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**Question 1**
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The total length of a spring when a mass of 20g is hung from its end is 14cm, while its total length is 16cm when a mass of 30g is hung from the same end. Calculate the unstretched length of the spring assuming Hooke's law is obeyed.

**Answer Details**

Let unstretched length = L

e1 = 14 - L and e2 = 16 - L

Using, m1e1 $\frac{{m}_{1}}{{e}_{1}}$ = m2e2 $\frac{{m}_{2}}{{e}_{2}}$

2014−L $\frac{20}{14-L}$ = 3016−L $\frac{30}{16-L}$

L = 10cm

**Question 2**
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Which of the following arrangements in the sequence shown can be used to obtain a pure spectrum of white light?

**Question 3**
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A short response to time is obtained in liquid-in-glass thermometer when the

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**Question 4**
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Four resistors R1, R2, R3 and R4 are connected in series as shown above, V1, V2, V3 are voltmeters connected as indicated above. Which of the following relations is correct??

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**Question 5**
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Which of the following conditions are necessary and sufficient for total internal reflection to take place at the boundary between two optical media? i. light is passing from optically denser medium to optically less dense medium. ii. light is passing from optically less dense medium to optically denser medium. iii. angle of incidence is greater. iv. angle of incidence is lesser

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**Question 6**
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Which of the following statements is CORRECT? i. the mass number is equal to the total number of protons and electrons in an atom. ii. the atomic number is equal to the number of protons in an atom. iii. the number of electrons in an atom is equal to the total number of protons and neutrons in the nucleus.

**Question 7**
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In a resonance tube experiment, a tube of fixedlength in closed at one end and several turningforks of increasing frequency used to obtainresonance at the open end. If the turning fork withthe lowest frequency which gave resonance had a frequency f1 and the next turning fork to giveresonance had a frequency f2, find the ratio f2/ f1.

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**Question 8**
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which of the following is NOT correct? i. the pitch of a sound note depends on the frequency of vibrations. ii. the intensity of a sound note is proportional to the amplitude of vibrations. iii. beats are produced by two sources of sound because one wave is travelling faster than the other. iv. when two sources of sound of frequencies 500Hz and 502Hz are sounded together, a beat frequency of 2Hz is observed. v. the first harmonic of a tone have double the frequency of the fundamental note.

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**Question 9**
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Which of the following may be used to determine the relative humidity in a physics laboratory I. Manometer

II. Wet-and-Dry Bulb Hygrometer

III. Hair Hygrometer

IV. A Hydrometer

**Answer Details**

**Question 10**
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PQ is a thin rod on a horizontal table, RS is a plane mirror inclined at 45∘C
${45}^{\circ}C$ to the horizontal as shown above. The image of PQ as seen in the mirror by the eye T is

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**Question 11**
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If the force of a charge of 0.2 coulomb in an electric field is 4N, then the electric field intensity of the field is

**Answer Details**

Field intensity = forcecharge $\frac{force}{charge}$

40.2 $\frac{4}{0.2}$ = 20N/C

**Question 13**
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The image above shows an inverted U-tube with the open end, O of one limb below the level, W of water in the tank, in order that water should begin to flow from the tank it is is necessary that

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**Question 14**
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The range of wavelengths of the visible spectrum is 400nm - 700nm. The wavelength of gamma rays is

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**Question 15**
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A machine has a velocity ratio of 5. It requires a 50kg weight to overcome a 200kg weight. The efficiency is

**Answer Details**

Efficiency = M.A x 100%

= 20050 $\frac{200}{50}$ x 15 $\frac{1}{5}$ x 100

= 80%

**Question 16**
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Which of the following statements about defects of vision is/are CORRECT? i. for a long sighted person, close objects appear blurred. ii. for a short sighted person, distant objects appear blurred. iii. short sight is corrected by using a pair of converging lenses.

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**Question 17**
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If relative density of a metal is 19, what will be the mass of 20cm3 of the metal when immersed in water?

**Answer Details**

R.d = 19, therefore, density = 19gcm-3

mass = velocity x density

= 20 x 19

= 380g

**Question 18**
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A ship travelling towards a cliff receives the echo of its whistle after 3.5 seconds. A short while later, it receives the echo after 2.5 seconds. If the speed of sound in air under the prevalling condition is 250ms -1, how much closer is the ship to the cliff?

**Answer Details**

Difference in time = 1 sec.

echo time = 1 ÷ $\xf7$ 2 = 0.5 sec.

= 0.5 x 250

= 125m

**Question 19**
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A piece of wood is floating on water. The forces acting on the wood are

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**Question 20**
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A train has an initial velocity of 44ms-1 and an acceleration of -4ms-1. Its velocity after 10 seconds is

**Question 21**
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The electrochemical equivalent of a metal is 0.126 x 10-6 kgC-1. The mass of the metal that a current of 5A will deposit from a suitable bath in 1 hour is

**Answer Details**

m = Itz

= 5 x 3600 x 0.126 x 10-6

= 2.268 x 10-3kg

**Question 22**
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The force with which an object is attracted to the earth is called its

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**Question 24**
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A 24V potential difference is applied across a parallel combination of four 6-ohms resistor, The current in each resistor is

**Question 25**
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A man of mass 50kg ascends a flight of stairs 5m high in 5 seconds. If acceleration due to gravity is 10ms-2, the power expended is

**Answer Details**

Power = force x distancetime $\frac{\text{force x distance}}{\text{time}}$

= 50 x 10 x 5 = 500W

**Question 26**
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Which of the following figures gives the correct resultant R of two vectors P and Q?

