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This mock test of VITEEE PCME Mock Test - 4 for JEE helps you for every JEE entrance exam.
This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 4 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The instantaneous rate of change at t = 1 for the function f(t) = te^{-1 }+ 9 is

Solution:

QUESTION: 2

Area bounded by the curves y = x, y = x^{3}

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QUESTION: 3

2x - y - 2z = 2, x - 2y + z = -4, x + y + λz = 4 then the value of λ such that system of equations has no solutions is

Solution:

QUESTION: 4

(1 + 2i)/(1 - i) lies in the

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QUESTION: 5

The complex numbers z₁, z₂ and z₃ satisfying (z₁-z₃)/(z₂-z₃) = (1 - i√3)/2 are the vertices of a triangle which is

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QUESTION: 6

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QUESTION: 7

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QUESTION: 8

Given that the function *f* defined by is continuous . Then the value of *k* is

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QUESTION: 9

If f(x) = sin π [ x ] then f ′(1 − 0) is equal to

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QUESTION: 10

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QUESTION: 11

The degree of the differential equation d^{2}y/dx^{2}+(dy/dx)^{3}+6y=0 is

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QUESTION: 12

The differential equation representing the family of curves y^{2} = 2c(x + √c), where c>0, is a parameter, is of order and degree as follows

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QUESTION: 13

The solution of differential equation (dy/dx)=x^{2}+sin3x is

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QUESTION: 14

The differential of sin^{-1}[(1-x)/(1+x)] w.r.t. √x is equal to

Solution:

QUESTION: 15

∫(1/√x)sin√x dx=

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QUESTION: 16

The range of the function f(x) = tan^{-1}x is

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QUESTION: 17

∫(sin^{-1}x+cos^{-1}x)dx=

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QUESTION: 18

tan^{-1}(x/y) - tan^{-1}[(x-y)/(x+y)]=

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QUESTION: 19

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QUESTION: 20

if f : R→R be such that f(1) = 4 and f^{'}(1) = 12 then

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QUESTION: 21

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

Solution:

Remember what is TRUE: 3 is prime, odd and 2(3) is even.

Choice 1: T and T is TRUE

Choice 2: T or F is TRUE

Choice 3: F and T is FALSE

Choice 4: T and T is TRUE

QUESTION: 22

If 3X+2Y=I and 2X-Y=0, where I and 0 are unit and null matrices of order 3, then

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QUESTION: 23

If I₃ is unit matrix then, (I₃)^{-1}=

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QUESTION: 24

How many even numbers can be formed by using all the digits 2, 3, 4, 5, 6?

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QUESTION: 25

What is the chance that a leap year should have 53 sundays?

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QUESTION: 26

If P(B)=(3/4), P(A∩B∩C̅) = (1/3) and P(A̅∩B∩C̅) = 1/3, then P(B∩C) is

Solution:

QUESTION: 27

The probabilities of solving a problem by three student A,B,C are 1/2, 1/3, 1/4 respectively. The probability that problem will be solved is

Solution:

We have, probability that A can solve the problem = P(A) = 1/2 ,

And in this way P(B) = 1/3 and P(C) = 1/4.

P(A cannot solve the problem) = 1 – P(A) = 1/2 ,

P(B cannot solve the problem) = 1 – P(B) = 1 – 1/3 = 2/3,

P(C cannot solve the problem) = 1 – P(C) = 1 – 1/4 = 3/4.

P(A, B, and C cannot solve the problem) = 1/2 x 2/3 x 3/4 = 1/4.

Therefore , P(Problem will be solve) = 1 – P(Problem is not solved by any of them)

= 1 – 1/4 = 3/4

QUESTION: 28

If a = 2, b = 3, c = 5 in triangle ABC, then C =

Solution:

QUESTION: 29

If x is a positive real number different from 1, then the number 1/1 + √x, 1/1 - x , 1/1 - √x, .... are in

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QUESTION: 30

The mean deviation of the numbers 3, 4, 5, 6, 7 is

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QUESTION: 31

The value of covariance of two variables x and y is -(148/3) and the variance of x is (272/3) and the variance of y is (131/3). Then the coefficient of correlation is

Solution:

