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This mock test of JEE Main Mock Test 3 for JEE helps you for every JEE entrance exam.
This contains 90 Multiple Choice Questions for JEE JEE Main Mock Test 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The frequency for which a 5 μF capacitor has a reactance of 1/1000 ohm is given by

Solution:

QUESTION: 2

Neutrino is a particle, which is

Solution:

QUESTION: 3

Which of the following is true?

Solution:

QUESTION: 4

The phase difference between the alternating current and e.m.f. is π/2. Which of the following can not be the constituent of the circuit?

Solution:

QUESTION: 5

The approximated wavelength of a photon of energy 2.48eV is

Solution:

QUESTION: 6

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plump bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is

Solution:

QUESTION: 7

A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole), then the electric field at Q is proportional to :

Solution:

QUESTION: 8

A lift of mass 1000 kg is moving with an acceleration of 1 m−s⁻^{2} in upward direction. Tension developed in the string, which is connected to the lift, is

Solution:
Use T-mg=ma with g=9.8You will get T=m(a+g)T=1000(1+9.8)T=1000(10.8)T=10800

QUESTION: 9

Electric field at the centroid of a triangle carrying q charge at each corner is

Solution:

QUESTION: 10

A machine gun fires a bullet of mass 40 g with a velocity 1200 m−s⁻1. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?

Solution:

QUESTION: 11

The logic behind 'NOR' gate is that, it gives

Solution:

QUESTION: 12

A long solenoid has n turns per metre and current I ampere is flowing through it. The magnetic field at the ends of solenoid is

Solution:

QUESTION: 13

Two pieces of a glass plate, placed one upon the other with a little water in between them, can not be separated easily, because of

Solution:

QUESTION: 14

The sum of two vectors A → and B → is at right angles to their difference. Then

Solution:

QUESTION: 15

The function of the moderator in a nuclear reactor is

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):In a nuclear reactor cadmium acts as a moderator.

Reason(R):The cadium rods are so inserted in the graphite block so that they can be slided in and out as per requirement.

Solution:
The role of moderator is to slow down the neutron produced due to nuclear fission reaction occurring in nuclear reactors. The cadmium rod is good neutron absorber so it is used to control the number and not to slow them down for reuse.

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): Energy density in the solenoid is greater at centre than near its ends.

Reason(R): Energy density is defined as

Solution:

QUESTION: 18

A solid cylinder of mass M and radius R rolls down an inclined plane without slipping. The speed of its centre of mass when it reaches the bottom is

Solution:

QUESTION: 19

There are two lead spheres at the same temperature, the ratio of radii being 1:2 The ratio of head capacities are

Solution:

QUESTION: 20

For the constructive interference the path difference between the two interfering waves must be equal to

Solution:

QUESTION: 21

The fundamental unit which has the same power in the dimensional formula of surface tension and viscosity is

Solution:

QUESTION: 22

If a star is moving towards earth, then the lines are shifted towards

Solution:
Its shifts towards blue because of increases in frequency by Doppler Effect in optics.

QUESTION: 23

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:

QUESTION: 24

When a tuning fork of frequency 341 is sounded with another tuning fork, six beats per second are heard. When the second tuning fork is loaded with wax and sounded with the first tuning fork, the number of beats is two per second. The natural frequency of the second tuning fork is

Solution:

QUESTION: 25

d dx [tan^{-1} cos x 1 + sin x ] =

Solution:

d dx

[tan^{-1} cos x (1 + sin x) ]

tan^{-1} [ cos x 1 + sin x ]

= tan^{-1} [ sin( π 2 - x) 1 + cos( π 2 - x) ]

= tan^{-1} [tan( π 4 - x 2 )]

= π 4 - x 2

∴ d dx ( π 4 - x 2 ) = - 12

QUESTION: 26

Singly ionized helium (*He*^{+}) atom is hydrogen like in the sense that a solitary electron revolves around a positively charged nucleus. If the energy of this electron in its first orbit (*n* = 1) is -54.4 eV, what will be its energy in the first excited state?