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**Question 27**
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The refractive index of liquid is 1.5. If the velocity of light in vacuum is 3.0 x 108ms-1, the velocity of light in the liquid is

**Answer Details**

n = speed in airspeed in glass $\frac{\text{speed in air}}{\text{speed in glass}}$

1.5 = 3×104speed in glass $\frac{3\times {10}^{4}}{\text{speed in glass}}$

speed in glass = 2 x 108ms-1

**Question 28**
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The diagram above shows three circuits, the internal resistances of the batteries are negligible. which of the currents is the largest

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**Question 29**
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Of the following derived units, the one that is not a unit of power is

**Question 30**
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Each of the figures in the diagram above represent two current carrying conductors situated close to each other. In which two diagrams, are the forces between the two wires attractive

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**Question 31**
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a force of 16N applied 4.0kg block that is at rest on a smooth, horizontal surface. What is the velocity of the block at t = 5 seconds?

**Answer Details**

F = ma

= m(u−v)t $\frac{m(u-v)}{t}$

16 = 4(v−0)5 $\frac{4(v-0)}{5}$

v = 20ms-1

**Question 32**
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1,000 identical drops of oil of density 500kgm-3 have a total mass of 5 x 10-4kg. One of the drops forms a thin film of area 0.5m2 on water. The thickness of the film is

**Answer Details**

Mass of one oil = 5×10−41000 $\frac{5\times {10}^{-4}}{1000}$

= 5 x 10-4kg

Density = massarea x thickness $\frac{\text{mass}}{\text{area x thickness}}$

500 = 5×10−70.5 x thickness $\frac{5\times {10}^{-7}}{\text{0.5 x thickness}}$

thickness = 2 x 10-9m

**Question 33**
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The difference of potential between the terminals of cells is 2.2 volts. When a 4ohm resistor is connected across the terminals of this cells, the potential difference is 2 volts. What is the internal resistance of the cell?

**Answer Details**

IR = 2 and Ir = 0.2

I = 2R $\frac{2}{R}$ ; I = 0.2r $\frac{0.2}{r}$

24 $\frac{2}{4}$ = 0.2r $\frac{0.2}{r}$

r = 0.4Ω

**Question 34**
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Which of the following statements is true about liquid pressure is NOT correct? The pressure

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**Question 35**
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If the normal atmospheric pressure in a laboratory supports a column of mercury 0.76m high and the relative density of mercury is 13.8, then the height of water column which atmospheric pressure will support in the same laboratory at the same time is

**Answer Details**

Density of H2O = 1gcm3

Density x pressure = constant

D1 x P1 = D2 x P2

13.6 x 0.76 = 1 x P2

P2 = 10m

**Question 36**
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Which of the following may be used to determine relative humidity in a physics laboratory?

I. Manometer

II. Wet-and-dry bulb hygrometer

III. Hair hygrometer

IV. A hydrometer.

**Answer Details**

**Question 37**
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The linear expansivity of brass is 2 x 10-5oC-1. If the volume of a piece of brass is 10cm3 at 0oC, what will be its volume at 100oC?

**Answer Details**

3 x α $\alpha $ = V2−V1Δθ×V1 $\frac{{V}_{2}-{V}_{1}}{\mathrm{\Delta}\theta \times {V}_{1}}$

3 x 2 x 10-5 = V2−1010×100 $\frac{{V}_{2}-10}{10\times 100}$

V2 = 10.06cm3

**Question 38**
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The speed of light in vacuum is 3.0 x 108ms-1. If the refractive index of a transparent liquid is 43 $\frac{4}{3}$, then the speed of light in the liquid is

**Answer Details**

n = speed in air speed in water $\frac{\text{speed in air}}{\text{speed in water}}$

43 $\frac{4}{3}$ = 3×108v $\frac{3\times {10}^{8}}{v}$

v = 2.25 x 10 8ms-1

**Question 39**
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An electric current of 3Aflowing through an electric heating elements of resistance 20 embedded in 1,000g of an oil raises the temperature of the oil by 10oC in 10 seconds then the specific heat capacity of the oil is

**Answer Details**

Heat energy = Electrical energy

mcΩ $\Omega $ = I2RTt

1000 x c x 10 = 3 x 3 x 20 x 10

0.18Jg-1oC

**Question 43**
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In the Figure above, QR is a vertical conductor and the current I flows from R to Q, P is a point on the horizontal plane and is to the south of the wire. The direction of the magnetic field at P due to the current is

**Question 44**
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Which of the following best describes the energy changes which take place when a steam engine drives a generator which lights a lamp?

**Answer Details**

**Question 45**
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If the pressure on 100cm3 of an ideal gas is doubled while its kelvin temperature is halved, then the new volume of the gas will become

**Answer Details**

P1V1T1 $\frac{{P}_{1}{V}_{1}}{{T}_{1}}$ = P2V2T2 $\frac{{P}_{2}{V}_{2}}{{T}_{2}}$

P2 = 2P ; T1 = 2T2

therefore, P1×10002T2 $\frac{{P}_{1}\times 1000}{2{T}_{2}}$ = 2P2×V2T2 $\frac{2{P}_{2}\times {V}_{2}}{{T}_{2}}$

= 25cm

**Question 46**
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A milliameter with full scale deflection of 10mA has an internal resistance of 5 ohms. It would be converted to an ammeter with a full scale deflection of 1A by connecting a resistance of