QUESTION: 32

The roots of the equation x^{3} + x^{2} + x + 1 = 0 are___

Solution:

The given equation is

x^{3} + x^{2} + x + 1 = 0

or , (x^{2} + 1)( x + 1) = 0

or , x = i , x = − 1

QUESTION: 33

In ∆ABC angle A is defined by 5 cos A + 3 = 0, the equation whose roots are sinA and tanA, is

Solution:

QUESTION: 34

The points (5,2,4),(6,-1,2) and (8,-7,k) are collinear if k is equal to

Solution:

QUESTION: 35

The equation of the sphere concentric with the sphere x^{2}+y^{2}+z^{2}-4x-6y-8z=0 and which passes thro' (0.1,0) is

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QUESTION: 36

In any right angled triangle hypotenuse is equal to 2√2 times the perpendicular drawn from the opposite vertex on it, then other angles are

Solution:

QUESTION: 37

The equation y^{2} - x^{2}+ 2x - 1 = 0 represents

Solution:

QUESTION: 38

The line passing through (0, 1) and perpendicular to the line x - 2y + 11 = 0 is

Solution:

QUESTION: 39

If a is any vector then |a x i| ^{2} +|a x j|^{2} +|a x k|^{2} =

Solution:

QUESTION: 40

If are non-zero non-collinear vectors and

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QUESTION: 41

A loss free transformer has 500 turns on its primary winding and 2500 in secondary. The meters of the secondary indicate 200 volts at 8 amperes under these conditions. The voltage and current in the primary is

Solution:

QUESTION: 42

Two ions of the same charge and energy but different mass are passing through a uniform magnetic field. The radii of their paths are proportional to

Solution:

QUESTION: 43

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?

Solution:

The emission lines are II, III and IV. The line having maximum energy is III, because energy difference between successive levels decreases rapidly with increase of n

QUESTION: 44

A capacitor is charged to store an energy U. The charging battery is disconnected. An identical capacitor is now connected to the first capacitor in parallel. The energy in each of the capacitor is

Solution:

QUESTION: 45

If a cell of constant electromotive force produces the same amount of heat during the same time in two independent resistances R₁ and R₂, when connected separately one after the other, across the cell, then the internal resistance of the cell is

Solution:

QUESTION: 46

Optical fibres uses the phenomenon of

Solution:

QUESTION: 47

A wire has a resistance of 6 Ω. If it is cut into two parts and connected in parallel, then the new resistance will be

Solution:

QUESTION: 48

In a circuit 5 percent of total current passes through a galvanometer. If resistance of the galvanometer is G then value of the shunt is

Solution:

QUESTION: 49

The temperature coefficient of resistance of a wire is 0.00125^{0}K^{-1 }. Its resistance is 1 Ω at 300 K. Its resistance will be 2 Ω at

Solution:

QUESTION: 50

A dry cell has an e.m.f. of 1.5 V and an internal resistance of 0.05 Ω. The maximum current obtainable from this cell, for a very short interval is

Solution:

QUESTION: 51

When a proton is accelerated through 1 V, then its kinetic energy will be

Solution:

QUESTION: 52

Choke coil works on the principle of

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QUESTION: 53

Two inductors of inductance L each are connected in series with opposite magnetic fluxes. What is the resultant inductance ?

Solution:

QUESTION: 54

In an ideal transformer, the voltage and the current in the primary are 200 V, 2A and that in the secondary are 2000 V, 1A. The value of is (in A).

Solution:

QUESTION: 55

A charged particle q is placed at the centre O of a cube of length L. Another same charge q is placed at a distance L from O. Then electric flux through the cube is

Solution:

QUESTION: 56

What is the cause of "Green house effect"?

