50 questions. Try each one, then open the answer to check yourself and read the explanation.
The density of 400 cm3 of palm oil was 0.9 g cm−3 before frying. If the density of the oil was 0.6 g cm−3 after frying, assuming no loss of oil due to spilling, its new volume was
Answer: B (600 cm3)
The mass does not change: 0.9 × 400 = 360 g. New volume = mass ÷ new density = 360 ÷ 0.6 = 600 cm3.
Which of the following statements defines correctly the efficiency of a machine?
Answer: C (The useful work done by the machine divided by the total work put into it.)
Efficiency = useful work output ÷ total work input (usually × 100%). Option A is mechanical advantage and B is the inverse of velocity ratio.
A 500 kg car which was initially at rest travelled with an acceleration of 5 m s−2, its kinetic energy after 4 seconds was
Answer: A (105 J)
After 4 s, v = at = 5 × 4 = 20 m s−1. KE = ½mv² = ½ × 500 × 400 = 100 000 J = 105 J.
Two closed vessels contain equal volumes of boiling water and are identical except that one is blackened on the outside while the other is polished. Which of the following is correct?
Answer: E (The black vessel will cool faster because a black surface radiates heat faster than a polished one.)
Dull black surfaces are good emitters of radiant heat, while polished surfaces are poor emitters. So the blackened vessel loses heat faster.
The temperature at which the water vapour present in the air saturates the air and begins to condense is known as
Answer: D (dew point)
The dew point is the temperature at which the air becomes saturated with the water vapour it holds, so the vapour starts to condense as dew.
Which one of the following types of waves cannot travel through a vacuum?
Answer: A (sound waves)
Sound is a mechanical wave and needs a material medium. Light, infra-red, X-rays and radio waves are electromagnetic and can cross a vacuum.
If in a simple pendulum experiment the length of the inextensible string is increased by a factor of four, its period is increased by a factor of
Answer: E (2)
T = 2π√(L/g), so T is proportional to √L. Making L four times larger multiplies T by √4 = 2.
PQR is an equilateral glass prism of refractive index 1.5. Light incident normally on face PQ as shown in Fig. 1 will
Answer: A (undergo total internal reflection at face PR and then emerge normal to the face QR)
The ray enters PQ without bending and meets PR at 60°, which is more than the critical angle (about 42° for n = 1.5), so it is totally reflected. In an equilateral prism the reflected ray then meets QR along the normal and leaves without bending.
In what range of temperature is the expansion of water anomalous?
Answer: E (0°C to +4°C)
Between 0°C and 4°C water contracts as it is warmed, instead of expanding; it is densest at 4°C.
When the vapour of a substance is in equilibrium with its own liquid, it is said to be
Answer: E (saturated)
A vapour in dynamic equilibrium with its liquid (as many molecules returning as leaving) is a saturated vapour.
The diagram in Fig. 2 shows the lens arrangement in
Answer: B (an astronomical telescope)
Two converging lenses separated by fo + fe, with parallel rays from a distant object entering the objective, is the arrangement of an astronomical telescope in normal adjustment.
In the given circuit of Fig. 3 the cell P has an e.m.f. 1.5 V and an unknown internal resistance r while the cell Q has an e.m.f. 2.0 V and an internal resistance 1 ohm. If the ammeter reads 50 mA, then r is equal to
Answer: D (2.0 ohms)
The cells oppose each other, so the net e.m.f. is 2.0 − 1.5 = 0.5 V. Then 0.5 = 0.05 × (7 + 1 + r), so 7 + 1 + r = 10 and r = 2 Ω.
If the wavelength of a wave travelling with a velocity of 360 m s−1 is 60 m, the period of the wave is
Answer: C (0.17 s)
Frequency f = v/λ = 360/60 = 6 Hz, so the period T = 1/f = 1/6 ≈ 0.17 s.
