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This mock test of Sample JEE Main Full Mock Test for JEE helps you for every JEE entrance exam.
This contains 90 Multiple Choice Questions for JEE Sample JEE Main Full Mock Test (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The transition from the state n = 3 to n=1 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from.

Solution:

Infrared radiation is found in Paschen, Brackett and pfund series nd it is obtained when electron transition occurs from high energy level to minimum third level.

QUESTION: 2

Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is

Solution:

Volume of 8 small drops = Volume of big dropAs capacity is r, hence capacity becomes 2 times.

QUESTION: 3

If the body is moving in a circle of radius r with a constant speed υ, its angular velocity is

Solution:
In circular motion, angular velocity (w)= v( linear velocity) / radius if circle (r)

QUESTION: 4

To convert a 800 mV range milli voltmeter of resistance 40 Ω into a galvanometer of 100 mA range, the resistance to be connected as shunt is

Solution:

QUESTION: 5

A point charge *q* is placed at the centre of a skeleton cube made of thin non-conducting wire. The electric flux passing through one face of the cube is

Solution:
Because total flux coming out from a closed body is q/Ä›. So flux through 1 face is 1/6th of it.

QUESTION: 6

The magnetic moment of a circular coil carrying current is

Solution:

QUESTION: 7

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

__Assertion(A)__: a + i b c + i d = p where p > 0 , then a^{2} + b^{2} c^{2} + d^{2} = p^{2} c

__Reason(R)__ : cos θ + i sin θ n = cos n θ + i sin n θ

Solution:

The expressions in Assertion(A) and Reason(R) are not clear. The operation between the terms is not given.

QUESTION: 8

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24^{th} division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

Solution:

QUESTION: 9

The natural frequency of a L-C circuit is equal to

Solution:
At resonance, X(L)=X(C)

It means that the inductive & capacitive reactances are equal.

Value of inductive reactance is given byâ€“

X(L)=2Ï€fL

And that of capacitive reactance is given byâ€“

X(C)=1/(2Ï€fC)

Therefore, at resonanceâ€“

2Ï€fL=1/(2Ï€fC)

fÂ²=1/[(2Ï€C)Ã—(2Ï€L)]

fÂ²=1/(4Ï€Â²LC)

f=1/[2Ï€âˆš(LC)] => Resonant Frequency f(R) or f(0)

It means that the inductive & capacitive reactances are equal.

Value of inductive reactance is given byâ€“

X(L)=2Ï€fL

And that of capacitive reactance is given byâ€“

X(C)=1/(2Ï€fC)

Therefore, at resonanceâ€“

2Ï€fL=1/(2Ï€fC)

fÂ²=1/[(2Ï€C)Ã—(2Ï€L)]

fÂ²=1/(4Ï€Â²LC)

f=1/[2Ï€âˆš(LC)] => Resonant Frequency f(R) or f(0)

QUESTION: 10

A coil of inductance 40 henry is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is

Solution:

Time constant in in RL circuit is t = L/R

L = 40 henry

R = 8 ohm

t = L/R = 40/8 = 5 second

It is the time in which the current in RL circuit grows to 63.2 % of its peak value.

QUESTION: 11

Proton and α-particles have the same de-Broglie wavelength. What is the same for both of them ?

Solution:
De brogile wavelength has formula lambda =h/MV. h is Planck's constant. If they have same de brogile wavelength then they have same m.v as h is constant.

QUESTION: 12

After an interval of one day, 1/16th of the initial amount of a radioactive material remains in a sample. It's half life will be

Solution:
If 1/16 of the initial material is left after a day or 24 hours means it has gone through 4 half lives. So the answer will be 24/4 = 6 hours.

QUESTION: 13

The angular velocity of the second needle in watch (in rad/s) is

Solution:

The seconds hand of a clock completes one rotation in 1 minute i.e 60 seconds.

