Correct Answer: $x^{2}+2x+1=0$

Solution : $\alpha$ and $\beta$ are roots of the equation $x^{2}-x+1=0$
⇒ $\alpha+\beta=1$ and $\alpha\beta=1$
Now we need to find the equation whose roots are $\alpha ^{3}$ and $\beta ^{3}$.
⇒ $(\alpha^{3}+\beta^{3})=(\alpha+\beta)^{3}-3\alpha\beta\times(\alpha+\beta)$
⇒ $(\alpha^{3}+\beta^{3})=(1)^{3}-3\times 1 \times (1)$
⇒ Sum of roots = $(\alpha^{3}+\beta^{3})=-2$
Also, Product of roots

Correct Answer: taking an exam

Solution : The second option is correct.

Given the context of someone's engagement or action related to an exam five years from now, taking an exam is the appropriate choice to complete the sentence, indicating participation in an exam at that future time.

The meanings

Correct Answer: BDF

Solution : Let's check the options –
First option: ADG; A + 3 = D; D + 3 = G
Second option: HKN; H + 3 = K; K + 3 = N
Third option: ORU; O + 3 = R; R + 3 = U
Fourth

Correct Answer: Chiranjeevi

Solution : The correct answer is Chiranjeevi.

The Indian Film Personality Award was awarded to Chiranjeevi. He belongs to the Telugu industry. This was the 53rd edition of the International Film Festival of India (IFFI) award.

IFFI was first held in 1952, making it one of the

Correct Answer: 7200

Solution : Let there be 36x job applicants of whom 19x were selected, while 17x were rejected.
If (36x – 1200) had applied and (19x – 800) were selected, then
Rejected = (36x – 1200 – 19x + 800) = (17x – 400)
Given, Rejected : Selected

Correct Answer: $96 + 64\sqrt2$

Solution : Diagonal of the face = (side of cube) × $\sqrt{2} = 8\sqrt{2}$ cm
The total surface area of the part
= Area of one face of cube + 2 × $\frac{1}{4}$ × area of top face + 2 × side of cube ×

Correct Answer:

Solution : According to the given figure series – 
From Box 1 to Box 2 – The square becomes unshaded and shifts at the first position followed by the unshaded triangle at the second position and the circle at the third position. The symbol at the third position,

Correct Answer:

Solution : According to the given figures –

In Images first, second, third, and fifth, the half arrow is drawn to the right-hand side of the arrows at the other end of the line.
But in image 4, the half arrow is drawn to the left-hand side of

Correct Answer: Monarch

Solution : The second option is the correct choice.

A monarch is typically a king or queen who holds a position of authority and often inherits the position through a hereditary line. The word monarch accurately captures the idea of a sovereign head of state, making it

Correct Answer: OFU

Solution : Given:
WNM, ULO, SJQ, QHS, ?

Here, subtract 2 from the place value of the first and second letters and add 2 to the place value of the third letter of the previous term to get the next term of the series.
WNM→W – 2