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QUESTION: 57

Two charges -10 C and + 10 C are placed 10cm apart. Potential at the centre of the line joining two charges is

Solution:

QUESTION: 58

*n* small drops of same size are charged to *V* volt each. They coalesce to form a bigger drop. The potential of the bigger drop is

Solution:

QUESTION: 59

When a dielectric material is kept in between the plates of a condenser, its capacity

Solution:

QUESTION: 60

The distance between the plates of a condenser is reduced to 1/4 th and the space between the plates is filled up by a medium of dielectric constant (K) 2.8. The capacity is increases by

Solution:

QUESTION: 61

An electron revolves in a circle of radius 0.4 Å with a speed of 10^{6} m s^{-1} in a hydrogen atom. The magnetic field produced at the centre of the orbit due to the motion of the electron in tesla is [ μ_{0} = 4 π x 10^{-7} H m^{-1} ; change on the electron = 1.6 x 10^{-19} C ]

Solution:

QUESTION: 62

Two infinitely long parallel conducting plates having surface charge densities +σ and -σ respectively, are separated by a small distance. The medium between the plates is vacuum. If ε₀ is the dielectric permittvity of vacuum, then electric field in the region between the plates is

Solution:

QUESTION: 63

The first atomic reactor was constructed by

Solution:

QUESTION: 64

If in a nuclear reactor using U^{235} as fuel, the power output is 4.8 mega watts, the number of fissions per second is:

(energy released per fission of U^{235} = 200 MeV; 1eV = 1.6 x 10^{-19} J)

Solution:

QUESTION: 65

A nucleus with *Z* = 92 emits the following in sequence: α , α , β − , β − , α , α , α , α ; β − , β − , α , β + , β + , α . The *Z* of the resulting nucleus is

Solution:

QUESTION: 66

Which of the following is not dependent on the intensity of incident radiation in a photoelectric experiment ?

Solution:

QUESTION: 67

A convex lens made of glass has focal length 0.15*m* in air. If the refractive index of glass is 3/2 and that of water is 4/3, the focal length of lens when immersed in water is

Solution:

QUESTION: 68

The maximum energy of photo-electrons emitted in a photo cell is 2eV. For no photo-electrons to reach the anode, the stopping potential should be

Solution:

QUESTION: 69

The distance travelled by light in glass (refractive index =1.5) in a nanosecond will be

Solution:

Speed of light in glass

Distance travelled in one nanosecond

= 2 x 10^{8} x 10^{-9} = 0.2 m = 20 cm

QUESTION: 70

An *n* - type and *p* - silicon can be obtained by doping pure silicon with:

Solution:

For obtaining ‘n’ type semi conductor V group element is doped with silicon.

Ex: Phosphorus

For obtaining ‘p’ type semiconductor III group element is doped with silicon.

Ex: Indium

QUESTION: 71

The region with free electrons and holes in a p-n junction diode is

Solution:

QUESTION: 72

If a full wave rectifier circuit is operating from 50 Hz mains, then fundamental frequency in the ripple will be

Solution:

QUESTION: 73

In a common base amplifier circuit, calculate the change in base current if that in the emitter current is 2 mA and α = 0.98

Solution:

QUESTION: 74

Function of rectifier is

Solution:

QUESTION: 75

A P-type semiconductor can be obtained by adding

Solution:

QUESTION: 76

A semi-conducting device is connected in a series circuit with a battery and a resistance. A current is found to pass through the circuit. If the polarity of the battery is reversed, the current drops to almost zero the device may be

Solution:

QUESTION: 77

Laser light is considered to be coherent as it consists of

Solution:

QUESTION: 78

Two identical light waves, propagating in the same direction, have a phase difference δ . After they superpose the intensity of the resulting wave will be proportional to

Solution:

QUESTION: 79

Inverse square law of intensity (illuminance) is valid for

Solution:

QUESTION: 80

Light was producing interference have their amplitudes in the ratio 3:2. The intensity ratio of maximum and minimum of interference fringes is

Solution:

QUESTION: 81

When 3,3-Dimethyl-2-butanol is heated with H₂SO₄, the major product obtained is

Solution:

QUESTION: 82

At room temperature formaldehyde is

Solution:

QUESTION: 83

In which of the following reactions, aldehydes and ketones are distinguished?