Angular speed=angle swept by the radius vector/time taken

Angle swept for one complete rotation is 2Ï€ radians

Therefore, 2Ï€/60=Ï€/302Ï€/60=Ï€/30

QUESTION: 14

The energy released in a typical nuclear fusion reaction is approximately

Solution:

QUESTION: 15

Two infinite plane parallel sheets, separated by a distance d have equal and opposite uniform charge densities σ. Electric field at a point between the sheets is

Solution:

QUESTION: 16

A straight wire of length l and electric dipole moment p is bent to form a semicircle. The new dipole moment would be

Solution:

QUESTION: 17

A block of mass 10 kg is placed on rough horizontal surface whose coefficient of friction is 0.5. If a horizontal force of 100 N is applied on it, then acceleration of block will be

Solution:

Friction = (0.5)mg = 50 N

Net force in horizontal dirn = 100 N - 50 N = 50N

acceleration= 50/10 = 5 m/s^{2}

QUESTION: 18

A bird weighs 2 kg and is inside a closed cage of 1 kg. If it starts flying, then what is the weight of the bird and cage assembly

Solution:

When the bird flies, it pushes air down to balance its weight. So the weight of the bird and closed cage assembly remains unchanged.

QUESTION: 19

A particle of mass *M* and charge *Q* moving with velocity V → describes a circular path of radius *R* when subjected to a uniform transverse magnetic field of induction *B*. The work done by the field when the particle completes one full circle is

Solution:

When particle describes circular path in a magnetic field, its velocity is always perpendicular to the magnetic force?

Hence, work done W = 0 (everywhere)

QUESTION: 20

NAND gate is

Solution:

QUESTION: 21

Which of the following is more effective in inducing nuclear fission

Solution:

QUESTION: 22

The kinetic energy k of a particle moving along a circle of radius R depends on the distance covered s as K = as^{2} where a is a constant. The force acting on the particle is

Solution:

Given K.E = 1/2 mv^{2} = as^{2}

= mv^{2} = 2as^{2}

now differenciating with respect to t

2mv = dv/dt = 4as ds/dt = 4asv

mat = 2 as

Hence Ft = 2 as here (Ft = tangential force) .... 1>

centripetal force = Fc = mac = mv^2/R = 2 mas^2/ mR = 2as^2/R .... 2>

now net force of particle is = √Ft^2 + F^2 c = √(2as)^2 + (2as^2/R)^2

= 2 as(√1 + s^2/R^2or 2as(1 + s^2/R^2) raise to power 1/2

QUESTION: 23

If a liquid does not wet the glass, then its angle of contact is

Solution:

If a liquid does not wet the sides of containing vessel, then the value of angle of contact is obtuse i.e. greater than 90degree .e.g. mercury.

QUESTION: 24

A 1 kg stationary bomb exploded in three parts having mass ratio 1:1:3 . Parts having same mass are moving in perpendicular direction with velocity 30m/s, then the velocity of bigger part will be

Solution:

Conservation of momentum

1×0=1 ×30i +1×30j +3v

3v= -(30i +30j)

v = -(10i +10j)

v ( magnitude)= √(10)²+(10)²

=10√2 m/s

QUESTION: 25

Of two masses of 5 kg each falling from height of 10m, by which 2 kg water is stirred. The rise in temperature of water will be

Solution:

W = J Q

2m * g* h = J * m' * Cp * Delta T

2 *5*10*10 = 4.2 *(2* 1000* delta T)

Delta T = 0.12°c

QUESTION: 26

A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of slit is

Solution:

The phase difference between the wavelets from the top and bottom edge of the slit=2π/λd sinθ

where d=width of slit

The first minimum of diffraction patterns occurs at,

QUESTION: 27

Dimension of CR are same as

Solution:

QUESTION: 28

Both light and sound waves produce diffraction. It is more difficult to observe the diffraction with light waves because

Solution:
WAVELENGTH AND DIFFRACTION. The reason for the differenceâ€”that is, why sound diffraction is more pronounced than light diffractionâ€”is that sound waves are much, much larger than light waves. Sound travels by longitudinal waves, or waves in which the movement of vibration is in the same direction as the wave itself.

QUESTION: 29

The velocities of sound at the same temperature in two monoatomic gases of densities ρ₁ and ρ₂ are ν₁ and ν₂ respectively. If ρ₁/ρ₂= 4, then the value of ν₁/ν₂ is

Solution:

QUESTION: 30

In Huygens wave theory, the locus of all points osculating in the same phase is called a

Solution:

Huygen, a Dutch mathematician, in 1678, gave a theory regarding nature of light. The theory is popularly known as Huygen’s wave theory. According to this theory, light is a sort of disturbance. The particles of the medium, vibrate in a direction, at right angle to the direction of propagation of disturbance. The process is called wave motion.

