Correct Answer: (1)

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

The original sentence "Hope you had a pleasant stay on the hotel" contains a prepositional error. When referring to staying at a hotel, one should use the preposition at to indicate the location where the stay occurred, as "at" is used for a specific place.

Therefore, the correct sentence is: "Hope you had a pleasant stay at the hotel."

Correct Answer: South-east

Solution : Firstly, we will draw the diagram as per the given instructions –

So, from the above diagram, B is in the South-east direction concerning M's position. Hence, the third option is correct.

Correct Answer: O

Solution : The correct answer is O.

The term universal donor refers to those with blood type O (especially O-). Because their red blood cells lack A and B antigens and the Rh factor (D antigen), they are considered universal donors. It indicates that substantial immunological reactions cannot be caused by transfusing their blood to recipients of different blood types.

Correct Answer: 45

Solution : Given:
3, 10, 24, ?, 73, 108

Add the multiples of 7 to the previous term to obtain the next term.
3 + 7 = 10; 10 + 14 = 24; 24 + 21 = 45; 45 + 28 = 73; 73 + 35 = 108

So, 45 is the missing term in the given series. Hence, the second option is correct.

Correct Answer: 1956

Solution : The correct option is 1956.

The National Council of Applied Economic Research (NCAER) was established in 1956. It is one of India's oldest and largest independent, non-profit economic policy research institutes. NCAER was founded by a group of leading industrialists, economists, and scientists, including notable figures like J. R. D. Tata, P. Thakurdas, C. D. Deshmukh, and others.

Correct Answer: Babur

Solution : The correct answer is Babur.

On April 21, 1526, in North India, the Lodi Empire and Babur's invading forces engaged in combat in the First Battle of Panipat. It signalled the start of the Mughal Empire. This battle was one of the first conflicts involving field artillery and gunpowder.

Correct Answer: + and ×

Solution : Given:
(35 ÷ 7 × 50) ÷ 11 × 1 + 3 = 8

Let's check the given options –
First option: + and –
= (35 ÷ 7 × 50) ÷ 11 × 1 – 3
= (5 × 50) ÷ 11 × 1 – 3
= 250 ÷ 11 × 1 – 3 
= 22.72 – 3
= 19.72 ≠ 8
Second option: ÷ and +
= (35 + 7 × 50) + 11 × 1 ÷ 3
= (35 + 350) + 11 × 1 ÷ 3
= 385 + 11 × 1 ÷ 3
= 385 + 11 × 0.33
= 385 + 3.63
= 388.63 ≠ 8
Third option: × and ÷
= (35 × 7 ÷ 50) × 11 ÷ 1 + 3
= (35 × 0.14) × 11 ÷ 1 + 3
= 4.9 × 11 ÷ 1 + 3
= 4.9 × 11 + 3
= 53.9 + 3
= 56.9 ≠ 8
Fourth option: + and ×
= (35 ÷ 7 + 50) ÷ 11 + 1 × 3 
= 55 ÷ 11 + 1 × 3 
= 5 + 3
= 8

Here, only the fourth option satisfies the R.H.S. of the given equation. Hence, the fourth option is correct.

Correct Answer: Raja Ram Mohan Roy

Solution : The correct option is Raja Ram Mohan Roy.

The Brahmo Samaj, a prominent reform movement in 19th-century India, was founded by Raja Ram Mohan Roy. He established the Brahmo Samaj in 1828 in Calcutta (now Kolkata). The Brahmo Samaj aimed to promote monotheism and reject idol worship, caste discrimination and other social and religious practices deemed as superstitions.

Correct Answer: Damodar

Solution : The correct option is Damodar.

The Damodar River is the river which was formerly called the "Sorrow of Bengal". The Damodar River, which passes through the Indian states of West Bengal and Jharkhand, is well-known for its destructive floods, which have inflicted enormous devastation on the area. The state of West Bengal is severely damaged by floods from the Damodar River, especially during the monsoon season.

Correct Answer: 510

Solution : Given:
12 : 1726 :: 8 : ?

(12)³ – 2 = 1728 – 2 = 1726
Similarly, (8)³ – 2 = 512 – 2 = 510

Hence, the second option is correct.