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This mock test of VITEEE PCME Mock Test - 15 for JEE helps you for every JEE entrance exam.
This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 15 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The function which is neither decreasing nor increasing in (π/2, 3π/2) is

Solution:

QUESTION: 2

If complex numbers z₁, z₂ and origin form an equilateral triangle then z₁^{2} + z₂^{2} =

Solution:

QUESTION: 3

The area of the region bounded by the curve y = x - x^{2} between x = 0 and x = 1 is

Solution:

QUESTION: 4

The curve represented by Im (z^{2}) = K where K is a non-zero real number is

Solution:

QUESTION: 5

The area of the curve |x|+|y|=4 is

Solution:

QUESTION: 6

Solution:

QUESTION: 7

for x ≠ 5 and *f* is continuous at *x* = 5 then *f*(5) =

Solution:

QUESTION: 8

The order of differential equation (d^{2}y/dx^{2})^{2 }= (1+dy/dx)^{1/2} is

Solution:

QUESTION: 9

If the function *f* is defined by f(x) = x/1 + | x | then at what points is *f* differentiable

Solution:

QUESTION: 10

If x^{y}=e^{(x-y)}, (dy/dx)=

Solution:

QUESTION: 11

Let *f(x)* = [*x*], where [*x*] denotes the greatest integer contained in *x*. Which one of the following is correct?

Solution:

QUESTION: 12

If *c* is parameter then the differential equation whose solution is y = c^{2} + c/x is

Solution:

QUESTION: 13

Solution of (x+y-1) dx+(2x+2y-3) dy = 0 is

Solution:

QUESTION: 14

The equation of the curve passing through the origin and satisfying the differential equation dy/dx = (x − y)^{2} is

Solution:

QUESTION: 15

∫cos√x dx=

Solution:

QUESTION: 16

∫tan^{-1}x dx =

Solution:

QUESTION: 17

If Tan^{-1}x + 1 + Tan^{-1}(x − 1) =Tan^{-1}(18/31) , then x =

Solution:

QUESTION: 18

The value of

Solution:

QUESTION: 19

Solution:

QUESTION: 20

If n is any odd number, which of the following is true about n +1?

Solution:

Every whole number is either odd or even.

A whole number is even if it can be divided evenly by two; the numbers 2, 4, 6, 8, 10, 12, . . . are even.

In this question we are given the information that n is an odd number.

Because n is odd, it must be one of the numbers 1, 3, 5, 7, 9, 11, 13, 15, and so on.

Now we have to reason mathematically.

If n is a member of this “odd” list, then what can we say for sure about n +1?

If we add 1 to each number in the odd list, we get the “ n +1 ” list: 2, 4, 6, 8, 10, 12, 14, 16, and so on, which are even numbers.

QUESTION: 21

The system of equations

*2x + 2y - 3z - 1 = 0*

*4x + 4y + z -2 = 0*

*6x + 6y - z -3 = 0*

has-

Solution:

QUESTION: 22

If *A = [x y z]* ,

then [ a x^{2} + b y^{2} + c z^{2} + 2 hxy + 2 gzx + 2 fyz ] is

Solution:

QUESTION: 23

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of there parallel lines is :

Solution:

QUESTION: 24

The number of ways in which 7 men and 7 women can sit on a round table such that no two woman sit together is, are

Solution:

QUESTION: 25

The probability of an event A occuring is 0.5 and of B occuring is 0.3. If A and B are mutually exclusive events,then the probability of neither A nor B occuring is

Solution:

QUESTION: 26

A coin is tossed 10 times. The probability of getting exactly six heads, is

Solution:

QUESTION: 27

If the sum of first n terms of an A.P. be 3n^{2} - n and its common difference is 6, then its first term is

Solution:

QUESTION: 28

If in a ∆ABC 2cosA=sinB cosecC, then

Solution:

QUESTION: 29

If the matrix is singular, then θ =

Solution:

QUESTION: 30

The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3 and the standard deviations are 8 and 7. The mean and standard deviations of the combined sample is

Solution:

QUESTION: 31

Given n = 10, ∑x = 4, ∑y = 3, ∑x^{2} = 8, ∑y^{2 }= 9 ∑xy = 3, then the co-eff. of correlation is

Solution:

QUESTION: 32

The number of roots of the equation |x|^{2 }- 7|x|+12=0 is

Solution:

QUESTION: 33

If there is a multiple root of order 3 for the equation x^{4} − 2 x^{3} + 2 x − a = 0 , then the other roots is

Solution:

QUESTION: 34

The ratio in which the plane r̅.(i̅−2j̅+3k̅)=17 divides the line joining the points -2i̅+4j̅+7k̅ and 3i̅+5j̅+8k is̅

Solution:

QUESTION: 35

The angle between the two planes 3x-4y+5z=0 and 2x-y-2z=5 is

Solution:

QUESTION: 36

If sin2x+sin4x=2sin3x, then x=

Solution:

QUESTION: 37

The equation of the parabola whose focus is (1,-1) and directrix is x + y + 7 = 0 is

Solution:

QUESTION: 38

The vertex of the parabola

y^{2} = 4(a' - a) (x - a) is

Solution:

