It's a Question of your Career!

Correct Answer: $-\frac{4}{15}$

Solution : $x\sin ^{2}60^{\circ}-\frac{3}{2}\sec 60^{\circ}\tan^{2}30^{\circ}+\frac{4}{5}\sin^{2}45^{\circ}\tan ^{2}60^{\circ}=0$
$⇒x(\frac{\sqrt3}{2})^2-\frac{3}{2}×2×(\frac{1}{\sqrt3})^2+\frac{4}{5} ×\frac{1}{2}×(\sqrt{3})^2=0$
$⇒\frac{3x}{4}-1+\frac{6}{5}=0$
$⇒\frac{3x}{4}=-\frac{1}{5}$
$⇒x=-\frac{4}{15}$
Hence, the correct answer is $-\frac{4}{15}$.

Correct Answer: $-1$

Solution : As we know,
$(x + \frac{1}{x})^2 = x^2 + \frac{1}{x^2} + 2$
⇒ $(\sqrt{x} + \frac{1}{\sqrt{x}})^2 = x+\frac{1}{x} +2$
⇒ $x + \frac{1}{x} + 2 = 3^2 = 9$
⇒ $x + \frac{1}{x} = 9 - 2 = 7$
⇒ $(x + \frac{1}{x})^2= 7^2$
⇒

Correct Answer: (3)

Solution : The sentence can be improved using the third option.

The sentence discusses the requirement or obligation for citizens to help the administration maintain the cleanliness of the city. The preposition "to" expresses the purpose or intention of an action; we often use the infinitive form

Correct Answer: watchfully

Solution : The correct choice is the third option.

This choice aligns with the sentence structure, indicating that he ruled well while being attentive and cautious, leaning towards justice rather than mercy. The sentence requires an adverb to modify the verb. Thus, watchfully is the appropriate choice.

Correct Answer: Megha said, "I took the shortcut to my college."

Solution : The correct answer is the third option.

Direct speech is a form of speech or writing where the actual words spoken by a person are quoted within quotation marks and attributed to the speaker.

Narration Conversion:

• The

Correct Answer: OWM

Solution : Given:
CZA, GYE, KXI, ?

In the given series, add 4 to the place value of the first and third letters and subtract 1 from the place value of the second letter of the previous term to get the next term.
CZA→C + 4 =

Correct Answer: Shah Jahan

Solution : The correct answer is Shah Jahan.

Pandit Raj Jagannath was a famous poet and literary critic in the court of the Mughal Emperor Shah Jahan. As a literary theorist or rhetorician, He was renowned for his Rasagangadhara, a work on poetic theory. He was

Correct Answer: of

Solution : The correct choice is the second option.

Of is the correct preposition, as it helps in indicating the substance the table is made from. It helps specify the material (wood) from which the table is constructed.

Therefore, the complete sentence is: Tables are usually

Correct Answer: Loudspeaker

Solution : Given:
Grip : Spanner :: Amplify : ?

Like, Grip : Spanner→A spanner is a tool used to enhance or improve one's grip on objects
Similarly, follow the same pattern for Amplify : ?→A loudspeaker amplifies sound.

Hence, the third option is correct.

Correct Answer: 4, 2 and 1

Solution : Let us assume the third number is  $x$.
Second number = 2$x$
First number = 2(2$x$) = 4$x$
Reciprocals of the three numbers = $\frac{1}{4x}, \frac{1}{2x}, \frac{1}{x}$
Average of the reciprocals = $\frac{7}{12}$
Sum of the reciprocals = $\frac{1}{4x}+\frac{1}{2x}+\frac{1}{x}=\frac{7}{4x}$
Average of reciprocals