The heights of the mercury thread in a mercury-in-glass thermometer when in melting ice and then in steam are 3 cm and 18 cm respectively. At a temperature of 60°C the height would be
Answer: D (12 cm)
The 100 degrees span 18 − 3 = 15 cm. At 60°C the thread is 60% of the way up: 3 + 0.6 × 15 = 12 cm.
The sum of the currents I1 and I2 in Fig. 4 is
Answer: D (2 A)
Each branch has the full 12 V across it. I2 = 12/10 = 1.2 A and I1 = 12/(5 + 10) = 0.8 A, so the sum is 2 A.
An object is placed 30 cm from a concave mirror of focal length 15 cm. The linear magnification of the image produced is
Answer: C (1)
The object is at the centre of curvature (2f = 30 cm), so the image is also at 30 cm. Magnification = v/u = 30/30 = 1.
If a given mass of gas at constant pressure obeys the relation...volume is proportional to the absolute temperature...the gas is said to obey
Answer: D (Charles' law)
Charles' law: at constant pressure, the volume of a fixed mass of gas is proportional to its absolute temperature.
A man standing between two parallel mirrors in a barber's shop will see the following number of his own image
Answer: E (Infinite)
For parallel mirrors the angle between them is 0°, so n = 360°/θ − 1 is infinite: each image is reflected again and again.
Which of the following statements is incorrect? The sensitivity of a galvanometer which incorporates an optical lever arrangement may be increased by providing:
Answer: E (a light source with a greater intensity.)
More turns, a weaker (thinner) suspension and a stronger magnet all give a bigger deflection per unit current, so A to C are correct. A brighter lamp only makes the spot easier to see; it does not change the deflection, so E is the incorrect statement.
A landlord has eight 40 W electric light bulbs, four 60 W bulbs and two 100 W bulbs in his house. If he has all the points on for five hours daily and if N.E.P.A. charges 5k per unit, his bill for 30 days is
Answer: A (N5.70)
Total power = 320 + 240 + 200 = 760 W = 0.76 kW. Energy = 0.76 × 5 × 30 = 114 kWh. Cost = 114 × 5k = 570k = N5.70.
An air column 10 cm in length is trapped into the sealed end of a capillary tube by a 15 cm column of mercury with the tube held vertically as shown in Fig. 5. On inverting the tube, the air column becomes 15 cm long. The atmospheric pressure during the experiment is
Answer: C (75 cm)
With the open end up the air is at (H + 15) cmHg; inverted it is at (H − 15). Boyle's law: (H + 15) × 10 = (H − 15) × 15, so 5H = 375 and H = 75 cmHg.
Which of the following statements is correct? The reading of pressure on a mercury barometer is independent of
Answer: A (the cross-sectional area of the tube)
Pressure depends on the height of the column (p = hρg), not on how wide the tube is.
In a resonance tube experiment which is illustrated in Fig. 6, the velocity of sound in air is 327.68 m/s, the frequency of the tuning fork used is therefore
Answer: C (512 Hz)
At the first resonance the 16 cm air column is a quarter wavelength, so λ = 64 cm = 0.64 m. f = v/λ = 327.68/0.64 = 512 Hz.
What are the units of thermal conductivity?
Answer: B (Joule sec−1 m−1 K−1)
Thermal conductivity is the rate of heat flow (J s−1) per unit length and per kelvin of temperature difference: J s−1 m−1 K−1 (W m−1 K−1).
A uniform beam HK of length 10 m and weighing 200 N is supported at both ends as shown in Fig. 7. A man weighing 1000 N stands at a point P on the beam. If the reactions at H and K are respectively 800 N and 400 N, then the distance HP is
Answer: C (3 m)
Take moments about H: 1000 × HP + 200 × 5 = 400 × 10. So 1000 × HP = 3000 and HP = 3 m.
