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This mock test of JEE Main Mock Test 6 for JEE helps you for every JEE entrance exam.
This contains 90 Multiple Choice Questions for JEE JEE Main Mock Test 6 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

A d.c. motor having an armature of resistance 2 Ω is designed to operate at 220 V mains. At full speed, it develops a back e.m.f. of 210 V. When the motor is running at full speed, the current in the armature is

Solution:

When motor is running at full speed the electric current is given by:

QUESTION: 2

A solenoid has an inductance of 60 henrys and a resistance of 30 ohms. If it is connected to a 100 volt battery, how long will it take for the current to reach e-1/e=63.2% of its final value

Solution:

QUESTION: 3

A dipole of dipole moment p̅ is placed in uniform electric field E̅, then torque acting on it is given by

Solution:

QUESTION: 4

What fraction of a radioactive material will get disintegrated in a period of two half-lives

Solution:

QUESTION: 5

What percentage of original radioactive atoms is left after five half lives ?

Solution:

QUESTION: 6

Photons of energy 5.5eV fall on the surface of the metal emitting photoelectrons of maximum kinetic energy 4.0eV. The stopping potential required for these electrons are :

Solution:

QUESTION: 7

An electric dipole is placed along the X-axis at the origin O. A point P is at a distance of 20 cm from this origin such that OP makes an angle π/3 with the X axis. If electric field at P makes an angle θ with X-axis, the value of θ is

Solution:

QUESTION: 8

The angular speed of an engine wheel making 90 revolutions per minute is

Solution:

QUESTION: 9

A man of mass 60 kg. records his wt. on a weighing machine placed inside a lift. The ratio of wts. of man recorded when lift is ascending up with a uniform speed of 2 m/s to when it is descending down with a uniform speed of 4 m/s will be

Solution:

QUESTION: 10

A boat of mass 40 kg is at rest. If a dog of mass 4 kg moves in the boat with a velocity of 10 m/s, then velocity of a boat will be

Solution:

According to law of conservation of momentum

(m_{d} + m_{b})υ_{b} = m_{d} υ_{d}

⇒ 44 υ_{b} = 4 x 10

⇒ υ_{b} = 1 m/s

QUESTION: 11

A microammeter has a resistance of 100 Ω and full scale range of 50 μ A. It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combination

Solution:

QUESTION: 12

Spherical balls of radius *R* are falling in a viscous fluid of viscosity η with a velocity *v*. The retarding viscous force acting on the spherical ball is

Solution:

QUESTION: 13

The symbolic representation of four logic gates are given below:

The logic symbols for OR, NOT and NAND gates are respectively:

Solution:

QUESTION: 14

The size of nucleus of an atom of mass number *A* is proportional to

Solution:

QUESTION: 15

A ball is moving to and fro about the lowest point A of a smooth hemisphrical bowl. If it is able to rise up to a height of 20 cm on either side of A, its speed at A must be (Take = 10 m/s^{2.} mass of the body 5 g)

Solution:

QUESTION: 16

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): By the study of positive rays, Thomson discovered the existence of isotopes.

Reason(R): Thomson obtained two parabolas for neon gas whose atomic mass is 20.2 .

Solution:

QUESTION: 17

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): When a massive projectile collides with a lighter stationary target then maximum speed of target is twice that of projectile.

Reason(R): It is explained by the momentum and energy conservation.

Solution:

QUESTION: 18

Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the ring is (mass = and radius = r)

Solution:

QUESTION: 19

A process in which volume remains constant is called

Solution:

QUESTION: 20

Erg-m^{⁻1 }can be the unit of measure for

Solution:

QUESTION: 21

In Young's experiment of double slit, the intensity of central bright band is ---- times the individual intensities of the interfering waves

Solution:

QUESTION: 22

A train is approaching a platform with a velocity Î½. The frequency heard by an observer standing at the station is

Solution:

QUESTION: 23

To demonstrate the phenomenon of interference we require two sources which emit radiations of

Solution:

QUESTION: 24

Standing stationary waves can be obtained in an air column even if the interfering waves are

Solution:

QUESTION: 25

The H α line is the first member of the Balmer series of the hydrogen spectrum and it occurs due to the transition of the electron from the 3^{rd} orbit to the 2^{nd}orbit. If its wave length is λ , the wave length of the last member of the Balmer series will be

Solution:

QUESTION: 26

If the charge on a capacitor is increased by 2 coulomb, the energy stored in it increases by 21%. The original charge on the capacitor is

Solution:

QUESTION: 27

A particle is moving on a circular path with constant speed, then its acceleration will be

Solution:

QUESTION: 28

At what temperature will the resistance of a copper wire be three times its value at 0ºC? (Given Temperature coefficient of resistance for copper = 4x10⁻^{3}ºC⁻^{1})

Solution:
For temp. coeff (a)=4Ã—10^-3,

3R=R(1+(a)t)

2/4Ã—10^-3=t

t=500

3R=R(1+(a)t)

2/4Ã—10^-3=t

t=500

QUESTION: 29

How many electrons must be removed from each of two 5.0-kg copper spheres to make the electric force of repulsion between them equal in magnitude to the gravitational attraction between them?

