Explanation

To find the area of the path, we need to find the area of the larger rectangle and subtract the area of the smaller rectangle.

Area of larger rectangle = Length × Width

= 60 × 40

= 2400 m²

Length of inner rectangle = 60 - 2 × 2.5 = 55 m

Width of inner rectangle = 40 - 2 × 2.5 = 35 m

Area of inner rectangle = 55 × 35

= 1925 m²

Area of path = Area of larger rectangle - Area of inner rectangle

= 2400 - 1925

= 475 m²

Explanation

First bottle: 3 liters 240 milliliters

Second bottle: 5 liters 350 milliliters

Liters: 3 + 5 = 8 liters

Milliliters: 240 + 350 = 590 milliliters

Total = 8 liters 590 milliliters

Explanation

We know the identity:

a³ - b³ = (a - b)(a² + ab + b²)

Here, 8x³ - 27y³ = (2x)³ - (3y)³

= (2x - 3y)((2x)² + (2x)(3y) + (3y)²)

Given 2x - 3y = 8 and xy = 2:

(2x)² + (2x)(3y) + (3y)² = 4x² + 6xy + 9y²

= 4x² + 6(2) + 9y²

= 4x² + 12 + 9y²

We need to express 4x² + 9y² in terms of 2x - 3y and xy:

(2x - 3y)² = 4x² - 12xy + 9y²

64 = 4x² - 12(2) + 9y²

64 = 4x² - 24 + 9y²

4x² + 9y² = 88

Now, 4x² + 6xy + 9y² = 88 + 12 = 100

So, 8x³ - 27y³ = (2x - 3y)((2x)² + (2x)(3y) + (3y)²)

= 8 × 100

= 800

Explanation

The Halting problem is about determining whether a given program will terminate (halt) or run indefinitely for a specific input.

It was proven by Alan Turing that there is no general algorithm to solve this problem for all possible programs.

Explanation

Over 6000 languages are spoken globally, including many with distinct dialects and regional variations.

This linguistic diversity is mainly concentrated in Asia and Africa, where countries like Papua New Guinea alone have over 800 languages.

Explanation

In 1961, under Ayub Khan’s regime, the Muslim Family Laws Ordinance was introduced.

It made registration of marriages compulsory in the Union Council to maintain official records and prevent disputes.

Explanation

The formula to find the arc length (I) is:

I = rθ

Given values:

I = 30 cm

r = 6 cm

Rearrange the formula to solve for θ:

θ = I / r

= 30 / 6

= 5 radians

Explanation

This is the cow that lows.

"Cow" is singular, so the verb must be "lows" (singular form).

"That" is correctly used for animals in defining clauses.

Explanation

Hazrat Abu Bakr (RA) paid the cost of the land purchased for the construction of the Prophet's Mosque (Masjid-e-Nabvi) in Medina.

The land was initially owned by two orphans, and Hazrat Abu Bakr (RA) helped buy it for the mosque.

Explanation

Expansion of metal on heating is a physical change because it does not alter the metal’s chemical composition.

When cooled, the metal returns to its original size, showing that the change is reversible.