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

Cost price of 1 apple = 34 ÷ 8 = Rs. 4.25

Cost price of 12 apples = 4.25 × 12 = Rs. 51

Selling price of 12 apples = Rs. 57

Profit = 57 − 51 = Rs. 6 per dozen.

Explanation

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

With 4 persons: 12 ÷ 4 = 3 days.

Explanation

Explanation

10% of 5400 = 540

5400 - 540 = 4860

Explanation

A pie chart represents data in a circular form, and the sum of all the angles in the chart always equals 360°.

Each slice of the pie chart corresponds to a portion of the total, and their angles add up to 360°.

Explanation

The correct phrase is "quick in mind," meaning intellectually sharp or intelligent.

"In" is the proper preposition to describe a quality within someone, like the mind.

Explanation

The phrase "goes on for some time" is the correct usage when referring to a duration of time.

"For" is used with periods of time (e.g., for hours, for years, for some time).

Explanation

The sentence refers to the location where the branches were joined — specifically “at the top.”

The correct preposition for pointing to a specific point or location is “at.”

Explanation

The sentence means that teachers follow or model their actions based on the example of the Prophet (S.A.W).

The correct preposition to express imitation or following someone’s example is “after.”