Frequency (f) is inversely proportional to wavelength (λ). If λ is halved, f is doubled.

Energy is inversely proportional to wavelength. Halving the wavelength doubles the energy.

The angular separation (θ) is directly proportional to the wavelength (λ). Therefore, increasing λ increases the angular separation.

Fringe separation is directly proportional to the wavelength. If the wavelength increases, the fringe separation also increases.

The fringe width is directly proportional to the wavelength. Therefore, increasing the wavelength increases the distance between the fringes.

The position of the first minimum in single-slit diffraction is given by a sin(θ) = λ. Increasing λ will cause θ to increase, moving the minimum away from the center.

The width of the central maximum in single-slit diffraction is directly proportional to the wavelength. Increasing the wavelength increases the width.

At the midpoint, the electric fields due to +Q and -Q cancel each other out, resulting in a net electric field of 0.

The possible outcomes are HH, HT, TH, TT. The outcomes with at least one tail are HT, TH, TT (3 outcomes). So, the probability is 3/4.

Possible combinations for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.

C_eq = 1 / (1/C1 + 1/C2) = 1 / (1/4 + 1/4) = 2 µF.

In series, R_eq = R1 + R2 = 4Ω + 6Ω = 10Ω.

Total resistance R = 4Ω + 6Ω = 10Ω. Voltage V = I * R = 2A * 10Ω = 20V.

The complement A' consists of all elements in U that are not in A. Therefore, A' = {3, 4, 5}.

2(3^2) - 5(3) + 1 = 18 - 15 + 1 = 4.

Substituting x = 5, we get 2(5) + 3 = 10 + 3 = 13.

3(5) + 2 = 15 + 2 = 17.

Molar mass of H2SO4 = 2*1 + 32 + 4*16 = 98 g/mol. Mass = 0.25 moles x 98 g/mol = 24.5 g.

|z| = √((-2)^2 + (2)^2) = √(4 + 4) = √8 = 2√2.

z^2 = (1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2i.

z² = (1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.

The argument is given by tan^(-1)(√3/1) = π/3.

|z|^2 = (2^2 + 2^2) = 4 + 4 = 8.

The conjugate of z = 2 - 3i is 2 + 3i.

The imaginary part of the complex number z = 3 + 4i is 4.

z + z* = (3 + 4i) + (3 - 4i) = 6.

z + z̅ = (3 + 4i) + (3 - 4i) = 6.

|z|^2 = 3^2 + 4^2 = 9 + 16 = 25.

The real part of the complex number z = 4 + 3i is 4.

The argument of z = 5 + 12i is given by arctan(12/5).