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VITEEE PCME Mock Test - 4


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125 Questions MCQ Test VITEEE: Subject Wise and Full Length MOCK Tests | VITEEE PCME Mock Test - 4

VITEEE PCME Mock Test - 4 for JEE 2023 is part of VITEEE: Subject Wise and Full Length MOCK Tests preparation. The VITEEE PCME Mock Test - 4 questions and answers have been prepared according to the JEE exam syllabus.The VITEEE PCME Mock Test - 4 MCQs are made for JEE 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for VITEEE PCME Mock Test - 4 below.
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VITEEE PCME Mock Test - 4 - Question 1

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

VITEEE PCME Mock Test - 4 - Question 2

Area bounded by the curves y = x, y = x3

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 4

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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 6

VITEEE PCME Mock Test - 4 - Question 7

VITEEE PCME Mock Test - 4 - Question 8

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

VITEEE PCME Mock Test - 4 - Question 9

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

Detailed Solution for VITEEE PCME Mock Test - 4 - Question 9

VITEEE PCME Mock Test - 4 - Question 10

VITEEE PCME Mock Test - 4 - Question 11

The degree of the differential equation d2y/dx2+(dy/dx)3+6y=0 is

VITEEE PCME Mock Test - 4 - Question 12

The differential equation representing the family of curves y2 = 2c(x + √c), where c>0, is a parameter, is of order and degree as follows

VITEEE PCME Mock Test - 4 - Question 13

The solution of differential equation (dy/dx)=x2+sin3x is

VITEEE PCME Mock Test - 4 - Question 14

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

VITEEE PCME Mock Test - 4 - Question 15

∫(1/√x)sin√x dx=

VITEEE PCME Mock Test - 4 - Question 16

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

VITEEE PCME Mock Test - 4 - Question 17

∫(sin-1x+cos-1x)dx=

VITEEE PCME Mock Test - 4 - Question 18

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

VITEEE PCME Mock Test - 4 - Question 19

VITEEE PCME Mock Test - 4 - Question 20

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

VITEEE PCME Mock Test - 4 - Question 21

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

Detailed Solution for VITEEE PCME Mock Test - 4 - Question 21

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

VITEEE PCME Mock Test - 4 - Question 22

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

VITEEE PCME Mock Test - 4 - Question 23

If I₃ is unit matrix then, (I₃)-1=

VITEEE PCME Mock Test - 4 - Question 24

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

VITEEE PCME Mock Test - 4 - Question 25

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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - 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

Detailed Solution for VITEEE PCME Mock Test - 4 - Question 27

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

VITEEE PCME Mock Test - 4 - Question 28

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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 30

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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 32

The roots of the equation x3 + x2 + x + 1 = 0 are___

Detailed Solution for VITEEE PCME Mock Test - 4 - Question 32

The given equation is
x3 + x2 + x + 1 = 0
or , (x2 + 1)( x + 1)   = 0
or , x = i , x = − 1

VITEEE PCME Mock Test - 4 - Question 33

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

VITEEE PCME Mock Test - 4 - Question 34

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

VITEEE PCME Mock Test - 4 - Question 35

The equation of the sphere concentric with the sphere x2+y2+z2-4x-6y-8z=0 and which passes thro' (0.1,0) is

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 37

The equation y2 - x2+ 2x - 1 = 0 represents

VITEEE PCME Mock Test - 4 - Question 38

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

VITEEE PCME Mock Test - 4 - Question 39

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

VITEEE PCME Mock Test - 4 - Question 40

If  are non-zero non-collinear vectors and

VITEEE PCME Mock Test - 4 - 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
VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - 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?

 

Detailed Solution for VITEEE PCME Mock Test - 4 - Question 43

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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 46

Optical fibres uses the phenomenon of

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 49

The temperature coefficient of resistance of a wire is 0.001250K-1 . Its resistance is 1 Ω at 300 K. Its resistance will be 2 Ω at

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 51

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

VITEEE PCME Mock Test - 4 - Question 52

Choke coil works on the principle of

VITEEE PCME Mock Test - 4 - Question 53

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

VITEEE PCME Mock Test - 4 - 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).

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 56

What is the cause of "Green house effect"?

VITEEE PCME Mock Test - 4 - Question 57

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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 59

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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 61

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

VITEEE PCME Mock Test - 4 - Question 62

An electron revolves in a circle of radius 0.4 Å with a speed of 106  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 [ μ0  = 4 π x 10-7  H m-1 ; change on the electron = 1.6 x 10-19  C ]

VITEEE PCME Mock Test - 4 - Question 63
The first atomic reactor was constructed by
VITEEE PCME Mock Test - 4 - Question 64

If in a nuclear reactor using U235 as fuel, the power output is 4.8 mega watts, the number of fissions per second is:
(energy released per fission of U235 = 200 MeV; 1eV = 1.6 x 10-19  J)

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 66

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

VITEEE PCME Mock Test - 4 - Question 67

A convex lens made of glass has focal length 0.15m 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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 69

