Correct Answer: $\frac{1}{(x+y)(y+z)(z+x)}$

Solution : Given:
$\frac{(x-y)^3+(y-z)^3+(z-x)^3}{\left(x^2-y^2\right)^3+\left(y^2-z^2\right)^3+\left(z^2-x^2\right)^3}$
= $\frac{3(x-y)(y-z)(z-x)}{3(x^2-y^2)(y^2-z^2)(z^2-x^2)}$ [since $(x-y)+(y-z)+(z-x)=0$]
= $\frac{(x-y)(y-z)(z-x)}{(x+y)(x-y)(y+z)(y-z)(z+x)(z-x)}$
= $\frac{1}{(x+y)(y+z)(z+x)}$
Hence, the correct answer is $\frac{1}{(x+y)(y+z)(z+x)}$.

Correct Answer: Regulator

Solution : The correct answer is Regulator.

Typically, the tool used to adjust the speed of an electric fan is referred to as a "fan speed controller"; or "fan speed regulator". These gadgets are made to vary the voltage supplied to the fan's motor, which alters

Correct Answer: 3

Solution : The error lies in the third part of the sentence.

The preposition "in" is not suitable in this context and should be substituted with "regarding". "In" has a different meaning, while "regarding" implies a connection or relation.

Therefore, the correct sentence should be: "Tell me

Correct Answer: Silent

Solution : The correct choice will be the first option.

The most appropriate antonym for the word vociferous is silent.

Vociferous: This term describes someone or something loud, outspoken, or vocal, often intensely or vehemently.

Silent: The antonym of vociferous, silent refers to the absence of

Correct Answer: are looking for

Solution : The correct choice is the third option.

Explanation:

The preposition to in the original sentence is not suitable for expressing the idea of searching for a place. Instead, the appropriate preposition to convey the intended meaning is for. The correct expression

Correct Answer: 13 : 18 : 22

Solution : The salaries of A, B, and C are in ratio 2 : 3 : 4.
Let the salaries of A, B, and C be $2x,3x$, and $4x$, respectively.
Their salaries increase 30%, 20%, and 10%, respectively.
$\therefore$ The new ratio of

Correct Answer: Clostridium

Solution : The correct option is Clostridium.

Tetanus is a deadly disease caused by the bacteria Clostridium tetani. The bacteria can be found in soil and animal faeces. It may enter the body through wounds such as cuts, scrapes, and perforations. Once inside the body, the

Correct Answer: Both I and II

Solution : The correct option is Both I and II.

After the new moon, the portion of the moon that is visible from Earth gets brighter every day. The portion of the moon that is visible and illuminated by the sun gets smaller

Correct Answer: 0.9

Solution : The value of $\sqrt{0.9}= \sqrt{\frac{9}{10}}$
= ${\frac{3}{\sqrt{10}}}$
= ${\frac{3\sqrt{10}}{10}}$
$\sqrt{10}$ is greater than 3 but less than 4.
So, 9 < 3$\sqrt{10}$ < 10
⇒ 0.9 < ${\frac{3\sqrt{10}}{10}}$ < 1
⇒ 0.9 < $\sqrt{0.9}$ < 1
Hence, the correct answer is 0.9.

Correct Answer: Hydrogen

Solution : The correct answer is Hydrogen.

Hydrogen fuel produces no harmful substance and water is the byproduct of this combustion reaction i.e. why they are least harmful to the environment.