Correct Answer: 105°

Solution :
KI = IT and EK = ET
$\angle$ KET = 150°
In $\triangle$ KEI and $\triangle$ TEI,
KI = IT [Given]
EK = ET [Given]
EI = EI [Common]
So, $\triangle$ KEI $\cong$ $\triangle$ TEI,
⇒ $\angle$ KEI = $\angle$ TEI
Now,
$\angle$ KET + $\angle$ KEI + $\angle$ TEI = 360°
⇒ 150° + 2 × $\angle$ TEI = 360°
⇒ 2 $\angle$ TEI = 210°
⇒ $\angle$ TEI = 105°
Hence, the correct answer is 105°.

Correct Answer: FKQDWE

Solution : Given:
SLAIN is written as PKCNU and DENT is written as VPGF.

Follow the pattern to obtain the required code –

Thus, SLAIN is coded as PKCNU.
And, DENT is written as VPGF.

Thus, DENT is coded as VPGF.
Similarly, follow the same pattern for CUBOID –

So, CUBOID is coded as FKQDWE. Hence, the first option is correct.

Correct Answer: Abridgement

Solution : The correct choice is the fourth option.

Abridgement is a term used to describe a version of a larger work that has been condensed. This involves shortening the original work by omitting details while still preserving the essential content and narrative.

The meanings of the other options are as follows:

• Summary: It is a brief statement or account that covers the main points of a piece of writing, a speech, a film, etc., but omits the less important details.
• Precis: It is a concise summary of a text or speech. It focuses on the key points and the structure of the original work.
• Shorts: In the context of films, it means a shortened version of a story, but this isn't a standard literary term like the others.

Correct Answer: 48

Solution : Given: The ratio of the triangle's sides
$=\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$.
$=\frac{1}{2} × 12 : \frac{1}{3} × 12 : \frac{1}{4} × 12$
$=6: 4: 3$
The perimeter of the triangle is $104$ cm.
$\therefore$ The longest length of the triangle = $\frac{104}{6+4+3}×6= 48$ cm
Hence, the correct answer is 48.

Correct Answer: exchange

Solution : The correct choice is the third option.

The word exchange is appropriate in this context as it implies a mutual or reciprocal action of giving and receiving greetings.

People at the marketplace take time from their busy schedules not just to offer greetings but also to receive greetings from friends or neighbours, creating a sense of interaction and connection.

Therefore, the use of exchange in this sentence conveys the idea of a two-way communication of greetings between individuals in the social setting of the marketplace.

Correct Answer: $\frac{1}{2}\left(5+\frac{1}{5}\right)$

Solution : Given: $\sec \theta+\tan \theta=5$ ..... equation1
$\sec^{2}\theta - \tan^{2}\theta =1$
⇒ $(\sec \theta+\tan \theta)(\sec \theta-\tan \theta)=1$
⇒ $\sec \theta-\tan \theta=\frac{1}{5}$......equation2
Adding equation1 and equation2
$2\sec\theta = 5 + \frac{1}{5}$
⇒ $\sec\theta=\frac{1}{2}\left(5+\frac{1}{5}\right)$
Hence, the correct answer is $\frac{1}{2}\left(5+\frac{1}{5}\right)$.

Correct Answer: the postman would be

Solution : The fourth option contains the error.

Would is used to express a past event and is the past tense of will, which is used to predict a future event. Since we are talking about a future event, we should use will instead of would.

Therefore, the correct sentence is: "I am sure that the postman will be coming shortly to deliver the letter."

Correct Answer: Rs. 2,850

Solution : Ankita sold her watch at a 5% loss.
Here, SP = Selling price and CP = Cost price
Let the SP of the watch be $x$.
Then, CP $= \frac{100}{(100 - \text{Loss}\%)} \times SP =\frac{100}{(100- 5)} \times x = \frac{100}{95}x$
If she sold for 300 more, then $SP = 300 + x$
Then, gain = 5%
$CP =\frac{100}{(100 + P)} \times SP = \frac{100}{(100  +5)} \times (x + 300)$ = $\frac{100}{105}(300 + x)$
According to the question,
$\frac{100}{105}(300 + x) = \frac{100}{95}x$
$⇒\frac{(300 + x)}{x} = \frac{105}{95}$
$⇒95 \times (300 + x) = 105x$
$⇒28500 + 95x = 105x$
$⇒10x = 28500$
$\therefore x = 2850$
Hence, the correct answer is Rs. 2,850.

Correct Answer: Gandhi advocated complete sepration of Politics from religion.

Solution : Correct Answer is Gandhi advocated complete sepration of Politics from religion.

He argued for a religion-based form of secularism, based on the principle of tolerance and plurality as a means of promoting the peaceful co-habitation of various religious communities in India. He did not call for a complete separation of religion from politics. Instead, he used a new form of mass agitation that emphasized truth, tolerance and non-violence, as well as peaceful protests.

Correct Answer: 2

Solution : Amount = INR 7500
1. Two successive discounts of 5% and 5%
Net discount % = $5 +5- \frac{5×5}{100}$ = $9.75$
2. Single discount of 10%
3. Two successive discounts of 8% and 2%
Net discount % = $8 +2- \frac{8×2}{100}$ = $9.84$
So, the maximum discount is from option 2, which is a single discount of 10%.
Hence, the correct answer is 2.