Solution:

QUESTION: 30

There are three voltmeters of the same range but of resistance 10000 Ω, 8000 Ω and 4000 Ω respectively. The best voltmeter among these is the one whose resistance is

Solution:

QUESTION: 31

Final product formed on reduction of glycerol by hydriodic acid is

Solution:

QUESTION: 32

RCH = O + H₂ → RCH₂OH. For this reaction, catalyst is

Solution:

QUESTION: 33

For the equilibrium

K p = 9 a t m 2 at 37 º C . A 5 litre vessel contains 0.1 mole of *LiCl.NH _{3}*. How many moles of

Use

Solution:

QUESTION: 34

Night blindness is caused by the deficiency of

Solution:

QUESTION: 35

If initial concentration is reduced to (1/4)th in a zero order reaction, the time taken for half the reaction to complete

Solution:

QUESTION: 36

Given that heat of neutralisation of strong acid and strong base is -57.1 kJ. Calculate the heat produced when 0.25 mole of HCl is neutralised with 0.25 mole of NaOH in aqueous solution.

Solution:

The heat produced when 0.25 mole of HCl is neutralised with 0.25 mole of NaOH in aqueous solution is 57.1x1/4=14.275kJ

QUESTION: 37

The decreasing order of the ionisation potential of the following elements is

Solution:

As we move across a period from left to right, the nuclear charge increases and the atomic radius decreases though the principal quantum number of the valence shell remains the same. As a result, the valence electrons are more are more tightly held by the nucleus, hence ionisation potential keep on increasing. However, closed shell configuration (Ne), half-filled configuration (P) and completely-filled configuration (Mg) are responsible for higher values of ionisation energy.

QUESTION: 38

In the complex compound K₄[Ni(CN)₄], the oxidation no. of nickel is

Solution:

QUESTION: 39

Which of the following reagent can be used to convert benzene diazonium chloride into benzene ?

Solution:

QUESTION: 40

The element, which forms oxides in all oxidation states + 1 to + 5, is

Solution:

QUESTION: 41

The e.m.f. of a galvanic cell with electrode potentials of silver equal to + 0.80 V and that of copper equal to + 0.34 V is

Solution:

QUESTION: 42

Which of the following compound is the most soluble in water?

Solution:

QUESTION: 43

The best indicator for the detection of end point in titration of a strong base is

Solution:

QUESTION: 44

The pH indicates are

Solution:

QUESTION: 45

The pH of blood does not appreciably change by a small addition of acid or a base because blood

Solution:

QUESTION: 46

Which of the following does not give yellow ppt. with I₂/NaOH?

Solution:

QUESTION: 47

Product(s) of the following S N 1 reaction is/are :

Solution:

QUESTION: 48

An example of natural biopolymer is

Solution:

QUESTION: 49

Which of the following isomers will have the highest octane number ?

Solution:

QUESTION: 50

Which of the following metal oxides is antiferromagnetic in nature?

Solution:

QUESTION: 51

The radius of an atom of an element is 500 pm, if it crystallizes as a face-centred cubic lattice, then the edge length of the unit cell is

Solution:

QUESTION: 52

The normality of orthophosphoric acid having purity of 70% by weight and specific gravity 1.54 would be (H=1;O=16; P=31)

Solution:

QUESTION: 53

A solution contains non-volatile solute of molecular mass M₂. which of the following can be used to calculate the molecules mass of solute in terms of osmotic pressure ?

Solution:

QUESTION: 54

Catalyst used in dimerisation of acetylene to prepare chloroprene is

Solution:

QUESTION: 55

The ionisation potential of hydrogen atom is 13.6 eV. The energy required to remove an electron in the n = 2 state of the hydrogen atom is __

Solution:

QUESTION: 56

The electronic configuration of the atom with atomic number 47 is ___

Solution:

Element with atomic number 47 is silver (Ag) with configuration (actual is 1s^{2} 2^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{10} 4s^{2} 4p^{6} 4d^{10} 5s^{1}, i.e. its shows preference for completely filled orbital.

QUESTION: 57

The change in entropy ∆S is positive for certain reaction and enthalpy change ∆H is also greater than zero at temperature T.The reaction is

Solution:

QUESTION: 58

The reaction of acidified, aqueous potassium iodide with aqueous hydrogen peroxide

is thought to involve the following steps

Which one of the following conclusions cannot be drawn from this information?

Solution:

QUESTION: 59

Which of the following sequence follows the Irwing-William order?