**Straight wave front**

Huygens's principle applied to a straight wave front. Each point on the wave front emits a semicircular wavelet that moves a distance s=vt. The new wavefront is a line tangent to the wavelets.

QUESTION: 31

The alcohol which does not give a stable compound on dehydration is

Solution:

If you take out H_{2}O from the Methyl Alcohol you will be left with CH^{2+} cation which is not stable.

QUESTION: 32

Vanaspati ghee is prepared by which of the following reactions of vegetable oils?

Solution:
Vanaspati ghee is made by hydrogenation of vegetable oils that is why it is considered harmful while vegetable oils are safe.

QUESTION: 33

Cinnamic acid is formed when C₆H₅CHO condenses with (CH₃CO)₂ in presence of

Solution:

QUESTION: 34

According to Le-Chatelier's principle, adding heat to a solid and liquid in equilibrium will cause the

Solution:

When we add heat to the equilibrium between solid and liquid, then the equilibrium shifts towards liquid and hence, the amount of solid decrease and amount of liquid increase.

QUESTION: 35

A catalyst increases rate of reaction by

Solution:
A catalyst increases the rate of reaction by decreasing the energy of activation (Ea). a catalyst provides a new reaction path for the reaction. Because a catalyst forms an unstable intermediate with the reactants and it decomposes to give products and the catalyst is regenerated.

QUESTION: 36

C + O_{2} → C O_{2} , Δ H = − 94 K . c a l s , → C O_{2} , Δ H = − 67.7 K . cal .

On the basis of above data, the heat of formation of *CO* is

Solution:
Add equations 1 and (-2) and you'll see there's the formation of CO. So âˆ†H of formation of CO=(-94)-(-67.7)= -26.3 Kcal.

QUESTION: 37

Electron affinity depends on

Solution:

As the size of the atom increases, the electron affinity decreases, whereas when the nuclear charge increases the electron affinity increases.

QUESTION: 38

In the diazotisation of aniline with sodium nitrite and hydrochloric acid, the excess of hydrochloric acid is used primarily to

Solution:

An excess of HCl will suppress the hydrolysis of diazonium salt to phenol.

QUESTION: 39

The type of isomerism present in nitropentaamminechromium (III) chloride is

Solution:
Nitropentamine chromium (III) chloride exhibits linkage isomerism as -NO2 is an ambidendate ligand.

QUESTION: 40

On passing 0.1 faraday of electricity through fused sodium chloride, the amount of chloride liberated is (At. mass of Cl = 35.45)

Solution:
On passing 0.1F of electricity in NaCl, the amt of chloride liberated = 35.45*0.1 = 3.545

QUESTION: 41

In which of the following acid-base titration, pH is greater at eqivalence point?

Solution:

QUESTION: 42

Why are strong acids generally used as standard solutions in acid-base titrations ?

Solution:

QUESTION: 43

The electrolysis of aqueous *NaCl* produces at cathode and anode respectively

Solution:
Electrolysis of aqueous sodium chloride: Electrolysis of aqueous NaCl results in hydrogen and chloride gas. **At the anode (A), **chloride (Cl-) is oxidized to chlorine. The ion-selective membrane (B) allows the counterion Na+ to freely flow across, but prevents anions such as hydroxide (OH-) and chloride from diffusing across. **At the cathode (C), **water is reduced to hydroxide and hydrogen gas. The net process is the electrolysis of an aqueous solution of NaCl into industrially useful products sodium hydroxide (NaOH) and chlorine gas.

QUESTION: 44

If H⁺ ion conc. of a solution is increased by 10 times, its pH will

Solution:
Concept: pH = -log (H+)

If its concentration is increased 10 times its

pH = - log (10) = -1.

so it decreases by 1.

So, correct answer is C

If its concentration is increased 10 times its

pH = - log (10) = -1.

so it decreases by 1.

So, correct answer is C

QUESTION: 45

When NaCl is added to the reaction mixture of an oil and caustic soda , the soap is thrown out because

Solution:

Formation of soap involves reaction with ester and NaOH when NaCl has added it results in the increase in repulsion between the ions namely NA^{+} which shifts the reaction in the formation of soap.