Solution:

QUESTION: 27

The charge deposited on 4 μ F capacitor in the circuit is

Solution:

QUESTION: 28

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

Solution:

QUESTION: 29

We are able to obtain fairly large currents in a conductor because

Solution:

QUESTION: 30

A charge *+4q* is located on the *X*-axis of a Cartesian coordinate system at *x = -2a* as shown. Another charge *+(q/4)* is located on the *X*-axis at *x = a*. Where on the *Y*-axis should a third charge *-3q* be placed so that the resultant electric field at the origin *O* has equal positive *X* and *Y* components?

Solution:

QUESTION: 31

A charged particle with velocity 2 x 10^{3} m/s passes undeflected through electric and magnetic field. Magnetic field is 1.5 telsa. The electric field intensity would be

Solution:

QUESTION: 32

The correct order of boiling points for primary (1º), secondary (2º) and tertiary (3º) alcohols is

Solution:

QUESTION: 33

DNA has deoxyribose, base and a third compound, known as

Solution:

QUESTION: 34

Which of the following does not undergo Cannizzaro's reaction?

Solution:

QUESTION: 35

For reaction at equilibrium, Le Chatelier's principle predicts the effects of

Solution:

QUESTION: 36

For an endothermic reaction, energy of activation is E_{a} and enthalpy of reaction is ΔH (both of these in kJ/mol). Minimum value of E_{a} will be

Solution:

QUESTION: 37

In the reaction CH_{2}COOH_{aq} + OH_{(aq)} → CH_{3}COO^{-} + H_{2}O_{(l)} ; ΔH = -55.2kJ mol^{-1} What is the heat of dissociation (in kJ mol^{-1}) of acetic acid?

Solution:

ΔH = -55.2 KJ.mol^{-1}

-[H^{+} _{(aq)} + OH^{-} _{(aq)} → H_{2}O_{(l)} ΔH = -57.3 KJ .mol^{-1}]]

CH_{2}COOH_{aq} → CH_{3}COO^{-} _{(aq)} + H^{+} _{(aq)} ΔH = ?

CH_{2}COOH_{(aq)} + OH^{-} _{(aq)} → CH_{3}COO^{-} _{(aq)} + H_{2}O_{(l)} ΔH = -55.2 KJ .mol^{-1}

-H^{+} + OH^{-} _{(aq)} → - H_{2}O_{(l)} ΔH = + 57.3KJ .mol^{-1}

CH_{3}COOH_{(aq)} → CH_{3}COO^{-} _{(aq)} + H^{+}_{(aq)} ΔH = 2.1 KJmol^{-1}

QUESTION: 38

Element with Atomic number 38, belongs to

Solution:

Element with atomic number-38 is strontium (symbol-Sr), which belongs to II A group i.e. alkaline earth metals and 5^{th} period.

QUESTION: 39

Which of the following complexes will have four isomers?

Solution:

QUESTION: 40

The amount of Aluminium deposited when 0.1 Faraday current is passed through aluminium chloride will be (R = 27)

Solution:

QUESTION: 41

Compound A has a molecular formula C₇H₇NO on treatment with Br₂/KOH, A gives an amine B which respond to carbylamine test. B on diazotisation and coupling with phenol give an azo dye. A can be

Solution:

QUESTION: 42

pH of a solution is defined by the expression

Solution:

QUESTION: 43

A solution of *AgNO*_{3} during electrolysis between silver electrodes required a quantity of 241.25 coulombs of electricity the weight of silver deposited is

Solution:

QUESTION: 44

Identify the indicator used to titrate Na₂CO₃ solution with HCl

Solution:

QUESTION: 45

To a solution containing equimolar mixture of sodium acetate and acetic acid, some more amount of sodium acetate solution is added. The pH of mixture solution

Solution:

QUESTION: 46

A white salt is readily soluble in water and gives a colourless solutions with a pH of about 9.The salt would be

Solution:

QUESTION: 47

Which of the following compounds will show positive silver mirror test?