Which of the following statements is correct? The magnetized state of an iron bar can be destroyed completely by
Answer: A (heating the bar to a high temperature)
Strong heating makes the atoms vibrate violently and throws the magnetic domains out of line, destroying the magnetism. Breaking the bar just makes smaller magnets.
An electric cell has an internal resistance of 2 ohms. A current of 0.5 A is found to flow when a resistor of 5 ohms resistance is connected across it. What is the electromotive force of the cell?
Answer: B (3.5 volts)
E = I(R + r) = 0.5 × (5 + 2) = 3.5 V.
Which of the following is the correct definition of 'half-life'?
Answer: B (The time it takes a radioactive material to decay to half of its original quantity.)
Half-life is the time taken for half of the radioactive nuclei in a sample to decay.
The bulb of a motorcycle head-lamp is marked 40 W, 6 V. The resistance of the filament when it is switched on is
Answer: E (62/40 ohms.)
P = V²/R, so R = V²/P = 6²/40 Ω (0.9 Ω).
In an electrolysis experiment, a cathode of mass 5 g is found to weigh 5.01 g after a current of 5 A flows for 50 seconds. What is the electrochemical equivalent of the deposited substance?
Answer: A (0.00004 g/C)
Mass deposited m = zIt. Here m = 0.01 g and It = 5 × 50 = 250 C, so z = 0.01/250 = 0.00004 g/C.
Which of the following statements about radioactivity are true? (i) Alpha particle is positively charged (ii) Beta particle is negatively charged (iii) Gamma ray is neutral (iv) Beta particle has the same mass as helium atom (v) Gamma ray is charged.
Answer: C (i, ii and iii only)
Alpha particles are positive, beta particles (electrons) are negative and gamma rays have no charge. A beta particle is far lighter than a helium atom, and gamma rays are not charged.
A concave lens of focal length 20 cm forms an image ½ the size of the object. The object distance is
Answer: E (none of these value.)
A concave lens forms a virtual image on the same side, so with f = −20 cm and v = −u/2: 1/u − 2/u = −1/20, giving u = 20 cm. That is not among A to D.
Fig. 8 shows a current I flowing in a copper wire situated in the magnetic field existing between the pole-pieces of a horse-shoe magnet. Which of the following statements is correct?
Answer: A (The wire will experience a force in the direction into the paper.)
The field runs from N to S (left to right) and the current runs up the page. By Fleming's left-hand rule the force is perpendicular to both, into the paper.
Consider a thick glass tumbler and a thin glass tumbler which are made of the same kind of glass. Some hot liquid is poured into them. Which of the following statements is correct?
Answer: D (The thick tumbler is more likely to crack because uneven expansion persists for a longer time within the thicker glass)
Glass conducts heat poorly, so in thick glass the inside surface expands while the outside stays cool. This uneven expansion sets up strains that crack it; thin glass warms through quickly and evenly.
A capacitor and a resistor are connected in series with each other and in series with an accumulator of negligible internal resistance. The potential difference across the terminals of the capacitor is
Answer: D (the same as the e.m.f.)
Once the capacitor is fully charged no current flows, so there is no p.d. across the resistor and the capacitor's p.d. equals the e.m.f.
For the wave motion represented in Fig. 9 the wavelength is given by
Answer: D (s)
The wavelength is the distance between two neighbouring crests, marked s on the diagram.
Which of the following statements is true? The frequency of a vibrating string is
Answer: E (proportional to the square root of the tension within it.)
For a string, f = (1/2L)√(T/μ), so the frequency is proportional to the square root of the tension and inversely proportional to the length.
An air bubble rises from the bottom to the top of a water dam which is 40 m deep. The volume of the bubble just below the surface is 2.5 cm3. Find its volume at the bottom of the dam, if atmospheric pressure is equivalent to 10 m of water.
Answer: E (0.5 cm3)
Pressure at the surface = 10 m of water; at the bottom = 10 + 40 = 50 m. Boyle's law: 10 × 2.5 = 50 × V, so V = 0.5 cm3.