QUESTION: 46

The compound which can form intramolecular hydrogen bond is

Solution:

QUESTION: 47

Increasing order of pk_{a} values (pK_{a} = - log k_{a }) of H_{2}O , C H_{3}OH and C_{6}H_{5}OH is :

Solution:

Option d is correct. Methanol is more acidic than water. So its pk_{a} value will be less than water. However C_{5}H_{5}OH wll be most acidic among all three.SO he order of pk_{a} is C_{6}H_{5}OH < CH_{3}OH < H_{2}O

QUESTION: 48

Which one is a polymer compound?

Solution:

Pvc is polymer compound and many other compound that made plastic are called polymer compound while pvc is present in plastic bottle.

QUESTION: 49

Ionic solids with Schottky defects contain in their structure

Solution:

QUESTION: 50

Diamond is a

Solution:

QUESTION: 51

If 107 g of an aqueous solution contains 39.5 g of a solute (mol. weight = 158), then mole fraction of the solute is

Solution:
First find no. of moles of solute that is 0.25(39.5/158)then moles of solvent that is 107-39.5/18 = 3.75 mole reaction of solute = no of moles of solute/total moles 0.25/4 into 100 = 6.25

QUESTION: 52

Which of the following compound corresponds Vant's Hoff factor (i) to be equal to 2 in a dilute solution?

Solution:

This is because, it will dissociate into Mg^{2+} and SO4^{2-}, i.e. two ions.

QUESTION: 53

One mole of 1, 2-Dibromopropane on treatment with X moles of NaNH₂ followed by treatment with ethyl bromide gave a pentyne. The value of X is

Solution:

QUESTION: 54

Ethyl bromide on treatment with alcoholic KOH gives

Solution:

QUESTION: 55

If the energy of an electron in the second energy level of hydrogen atom is -E, its value in the third energy level will be __

Solution:

According to question :

− E = -13.6 x Z^{2} /n^{2}

o r − 13.6 = − E x 4 (i)

Energy for third energy level:

E_{3} = − 13.6 x Z^{2} 3^{2 }

E_{3 } x 9 = − 13.6 i i

By (i) and (ii)

− E x 4 = E _{3 } x 9

or E_{3} = − 4E /9

QUESTION: 56

Suppose 10^{-17} J of energy is needed by the interior of human eye of to see an object. How many photons of green light (λ = 500 nm) are needed to generate this minimum amount of energy?

Solution:

Let the number of photons required be n

QUESTION: 57

Which of the following is correct relation of first law of thermodynamics ?

Solution:

QUESTION: 58

An activated complex molecule differs from a normal molecule of the same atomicity in that it has__

Solution:

QUESTION: 59

Which of the following ions has zero crystal field stabilization energy in octahedral field?

Solution:

QUESTION: 60

An organic compound with C = 40% and H = 6.7% will have the empirical formula

Solution:

C is 40% and H is 6.7% so O is 53.3%

now calculate % / at. weight

c= 40/12

H=6.7/1

O=53.3/16

now get the simplest ratio as CH_{2}O

QUESTION: 61

For which one of the following values of k, the equation

2x^{3} + 3x^{2} − 12x − k = 0 has three distinct real roots?

Solution:

QUESTION: 62

If x^{h} y^{k} is an integrating factor of the differential equation

y(1 + xy) dx + x(1 − xy) dy = 0,

then the ordered pair (h, k) is equal to

Solution:

QUESTION: 63

Let *A* be the square of natural numbers and *x, y* are any two elements of *A*. Then

Solution:

Because as x is a squared quantity and y is also a squared quantity so xy will also be perfect square of a number but in case of x+y and x-y it may be perfect square or not.

QUESTION: 64

If *'n'* is a positive integer, then *n*^{3} + 2*n* is divisible by

Solution:

QUESTION: 65

The area enclosed between the parabola y^{2} = 4ax and the lines *x = a, x = 9a* is

Solution:

QUESTION: 66

Area of the curve x^{2}+y^{2}=2ax is

Solution:

It is a circle whose equation is (x-a)^{2}+y^{2}=a^{2}

with radius a. So area of such a circle is πa^{2}

QUESTION: 67

The equation of the circle passing through (0,0),(0,a),(a,0) is

Solution:

The general equation of circle is x^2+y^2+2gx+2fy+c=0 where center is (-g,-f)

Given the point (0,0 ) Equation of the circle through that point is c=0

Given the point (a,0).Equation of the circle through that point is a^2+2ga+c=0

â‡’a^2+2ag=0

a(a+2g)=0â†’g=âˆ’a2â‡’g=âˆ’a/2

Given the point (0,a) Equation of the circle through that point is a^2+2fa+c=0

â‡’a^2+2fa=0â†’a(a+2f)=0â†’a=-2f

f=-a/2

the equation will be

x^2+y^2+2(-a/2)x+2(-a/2)y+0=0

x^2+y^2-ax-ay=0

x^2+y^2-a(x+y)=0

QUESTION: 68

If the imaginary part of [(2z+1)/(iz+1)] is -2, then the locus of z in complex plane represent.

