Explanation

"With keen interest" is the correct phrase to express the manner or attitude of studying.

"In Japan" correctly refers to the location where the studying took place.

Explanation

The equation 3(4x) = (4x)3 shows that the order of multiplication does not affect the result.

This is the Commutative Property of Multiplication, where a × b = b × a.

Explanation

Work = Persons × Days = 3 × 4 = 12 person-days

With 4 persons: 12 ÷ 4 = 3 days.

Explanation

To find the loss percentage:

Cost Price (CP) = Rs. 120,000

Selling Price (SP) = Rs. 96,000

Loss = CP - SP = 120,000 - 96,000 = Rs. 24,000

Loss percentage = (Loss / CP) × 100

= (24,000 / 120,000) × 100

= 0.2 × 100

= 20%

Explanation

Given:

x̄ (mean) = 12

∑x (sum) = 132

The formula for mean is:

x̄ = ∑x / n

Rearrange to find n:

n = ∑x / x̄

= 132 / 12

= 11

Explanation

Stealing a book is a physical theft, not done through digital means — so it’s not a cybercrime.

Cybercrimes include actions like stealing passwords, hacking, and online fraud, all involving computers or the internet.

Explanation

a² - b² = (a - b)(a + b).

Explanation

"Before entering" is the correct phrase, indicating the action should happen prior to entering.

It properly links with the verb "ask permission" to show timing and respect.

Explanation

"Through the tunnel" means entering at one end and coming out the other.

It accurately describes movement inside a passage like a tunnel.

Explanation

A Municipal Corporation is a geographical and administrative division in urban areas to manage local governance and services.

It handles functions like sanitation, water supply, infrastructure, and urban planning for cities.