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

Detailed Solution for VITEEE PCME Mock Test - 4 - Question 69

Speed of light in glass 
Distance travelled in one nanosecond
= 2 x 108 x 10-9 = 0.2 m = 20 cm

VITEEE PCME Mock Test - 4 - Question 70

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

Detailed Solution for VITEEE PCME Mock Test - 4 - Question 70

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

VITEEE PCME Mock Test - 4 - Question 71

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

VITEEE PCME Mock Test - 4 - Question 72

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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 74

Function of rectifier is

VITEEE PCME Mock Test - 4 - Question 75

A P-type semiconductor can be obtained by adding

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 77

Laser light is considered to be coherent as it consists of

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 79

Inverse square law of intensity (illuminance) is valid for

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 81

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

VITEEE PCME Mock Test - 4 - Question 82

At room temperature formaldehyde is

VITEEE PCME Mock Test - 4 - Question 83

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

VITEEE PCME Mock Test - 4 - Question 84

Aldehydes and ketones do not give addition reaction with

VITEEE PCME Mock Test - 4 - Question 85

The reaction/method that does not give an alkane is

VITEEE PCME Mock Test - 4 - Question 86

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

VITEEE PCME Mock Test - 4 - Question 87

Oxytocin is

VITEEE PCME Mock Test - 4 - Question 88

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

VITEEE PCME Mock Test - 4 - Question 89

Reference proteins are those obtained from

VITEEE PCME Mock Test - 4 - Question 90

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

VITEEE PCME Mock Test - 4 - Question 91

Acetamide and NaOBr/OH⁻ produce

VITEEE PCME Mock Test - 4 - Question 92

One of the essential α-amino acids is

VITEEE PCME Mock Test - 4 - Question 93

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

VITEEE PCME Mock Test - 4 - 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

VITEEE PCME Mock Test - 4 - Question 95

A reaction reaches a state of chemical equilibrium only when

VITEEE PCME Mock Test - 4 - Question 96

Rancidity of butter is due to the formation of

VITEEE PCME Mock Test - 4 - Question 97

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

VITEEE PCME Mock Test - 4 - Question 98

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

VITEEE PCME Mock Test - 4 - Question 99

The IUPAC name of the following compound
CH₃-C(CH₃)₂-CH = C(CH₃)₂ is

VITEEE PCME Mock Test - 4 - Question 100

Which of the following is true for an isochoric processes

VITEEE PCME Mock Test - 4 - Question 101

2, 4-Dichlorophenoxyacetic acid is used as

VITEEE PCME Mock Test - 4 - Question 102

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

VITEEE PCME Mock Test - 4 - Question 103

The shape of [Cu(NH₃)₄]2+ is

VITEEE PCME Mock Test - 4 - Question 104

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

VITEEE PCME Mock Test - 4 - Question 105

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

VITEEE PCME Mock Test - 4 - Question 106

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

VITEEE PCME Mock Test - 4 - Question 107

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

VITEEE PCME Mock Test - 4 - Question 108

The substance not likely to contain CaCO₃ is

VITEEE PCME Mock Test - 4 - Question 109

What is the time (in sec) required for depositing all the silver present in 125ml of 1M AgNO3 solution by passing a current of 241.25 amperes? (1F = 96500 coulombs)

VITEEE PCME Mock Test - 4 - Question 110

The ether that undergoes electrophilic substitution reactions is

VITEEE PCME Mock Test - 4 - Question 111

A sample of gas occupise 100 ml at 270C and 740 mm pressure. When its volume is changed to 80 ml at 740 mm pressure, the temperature of the gas will be

VITEEE PCME Mock Test - 4 - Question 112

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

VITEEE PCME Mock Test - 4 - Question 113

The number of P - O bonds and the lone pairs of eletrons present in P4O6 molecule, respectively

VITEEE PCME Mock Test - 4 - Question 114

Red P can be obtained from white P by

VITEEE PCME Mock Test - 4 - Question 115

When KMnO₄ acts as an oxidising agent and ultimately forms MnO₄2- , MnO₂, Mn₂O₃ and Mn2+, then the number of electrons transferred in each case is

VITEEE PCME Mock Test - 4 - Question 116

Potassium crystallizes with a

VITEEE PCME Mock Test - 4 - Question 117

Physical adsorption is inversely proportional to the

VITEEE PCME Mock Test - 4 - Question 118

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

VITEEE PCME Mock Test - 4 - Question 119

Select correct statement(s):

VITEEE PCME Mock Test - 4 - Question 120

Iron loses magnetic property at

VITEEE PCME Mock Test - 4 - 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.

VITEEE PCME Mock Test - 4 - Question 122

Find the antonym of AFFLUENCE

VITEEE PCME Mock Test - 4 - Question 123

Find the Synonym of FATIGUE

VITEEE PCME Mock Test - 4 - 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.

VITEEE PCME Mock Test - 4 - Question 125

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

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