Correct Answer: 176 m²

Solution : Given:
Original length of rope = 9 m
The new length of rope = 5 m
(Length of rope taken as the radius of the circle)
So,
Old area = $\pi (9^{2}) = 81\pi $
New area =  $\pi (5^{2}) = 25\pi $
So, the net change in the area
$=81\pi -25\pi $
$=56\pi $
$= (56\times \frac{22}{7})$
$= \frac{1232}{7}$
$= 176\ \text{m}^{2}$
So, the decrease in the area that can be grazed by the calf is 176 m².
Hence, the correct answer is 176 m².

Correct Answer: Cytoplasm

Solution : The correct answer is Cytoplasm.

Each cell is filled with cytoplasm, which is a thick solution. The cell membrane encloses it. It consists of water, salts, and proteins. The cytoplasm in eukaryotic cells includes all of the material inside the cell and outside of the nucleus.

Correct Answer: 1 : 3

Solution : Given,
Number of red balls in the bucket = 40
Number of blue balls in the bucket = 120
⇒ Ratio = 40 : 120 = 1 : 3
Hence, the correct answer is 1 : 3.

Correct Answer: Raja Ram Mohan Roy

Solution : The correct answer is Raja Ram Mohan Roy.

The social manifestation of Brahmoism is known as Brahmo Samaj. It began as a Hindu reformist movement that was monotheistic and was valued during the Bengal Renaissance. On August 20, 1828, Raja Ram Mohan Roy and Dwarkanath Tagore founded it in Calcutta. Raja Ram Mohan Roy also founded the Atmiya Sabha in 1815.

Correct Answer: 10%

Solution : Given: Principal = Rs. 16,000
Time = 2 years
We know, Difference between compound interest and simple interest = $P(\frac{r}{100})^2$, where $P$ = Principal, $r$ = Rate of interest
⇒ $160=16000(\frac{r}{100})^2$
⇒ $\frac{r^2}{10000}×100=1$
⇒ $r^2=100$
$\therefore r =10$%
Hence, the correct answer is 10%.

Correct Answer: Sir Syed Ahmad Khan

Solution : The correct answer is Sir Syed Ahmad Khan.

In 1875, Sir Sayed Ahmad Khan established the Mohammedan Anglo-Oriental College in Aligarh, drawing inspiration from the Cambridge education system. The institution later evolved into the renowned Aligarh Muslim University, pivotal in educational and social development in British India.

Correct Answer: Alchemy

Solution : The third option is correct.

The word alchemy refers to the mediaeval forerunner of chemistry, making it the most appropriate choice.

Therefore, the correct answer is alchemy.

Correct Answer: 42

Solution : In each row, add 9 to the first number to obtain the second number and add 9 to the second number to obtain the third number.
First row – 82, 91, 100→82 + 9 = 91; 91 + 9 = 100
Second row – 63, 72, 81→63 + 9 = 72; 72 + 9 = 81
Third row – 24, 33, ?→24 + 9 = 33; 33 + 9 = 42

So, 42 is the missing number. Hence, the third option is correct.

Correct Answer: Dunes

Solution : The correct answer is Dunes.

Dunes are landforms which are composed of wind-driven sand. Dunes are formed when wind deposits the sand on top of each other until a mound starts to form. 

Correct Answer: Errand

Solution : The correct choice is the third option.

Errand means to take a brief trip in order to achieve small tasks, like picking up groceries, collecting mail, etc. This helps convey the intended meaning that, as he went on a short trip to do something in the morning, he saw a woman with a cat under her arm.

The meanings of the other options are as follows:

• Objection means a feeling of disapproval.
• Assessment means the act of judging the quality or value of something.
• Encasement is the act of enclosing something in a protective covering.