Correct Answer: – 29

Solution : Given equation,
$K+\frac{1}{K}=-3$ ..........(1)
Squaring the equation, we get,
$(K+\frac{1}{K})^2=(-3)^2$
$K^2 + \frac{1}{K^2} + 2 = 9$
⇒ $K^2 + \frac{1}{K^2} = 7$ ...........(2)
Cubing equation (1), we get
$(K+\frac{1}{K})^3 = (-3)^3$
⇒ $K^3 + \frac{1}{K^3} + 3\cdot K\cdot\frac{1}{K}(K+\frac{1}{K}) = -27$
⇒ $K^3+\frac{1}{K^3}+3(-3) =

Correct Answer: Li and Mg

Solution : The correct answer is Li and Mg.

The relationship exists between Li (Lithium) and Mg (Magnesium). This means that they are in different parts of the periodic table, they share some similar properties because their atoms and ions are roughly the same

Correct Answer: $\frac{12}{13}$

Solution :
Given, $\tan Q = \frac{5}{12}$
We know, $\tan\theta = \frac{\text{Perpendicular}}{\text{Base}}$
Applying Pythagoras theorem,
$\small\text{Hypotenuse}^2 = \text{Perpendicular}^2+\text{Base}^2$
⇒ $\text{H}^2=5^2+12^2$
⇒ $\text{H}^2 = 25 + 144$
⇒ $\text{H}=\sqrt{169}$
⇒ $\text{H} = 13\ \text{units}$
Now, $\cos\theta = \frac{\text{Base}}{\text{Hypotenuse}}$
⇒ $\cos Q = \frac{12}{13}$
Hence, the correct answer is

Correct Answer: Swami Dayananda Saraswati

Solution : The correct answer is Swami Dayananda Saraswati.

The Arya Samaj was founded by Swami Dayananda Saraswati in 1875. Swami Dayananda Saraswati advocated for a return to the teachings of the Vedas, emphasising monotheism, social equality, and the right of individuals to interpret

Correct Answer: Football

Solution : Football was liked by 122 students.
Hockey was liked by 58 students.
Cricket was liked by 115 students.
Kabaddi was liked by 50 students.
Tennis was liked by 105 students.
$\therefore$ Football is the favourite sport of most students.
Hence, the correct answer is Football.

Correct Answer: 10

Solution :
Given: $\angle PRS=(9x-15^{\circ}), \angle RPQ=2x$ and $\angle PQR=(4{x}+15^{\circ})$
Applying exterior angle property, we get:
$\angle PRS=\angle RPQ+\angle PQR$
⇒ $(9x-15^{\circ}) = 2x+(4{x}+15^{\circ})$
⇒ $3x=30^{\circ}$
⇒ $x=10^{\circ}$
Hence, the correct answer is 10.

Correct Answer: 53

Solution : Let the number be X.
Then, according to the question,
X – 31 = 75 – X
⇒ 2X = 75 + 31
⇒ 2X = 106
⇒ X = $\frac{106}{2}$
⇒ X = 53
Hence, the correct answer is 53.

Correct Answer: Summer of Soul

Solution : The correct answer is Summer of Soul.

"Summer of Soul" won the Documentary Feature Oscar at the 2022 Oscars. The film revolves around a monumental event in the summer of 1969 that celebrated black history, culture, and fashion. It illuminates the significance

Correct Answer: Vinai Kumar Saxena

Solution : The correct option is Vinai Kumar Saxena.

Vinai Kumar Saxena is serving as the 22nd Lieutenant Governor of Delhi. Previously, he was the chairman of the Khadi and Village Industries Commission (KVIC). In 1991, he incorporated the National Council for Civil Liberties

Correct Answer: announcement

Solution : The correct choice is the second option.

Since the lady is trying to complete her action using speakers. They are generally used to make announcements, so it is the most appropriate word to fill in the blank.