TS EAMCET 2023 (Online) 14th May Evening Shift | Complex Numbers Question 48 | Mathematics

The least positive integral value of $n$ such that $\left[\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right]^n=1$ is

TS EAMCET 2023 (Online) 14th May Evening Shift

MCQ (Single Correct Answer)

-0

If a polynomial $P(x)$ given by

$P(x)=2 x^4+a x^3+b x^2+c x+d$ is such that $P(1)=4$,

$P(2)=7, P(3)=12$ and $P(4)=19$, then $P(5)=$

TS EAMCET 2023 (Online) 14th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+x^2+x+1=0$, then match the items of List I with those of List II

List - I		List - II
(i)	$$ \frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma} $$	(a)	-1
(ii)	$$ \alpha^3+\beta^3+\gamma^3 $$	(b)	-4
(iii)	$$ \alpha^4+\beta^4+\gamma^4 $$	(c)	1
(iv)	$$ (\alpha-\beta)^2+(\beta-\gamma)^2+(\gamma-\alpha)^2 $$	(d)	3
		(e)	0

Then, the correct match is

(i) $\rightarrow \mathrm{a}$, (ii) $\rightarrow \mathrm{a}$, (iii) $\rightarrow \mathrm{d}$, (iv) $\rightarrow \mathrm{b}$

(i) $\rightarrow \mathrm{c}$, (ii) $\rightarrow \mathrm{a}$, (iii) $\rightarrow \mathrm{e}$, (iv) $\rightarrow \mathrm{b}$

(i) $\rightarrow \mathrm{a}$, (ii) $\rightarrow \mathrm{c}$, (iii) $\rightarrow \mathrm{d}$, (iv) $\rightarrow \mathrm{b}$

(i) → c, (ii) → a, (iii) → b, (iv) → e

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

-0

If $i=\sqrt{-1}$, then $\operatorname{Arg}\left[\frac{(1+i)^{2025}}{(1-i)^{2022}}\right]=$

$\frac{-\pi}{4}$

$\frac{\pi}{4}$

$\frac{3 \pi}{4}$

$\frac{-3 \pi}{4}$

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