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JEE Main Mock Test - 13 - JEE MCQ


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30 Questions MCQ Test Mock Tests for JEE Main and Advanced 2025 - JEE Main Mock Test - 13

JEE Main Mock Test - 13 for JEE 2025 is part of Mock Tests for JEE Main and Advanced 2025 preparation. The JEE Main Mock Test - 13 questions and answers have been prepared according to the JEE exam syllabus.The JEE Main Mock Test - 13 MCQs are made for JEE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Main Mock Test - 13 below.
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JEE Main Mock Test - 13 - Question 1
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If the binding energy of an electron in a hydrogen atom is 13.6 eV, then the energy required to remove the electron from the first excited state of Li++ is

Detailed Solution for JEE Main Mock Test - 13 - Question 1

Binding energy of the electron,

Hence, for n = 2:

Binding energy, E2 =

E2 = -30.6 eV

Energy required to remove the electron from the first excited state of Li++ = 30.6 eV

JEE Main Mock Test - 13 - Question 2
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A particle is dropped from height 3R from surface of earth then velocity of particle at height R is (given R is radius of earth, g is acceleration due to gravity) :

Detailed Solution for JEE Main Mock Test - 13 - Question 2

Principle of conservation of energy is to be applied. Since acceleration is variable

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JEE Main Mock Test - 13 - Question 3
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A satellite of mass m, is orbiting around the earth at a distance r from centre of earth, if it is stopped suddenly the loss in total energy will be

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JEE Main Mock Test - 13 - Question 4
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A uniform cylinder of density σ and length L floats vertically completely immersed in two liquids with length L1 immersed in a liquid of density ρ1 and the remaining length L2 immersed in the other liquid of density ρ2 as shown in Fig. The ratio L1/L2 will be (ρ1 > ρ2) equal to
Detailed Solution for JEE Main Mock Test - 13 - Question 4

Mass of the body is m = σAL, where A is the cross-sectional area of the cylinder. Weight of cylinder is W = mg = σALg.
Weight of volume of liquid of density ρ1 displaced by the length L1 is
W1 = ρ1AL1g
Weight of volume of liquid of density ρ2 displaced by length L2 is
W2 = ρ2AL2g
According to the law of floatation, the weight of the cylinder must be equal to the total weight of the liquids displaced, i.e.
W = W1 + W2

Similarly, using L1 = L − L2 in Eq. (i), we get

JEE Main Mock Test - 13 - Question 5
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The K.E. and P.E. of a particle executing SHM with amplitude A will be equal when its displacement is:
Detailed Solution for JEE Main Mock Test - 13 - Question 5

JEE Main Mock Test - 13 - Question 6
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An electric dipole of moment  is placed at the origin along the X-axis. The electric field at a point P, whose position vector makess an angle θ with the X-axis, will make an angle φ with the X-axis, then φ is (α = tan−1(1/2 tanθ))
Detailed Solution for JEE Main Mock Test - 13 - Question 6

An electric dipole of moment =
electric field x-axis at a point = p
angle = θ with x − axis
tana = 1/2 tanθ
(θ + α) = the value of the position vector makes an angle θ
θ = 60∘ + α
now resolving E into its components

JEE Main Mock Test - 13 - Question 7
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Two coils A and B, each of 10 turns and radius 20 cm, are held such that coil A lies in the vertical plane and coil B in the horizontal plane with their centres coinciding. What current should be passed through the coils so as to nullify the earth's magnetic field at their common centre? Horizontal component of earth's field = 0.314 × 10−4 T and angle of dip = 26.6°. Given tan 26.6° = 0.5
Detailed Solution for JEE Main Mock Test - 13 - Question 7

Angle of dip(θ)  where BV and BH are the vertical and horizontal components of earth's field respectively. Thus
BV = BH tan(θ) = 0.314 × 10−4 × tan 26.6°
= 0.157 × 10−4 T
If the plane of the vertical coil A is perpendicular to the magnetic meridian, the field produced by it can neutralize the horizontal component of earth's field if

Similarly, the magnetic field produced by the horizontal coil B will be vertical and will neutralize the vertical component BV of the earth's field, if

JEE Main Mock Test - 13 - Question 8
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A cube of side 2 m is placed in front of a concave mirror of focal length 1 m with its face A at a distance of 3 m and face B at a distance of 5 m form the mirror. The distance between the images of faces A and B and heights of images of A and B are, respectively,
Detailed Solution for JEE Main Mock Test - 13 - Question 8


the distance between two points is then 1.5 − 1.25 = 0.25 m
Now, using the magnification relation,

JEE Main Mock Test - 13 - Question 9
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A point source of light is placed in front of a plane mirror as shown in the figure.

