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JEE Main 2017 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 2 April 2017 (offline), Maths Q63

Question 63 of 90 in this shift, Maths question 3 of 30.

Let

\omega

be a complex number such that

2\omega+1=z

where

z=\sqrt{-3}

. If

\begin{vmatrix}1&1&1\\1&-\omega^2-1&\omega^2\\1&\omega^2&\omega^7\end{vmatrix}=3k

, then k is equal to :

(1) $z$
(2) $-1$
(3) $1$
(4) $-z$ Official answer

Official answer

Option 4

CBSE answer key (25/04/2017, used for result).

Chapter: Determinants
Topic: Roots of Unity
Idea tested: Evaluating Determinants with Cube Roots

Same idea in other shifts

Asked 2× in all

31 Aug 2021, Shift 1 · Q63If $\mathrm{a_r}=\cos\frac{2\mathrm{r}\pi}{9}+i\sin\frac{2\mathrm{r}\pi}{9}$ , $\mathrm{r}=1, 2, 3, ..., i=\sqrt{-1}$ , then the determinant…HardSingle correct

Question text from the official JEE Main paper published by NTA (CBSE ran the 2017 exam); answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.