List-II is

         List-I                       List-II

(i)      aa                            - π3

(ii)    arg1a                       - i3

(iii)    a - a                        2i3 

(iv)     Im43a                    1

                                        π3

                                        23

correct match is 

A. (i) (ii) (iii) (iv) (i) D E C B
B. (i) (ii) (iii) (iv) (ii) D A B F
C. (i) (ii) (iii) (iv) (iii) F E B C
D. (i) (ii) (iii) (iv) (iv) D A B C

 Multiple Choice QuestionsMultiple Choice Questions

228.

The points in the set z  C : argz - 2z - 6i = π2 (where C denotes the set of all complex numbers) lie on the curve which is a

  • circle

  • pair of lines

  • parabola

  • hyperbola


Advertisement
Advertisement

229.

If w is a complex cube root of unity, then sinw10 + w23π - π4 is equal to

  • 12

  • 12

  • 1

  • 32


A.

12

Since, w is a cube root of unity. sinw10 + w23π - π4  = sinw + w2π - π4  = sin- π - π4               1 + w + w2 = 0  = - sinπ + π4 = sinπ4  = 12


Advertisement
230.

If m1, m2, m3 and m4 respectively denote the moduli of the complex numbers 1 + 4i, 3 + i, 1 - i and 2 - 3i, then the correct one, among the following is

  • m1 < m2 < m3 < m4

  • m4 < m3 < m2 < m1

  • m3 < m2 < m4 < m1

  • m3 < m1 < m2 < m4


Advertisement