Fig. 10 shows a see-saw which is exactly in balance. The weights of the people sitting on it are 50 kg, X kg and 15 kg as shown. They sit at distances of 1½ m, 1½ m and 2 m from the pivot respectively. The value of X is
Answer: A (30)
Clockwise and anticlockwise moments are equal: 50 × 1.5 = X × 1.5 + 15 × 2, so 75 = 1.5X + 30 and X = 30.
Which of the following electromagnetic waves has the shortest wavelength?
Answer: B (X-rays)
Of those listed, X-rays have the highest frequency and so the shortest wavelength.
All the heat generated in a 5 ohm resistor by 2 A flowing for 30 seconds is used to evaporate 5 g of a liquid at its boiling point. Which of the following is the correct value of the specific latent heat of the liquid?
Answer: C (120 J g−1)
Heat = I²Rt = 2² × 5 × 30 = 600 J. Latent heat = 600 J ÷ 5 g = 120 J g−1.
The speed of light in air is 3 × 108 m s−1. If the refractive index of light from air-to-water is 4/3, then which of the following is the correct value of the speed of light in water?
Answer: B (2.25 × 108 m s−1)
Refractive index = speed in air ÷ speed in water, so speed in water = 3 × 108 ÷ (4/3) = 2.25 × 108 m s−1. Option D has the wrong unit.
On which of the following is the operation of a moving coil galvanometer based?
Answer: D (Force on a current carrying conductor in a magnetic field)
The current in the coil sits in the field of a permanent magnet, so the coil feels a turning force (couple) and rotates against the hairsprings.
A body is released from rest and allowed to fall freely from a given height under gravity. The kinetic energy at its half-way point is
Answer: C (a half of its initial energy)
In free fall the potential energy lost turns into kinetic energy. Halfway down it has lost half its initial (potential) energy, so its KE is half the initial energy.
An electrical circuit of Fig. 11 is connected up as shown; which of the following is the correct value of the current through the 1 ohm resistance?
Answer: D (3 A)
There are two 6 Ω paths (3 Ω + 3 Ω each) in parallel, giving 3 Ω, in series with the 1 Ω resistor: total 4 Ω. All the current passes through the 1 Ω resistor: I = 12/4 = 3 A.
It is known that a neutron exists in a light atomic nucleus. Which of the following also exists in the nucleus?
Answer: D (a proton)
A nucleus is made of protons and neutrons; electrons are outside it.
A weight of 1000 grams hangs from a lever 20 cm to the right of the fulcrum. At the left is a 500-gram weight 20 cm from the fulcrum, and a 200-gram weight x cm away from the fulcrum. What is the value of x that will make the lever balanced?
Answer: A (50 cm)
Moments about the fulcrum: 500 × 20 + 200 × x = 1000 × 20, so 200x = 10 000 and x = 50 cm.
Radio carrier waves are generated by causing electrons to oscillate rapidly in
Answer: E (a transmitter.)
The radio transmitter contains the oscillator circuit that makes electrons oscillate at the carrier frequency; the antenna then radiates the wave.
Fig. 12 shows the velocity-time graph of a car which starts from rest and is accelerated uniformly at the rate of 3 m sec−2 for 5 seconds. It attains a velocity which is maintained for 1 minute. The car is then brought to rest by a uniform retardation after another 3 seconds. Calculate the total distance covered.
Answer: D (960 metres)
Top speed = 3 × 5 = 15 m s−1. Distance = area under the graph = ½ × 5 × 15 + 15 × 60 + ½ × 3 × 15 = 37.5 + 900 + 22.5 = 960 m.
Which of the following statements is correct? Silvered walls of a vacuum flask are used to prevent
Answer: D (heat loss due to radiation)
Shiny silvered surfaces are poor emitters and good reflectors of radiant heat, so they cut down heat transfer by radiation. The vacuum deals with conduction and convection.