'Under the weather' means feeling ill or unwell.

'Diligent' means showing care and effort in one's work, making 'industrious' the correct synonym.

'Hasty' means done with excessive speed or urgency; thus, the synonym is 'quick'.

'Meticulous' means showing great attention to detail; thorough.

The absolute value of -7 is 7.

The slopes are m1 = 2 and m2 = -1/2. The angle θ between the lines is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)|, which results in 90 degrees.

The angular distance is calculated as |90° - 30°| = 60°.

The Earth rotates 360 degrees in 24 hours, so in 1 hour, it rotates 360/24 = 15 degrees.

'Contract' is the opposite of 'expand', meaning to decrease in size.

'Diminish' is the opposite of 'increase', which means to make smaller or reduce.

'Quiet' is the opposite of 'noisy', referring to a lack of sound.

'Complicated' is the opposite of 'simple', meaning something that is difficult to understand.

'Fail' is the opposite of 'succeed', indicating a lack of success.

'Defeat' is the opposite of 'victory', indicating loss.

'Obscure' means not visible or hard to see, which is the opposite of 'visible'.

The approximate area of India is 3.28 million square kilometers.

The circumference of the Earth at the equator is approximately 24000 km.

The temperature at the Earth's inner core is estimated to be around 5000°C to 6000°C.

The Earth's crust varies in thickness, averaging about 30-50 km under continents and about 5-10 km under oceans.

Area = π * radius² = 3.14 * 3² = 3.14 * 9 = 28.26 cm².

Area = πr² = 3.14 * (4)² = 3.14 * 16 = 50.24 cm²

Area = πr² = (22/7) × (7)² = (22/7) × 49 = 154 cm².

Area = 1/2 * base * height = 1/2 * 10 * 5 = 25 square units.

Area = 1/2 * base * height = 1/2 * 12 * 5 = 30 cm².

Area = 1/2 × base × height = 1/2 × 6 cm × 4 cm = 12 cm².

The area of a triangle is given by A = 1/2 * base * height. Here, A = 1/2 * 8 * 5 = 20 cm².

The area under the curve is given by ∫(from 1 to 4) (1/x) dx = [ln(x)] from 1 to 4 = ln(4) - ln(1) = ln(4).

The area under the curve is given by ∫(from 0 to 2) (2x^2 + 3) dx = [(2/3)x^3 + 3x] from 0 to 2 = (16/3 + 6) = 10.

The average atmospheric pressure at sea level is defined as 1013.25 millibars.

The average density of the Earth is about 5.5 g/cm³, which is higher than the density of the crust.