SAT (Stage-1) Mock Test

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SAT (Stage-1) Mock Test - 89

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Weekly Quiz Competition

Question 1
1 / -0

Two satellites of Earth, S₁ and S₂, are moving in the same orbit. The mass of S₁ is four times the mass of S₂. Which of the following statements is true?

A
The time period of S₁ is four times that of S₂.

B
The potential energy of Earth and satellite in both the cases is the same.

C
S₁ and S₂ are moving with the same speed.

D
The kinetic energies of the two satellites are equal.

Solution

Orbital speed of a satellite is independent of the mass of the satellite and depends upon the mass of the planet (M) and the radius of the orbit (r).
Question 2
1 / -0

A sonometer wire of density 'd' and radius 'a' is held between two bridges at a distance 'l' apart. The wire has a tension 'T'. The fundamental frequency of the wire is

A

B

C

D

Solution

In case of the sonometer wire, the two bridge points are treated as clamped points.
So, the fundamental wavelength is λ = 2I.

Corresponding fundamental frequency,

Velocity of the wave in the string,

, where T is the tension in the wire and μ is the mass per unit length.

If 'd' is the density of the wire,

Then, ; where A is the cross-sectional area of the wire (A = πa²).
Question 3
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An object is placed 12 cm in front of a concave mirror and an image of the same size is obtained on the screen. How far back should the object be moved so that the image is formed 6 cm nearer to the mirror?

A
Infinite

B
12 cm

C
6 cm

D
0 cm

Solution
Question 4
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The critical angle for a denser medium is 35°. If the light travelling from a denser medium to a rarer medium makes an angle of 60° with the boundary of two media, then which of the following statements is true?

A
Light will be refracted into the rarer medium.

B
Light will travel parallel to the boundary.

C
Light will be totally reflected back into the same medium.

D
None of these

Solution

As the angle of incidence is 30°, which is less than the critical angle of incidence, so the light travelling from the denser medium to rarer medium will undergo normal refraction.
Question 5
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If a ray of light in a denser medium enters into a rarer medium at an angle of incidence i, the angles of reflection and refraction are r and r', respectively. If the reflected and refracted rays are at right angle to each other, then the critical angle for the given pair of media is

A
tan^-1(sin r)

B
sin^-1(tan r)

C
tan^-1(tan i)

D
cot^-1(tan i)

Solution
Question 6
1 / -0

¹⁴N₇ is bombarded with ⁴He₂. The resulting nucleus is ¹⁷O₈ with the emission of a/an

A
neutrino

B
antineutrino

C
proton

D
neutron

Solution

For the given reaction , we have

¹⁴N₇ + ⁴He₂ → ¹⁶O₈ + ¹p₁
Question 7
1 / -0

In the given diagram of an electric motor, if the key (k) in the circuit is closed, then the armature will

A
rotate in a clockwise direction

B
rotate in a counterclockwise direction

C
rotate in any of the clockwise or counterclockwise directions

D
not rotate

Solution

If the key (k) in the circuit is closed, then the current will flow in the circuit. The armature will rotate in a clockwise direction, i.e. from A to B to C to D in the diagram. Using Fleming's Left Hand rule, the direction of the force on section AB is upward and on section CD, the direction of force is downward. As a result, the coil will rotate in a clockwise direction.
Question 8
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A particle is moving with a uniform acceleration along a straight line AB. If its speeds at A and B respectively are 2 m/s and 14 m/sec, then

A
its speed at the mid-point of AB is 10 m/sec

B
its speed at a point P, such that AP : PB = 1 : 5, is 5 m/sec

C
the time it takes to go from A to the mid-point of AB is the same as that to go from the mid-point to B

D
None of these

Solution

Let a be the acceleration of the particle and distance AB = d.
Then, using v²- u²= 2as, we have
14² = 2² + 2 x a x d
At the mid-point, let the velocity be v.

Let the velocity at P be v₁.

Let the time taken to reach the mid-point from A be t₁ and the time taken to reach B from the mid-point be t₂_.
Question 9
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If equal volumes of two liquids with densities ρ₁ and ρ₂ are mixed, then the new density of the resultant mixture will be

A
ρ₁ + ρ₂

B

C
ρ₁ - ρ₂

D

Solution

Suppose if equal volumes of two liquids with densities ρ₁ and ρ₂ are mixed, then the density of the resultant mixture is ρ.
Question 10
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A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio of 2 : 3. The smaller fragment moves with a velocity of 6 ms^-1. The kinetic energy of the larger fragment is

A
96 J

B
216 J

C
144 J

D
360 J

Solution

Total mass of the shell = 20 kg
Ratio of the masses of the fragments = 2 : 3
∴ Masses of the fragments are 8 kg and 12 kg
Now, according to the conservation of momentum
m₁v₁ = m₂ v₂
∴ 8 x 6 = 12 x v
v (velocity of the larger fragment) = 4 m/s
Question 11
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In △ABC,∠ B is an obtuse angle with AD perpendicular to CB produced. If AB = 8 cm, BC = 6 cm and AC = 11 cm, then BD is equal to

A
1.75 cm

B
3.55 cm

C
4.91 cm

D
8.54 cm

Solution

In △ ADC
AC² = (BD + BC)² + (AD)² ....(1)
In △ ADB
(AB)² = (AD)² + (BD)² ....(2)
(1) → (11)² - (BD + BC)² = (AD)² .... (3)
(2) → (AD)² = 64 - (BD)².... (4)
From (3) and (4):
121 - (BD + BC)² = 64 - (BD)²
(121) - (BD² + 6² + 2 ×BD ×6) = 64 - BD²
121 - 36 - 12 BD = 64
∴ BD = 1.75 cm
Question 12
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In the figure below, the length of each edge of the cube is x.

If M and N are midpoints of two edges, then what is the perimeter of MNOP?

A
4x√5

B

C
2x + x √5

D
3x

Solution
Question 13
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The sum of the integers lying between 1 and 100, which are divisible by either 3 or 7, is

A
5050

B
5000

C
3000

D
None of these

Solution

Let A = Numbers divisible by 3 up to 100 = 33
B = Numbers divisible by 7 up to 100 = 14
A ∩ B is divisible by 3 and 7 both.
Sum of numbers of set A = 33/2 [2 × 3 + 32 × 3] = 33/2 × 102 = 33 × 51
Sum of numbers of set B = 14/2 [2 × 7 + 13 × 7] = 7(105)
Sum of numbers of set A ∩B = 4/2 [2 × 21 + 3 × 21] = 2(105)
So, using sum of numbers of set A ∪B = Sum of numbers of set A + Sum of numbers of set B - Sum of numbers of set A ∩ B
= 33 × 51 + 7 × 105 – 2 × 105 = 2208
Question 14
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In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If ∠CBE = 65°, then what is the value of ∠DEC ?

A
35°

B
55°

C
45°

D
25°

Solution
Question 15
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Answer the following question by using the given figure.

If O is the center of the circle and ∠BOC = 80°, then ∠ADB is equal to

A
80°

B
40°

C
50°

D
100°

Solution

∠BOC = 80° (Given)
Now, ∠AOB + ∠BOC = 180° (Linear pair axiom)
∠AOB = 180° - ∠BOC = 180° - 80° = 100°
Also, ∠ ADB = (1/2) × ∠ AOB = (1/2) × 100° = 50° (An angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.)