Correct Answer: $2$

Solution : Given: $\sqrt{x}=\sqrt{3}-\sqrt{5}$
By squaring both the sides, we get,
$x=3+5-2\sqrt{15}$
⇒ $x-8=-2\sqrt{15}$
Again, squaring both the sides, we get,
$x^2-16x+64=60$
⇒ $x^2-16x+4=0$
$\therefore x^2-16x+6=2$
Hence, the correct answer is $2$.

Correct Answer: Latanoprost

Solution : The correct option is Latanoprost.

Glaucoma, a disorder in which elevated pressure in the eye can cause a gradual loss of vision, is treated with Latanoprost. It is listed as one of the essential medicines by the World Health Organization. Latanoprost belongs to a class of medications known as prostaglandin analogues. It works by increasing the outflow of aqueous humour, the fluid inside the eye, which helps to lower intraocular pressure.

Correct Answer: 1 – x¹⁶

Solution : Given expression,
(1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) (1 – x)
= (1 − x²)(1 + x²)(1 + x⁴)(1 + x⁸)
= (1 − x⁴)(1 + x⁴)(1 + x⁸)
= (1 − x⁸)(1 + x⁸)
= (1 − x¹⁶)
Hence, the correct answer is (1 − x¹⁶).

Correct Answer: 1/1-c

Solution : The correct answer is 1/1-c.

The additional consumer spending that results from a rise in national income is known as the marginal propensity to consume (MPC). It is the extra spending brought on by an extra dollar in revenue. The multiplier is calculated as 1/(1 minus MPC).

Correct Answer: 72

Solution : The correct option is 72.

The Indian National Congress was founded in 1885 by A.O. Hume. Its first meeting was held in Bombay and was attended by 72 delegates. Mostly they were lawyers, journalists and intellectuals and it was founded by Allan Octavian Hume, a retired British civil servant. Dadabhai Naoroji was chosen as the president of the INC during its first session.

Correct Answer: 1

Solution : The correct answer is the first option because save should be replaced with salvage to convey the intended meaning that there were limited actions he could take to restore his reputation which had been severely tarnished.

Salvage which is similar in meaning to save is more suitable to use in the context of the sentence. The other options, such as wreck which means to destroy severely, and destroy do not go contextually with the intended meaning of the sentence.

Therefore, the correct sentence is, "There was little he could do to salvage his battered reputation".

Correct Answer: 60 

Solution : Let the base angle be $x$.
Given, that the vertex angle is twice the sum of base angles.
The sum of base angles = 2$x$
So, vertex angle = 4$x$
We know the sum of angles of a triangle is 180$^\circ$.
So, $x$ + $x$ + 4$x$ = 180$^\circ$
Or, $x$ = 30$^\circ$
Half of vertex angle = 2$x$ = 60$^\circ$
Hence, the correct answer is 60.

Correct Answer: source of Hindu philosophy

Solution : The correct answer is the source of Hindu philosophy.

The Upanishad is a Hindu philosophical literature written by various sages from the mid-5th century BC to the 2nd century BC. The Brihadaranyaka Upanishad is the first and the most famous one among the 108 Upanishads.

Correct Answer: Bahadur Shah Zafar

Solution : The correct option is Bahadur Shah Zafar.

Bahadur Shah Zafar was the last Mughal emperor. The 1857 rebellion, also known as the Indian Mutiny or Sepoy Mutiny, marked a significant moment in Indian history as a widespread uprising against British colonial rule.

Correct Answer: 2

Solution : The correct improvement for the sentence is: lacks

Explanation: This option suggests replacing "is wanting in" with "lacks." "He lacks a little common sense" is a more straightforward and commonly used expression. It means that the person does not possess some common sense, making it a suitable improvement for clarity and simplicity.

is lacking in 

• This option suggests replacing "is wanting in" with "is lacking in." "He is lacking in a little common sense" is also correct and conveys a similar meaning to the second option. However, it adds a bit more complexity to the sentence compared to the second option, without significantly improving clarity.

needs some

• This option suggests replacing "is wanting in" with "needs some." "He needs some a little common sense" is not a grammatically correct phrasing. The use of "needs some" in this context is redundant and does not improve the sentence.