SAT (Stage-1) Mock Test

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SAT (Stage-1) Mock Test - 74

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Weekly Quiz Competition

Question 1
1 / -0

If error in measurement of the radius of a sphere is 1%, then what will be the error in measurement of its volume?

A
1%

B
1/3%

C
3%

D
10%

Solution

As the volume of the sphere is
Question 2
1 / -0

A light passing through air has a wavelength of . The wavelength of the same light, when passing through a glass slab of refractive index 1.5, will be

A

B

C

D

Solution

As the refractive index of the glass is given
Question 3
1 / -0

Two thin lenses of powers 12 D and -2 D are placed in contact, the power, focal length and nature, respectively will be

A
8 D, 0.8 m, convex

B
14 D, 0.5 m, convex

C
5 D, 0.2 m, convex

D
10 D, 0.1 m, convex

Solution

Power of the combination of the lens

P = P₁+ P₂

P₁= 12 D and P₂ = -2 D

P = 12 - 2 = 10 D

Power of the combination is positive, so the combination is a convergent (convex) lens.

Focal length of the combination,
Question 4
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A body starting from rest moves along a straight line with a constant acceleration. The variation of speed (v) with distance (s) is represented by the graph:

A

B

C

D

Solution

Key Idea: Body starts from rest, hence initial velocity is zero.
From the equation of motion, we have
v² = u² = 2as
where v is final velocity, u is initial velocity, a is acceleration and t is time.
Since, body starts from rest, u = 0
∴ v²= 2as
which is general equation of a parabola.

y² = 4ax, hence graph is parabolic and is symmetrical along s-axis.
Question 5
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A stone released with zero velocity from the top of a tower reaches the ground in 4 s. The height of the tower is (Given: g = 10 m/s²)

A
20 m

B
40 m

C
80 m

D
160 m

Solution
Question 6
1 / -0

Hubble's law states that v = H₀r. What does the Hubble constant H₀mean?

A
Amount of dark energy

B
The expansion rate of universe

C
The mass of galaxies

D
The rotation rate of galaxies

Solution

Hubble's law states that the rate at which astronomical objects in the universe move apart from each other is proportional to their distance from each other, i.e. v = H₀r.
The Hubble Constant H₀ is the unit of measurement used to describe the expansion of the universe.
Question 7
1 / -0

The difference between the lengths of a mean solar day and a sidereal day is about

A
1 min

B
4 min

C
15 min

D
56 min

Solution

A solar day is the time it takes for the Earth to rotate about its axis so that the Sun appears in the same position in the sky.
A sidereal (means stars) day is the time it takes for the Earth to rotate about its axis so that the distant stars appear in the same position in the sky.

The sidereal day is approximately 4 minutes shorter than the solar day.
Question 8
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Mercury, Venus, Earth and Mars are also called

A
inner planets

B
terrestrial planets

C
outer planets

D
Both (1) and (2) are correct.

Solution

Terrestrial planets are Earth-like planets, made up of rocks or metals with a hard surface — making them different from other planets that lack a solid surface. Terrestrial planets also have a molten heavy metal core, few moons, and topological features such as valleys, volcanoes and craters. There are four terrestrial planets in our solar system and they are the four closest to the sun Mercury, Venus, Earth and Mars.

The inner planets are small, dense and composed mostly of rocks, while the outer planets are composed mostly of gas, with no solid surfaces and only liquid cores.
The inner planets also have few or no moons and no rings circling them, while the outer planets often have dozens of satellites and rings composed of particles of ice and rock.
Question 9
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Which of the following reactions is not an exothermic reaction?

A
Burning of natural gas

B
Respiration

C
Decomposition of calcium carbonate

D
Burning of carbon in oxygen

Solution

All decomposition processes are endothermic.
Hence, the decomposition of calcium carbonate is an endothermic reaction.
On the other hand burning of fuels is always exothermic.
Respiration is also an exothermic process and the energy released is stored in the form of A.T.P.
Question 10
1 / -0

Curdy white precipitates formed when soap solution is used with hard water is due to

A
calcium and magnesium ions present in hard water

B
potassium and sodium ions present in hard water

C
calcium and sodium ions present in hard water

D
magnesium and potassium ions present in hard water

Solution

Soap is a sodium salt of stearic acid or palmitic acid.
Hardness of water is due to Ca⁺² and Mg⁺² ions present in water as these ions form insoluble salts with soap which is seen as a curdy white precipitae or scum that settles on clothes that are washed in hard water using soap.
Question 11
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Which of the following energy resources is/are mined from the earth?

A
Petroleum

B
Coal

C
Coke

D
Natural gas

Solution

Coal is formed by the decomposition of vegetation and trees that got buried under the layers of the earth during natural calamities such as earthquakes and over millions of years, under the geothermal conditions, they got converted into coal.
Therefore, coal is the fossil fuel that has to be mined from the earth.
Question 12
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Select the correct sequence of steps undertaken in order to separate a mixture of kerosene, sand, alcohol and water.

A
Separating funnel, filtration, fractional distillation

B
distillation, separating funnel, filtration

C
Filtration, separating funnel, fractional distillation

D
Filtration, separating funnel, distillation

Solution

For effective separation of the components of the mixture, the sequence of steps followed should be:
Step 1: Filtration, to separate the insoluble component sand from the remaining mixture.
Step 2: Separating funnel is used to separate kerosene which is immiscisible with alcohol and water.
Step 3: Fractional distillation is carried out to separate alcohol from water because they are miscible and their boiling points differ by 21.6K
Question 13
1 / -0

The process of reduction of concentrated ore with carbon is known as

A
calcination

B
smelting

C
roasting

D
leaching

Solution

Metals are extracted by reduction of their oxides.
The process of reduction by carbon is called smelting, and is carried out in a brick lined blast furnace which is made up of steel, so that it can withstand the pressure of the gaseous products formed.
For example: Fe₂O₃(s) + C → Fe(s) + CO(g)
Question 14
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Which of the following statements is true with reference to the chemical properties of metals and non-metals?

A
Metals are highly electronegative in nature.

B
Non-metals react with dilute acids.

C
Some metals react with bases to form salts and carbon dioxide.

D
Metals react with oxygen to form metal oxides which are basic in nature.

Solution

Metals form oxides which are basic in nature and their solution will turn red litmus blue.
Question 15
1 / -0

The SI unit of latent heat is

A
J/kg

B
cal/g

C
J/g

D
None of these

Solution

Latent heat of fusion of a substance is the amount of heat required to change the state of 1 kg of a substance from solid to liquid at its melting point at the atmospheric pressure.
Similarly, latent heat of vaporisation of a substance is the amount of heat required to change the state of 1 kg of a substance from liquid to vapour at its boiling point at the atmospheric pressure.
Thus, the SI unit of latent heat is J/kg.