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.

Correct Answer: Array

Solution :  Correct answer is - Array

An array is a linear data structure that consists of a group of items kept in close proximity to one another in memory. It is a productive method of organizing memory. It is a type of data structure that can hold a group of values of the same type. Logically related data values are stored in arrays under a common name. For instance, in a search engine, web pages are stored in an array and then found through a user search. 

Correct Answer: Felicilate

Solution : The first option is the incorrectly spelled word.

The correct spelling is felicitate which means to congratulate or express happiness for someone's achievements.

The meanings of the other options are as follows:

• Coterminous: Sharing a common boundary; coextensive.

• Ambient: Relating to the immediate surroundings of something; creating a certain atmosphere.

• Announce: To make known or officially declare something.

Correct Answer: Looping

Solution : The correct answer is Looping.

In programming, repeating a series of commands is known as "looping." Loops are used to run code many times, either depending on a specific condition or for a set number of iterations, to speed up the process of executing repeated activities inside a programme.

Correct Answer: Easeful

Solution : The correct choice is the first option.

The adjective uncomfortable means causing or feeling slight pain or physical discomfort, whereas easeful is characterised by comfort and a lack of difficulty, making things easy and relaxed. Thus, it is the opposite of "uncomfortable".

The meanings of the other options are as follows:

• Difficult: Requiring a lot of effort, skill, or mental exertion; not easy to accomplish.
• Awkward: Lacking grace or ease in movement, causing discomfort or embarrassment.
• Troublesome: Causing problems, difficulties, or inconvenience; bothersome or vexatious.

Correct Answer: $\frac{5}{39}$

Solution :

$\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}$
$=\frac{1}{(3×5)}+\frac{1}{(5×7)}+\frac{1}{(7×9)}+\frac{1}{(9×11)}+\frac{1}{(11×13)}$
$= \frac{1}{2}×[( \frac{1}{3}− \frac{1}{5})+( \frac{1}{5}− \frac{1}{7})+( \frac{1}{7}− \frac{1}{9})+( \frac{1}{9}− \frac{1}{11})+( \frac{1}{11}− \frac{1}{13})]$
$= \frac{1}{2}×( \frac{1}{3}− \frac{1}{13})$
$= \frac{1}{2}×( \frac{13-3}{39})$
$= \frac{5}{39}$
Hence, the correct answer is $ \frac{5}{39}$.