Induced EMF (ε) = -N(dB/dt) = -100 * (0.5 - 0.2)/2 = -15 V.

Induced EMF = -N * (ΔB/Δt) = -100 * ((1.5 - 0.5)/2) = -100 * (1/2) = -50 V. The magnitude is 50 V.

Using Faraday's law, EMF = -N * (ΔB/Δt) = -100 * ((1.5 - 0.5) / 2) = -100 * (1 / 2) = -50 V. The magnitude is 50 V.

Probability of getting no heads (all tails) = (1/2)^3 = 1/8. Therefore, probability of at least one head = 1 - 1/8 = 7/8.

Each student receives = 1000 / 4 = $250.

Tax = 15% of $5000 = $750. Amount received = $5000 - $750 = $4250.

Amount for sports = 5000 - (0.6 * 5000) = 5000 - 3000 = $2000.

Amount for first place = 60% of $5000 = 0.60 * 5000 = $3000.

Number of students receiving trophy = 10% of 200 = 0.10 * 200 = 20.

25% of 120 is 30, so the number of employees not in the sales department is 120 - 30 = 90.

Profit = 20% of $50,000 = 0.20 * 50,000 = $10,000.

Net Profit = Revenue - Expenses = 1.5 million - 1 million = $500,000.

Profit = 20% of $500,000 = 0.2 * 500,000 = $100,000.

Profit amount = 25% of $200,000 = 0.25 * 200,000 = $50,000.

Selling Price = Cost Price + Profit = 200 + (30% of 200) = 200 + 60 = $260.

Profit = 30% of $500,000 = 0.3 * 500,000 = $150,000.

Selling Price = Cost Price + Profit = 200 + (25% of 200) = 200 + 50 = $250.

The total moment of inertia is I_cylinder + I_sphere = (1/2 MR^2) + (2/5 MR^2) = (7/10) MR^2.

Concave lenses always produce virtual and upright images regardless of the object distance.

Using the lens formula, 1/f = 1/v - 1/u, we find v = 8 cm.

For a concave lens, the image formed is virtual and erect when the object is placed beyond the focal length.

For a concave lens, the image formed is virtual and erect when the object is placed at any distance.

Using the lens formula, the image distance is calculated to be -16.67 cm.

Using the mirror formula, 1/f = 1/v + 1/u, where f = -10 cm (concave mirror), u = -30 cm. Solving gives v = -15 cm, which means the image is formed 15 cm in front of the mirror.

Using the mirror formula: 1/f = 1/v + 1/u, where f = -20 cm (concave mirror), v = -30 cm (image distance), we find u = 25 cm.

The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 20 cm = 40 cm.

Using the mirror formula, 1/f = 1/v + 1/u. Here, f = -5 cm (concave mirror), u = -10 cm. Solving gives v = -10 cm.

Volume of cone = (1/3)πr²h; Volume of cylinder = πr²h. Therefore, cone's volume is one-third of the cylinder's volume.

Volume of a cone = (1/3)πr²h = (1/3)π(2)²(6) = (1/3)π(4)(6) = 8π cm³.

The surface area of a cone is given by SA = πr(r + l), where l is the slant height. Here, l = √(r² + h²) = √(2² + 6²) = √40. Thus, SA = π(2)(2 + √40) = 20π.