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Mode = 42 42 occurred thrice.

The measures of central tendency are: Mean, Median, and Mode while the measures of dispersion/spread are: Range, Variance, Standard Deviation, Interquartile Range (IQR), and Coefficient of Variation.

The number of ways is given by (n−1)! For six people = (6−1)! = 5! = 120 Thus, the number of ways to seat 6 people around the table is: 120

To form a committee of 2 girls and 3 boys from 5 girls and 7 boys: Step 1: Combinations for Girls = \(^5C_2\) = \(\frac{5!}{(5-2)!2!}\) = 10 Step 2: Calculate the Combinations for Boys = \(^7C_3\) = \(\frac{7!}{(7-3)!3!}\) = 35 the total number of ways to form the committee, multiply the combinations of girls and boys: 10 x 35 = 350ways The total number of ways to form the committee is: 350.

To form a committee of 5 from 7 males and 3 females with at least one female: Choose 1 female from 3: \(^3C_1\) = 3 Choose 4 males from 7: \(^7C_4\) = 35 Total ways = 3 \times 35 = 105 The total number of ways to select the committee is: 105ways.

Total Balls 7 + 4 = 11 Probability of Picking Two Balls of the Same Colour = RR or BB = \(\frac{7}{11} \times \frac{7}{11}\) + \(\frac{4}{11} \times \frac{4}{11}\) = \(\frac{49}{121}\) + \(\frac{16}{121}\) = \(\frac{65}{121}\)

Pressure is defined as force per unit area. In the context of gas molecules colliding with the walls of a container, the force exerted by the gas can be understood as the rate at which momentum is transferred to the walls. As gas molecules collide with the walls, they change momentum, and this change occurs over time. Thus, the pressure can be described as the rate of change of momentum (change in momentum per collision multiplied by the number of collisions per second) divided by the area over which the collisions occur.

(a) A thermometric liquid is a liquid used in thermometers to measure temperature. It expands and contracts uniformly with changes in temperature, allowing for accurate readings. (ii) I. Narrow Bore Reason: Allows precise measurement by controlling the movement of the thermometric liquid, ensuring quick and accurate readings II. Thin Wall of the Bulb Reason: Enhances thermal conductivity, enabling faster heat transfer for quicker and more accurate temperature readings. (b) Heat is a measure of the change in total internal energy in a body while temperature is a measure of the average kinetic energy of a molecule of the body. (c) Evaporation leads to cooling for these reasons: Energy Absorption: Molecules at the surface absorb energy to break free, often from the liquid and its surroundings. Loss of High-Energy Molecules: Higher-energy molecules evaporate, reducing the average kinetic energy of the remaining liquid. Temperature Decrease: As the average kinetic energy drops, the temperature of the liquid decreases, resulting in cooling. (d)(i) Given: P = 2000W, \(\theta\) = 20ºC, t = 2 mins = 120 secs. P x t = mc\(\Delta\)\(\theta\) m = \(\frac{P \times t}{c \times \Delta \theta}\) m = \(\frac{2000 \times 120}{4200 \times (100 - 20)}\) = 0.714 kg Also, Pt = ml l = \(\frac{Pt}{m}\) where m = 45% of 0.714, t = 6mins = 360secs l = \(\frac{2000 \times 60 \times 6}{0.714 \times 0.45}\) = 2.29 x 10\(^6\)Jkg\(^{-1}\) (d)(i) Assumption made: there is no loss of heat to the surroundings, and the heat capacity of the material of the kettle is negligible.

The maximum displacement of particles from equilibrium position in a wave motion is known as "amplitude".

A rainbow is formed by the DISPERSION of sunlight by spherical raindrops floating in the air.

Object distance (u) = -25 cm (negative because the object is in front of the mirror) Image distance (v) = +5 cm (positive because the image is behind the convex mirror) Using \(\frac{1}{f}\) = \(\frac{1}{u}\) + \(\frac{1}{v}\) \(\frac{1}{f}\) = \(\frac{1}{-25}\) + \(\frac{1}{5}\) f = \(\frac{25}{4}\) = 6.250cm.

The Power is given by: P = \(\frac{1}{f}\) f = 20cm → 0.2m P = \(\frac{1}{0.2}\) = 5 dioptres

A monochromatic light is one that has a single wavelength or color. This means that it consists of light waves that all have the same frequency, resulting in a uniform appearance without any variation.

The diaphragm in a camera is similar to the D. Iris of the eyes. The diaphragm controls the amount of light entering the camera, just as the iris controls the amount of light entering the eye by adjusting the pupil's size.

The horizontal component F\(_x\) can be calculated using the formula: F\(_x\) = F⋅ cos (\(\theta\)) F = 150N and \(\theta\) = 60º F\(_x\) = 150 x 0.5 = 75N (cos 60º = 0.5)