Correct Answer: 343 : 169

Solution : The amount replaced by water each time is 8 litres.
The amount of milk = Original amount$\times(1- \frac{\text{Amount replaced by water}}{\text{Original Amount}})^n$, where $n$ = No. times process repeated
So, the amount of milk
$= 64\times (1-\frac{8}{64})^3$
$= 64\times (1-\frac{1}{8})^3$
$= 64\times (\frac{7}{8})^3$

Correct Answer: $40\frac{2}{3}\pi$

Solution : Given: Inner radius $(r)$ = 4 cm
Outer radius $(R)$ = 4 + 1 = 5 cm
According to the question,
The volume of steel used
= $\frac{2}{3}×\pi (R^3-r^3)$
= $\frac{2}{3}×\pi (5^3-4^3)$
= $\frac{2}{3}×\pi (125-64)$
= $\frac{2}{3}×\pi ×61$
= $\frac{122}{3}×\pi$
= $40\frac{2}{3}\pi\ \text{cm}^3$
Hence, the

Correct Answer: Z

Solution : Taking dice positions 2 and 3 with Z as the common face –

Moving clockwise from the common face with Z –

So, the opposite faces of the dice are –

Therefore, the opposite face of the A is Z. Hence, the fourth option is

Correct Answer: 20,00,000 tonnes

Solution : Production of company Z in 1998 = 45 (in lakh tonnes)
Production of company Y in 1996 = 25 (in lakh tonnes)
Difference = 45 – 25 = 20 (in lakh tonnes)
= 20,00,000 tonnes
Hence, the correct answer is 20,00,000 tonnes.

Correct Answer: Narendranath Dutt

Solution : The correct answer is Narendranath Dutt.

Swami Vivekananda's real name was Narendranath Dutt. He was born in Kolkata on January 12, 1863. The Indian philosophies of Vedanta and Yoga were first introduced to the West by the well-known Hindu spiritual figure Swami Vivekananda.

Correct Answer: 46, 40, 45

Solution : Let the missing numbers in a table be X, Y, Z.

In the given table, the sum of all the numbers in a row and in a column is equal, i.e., 132.

Row 1→43 + 48 + 41 = 132
Column 1→

Correct Answer: Just manage to avoid danger or trouble

Solution : The fourth option is the correct answer.

The phrase "have a narrow escape" implies a situation where someone barely avoids a potential danger or trouble, emphasising a close call. The fourth option, "just manage to avoid danger or trouble",

Correct Answer: Indira Gandhi

Solution : The correct answer is Indira Gandhi.

Indira Gandhi, a former prime minister of India, wrote a book titled "My Truth" in 1979. This book illustrates the nuance and complexity of leadership. Indira Gandhi was the first female recipient of the Bharat Ratna distinction.

Correct Answer: Milam Glacier

Solution : The correct option is the Milam Glacier.

The Milam Glacier is located in the state of Uttarakhand in India and is part of the Kumaon Himalayas. It is one of the largest glaciers in the region and is the source of the Gori Ganga

Correct Answer: Praseodymium

Solution : The correct option is Praseodymium.

Praseodymium is a chemical element with the symbol Pr and atomic number 59. It is a member of the lanthanide series, which is a group of 15 elements located in the f-block of the periodic table. Praseodymium, like many