Solution:

QUESTION: 48

Among the following compounds the decreasing order of reactivity towards electrophilic substitution is:

Solution:

QUESTION: 49

Which is not a macromolecule?

Solution:
The most common macromolecules in biochemistry are biopolymers (nucleic acids, proteins, carbohydrates and lipids) and large non-polymeric molecules (such as lipids and macrocycles).

QUESTION: 50

For preparing an alkane ,a concentrated aqueous solution of sodium or potassium salt of a saturated carboxylic acid is subjected to

Solution:

QUESTION: 51

AB is an ionic solid. If the ratio of ionic radii of A^{+} and B^{ − } is 0 . 52. What is the coordination number of B^{ − }

Solution:

Ratio r + r - = 0.414 - 0.732

Coordination no. is 6.

QUESTION: 52

The solubility of gas in liquid increases with

Solution:

QUESTION: 53

Which of the following is not a crystalline solid ?

Solution:

QUESTION: 54

A 100 g solution contains 25 g of water, 25 g ethanol and 50 g acetic acid. The mole fraction of water is

Solution:

QUESTION: 55

Pent-1-ene with HCl gives

Solution:

QUESTION: 56

Which of the following statements is incorrect?

Solution:

No two spectral lines of an element can have the same wave number.

QUESTION: 57

Entropy of universe:

Solution:
Entropy means randomness in accommodation of internal energy of gas and the randomness can only increase because in order to cool down a place we need the throw the heat energy somewhere else so randomness decreases at one point but increases at other point. overall it increases only. there since universe is an isolated system (assumed) it will always a increase in randomness of the universe.

QUESTION: 58

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

Solution:

QUESTION: 59

Which one of the following platinum complexes is used in cancer chemotherapy?

Solution:

Cis isomer of [PtCl_{2}(NH_{3})_{2}] is known as cisplatin and is used as an antitumor agent in treatment of cancer.

QUESTION: 60

The electrons, identified by quantum numbers n,l (i) n = 4, l = 1, (ii) n = 4, l = 0, (iii) n = 3, l = 2, (iv) n = 3, l = 1 can be placed in order of increasing energy, from the lowest to highest, as_

Solution:

On the basis of (n + l) rule, the values for (i), (ii), (iii) and (iv) are 5,4,5 and 4 respectively. In these in both, but n is minimum for (iv). Hence energy order = (iv) > (ii). Similarly in (i) and (ii), hence (iii) < (i).

QUESTION: 61

If 0.6387 of plantinichloride of a monoacid base on ignition gave 0.209g of platinum, then molecular weight of the base is

Solution:

QUESTION: 62

The area, in square unit, of the region bounded by the curve x^{2} = 4 y , the line *x* = 2 and the *x*-axis is

Solution:

QUESTION: 63

When 5^{99} is divided by 13 then the remainder is

Solution:

Rem [5^99/13] = 8

We need to find out the remainder when 5^99 is divided by 13

We should try and reduce the numerator in this case. Let us have a look at the method below.

Remainder [5^99 / 13]

= Remainder [5*5^98 / 13]

= Remainder [5*25^49 / 13]

= Remainder [5*(-1)^49 / 13]

= Remainder [(-5) / 13]

= 8

QUESTION: 64

What is the value of *x* satisfying the equation

?

Solution:

QUESTION: 65

The equation of the circle described on the common chord of the circles x^{2 }+ y^{2} -8x + y -15 = 0 and x^{2} + y^{2} - 4x + 4y - 42 = 0 as diameter is

Solution:

QUESTION: 66

The abcissae of two points A, B are roots of x^{2} + 4x - 45 = 0. The centre of the circle for which AB are diameter is

Solution:

QUESTION: 67

If z lies on |z| = 1 ,then 2/z lies on

Solution:
Let z=x+iy

so |z|=1. => xÂ²+yÂ²=1

Let 2/z = another complex no. c

c= 2/z

= 2/(x+iy)

