Correct Answer: Fauna

Solution : The correct choice is the third option.

Explanation:

The term fauna is a noun that refers to the animals of a particular region or period, especially as considered in relation to their total environment. In the context of the given group of words, fauna

Correct Answer: $\frac{2}{\left(\sin ^2 \theta-\cos ^2 \theta\right)}$

Solution : $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}+\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}$
Taking the LCM of the denominators:
= $\frac{(\sin \theta+\cos \theta)^2 + (\sin \theta-\cos \theta)^2}{\sin^2 \theta-\cos^2 \theta}$
= $\frac{(\sin^2 \theta+\cos^2 \theta+2\sin \theta \cos \theta) + (\sin^2 \theta+\cos^2 \theta-2\sin \theta \cos \theta)}{\sin^2 \theta-\cos^2 \theta}$

Correct Answer: Ultra-violet rays

Solution : The correct option is - Ultra-violet rays

The ozone layer above the surface of the Earth provides a shield against harmful ultraviolet (UV) radiation from the sun. It specifically filters out the majority of the sun's harmful ultraviolet  rays. This protection is crucial for

Correct Answer: $\frac{11}{20}$

Solution : $\sin A=\frac{3}{5}$
$⇒\cos A = \sqrt{1-\sin^2A}$
$⇒\cos A = \sqrt{1-(\frac{3}{5})^2}$
$⇒\cos A = \sqrt{\frac{25-9}{25}}$
$⇒\cos A = \sqrt{\frac{16}{25}}$
$⇒\cos A = \frac{4}{5}$
We know, $\tan A = \frac{\sin A}{\cos A}$
$⇒\tan A = \frac{\frac{3}{5}}{\frac{4}{5}}$
$⇒\tan A = \frac{3}{4}$
So, $\cos A+\tan A-1 = \frac{4}{5} +

Correct Answer: 11, 66, 12, 20, 57

Solution : Given:
BLACK

Number representations of each letter –
B→30, 01, 11, 41, 23
L→50, 75, 06, 66, 88
A→00, 21, 12, 43, 34
C→20, 02, 42, 33, 14
K→80, 05, 57, 67, 77

First option: 11, 66, 57, 20, 76; A

Correct Answer: Sugarcane

Solution : The correct option is Sugarcane.

The crop is sugarcane, which is suited for tropical and subtropical regions. It flourishes in hot, humid climates with temperatures between 21°C to 27°C and an annual rainfall of 75 cm to 100 cm. These conditions provide the ideal

Correct Answer:

Solution : According to the given figure –
1. The lower and upper region of N has consecutive numbers from 1 and 2 respectively.
2. On the right side, the numbers are the sum of the consecutive numbers on the left.
So, the next image will be as

Correct Answer: decreased by $6\tfrac{1}{4}$%

Solution : Given: A number is increased by 25%.
The resulting number is decreased by 25%.
Let the number be 100.
Increased by 25% = (100 + 25) = 125
125 is decreased by 25%, then it becomes = $125×\frac{75}{100}$ = $\frac{375}{4}$
So, the required

Correct Answer: $\frac{2 \mathrm{x}\left(1+\mathrm{x}^2\right)}{(\mathrm{x}-1)}$

Solution : Given expression,
$\frac{1+\mathrm{x}}{1-\mathrm{x}^2} \div \frac{1+\mathrm{x}}{1-\mathrm{x}^4}-\frac{1-\mathrm{x}^4}{1-\mathrm{x}} \times \frac{1+\mathrm{x}}{1-\mathrm{x}^2}$
$=\frac{\frac{1+\mathrm{x}}{1-\mathrm{x}^2}}{\frac{1+\mathrm{x}}{1-\mathrm{x}^4}}-\frac{(1-\mathrm{x}^2)(1+\mathrm{x}^2)\times(1+\mathrm{x})}{(1-\mathrm{x})\times(1-\mathrm{x}^2)}$
$=\frac{(1+\mathrm{x})(1-\mathrm{x}^4)}{(1-\mathrm{x}^2)(1+\mathrm{x})}-\frac{(1+\mathrm{x}^2)(1+\mathrm{x})}{1-\mathrm{x}}$
$=\frac{(1+\mathrm{x})(1-\mathrm{x^2})(1+\mathrm{x^2})}{(1-\mathrm{x^2})(1+\mathrm{x})}-\frac{(1+\mathrm{x}^2)(1+\mathrm{x})}{1-\mathrm{x}}$
$=\small 1+\mathrm{x^2}-\frac{(1+\mathrm{x}^2)(1+\mathrm{x})}{1-\mathrm{x}}$
$=\small (1+\mathrm{x^2})\times\frac{1-\mathrm{x}-1-\mathrm{x}}{1-\mathrm{x}}$
$=\frac{-2\mathrm{x}(1+\mathrm{x^2})}{1-\mathrm{x}}$
$=\frac{2\mathrm{x}(1+\mathrm{x^2})}{\mathrm{x}-1}$
Hence, the correct answer is $\frac{2\mathrm{x}(1+\mathrm{x^2})}{\mathrm{x}-1}$.

Correct Answer: Nation First, Always First

Solution : The correct option is Nation First, Always First.

India enthusiastically commemorated its 75th Independence Day on August 15, 2021. Prime Minister Narendra Modi raised the national flag at the Red Fort and gave a speech to the people from the famous