Solution:

QUESTION: 84

Aldehydes and ketones do not give addition reaction with

Solution:

QUESTION: 85

The reaction/method that does not give an alkane is

Solution:

QUESTION: 86

The product formed by the action of chlorine on ethene in saturated solution of KBr is/are

Solution:

QUESTION: 87

Oxytocin is

Solution:

QUESTION: 88

The number of moles of sodium oxide in 620 g of it is

Solution:

QUESTION: 89

Reference proteins are those obtained from

Solution:

QUESTION: 90

Molarity of liquid HCl with density equal to 1.17 g/cc is

Solution:

QUESTION: 91

Acetamide and NaOBr/OH⁻ produce

Solution:

QUESTION: 92

One of the essential α-amino acids is

Solution:

QUESTION: 93

In which of the following, the number of carbon atoms does not remain same when carboxylic acid is obtained by oxidation

Solution:

QUESTION: 94

A vessel at equilibrium, contains SO₃, SO₂ and O₂. Now some helium gas is added, so that total pressure increases while temperature and volume remain constant. According to Le-Chatelier's principle, the dissociation of SO₃

Solution:

QUESTION: 95

A reaction reaches a state of chemical equilibrium only when

Solution:

QUESTION: 96

Rancidity of butter is due to the formation of

Solution:

QUESTION: 97

In monatomic gases, ratio of specific heat at constant pressure to that at constant volume is

Solution:

QUESTION: 98

Which of the following gas molecule has the maximum specific heat at constant pressure?

Solution:

QUESTION: 99

The IUPAC name of the following compound

CH₃-C(CH₃)₂-CH = C(CH₃)₂ is

Solution:

QUESTION: 100

Which of the following is true for an isochoric processes

Solution:

QUESTION: 101

2, 4-Dichlorophenoxyacetic acid is used as

Solution:

QUESTION: 102

In the brown ring 'test', the brown colour of the ring is due to

Solution:

QUESTION: 103

The shape of [Cu(NH₃)₄]^{2+} is

Solution:

QUESTION: 104

Which of the following is produced by reaction of RCN in sodium and alcohol ?

Solution:

QUESTION: 105

To protect iron against corrosion, the most durable metal plating on it is

Solution:

QUESTION: 106

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

Solution:

QUESTION: 107

Which of the following metal is not attacked by the environment?

Solution:

QUESTION: 108

The substance not likely to contain CaCO₃ is

Solution:

QUESTION: 109

What is the time (in sec) required for depositing all the silver present in 125ml of 1*M* *AgNO*_{3} solution by passing a current of 241.25 amperes? (1*F* = 96500 coulombs)

Solution:

QUESTION: 110

The ether that undergoes electrophilic substitution reactions is

Solution:

QUESTION: 111

A sample of gas occupise 100 ml at 27^{0}C and 740 mm pressure. When its volume is changed to 80 ml at 740 mm pressure, the temperature of the gas will be

Solution:

QUESTION: 112

An oxide of lead which is used in lead storage batteries, in safety matches and is a powerful oxidising agent is

Solution:

QUESTION: 113

The number of P - O bonds and the lone pairs of eletrons present in P_{4}O_{6} molecule, respectively

Solution:

QUESTION: 114

Red P can be obtained from white P by

Solution:

QUESTION: 115

When KMnO₄ acts as an oxidising agent and ultimately forms MnO₄^{2-} , MnO₂, Mn₂O₃ and Mn^{2+}, then the number of electrons transferred in each case is

Solution:

QUESTION: 116

Potassium crystallizes with a

Solution:

QUESTION: 117

Physical adsorption is inversely proportional to the

Solution:

QUESTION: 118

Select correct statement(s):

Solution:

QUESTION: 119

Which one of the following elements shows maximum number of different oxidation states in its compounds ?

Solution:

QUESTION: 120

Iron loses magnetic property at

Solution:

QUESTION: 121

Fill in the blank with appropriate word.

The passengers and crew members of the aeroplane had a.......escape when it was taking off from the runway.

Solution:

QUESTION: 122

Find the antonym of AFFLUENCE

Solution:

QUESTION: 123

Find the Synonym of FATIGUE

Solution:

QUESTION: 124

**Out of the given alternatives, choose the one which can be substituted for the given capitalised word.**

OVER AND ABOVE the household work, she works in a factory on a part-time basis.

Solution:

QUESTION: 125

**Improve the sentence by choosing best alternative for capitalised part of the sentence.**

When are you LOOKING UP in dark?

Solution:

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