Determine the length of reflected path of light on its screen Σ.
Detailed Solution for JEE Main Mock Test - 13 - Question 9

Ray diagram is as shown in the figure below:

JEE Main Mock Test - 13 - Question 10
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An electromagnetic radiation given by
E = E0[sin(2πv1t) + sin(2πv2t)]
where v1 = 1.3 × 1015 Hz and v2 = 1.1 × 1015 Hz falls on a photocell whose work function is 2.0eV. Then the photoelectric current through the cell
Detailed Solution for JEE Main Mock Test - 13 - Question 10

Using trigonometric relation

the above equation can be written as

It follows from Eq. (ii) that the amplitude of the resultant wave varies periodically at beat frequency vb = v1 − v2. Hence the resultant intensity rises and falls periodically at this frequency. Since photoelectric current is directly proportional to the intensity of incident radiation, the correct choice is (d).

JEE Main Mock Test - 13 - Question 11
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On a particular day, the maximum frequency reflected from the ionosphere is 8MHz. On another day it was found to increase to 9MHz. The ratio of the maximum electron densities of the ionosphere on the two days is
Detailed Solution for JEE Main Mock Test - 13 - Question 11

vmax = 9(Nmax)1/2, where Nmax is the maximum electron density of the ionosphere. Hence Nmax ∝ v2max. Therefore, the ratio of maximum electron densities on the two days is (8/9)2, which is choice (d).

JEE Main Mock Test - 13 - Question 12
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A parallel plate air-filled capacitor has a capacitance of 2 μF . When it is half-filled with a dielectric of dielectric constant k = 3, its capacitance becomes
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JEE Main Mock Test - 13 - Question 13
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A coil having n turns and resistance RΩ is connected with a galvanometer of resistance 4RΩ. This combination is moved in time t seconds from a magnetic field W1 weber to W2 weber. The induced current in the circuit is
Detailed Solution for JEE Main Mock Test - 13 - Question 13
Induced current,

where ф = W = Flux x Per unit turn of the coil

Total resistance of the coil and the meter = R + 4R

Therefore,

JEE Main Mock Test - 13 - Question 14
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Which of the following relations is/are correct?
Detailed Solution for JEE Main Mock Test - 13 - Question 14
Rolling friction is always less than the sliding friction because in sliding friction layer rubs each other due to which a lot of kinetic energy is converted heat energy.
JEE Main Mock Test - 13 - Question 15
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The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K, is
Detailed Solution for JEE Main Mock Test - 13 - Question 15

Velocity of sound in gas,

or, (∵ Density Volume = M)

JEE Main Mock Test - 13 - Question 16
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A cannon on a level plain is aimed at an angle α above the horizontal and a shell is fired with a muzzle velocity v0 towards a vertical cliff, a distance R away. The height from the bottom at which the shell strikes the side walls of the cliff is
Detailed Solution for JEE Main Mock Test - 13 - Question 16
The time taken to move a horizontal distance R is t = . Therefore, the vertical distance moved in this time is given by

Hence, the correct answer is (c).

JEE Main Mock Test - 13 - Question 17
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Directions: This question has Statement-I and Statement-II. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-I: Higher the range, greater is the resistance of ammeter.

Statement-II: To increase the range of ammeter, additional shunt needs to be used across it.
Detailed Solution for JEE Main Mock Test - 13 - Question 17
For an ammeter, higher the range, lesser will be the value of the resistance of meter.

To increase the range of the ammeter, we have to add a resistance in parallel to the given device.

If R is the resistance of the given device, IA is the maximum current which can be passed through it and Rs is the value of the shunt resistance.

Effective value of the resistance of the new meter,

JEE Main Mock Test - 13 - Question 18
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The two physical quantities among the following which don't have the same dimensions are
Detailed Solution for JEE Main Mock Test - 13 - Question 18

E = hν, where h is Planck's constant.

h = E/ν

[h] = [M1L2T-2]/[T-1] = [M1L2T-1]

Momentum = m × v

[p] = [M1L1T-1]

Hence, Plank's constant and momentum have different dimensional formula.

JEE Main Mock Test - 13 - Question 19
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When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx2, where a and b are constants. The work done in stretching the unstretched rubber band by L is
Detailed Solution for JEE Main Mock Test - 13 - Question 19

JEE Main Mock Test - 13 - Question 20
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Find the angular speed of the meter stick, when a person throws it such that the centre of the stick is moving with a speed of 10 m s-1 vertically upwards & left end of stick with a speed of 20 m s-1 vertically upwards.
Detailed Solution for JEE Main Mock Test - 13 - Question 20

Given velocity of centre C of the rod, vC = 10 m s−1

and velocity of end A of the rod vA = 20 m s−1

Let ω be the angular velocity of the rod.

Since vA > vC, thus the stick will rotate in clockwise direction.

Now using the relation, vA − vC = ωr, we get,

⇒ 20 − 10 = ω(l/2)

⇒10 = ω/2 rad s−1

⇒ ω = 20 rad s-1

Hence, the angular speed of the stick is 20 rad s−1.

*Answer can only contain numeric values
JEE Main Mock Test - 13 - Question 21
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The adjacent graph shows the extension (Δl) of a wire of lengthlm suspended from the top of a roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is 10-6 m2, then the Young's modulus of the material of the wire comes out to be 2 × 10Q N/m2. State the value of Q.

