BITSAT Practice Test - 6 - JEE MCQ

Two bars of thermal conductivities K & 3K & 3 of 1 cm & 2 cm are connected in series,

Two thermal resistance are connected in series 
We know that, 

Here, L is the length of rod, A is the area of cross-section and K is the thermal conductivity of the rod. 
Rod AP and PB are in series , current flow is same in both rods.  
Let, temperature T on point P for rod AP be,
 
For rod BP, length is double in this case,

Dividing equation (i) by equation (ii), we get, 

⇒ 2T = 300 − 3T
⇒ 5T = 300
⇒ T = 60°C
Temperature at the junction point is 60°C.

• Viscosity is the property of fluids by the virtue of which it opposes any relative motion between the layers of fluid or between any object and fluid surrounding it. It is analogous to friction for fluids.
• It depends strongly on temperature. In liquids, it usually decreases with increasing temperature.
• Also, as the temperature rises, the atoms of the liquid become more mobile and the coefficient of viscosity falls.

All the given functions are in the form of f(x ± vt).

For travelling wave, these functions should be continuous and finite for all values of t.

Only the function  has finite values and is defined for all values of t.

Newton's law of gravitation says that the force acting between two bodies is given by, 

where M and m are the mass of the different bodies, R is the distance between them and K is the proportionality constant.
From the above formula, we can see force depends on mass as well distance between them. In the case of gravitational force M and R are the mass and radius of planet. We know that earth is massive compare to the moon and its radius is also bigger than the moon.
Then, the gravitational force due to earth is 6 times more than the moon. 

Efficiency of a rectifier is given by

For full wave rectifier


∴ Rectifier efficiency

η  will be maximum, if r_f is negligible as compared to R_L.
∴ Maximum rectified efficiency = 81.2%.

The internal resistance and the load will be in series connection, the total resistance across the circuit is given by,
R = RL + r = 4000 + 400 = 4400 Ω
The emf of the transformer is V = 440 V 
Current flowing through the circuit, 

Therefore, the voltage across the load is given as,

= R_Li = 4000 × 0.1 = 400

If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
Energy of incident photon's 
As we decrease wavelength to less than it's threshold wavelength corresponding energy of photon's increases. So, due to sufficient energy possessed by photon's , photo electons emission take place,after some time emission of electrons stops , as photo emmiting surface gained sufficient positive charge so ejected electron will experience attraction from surface electrons which becomes positively charged.

Using mirror formula,


Amplitude of image = 4 x 2 = 8 mm.

When particles vibrate in loops, they perform SHM. So particles have maximum speed when they cross mean position and their speed is zero at the extreme position. Also, all the particles in a loop have a phase difference of 0. So when all particles cross their mean position, kinetic energy is maximum and shape of the string is straight.

When the bird is at rest inside the cage, the spring balance records its weight, which is equal to the gravitational force acting on it, i.e., 25 N.

When the bird flies upward in the cage with an acceleration of 2 m/s^2, the net force acting on the bird is given by:

F = m*a

where F is the net force, m is the mass of the bird, and a is the acceleration.

F = 0.5 kg * 2 m/s^2 = 1 N

This means that the bird is exerting an additional force of 1 N upwards while flying.

Therefore, the spring balance will now record a weight of:

W = 25 N + 1 N = 26 N

So the spring balance will now record a weight of 26 N.

According to Gauss' law, the net  total electric flux through  a closed surface is proportional to the charge enclosed by the closed surface.
Mathematically, 

Net flux passing through closed surface =ϕ = 1.05 N m² C⁻¹

Total enclosed charge = q_enclosed = ?

Permittivity = ε₀ = 8.854 × 10⁻¹² 

Substituting the values and simplifying we get

q_enclosed = ϕε₀  = 1.05 × 8.854 × 10⁻¹² 
= 9.27 × 10⁻¹² C

For a quantity to be unit less, its dimensions = 1 = M⁰L⁰T⁰.

Hence, it has to be dimensionless.

Some examples are refractive index and relative density, these are unit less and dimensionless.

Quantities like angles are dimensionless, but they have a unit.

Hence, the correct answer is never has a non-zero dimension.

Two blocks of masses M and m are connected by a string passing over a pulley. Let T is the tension in the string and a is the downward acceleration. Applying II law of motion for the block of mass M.
T = Ma ...(i)
For block of mass m
ma = mg - T ...(ii)

From Equations, (i) and (ii), we get
ma = mg - Ma

Necessary centripetal force is provided by the gravitational force,


Time period of revolution is

or 

Yes, the critical velocity of a liquid flowing through a tube is inversely proportional to the radius of the tube: 

Yes, the velocity of a liquid flowing through a tube is inversely proportional to the cross-sectional area of the tube. This means that as the cross-sectional area increases, the velocity decreases. For example, if the cross-sectional area of a pipe is halved, the velocity of the liquid will double. 

Figure shows the longitudinal displacement y as a function of x for x lying between x = 0 and x = L, where L is the length of the pipe.

The fundamental frequency of a closed pipe is given by

In a closed pipe, only odd harmonics are present, i.e. the frequency v₁ of the first overtone is 3 times the fundamental frequency, that of the second overtone v₂ is 5 times the fundamental freuency and so on.
v₂ = 5v = 
⇒ L =  = 1.0 m

Let T be temperature of source, T₁ be initial temperature of sink in the first case and T₂ be temperature of sink in second case.
For the first case,

T₁ = 
For the second case,


T₁ - T₂ = 50

= 50
T = 25 × 15 = 375 K

By definition,

The velocity when the potential difference is V, is

and force F = evB
When the potential difference is doubled, i.e. V' = 2V, the velocity is

 Force F' = ev'B = √2 evB = √2F

i = 
Since, k = 
r^' = 2r, n' = 2n
Then k' =  = k
Then, the value of reduction factor remains the same.

The focal length of a convex lens of refractive index μ_g in air is
 ...(i)
Where R₁ and R₂ are the radius of curvatures of its first and second surface.
When lens immersed in a liquid of refractive index μ_l then refractive index of material of lens (glass) with respect to liquid is
 _{... (ii)}
∴ Focal length of lens in liquid is
 ...(iii)
Dividing (i) by (iii), we get

Putting f' = -0.5 m
f_air = 0.2 m
 = 1.5
 = ?
= 
⇒ 
⇒ 


∴ Refractive index of liquid = 15/8

The curve shows rise at A = 100 and fall at A = 200. Comparing with the actual curve, lighter nuclei in the range 51 < A < 100 will release energy on fusion and heavier nuclei in the range 200 < A < 260 will release energy on fission.