The correct answer is option 1 i.e. 540.

Given:

a² + b² = 72 and a - b = 6

Formula used:

(a - b)² = a² + b² - 2ab ----- (1)

a³ - b³ = (a - b)(a² + b² + ab) ---- (2)

Calculations:

Using equation (1), we get

⇒ 6² = 72 - 2ab

⇒ 2ab = 72 - 36

⇒ ab = 18

Now, using equation (2) and the value of ab = 18.

⇒ a³ - b³ = (6) × (72 + 18)

⇒ a³ - b³ = 6 × 90

⇒ a³ - b³ = 540

The correct answer is option 4 i.e. 177

Given: 12 : 133 :: 16: ?

(12 × 11) + 1 = 133 

Similarly, 

(16 × 11) + 1 = 177

Hence, the correct answer is 177.

The correct answer is option 2 i.e. F.

According to the question, the arrangement is as follows:

A made the plan in the fifth year from the start. Four persons went between E and F. B went after D. Neither E nor F went in the first or last year.

The number of persons who went between A and D is equal to the number of persons who went between A and F.

(Case 2 gets eliminated as the number of persons between A and F is not similar to the number of persons between A and D).

G went after H, but not in the 6th year from the start. C didn't go in 1991.

So, F went in 1997.

Hence, the correct answer is F.

The correct answer is option 3 i.e. MoHeavy Industries.

The implementation of the PM E-Drive scheme of the Ministry of Heavy Industries (MoHI) recently got approved by the Union Cabinet chaired by Prime Minister of India Shri Narendra Modi. The scheme stands for PM Electric Drive Revolution in Innovative Vehicle Enhancement (PM E-DRIVE) and has a total budget outlay of 10,900 crores for two years. The scheme is aimed at promoting electric mobility in the country.

The correct answer is Option 3 i.e. A force is applied to a sliding box, causing it to accelerate.

Work is defined as the process of a force causing displacement of an object. In this scenario, the applied force causes the box to accelerate, meaning there is a displacement in the direction of the force. This satisfies the condition for work being done, as work is the product of the force and the displacement in the direction of that force.

The correct answer is Option 3 i.e. four other carbon atoms.

In a diamond, each carbon atom is bonded to four other carbon atoms through strong covalent bonds, forming a rigid three-dimensional lattice structure known as a tetrahedral network. This network arrangement results in each carbon atom being surrounded by four other carbon atoms, creating a highly stable and densely packed structure. These strong covalent bonds between carbon atoms contribute to the remarkable hardness, high thermal conductivity, and optical properties characteristic of diamonds.

The correct answer is option 4 i.e. Charter Act of 1813.

• The Charter Act of 1813 marked the termination of the East India Company's monopoly in India, excluding its exclusive trade privileges with China and in tea.

• Additionally, it granted permission for Christian missionaries to spread their faith and conduct educational activities, including teaching English, in India.

• Furthermore, the Charter Act of 1833 transformed the company into an administrative entity.

The correct answer is Option 1 i.e. L20N.

Given series = R8E, P12H, N16K, ?, J24Q, H28T

For numbers, the pattern is:

8 + 4 = 12

12 + 4 = 16

16 + 4 = 20

20 + 4 = 24    

24 + 4 = 29   

The logic for letters =

R - 2 = P, P -  2 = N, N -  2 = L, L -  2 = J, J -  2 = H

E + 3 = H, H + 3 = K, K + 3 = N, N + 3 = Q, Q + 3 = T,

So, the missing term will be L20N.

Hence, the correct answer is L20N.

The correct answer is option 2 i.e. Rs. 280000.

Amounts invested by Pinku and Chinku are 125000 & 175000 which is in the ratio 5 : 7

Let the profit share of Pinku and Chinku be 5x and 7x respectively

⇒ 250000 = 50000 + 5x

⇒ 200000 = 5x

⇒ x = 40000

Profit of Chinku = 7x

⇒ 7(40000) = Rs. 280000

The correct answer is option 1 i.e. 1076

⇒ divided by 8 leaves a remainder of 6 = 8x - 2 form

⇒ divided by 9 leaves a remainder of 7 = 9y - 2

⇒ divided by 10 leaves a remainder of 8 = 10z - 2

Lowest such number = lcm(8, 9, 10) - 2

⇒ 360 - 2 = 358

Such numbers would be 358, 718

⇒ 358 + 718 = 1076