Solution:

QUESTION: 69

[(1 + sinθ + icosθ)/(1 +sinθ - icosθ)]^{n} =

Solution:

QUESTION: 70

(d/dx){log(secx+tanx)}=

Solution:

d/dx {log Sec x + tan x}

= 1 Sec x + tan x Sec x . tan x + sec 2x

= Sec x Sec x + tan x Sec x + tan x

= Sec x

QUESTION: 71

Solution of the differential equation tan y sec^{2} x dx + tan x sec^{2} y dy = 0 is

Solution:

QUESTION: 72

If f (x) = , then f of f(x) =

Solution:

QUESTION: 73

When y = 3, which of the following is FALSE?

Solution:

QUESTION: 74

If A is a non-zero column matrix of order m x1 and B is a non-zero row matrix of order 1 x n, then rank of AB is equal to

Solution:

Let

be two non-zero column and row matrices respectively

Since A, B are non-zero matrices. .% matrix AB will be a non-zero matrix. The matrix AB will have at least one non-zero element obtained by multiplying corresponding non-zero elements of A and B. All the two rowed minors of AB clearly vanish. Since AB is non-zero matrix,

∴ rank of AB = 1

QUESTION: 75

The line y=mx+c touches the parabola x^{2}=4ay if

Solution:

Concept: Straight line. x^{2}=4ay.............(1)

y=mx+c....,........(2)

From (1) and (2) we get x^{2} = 4a(mx+c)

=> x^{2}−4amx−4ac=0

=16a^{2}m^{2}+16ac(b^{2} -4ac). =16a(am^{2} + c ).

Line 2 will touch the parabola. if D=0. i.e if C=−am^{2}

Hence, correct answer is (C).

QUESTION: 76

Number of ways in which 6 persons can be seated around a table so that two particular persons are never seated together is equal to

Solution:

5! - 2×4! =72

QUESTION: 77

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

Solution:

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

Then, E = ((1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

QUESTION: 78

The most stable measure of central tendency is

Solution:

Mean is considered as most stable central tendency because it uses all the observation in any given distribution.

QUESTION: 79

The equation of a line passing through (-4,3) and this point divides the portion of line between axes in the ratio 5:3 internally, is

Solution:

Let the line through the point P(-A, 3) meets axis at A(h, 0) and 0(0, k)

Now according to the question AP : BP =5:3

QUESTION: 80

The length of the sub normal to the parabola y^{2}=4ax at any point is equal to

Solution:
The length of the subnormal is always constant and is equal to the semi-latus rectum i.e. 2a â€¦Hence D is the correct.

QUESTION: 81

The locus of x^{2}+y^{2}+z^{2}=0 is

Solution:

QUESTION: 82

cos^{2}α+cos^{2}(α+120º)+cos^{2}(α-120º)=

Solution:

QUESTION: 83

If , then the angle between the vectors a → + b → and a → − b →

is

Solution:

QUESTION: 84

The points with position vectors are collinear. The value of p is

Solution:

QUESTION: 85

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): At *x* = 0, the curve y = 11 + x^{2} has the greatest slope.

Reason(R) : dy/dx = 0 and d^{2} + yd x^{2} < 0 at x = 0

Solution:

QUESTION: 86

If A is a singular matrix, then A adj (A)

Solution:

QUESTION: 87

Solution:

QUESTION: 88

Solution:

QUESTION: 89

If f(x)=x^{5}-5x^{4}+5x^{3}-10 how local max and min at x=p and x=q respectively, then (p,q)=

Solution:

QUESTION: 90

Let α,β be the roots of x^{2}-x+p=0 and γ,δ be the roots of x^{2-}4x+q=0. If α,β,γ,δ are in G.P., then the integer values of p and q respectivley are :

Solution:

### Mock Test - 1 - Jee Mains

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