= 2(x-iy)/(xÂ²+yÂ²)

= 2(x-iy)

so |c| = 2|x-iy|

= 2(xÂ²+yÂ²)

= 2

so |c|= 2. which represents a circle

so |z|=1. => xÂ²+yÂ²=1

Let 2/z = another complex no. c

c= 2/z

= 2/(x+iy)

= 2(x-iy)/(xÂ²+yÂ²)

= 2(x-iy)

so |c| = 2|x-iy|

= 2(xÂ²+yÂ²)

= 2

so |c|= 2. which represents a circle

QUESTION: 68

*i*^{243} =

Solution:

QUESTION: 69

The solution of the equation y - x(dy/dx)=a[(y^{2})+(dy/dx)] is

Solution:

QUESTION: 70

"If Deb and Sam go to the mall, then it is snowing."

Which statement below is logically equivalent?

Solution:

A statement is logically equivalent to its contrapositive.

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):The angle between the lines 2x = 3y = -z and 6x = - y = - 4z , is 90^{0} .

Reason(R): If and and angle between them is θ , then

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-

A committee of *n* persons is to be formed out of 30 persons.

Assertion(A) : The value of *n* for which the number of committees is maximum is *n* = 15

Reason(R) : In the expansion of the middle term has the greatest binomial coefficient.

Solution:

QUESTION: 73

The equation of the normal to the curve *x*^{2} = 4*y* at (1, 2) is

Solution:

QUESTION: 74

If

Solution:

QUESTION: 75

A and B are square matrices of order n x n, then (A - B)^{2} is equal to

Solution:

(A - B) x (A - B)

(A - B) xA - (A - B) x B

= A^{2} - AB - BA + B^{2}

QUESTION: 76

If ^{2n}C_{3}:^{n}C_{2}=44:3.For which value of r, ^{n}C_{r}=15?

Solution:

QUESTION: 77

If a dice is thrown twice, the probability of occurrence of 4 at least once, is

Solution:
N(s)=6^2=36n(occurrence of 4 atleast once)={ (1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(4,1),(4,2),(4,3),(4,5),(4,6)}=11P(occurrence of 4 atleast once)=n(occurrence of 4 atleast once)/n(s)=11/36

QUESTION: 78

The angle between lines 3x+y-7=0 and x+2y+9=0 is

Solution:
Use the formula tan thita=|(m1-m2)/1+m1m2|

QUESTION: 79

A student obtain 75%, 80% and 85% in three subjects. If the marks of another subject are added, then his average cannot be less than

Solution:

QUESTION: 80

The equation of the sphere passing thro' the point (1,3-2) and the circle y^{2}+z^{2}=25 and x=0 is

Solution:

QUESTION: 81

If (axb)^{2}+(a.b)^{2}=144 and |a|=4, then |b|=

Solution:

QUESTION: 82

Given that θ is a acute and that sin θ =3/5. Let x,y be positive real numbers such that 3(x-y) =1, then one set of solutions for x and y expressed in terms of θ is given by

Solution:

QUESTION: 83

The length of subtangent to *x ^{2} + xy + y^{2}* = 7 at 1, − 3 is

Solution:

QUESTION: 84

If a=i+2j-2k, b=2i-j+k, c=i+3j-k, then ax(bxc)=

Solution:

QUESTION: 85

Solution:

QUESTION: 86

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):

Reason(R): If f(x) is a periodic function of period a, then

Solution:

QUESTION: 87

A and B are square matrices of the same order. Which is correct?

Solution:

QUESTION: 88

Solution:

QUESTION: 89

If minimum value of f(x) = x^{2} + 2bx + 2c^{2} is greater than maximum value of g(x) = - x^{2 }- 2cx + b^{2 }then for x is real

Solution:

QUESTION: 90

Let f(x) =ax^{2}+bx+c,a≠0 and triangle = b^{2}-4ac.If α+β, α^{2}+β^{2} and α^{2}+β^{2} are in G.P., then :

Solution:

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