Correct Answer: $3$

Solution : Given: The points are (5, –1) and (4, –4).
$\text{Slope}=\frac{y_2–y_1}{x_2–x_1}$
Substitute the given values in the above formula, we get,
$\frac{–4–(–1)}{4–5}=\frac{–3}{–1}$
So, the slope of the given line is 3. The slope of the line parallel to this line is also the same.
Hence, the

Correct Answer: $\frac{\sqrt{1-\cos A}}{\sqrt{1+\cos A}}$

Solution : Given: $\tan\frac{A}{2}=x$
We know,
$\cos A=1-2\sin^2(\frac{A}{2})$
⇒ $\sin(\frac{A}{2})=\sqrt{\frac{1–\cos A}{2}}$
Also, $\cos A=2\cos^2(\frac{A}{2})–1$
⇒ $\cos(\frac{A}{2})=\sqrt{\frac{1+\cos A}{2}}$
Now, $\tan\frac{A}{2}=\frac{\sin(\frac{A}{2})}{\cos(\frac{A}{2})}$
⇒ $x=\sqrt{\frac{1–\cos A}{2}}×\sqrt{\frac{2}{1+\cos A}}$
$\therefore x=\frac{\sqrt{1-\cos A}}{\sqrt{1+\cos A}}$
Hence, the correct answer is $\frac{\sqrt{1-\cos A}}{\sqrt{1+\cos A}}$.

Correct Answer: Lavender

Solution : The correct option is Lavender.

The goal of the project is to encourage commercial lavender farming and raise farmer incomes. The product is lavender oil, which retails for at least Rs. 10,000 per litre. Other well-liked goods include air fresheners, soaps, incense sticks, and

Correct Answer: EJTKUVKCP

Solution : Given:
BUDDHISM is coded as DWFFJKUO.

Add two to the place values of the letters of the given words to get the code.
BUDDHISM is coded as DWFFJKUO –
B + 2 = D; U + 2 = W; D + 2 = F; D

Correct Answer: $ 2 \cot 2x$

Solution : Given: $\cos x \operatorname{cosec} x – \sin x \sec x$
= $\frac{\cos x}{\sin x} - \frac{\sin x}{\cos x}$
= $\frac{\cos x \cos x - \sin x \sin x}{\cos x \sin x}$
= $\frac{2(\cos^2 x - \sin^2 x)}{2\sin x \cos x}$
= $\frac{2\cos

Correct Answer: (3)

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

The word "annoying" in the original sentence is used incorrectly. In this context, it seems like the intended meaning is that she felt annoyed or upset because her father had not accepted her suggestion. The correct

Correct Answer: Due to the southwest monsoon

Solution : The correct option is Due to the southwest monsoon.

Most parts of India experience rainfall from June to September due to the influence of the southwest monsoon, which is a seasonal wind pattern. During the summer months, there is a

Correct Answer: (3)

Solution : The correct choice is the third option.

The phrase "negotiations are completed" is incorrect as it should be the "negotiations were completed" because the context suggests that the negotiations have already been completed. So, the verb "were" is more appropriate to use. The present perfect

Correct Answer: Adrenaline

Solution : The correct option is Adrenaline.

Adrenaline, commonly known as epinephrine, is a hormone. Adrenaline is known as the "Emergency Hormone" because it is essential in the body's "fight or flight" reaction to stressful or dangerous conditions. Adrenaline is released into the circulation when the body

Correct Answer: Gujarat

Solution : The correct answer is Gujarat.

"Seema Darshan Project" was inaugurated at the Nadabet location on the Indo-Pak border in Banaskantha district of Gujarat. This multipurpose tourism project was completed under the guidance or mentorship of Prime Minister Narendra Modi. This project was aimed at