Correct Answer: $1-\sin \alpha \cos \alpha$

Solution : $\frac{\sin^3 \alpha+\cos^3 \alpha}{\sin \alpha+\cos \alpha}$
= $\frac{(\sin \alpha+\cos \alpha)(\sin^2 \alpha+\cos^2 \alpha–\sin \alpha\cos \alpha)}{\sin \alpha+\cos \alpha}$
= $(1–\sin \alpha\cos \alpha)$ [$\because \sin^2 \alpha+\cos^2 \alpha=1]$
Hence, the correct answer is $(1–\sin \alpha\cos \alpha)$.

Correct Answer: $-\frac{3}{4}$

Solution : Given: $\cos ^3 60°-\cos ^3 240°-\cos ^3 360°$
Now, $\cos60°=\frac{1}{2}$
$\cos240°=\cos(180°+60°)=-\cos60°=-\frac{1}{2}$
$\cos360°=\cos(360°+0°)=\cos0°=1$
So, $\cos^3 60°-\cos^3 240°-\cos^3 360°$
= $(\frac{1}{2})^3-(-\frac{1}{2})^3-(1)^3$
= $\frac{1}{8}+\frac{1}{8}-1$
= $-\frac{3}{4}$
Hence, the correct answer is $-\frac{3}{4}$.

Correct Answer: 12

Solution : Given: The ratio of two numbers = 5 : 4
Let the numbers be $5x$ and $4x$.
40% of the first number = 12
So, $\frac{40}{100}\times 5x=12$
$⇒x=6$
$\therefore$ The first number = 5 × 6 = 30
and the second number = 4 ×

Correct Answer: Humming bird

Solution : The correct answer is Humming bird.

The bee hummingbird is the world's tiniest bird. Native of Cuba, the bird measures around 2 inches long and weighs approximately 0.07 ounces. It is so little that it is sometimes misidentified as an insect. Bee hummingbirds are

Correct Answer: The contractor instructed the worker to remove all the stains carefully and clean the windows.

Solution : The fourth option is correct.

The given sentence is in the direct speech. As it is a case of instruction, instructed is used in the indirect speech to report.

Narration

Correct Answer:

Solution : According to the given figure series –
I. The chain of the symbol inside the box is moving forward in the increasing order of the places for example, in the first step, it is shifting one place forward then in the second step, two places forward,

Correct Answer: Astronomy

Solution : The correct option is Astronomy.

Varahamihira wrote the Pancha Siddhantika, a book on mathematical astronomy, in the sixth century CE. It is a synthesis of five older astronomical systems: the Surya Siddhanta, the Romaka Siddhanta, the Paulisa Siddhanta, the Vasishtha Siddhanta, and the Paitamaha Siddhanta.

Correct Answer: amateur

Solution : The correct choice is the third option.

The correct spelling is amateur. The word amateur refers to someone who engages in a particular activity, such as sculpting, for the love of it or as a hobby, rather than as a professional.

Therefore, the correct

Correct Answer: revenue deficit

Solution : The correct option is a revenue deficit.

The term "deficit budget" refers to a situation in which the government spends more money than it brings in for government initiatives. The excess of expenses over receipts on a revenue account is called a revenue

Correct Answer: $98.55\;\mathrm{cm^2}$

Solution :

In an equilateral triangle, the radius of the inscribed circle, where $a$ is the side of the equilateral triangle.
$r = \frac{a\sqrt{3}}{6}$
Put $a=24\text{ cm}$,
$r = \frac{24\sqrt{3}}{6} = 4\sqrt{3} \text{ cm}$
The area of the inscribed circle, where $r$ is the radius of the