Solution:

The correct order is according to decreasing charge to radius ratio.

QUESTION: 60

Which of the following compounds to does not show Lassaigne's test for nitrogen?

Solution:

QUESTION: 61

If (a^{2})+16(b^{2})+49(c^{2})-4ab-28bc-7ac=0, then a,b,c are in:

Solution:

QUESTION: 62

If 2^{ x} + 3 ^{y } = 17 and 2^{x + 2 } − 3^{ y + 1} = 5, then what is the value of x ?

Solution:

QUESTION: 63

*AOB* is the positive quadrant of the ellipse x ^{2 } ∕ a^{ 2 } + y 2 ∕ b^{ 2 } = 1, where *OA = a, OB = b*. The area between the arc *AB* and the chord *AB* of the ellipse is

Solution:

QUESTION: 64

The angle between the tangents drawn from (0,0) to the circle *x ^{2} + y^{2} + 4x - 6y + 4 = 0* is

Solution:

QUESTION: 65

If 2x - 3y = 0 is the equation of the common chord of the circles x^{2 }+ y^{2} + 4x = 0 and x^{2} + y^{2 }+ 2λy = 0, then the value of λ is

Solution:

QUESTION: 66

If the cube roots of unity are 1,ω,ω^{2} then the roots of the equation (x - 1)^{3} + 8 = 0,are

Solution:

QUESTION: 67

The differential equation obtained by eliminating the arbitrary constants *a* and *b* from

Solution:

QUESTION: 68

At x=3, (d/dx)[|x-1|+|x-5|]=

Solution:

QUESTION: 69

Let f(x) = x, g(x) = 1/x and h(x) = f(x)g(x). Then h(x) = 1 if

Solution:

QUESTION: 70

Which is logically equivalent to "If today is Sunday, Matt cannot play hockey."?

Solution:

Statements are logically equivalent to their contrapositives.

QUESTION: 71

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): Sum of the last 30 coefficients in the expansion of (1+x)^{59}, when expanded in ascending powers of x, is 2^{58}.

Reason(R): pth term from the end in the expansion of (x+y)^{n} is (n - p + 2)th term from the beginning.

Solution:

QUESTION: 72

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): The number of terms in the expansion of which are integers is equal to 32.

Reason(R): In the binomial expansion of (x+y)^{n} , the (r+1)th term from the beginning is called general term (T_{r+1}) i.e, T_{r+1} = ^{n}C_{r} x^{n+r}y^{r}.

Solution:
The correct option is B.

Using Binomial approximation every 4 th term and the first term is an integer

hence no. of integral values=1+(124/4)=1+31=32

this is not explained by the reason

Using Binomial approximation every 4 th term and the first term is an integer

hence no. of integral values=1+(124/4)=1+31=32

this is not explained by the reason

QUESTION: 73

If ^{n}P_{4}:^{n}P_{3}=1:2, then n=

Solution:

QUESTION: 74

The line, among the following, that touches the parabola *y*^{2} = 4*ax* is

Solution:

QUESTION: 75

Each coefficients in the equation ax^{2}+bx+c=0 is determined by throwing an ordinary die. The probability that the equation will have equal roots is

Solution:

QUESTION: 76

If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient ρ satisfies

Solution:

QUESTION: 77

The foot of perpendicular from (2,4) on the line x+y=1 is

Solution:

QUESTION: 78

The length of the subnormal to the curve *y ^{2} = 2px* is

Solution:

QUESTION: 79

Set of equations a+b-2c = 0, 2a-3b+c = 0 and a-5b+4c = α is consistent, if α equal to

Solution:

QUESTION: 80

If 1, ω, ω^{2} are cube roots of unity, the root of the equation (x-1)^{3} + 8 = 0 are

Solution:

QUESTION: 81

If cot (α+β)=0, then sin (α+2β) is equal to

Solution:

QUESTION: 82

The angle between the planes 2x - y + z = 6 and x + y + 2z = 7 is

Solution:

QUESTION: 83

The area of a parallelogram whose adjacent sides are a=i+2j+3k, b=3i-2j+k, is

Solution:

QUESTION: 84

Solution:

QUESTION: 85

Solution:

QUESTION: 86

Solution:

QUESTION: 87

Suppose a,b,c are in A.P. and a^{2,}b^{2},c^{2} are in G.P. If a < b< c and a + b + c =3/2,then the value of a is

Solution:

QUESTION: 88

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): The number of ways of selecting two elements x and y from the set S = {1, 5, 9, 13,...,1093} such that x + y = 1094 is 137.

Reason(R) : The elements of S are in A.P. with common difference 4 and number of terms 274.

Solution:

QUESTION: 89

If A and B are matrices such that A+B and AB are defined, then

Solution:

QUESTION: 90

The maximum value of *x ^{3}* - 3

Solution:

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