In series, R_eq = R1 + R2 = 10Ω + 20Ω = 30Ω.

In a series circuit, total resistance (R_total) is the sum of individual resistances: R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω.

In series, R_eq = R1 + R2 = 4Ω + 4Ω = 8Ω.

For parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/6. Finding a common denominator gives R_eq = 2.4Ω.

The Tyndall effect is the scattering of light by colloidal particles, making the path of the light visible.

The unit of electric charge is Coulomb (C).

The unit of electrical conductivity is Siemens (S).

The unit of the rate constant for a first-order reaction is s⁻¹.

The SI unit of work is Joule (J).

Magnesium has a valency of 2, as it can lose two electrons.

Oxygen has a valency of 2, as it needs two electrons to complete its outer shell.

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

Using BODMAS: (2 + 3) = 5 and (4 - 1) = 3, so 5 × 3 = 15.

(2 + 3) × 4 = 5 × 4 = 20.

Using the binomial theorem, (2 + 3)^3 = C(3,0)(2)^3 + C(3,1)(2)^2(3) + C(3,2)(2)(3)^2 + C(3,3)(3)^3 = 8 + 36 + 54 + 27 = 125.

Multiply numerator and denominator by the conjugate of the denominator: (2 + 3i)(1 - i) / (1 + i)(1 - i) = (2 - 2i + 3i + 3) / (1 + 1) = (5 + i) / 2 = 2.5 + 0.5i.

Using the difference of squares: (a + b)(a - b) = a² - b². Here, (2)² - (3i)² = 4 - (-9) = 4 + 9 = 13.

Using the binomial theorem, (2 - 3)^5 = (-1)^5 = -1.

Multiplying numerator and denominator by the conjugate of the denominator: (3 + 4i)(1 - i) / (1 + i)(1 - i) = (3 - 3i + 4i + 4) / 2 = (7 + i) / 2 = 2 + i.

(3 + 5) = 8 and (2 + 4) = 6, so 8 × 6 = 48.

(3 + 5) = 8 and (2 - 1) = 1, so 8 × 1 = 8.

(3 + 5) = 8 and (6 - 2) = 4, so 8 × 4 = 32.

(3 + 5) × 2 = 8 × 2 = 16.

Using the binomial theorem, (3 - 2)^5 = 1^5 = 1.

3^3 = 27 and 2^3 = 8, so 27 - 8 = 19.

Using the binomial theorem, (x + 1)^5 = C(5,0)(2)^5 + C(5,1)(2)^4 + C(5,2)(2)^3 + C(5,3)(2)^2 + C(5,4)(2)^1 + C(5,5)(2)^0 = 32 + 80 + 80 + 40 + 10 + 1 = 243.

100 - 37 = 63.

100 ÷ 4 = 25, so 25 + 6 = 31.

12 × 12 = 144.

12 × 8 = 96.