Detailed Solution for JEE Main Mock Test - 13 - Question 21

i.e. graph is a straight line passing through origin, the slope of which is l/YA

*Answer can only contain numeric values
JEE Main Mock Test - 13 - Question 22
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In an LCR series ac circuit, the voltage across each of the components L, C and R is 50 V. The voltage across the LC combination (in Volt) will be

Detailed Solution for JEE Main Mock Test - 13 - Question 22
As the voltage across each component is the same, so the given LCR circuit is in resonance and for an LCR series circuit, the voltage across components L and C are in opposite phase. The voltage across LC combination will be zero.
*Answer can only contain numeric values
JEE Main Mock Test - 13 - Question 23
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In an experiment with sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. If tension of the string remains constant, the frequency (in Hz) of the second tuning fork is:

Detailed Solution for JEE Main Mock Test - 13 - Question 23

For the sonometer wire

Frequency,

Μ is the mass per length

JEE Main Mock Test - 13 - Question 24
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If the equilibrium constant for the reaction, 2SO2 + O2 ⇌ 2SO3 is 64 at 500 K, then the equilibrium constant for the reaction  at the same temperature is
Detailed Solution for JEE Main Mock Test - 13 - Question 24


where, n = factor to the new equilibrium constant, which is nth root of the previous value and

∴ Option (b) is the correct answer.

JEE Main Mock Test - 13 - Question 25
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The tendency of BF3, BCl3 and BBr3 to behave as Lewis acid decreases in the sequence
Detailed Solution for JEE Main Mock Test - 13 - Question 25

A molecule is said to be a lewis acid if it can accept a lone pair.
When the halide is more electronegative the interelectronic repulsion increases making the molecule difficult to accept a lone pair. Size of halide also behaves in the same way. Also the degree of hydrolysis increases from fluorine to iodine,so the lewis acidic character increases in the same order,
So,the order of lewis acidity is BBr3 > BCl3 > BF3

JEE Main Mock Test - 13 - Question 26
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Standard electrode potential data are useful for understanding the suitability of an oxidant in a redox titration. Some half cell reactions and their standard potentials are given below
MnO−4(aq) + 8H+(aq) + 5e− → Mn+2(aq) + 4H2O(l) ; E∘ = 1.51 V
Cr2O72−(aq) + 14H+(aq) + 6e− → 2Cr+3(aq) + 7H2O(l) ; E∘ = 1.38 V
Fe+3(aq) + e− → Fe+2 ; E0 = 0.77 V
Cl2(g) + 2e− → 2Cl−(aq) ; E0 = 1.40 V
Identify the only incorrect statement regarding the quantitative estimation of aqueous Fe(NO3)2  
Detailed Solution for JEE Main Mock Test - 13 - Question 26

The reaction between MnO−4 and HCl may be represented as follows:
2MnO−4(aq) + 16H+ + 10Cl− →
2Mn2+(aq) + 8H2O(l) + 5Cl2(g)
Thus, on the basis of this reaction following electrochemical cell will be represented
Pt,Cl(g) (1atm) | Cl−(aq) ∥ MnO−4(g) | Mn2+(aq)
Hence, E0cell = E0cathode − E0anode 
From given data E0cell = 1.51−1.40 = 0.11 V
E∘ cell is positive, hence ΔG∘ is negative. Thus, above cell reaction is feasible but MnO−4ion can oxidise, Fe2+ to Fe3+ and Cl− to Cl2 in aqueous medium also. Therefore, for quantitative estimation of aqueous Fe(NO3)2 it is not a suitable reagent.

JEE Main Mock Test - 13 - Question 27
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Which of the following orders is true regarding the basic nature of NH2 group?
Detailed Solution for JEE Main Mock Test - 13 - Question 27

Electron-releasing group increases the availability of lone pair of electrons on nitrogen while electron attracting group decreases this availability.

The correct order of basic strength of aromatic amines is o − Toluidine < Aniline >0− Nitroaniline.

Aniline is more basic than ortho nitro aniline because the presence of electron withdrawing nitro group decreases the ease with which N can donate a lonepair of electrons.

o-Toluidine is less basic than aniline because whenever a substituent is present in the ortho position, it decreases its basicity.

JEE Main Mock Test - 13 - Question 28
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Which of the following diseases is not caused by bacteria?
Detailed Solution for JEE Main Mock Test - 13 - Question 28

Malaria is caused by protozoa.

JEE Main Mock Test - 13 - Question 29
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 and |z1| ≠ 3 then |z2| is
Detailed Solution for JEE Main Mock Test - 13 - Question 29



JEE Main Mock Test - 13 - Question 30
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If PQ is a double ordinate of hyperbola  such that OPQ is an equilateral triangle, O being the centre of the hyperbola, then the eccentricity e of the hyperbola satisfies
Detailed Solution for JEE Main Mock Test - 13 - Question 30

Let P(a secθ, b tanθ), Q(a secθ, − b tanθ) be end points of double ordinates and (0,0) is the centre of the hyperbola.

So, PQ = 2b tanθ


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