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Students that scored 4 and above = 5 + 3 + 3 + 0 + 2 + 2 + 2 = 17

2 + 3 + 4 + 5 + 6 + 3 +3 + 0 + 2 + 2 + 2 = 32

If the total number of students represents 100%, then 70% corresponds to the point on the graph where the cumulative frequency reaches 70 From the graph, find where the cumulative frequency line intersects the 70% mark. This typically corresponds to a specific age on the X-axis

(a)(i) The number of pupils who scored between 41 and 50 marks = \(\frac{90}{360} \times 200 = 50\) (ii) The angles for pupils above 60 marks = 54^\circ + 36^\circ + 18^\circ = 108^\circ \(\frac{108}{360} \times 200 = 60\) (b) The fraction of the pupils who scored at least 50 marks : \(\frac{54 + 90}{360} = \frac{2}{5}\) (c) The modal class = 51 - 60; It has the largest angle in the pie- chart.

x 2 3 6 2 5 0 4 2 24 x - \(\bar{x}\) -1 0 3 -1 2 -3 1 -1 \((x - \bar{x})^2\) 1 0 9 1 4 9 1 1 26 Mean = \(\frac{24}{8} = 3\) Standard deviation = \(\sqrt{\frac{26}{8}}\) = \(\sqrt{3.25}\) = 1.802 \(\approx\) 1.8

P(Kodjo passing) = \(\frac{3}{4}\); P(Adoga passing) = \(\frac{3}{5}\) P(Kodjo failing) = \(\frac{1}{4}\); P(Adoga failing) = \(\frac{2}{5}\) P(both fail) = \(\frac{1}{4} \times \frac{2}{5}\) = \(\frac{1}{10}\)

\(\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}\) Given \(V_{2} = 2V_{1}\) \(T_{1} = 27^\circC + 273 = 300k\) \(\frac{V_{1}}{300} = \frac{2V_{1}}{T_{2}}\) \(\frac{1}{300} = \frac{2}{T_{2}} \implies T_{2} = 600k or 327^\circC\)

The Relation between Power, Force and Velocity is given by the relation: P = F.V , this power is the product of force and velocity. Therefore, The power of the system is reduced to one-quarter of its original value when both the force and the velocity are reduced by half.

Resultant of two vector will be maximum when they are parallel That angle between them as zero.

As the temperature increases, the molecules in the gas move faster, impacting the gas's container more frequently and exerting a greater force. This increases the pressure. And similarly As the pressure goes up, the temperature also goes up. So the temperature and the pressure is directly proportional to each other. At a fixed point, temperature is kept constant. Hence, at this point, it can be deduced that \(P_{1} = P_{2}\)

a piece of magnet consist of north pole and south pole.

In a solenoid, the north pole is determined using the right-hand grip rule: if the current flows in the direction of the arrows, the north pole is at the end where the thumb points when the fingers follow the current. Therefore, the north pole is at the end labeled Q.

Energy imparted by the accelerating system = e x V, where V is the accelerating potential; and this energy is equal to the energy of the X-ray, give by hf e x V = hf ∴ V = hf/e (6.63 x 10\(^{-34}\) x 1.6 x 10\(^{16}\))/1.6 x 10\(^{-19}\) = 6.63 x 10 = 66.3V

Total internal reflection (TIR) is the optical phenomenon in which waves arrive at the interface (boundary) from one medium to another (e.g., from water to air). that is from a more optically denser medium to a less optically denser medium.

This is called dispersion . A beam of white light passes through a prism and changes into a spectrum of colours. The spectrum is a band of seven colours which is obtained by splitting of white light by a glass prism. The order of colours from the lower end of spectrum is violet (V), indigo (I), blue (B), green (G), yellow (Y), orange (O), and red (R).