JEE Advanced Mix Test 21

Result

JEE Advanced Mix Test 21

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

The spring block system lies on a smooth horizontal surface. The free end of the light spring is being pulled towards right with constant speed v0 = 2m/s. At t = 0 sec, the spring of spring constant k = 100 N/cm is unstretched and the block has a speed 1 m/s to left. The maximum

A
2 cm

B
4 cm

C
6 cm

D
8 cm

Solution

In the frame (inertial w.r.t earth) of free end of spring, the initial velocity of block is 3 m/s to left and the spring unstretched.
Question 2
4 / -1

The figure shows a hollow cube of side 'a' of volume V. There is a small chamber of volume V/4 in the cube as shown. This chamber is completely filled by m kg of water. Water leaks through a hole H. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is:

A
1/2 mg a

B
3/8 mg a

C
5/8 mg a

D
1/4 mg a

Solution

Let h be the height of water surface, finally
Question 3
4 / -1

Two blocks ‘A’ and ‘B’ each of mass ‘m’ are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on the two blocks ‘A’ and ‘B’ respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is:

A
F

B
F/2

C

D
3F

Solution
Question 4
4 / -1

A coin is released inside a lift at a height of 2 m from the floor of the lift. The height of the lift is 10 m. The lift is moving with an acceleration of 11 m/s2 downwards. The time after which the coin will strike the lift is :

A
4 s

B
2 s

C

D

Solution

Relative to lift initial velocity and acceleration of coin are 0 m/s and 1 m/s² upwards
Question 5
4 / -1

The extension in a uniform rod of length l, mass m, cross section radius r and young’s modulus Y when it is suspended at one of its end is :

A

B

C

D

Solution
Question 6
4 / -1

A spherical soap bubble of radius 1.0 cm is formed inside another of radius 2 cm. If a single soap bubble is formed which maintains the same pressure difference as inside the smaller and outside the larger bubble, the radius of this bubble is -

A
0.005 m

B
0.05 m

C
0.0067 m

D
0.067 m

Solution
Question 7
4 / -1

Block ‘ A ‘ is hanging from a vertical spring and is at rest. Block ‘ B ‘ strikes the block ‘A’ with velocity ‘ v ‘ and sticks to it. Then the value of ‘ v ‘ for which the spring just attains natural length is :

A

B

C

D
None of these

Solution

The initial extension in spring is x₀ = mg/k

Just after collision of B with A the speed of combined mass is v/2 .

For the spring to just attain natural length the combined mass must rise up by x₀ = mg/k(sec fig.) and comes to rest.
Question 8
4 / -1

A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities ρ and σ (ρ > σ) fill half of the tube as shown. θ is the angle which the radius passing through the interface makes with the vertical.

A

B

C

D

Solution

Pressure at 'A' from both side must balance. Figure is self–explanatory.
Question 9
4 / -1

A ball tied to the end of a string swings in a vertical circle under the influence of gravity

A
when the string makes an angle 90º with the vertical, the tangential acceleration is zero amd radial acceleration is somewhere between maximum and minimum

B
when the string makes an angle 90º with the vertical, the tangential acceleration is maximum and radial acceleration is somewhere between maximum and minimum

C
at no place in the circular motion, tangential acceleration is equal to radial acceleration

D
throughout the path whenever radial acceleration has its extreme value, the tangential acceleration is zero.

Solution

As shown in the figure , at A

Here, at is maximum because at other place, a_t = gcos θ . a_t and a_c will be equal at some point. a_c will have extreme
value at lowest points and there at = 0.
Question 10
4 / -1

A particle moves along the X-axis as x = u(t – 2) + a(t – 2)²

A
the initial velocity of the particle is u

B
the acceleration of the particle is a

C
the acceleration of the particle is 2a

D
at t =2s particle is at the origin

Solution