Inductive reactance (X_L) is given by X_L = 2πfL. If the frequency (f) is doubled, the inductive reactance also doubles.

The period T is the reciprocal of frequency f (T = 1/f). If frequency is doubled, the period halves.

30% of ₹500 crores = 0.30 * 500 = ₹150 crores.

Expected new cases = (Incidence rate × Population) / 1000 = (3 × 50000) / 1000 = 150.

Price after one year = Current Price * (1 + Inflation Rate) = 200 * (1 + 0.05) = 200 * 1.05 = $210.

Interest = Principal * Rate = 1000 * 0.04 = $40.

Time = Distance / Speed = 120 km / 5 km/h = 24 hours.

Time = Distance / Speed = 240 km / 4 km/h = 60 hours.

Area of square = side². If side is doubled, new area = (2 * side)² = 4 * side², so area quadruples.

Perimeter = 2 * (length + width) = 2 * (4 + 6) = 20 cm

A triangle with sides 3 cm, 4 cm, and 5 cm satisfies the Pythagorean theorem (3² + 4² = 5²), thus it is a right triangle.

Using Pythagoras theorem, 7² + 24² = 49 + 576 = 625 = 25², so it is a right triangle.

The maximum length of the third side is less than the sum of the other two sides, so it can be 22 cm.

Set y = 0: 2x + 6 = 0; x = -3.

Setting x = 0 in the equation gives 3y = 12, thus y = 4. The point of intersection is (0, 4).

Rearranging gives y = (4/3)x + 4. The slope is -4/3, so a parallel line has the same slope.

Substituting (1, 2) gives 2 = 3(1) + c, so c = -1.

Using y = mx + c: 3 = 2(2) + c => c = -1.

10% of 543 = 0.10 * 543 = 54.3, rounding down gives 54 members.

Number of women members = 20% of 545 = 0.20 * 545 = 109. Therefore, approximately 110.

E = mc^2 = 2 kg * (3 x 10^8 m/s)^2 = 1.8 x 10^16 J.

Mean of 10 numbers = 50, so total sum = 500. Sum of last 5 numbers = 500 - 200 = 300. Mean of last 5 = 300 / 5 = 60.

The sum of the numbers is calculated as mean * number of items = 25 * 12 = 300.

Sum = Mean * Number of observations = 10 * 5 = 50.

Variance is the square of the standard deviation. Therefore, variance = 5² = 25.

Variance = (Standard Deviation)² = 5² = 25.

Total sum = Mean * Number of values = 20 * 10 = 200

Total sum = Mean * Number of values = 20 * 5 = 100

Variance is the square of the standard deviation. Therefore, variance = 5² = 25.

Variance is the square of the standard deviation. Therefore, variance = 10² = 100.