QUESTION: 39

If a,b,c are position vectors of vertices ABC, then the position vector of a centroid of ∆ABC is

Solution:

QUESTION: 40

If vectors ai-2j+3k and 3i+6j-5k are mutually perpendicular, then the value of a is

Solution:

QUESTION: 41

A transformer is used to light 140 watt, 24 volt lamp from 240 volts A.C. mains. If the current in the mains is 0.7 A, then the efficiency of transformer is

Solution:

QUESTION: 42

Sodium has body centred packing. Distance between two nearest atoms is 3.7 Å . The lattice parameter is:

Solution:

QUESTION: 43

Light rays of wavelengths 6000 Å and of photon intensity 39 x 6 watts/m^{2} is incident on a metal surface. If only one percent of photons incident on the surface emit photo electrons, then the number of electrons emitted per second per unit area from the surface will be [ Planck constant = 6.64 x 10^{-34} J − s ; Velocity of light = 3 x 10^{8} m s^{-1} ]

Solution:

QUESTION: 44

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

Solution:

QUESTION: 45

Optical fibres uses the phenomenon of

Solution:

QUESTION: 46

We have two wires A and B of same mass and same material. The diameter of the wire A is half of that B. If the resistance of wire A is 24 ohm then the resistance of wire B will be

Solution:

QUESTION: 47

A cell whose e.m.f. is 2V and internal resistance is 0.1Ω, is connected with a resistance of 3.9Ω. The voltage across the cell terminal will be

Solution:

QUESTION: 48

The power of an electric bulb marked as 40 W and 200 V used in a circuit of supply voltage 100 V will be

Solution:

QUESTION: 49

At what temperature will the resistance of a copper wire become three times its value at 0^{o}C(Temperature coefficient of resistance for copper = 4x10^{-3} per ^{o}C)

Solution:

QUESTION: 50

What is the stopping potential when the metal with work function 0.6 eV is illuminated with the light of 2 eV?

Solution:

QUESTION: 51

The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux φ linked with the primary coil is given by φ = φ _{0} + 4t, where φ is in weber, t is time in second and φ _{0} is a constant, the output voltage across the secondary coil is

Solution:

No. of turns across primary N_{p} = 50

Number of turns across secondary N_{s} = 1500

Magnetic flux linked with primary, Φ = Φ_{0} + 4t

∴ Voltage across the primary,

QUESTION: 52

Which of the following figures correctly depicts the Lenz's law? The arrows show the movement of the labelled pole of a bar magnet into a closed circular loop and the arrows on the circle show the direction of the induced current.

Solution:

QUESTION: 53

When the current changes from *+2A* to *-2A* in 0.05s, an *emf* of 8*V* is induced in a coil. The coefficient of self induction of the coil is

Solution:

QUESTION: 54

The oscillating electric and magnetic field vectors of electromagnetic wave are oriented along

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

In bringing an electron towards another electron, the electrostatic potential energy of the system

Solution:

QUESTION: 57

If a point charge *q* be rotated in a circle of radius *r* around a charge *Q*, the work done will be

Solution:

QUESTION: 58

Two spherical conductors A and B having equal radii and carrying equal charges on them, repel each other with a force F, when kept apart at some distance. A third spherical conductor C having same radius as that of A, but uncharged, is brought in contact with A, then brought in contact with B and finally removed away from both. The new force of repulsion between the conductors A and B is

Solution:

QUESTION: 59

Two metal spheres have their surface in the ratio 9 : 16. They are put into contact with each other. A charge of 7 x10^{-6} C is given to the system and now they are separated so that each exerts no influence on the other . The potential due to smaller sphere at a distance of 50m from it is

Solution:

QUESTION: 60

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

Solution:

QUESTION: 61

A voltmeter has a resistance of G ohm and range V volt. The value of resistance used in series to convert it into voltmeter of range nV volt is

Solution:

QUESTION: 62

A radio active sample has a half life of 5 days. To decay from 8 micro curies to 1 micro-curie, the number of days taken will be

Solution:

QUESTION: 63

The radio of the radii of the nuclei _{13}Al^{27 }and _{52}Te^{152} is

Solution:

QUESTION: 64

Neutron was discovered by

Solution:

QUESTION: 65

As the intensity of incident light increases

Solution:

QUESTION: 66

In a Huygen's eye piece with an eyepiece of focal length *F*, the distance between the eye-piece and field lens should be

Solution:

QUESTION: 67

Einstein's work on the photoelectric effect provied support for the equation

Solution:

QUESTION: 68

*ABC* is a right angled glass prism of refractive index 1.5. ∠ A , ∠ B and ∠ C are 60^{o} , 30^{o} and 90^{o} respectively. A thin layer of liquid is on the face *AB*. For a ray of light which is incident normally on *AC* to be totally reflected at *AB*, the refractive index of the liquid on *AB* should be

Solution:

QUESTION: 69

Zener diode is used for

Solution:

QUESTION: 70

A zener diode works on the principle of

Solution:

QUESTION: 71

For a transistor working as common-base amplifier, the emitter current is 7.2 mA. If the current gain is 0.96, then the collector current is

Solution:

QUESTION: 72

If the lattice parameter for a crystalline structure is 3.6 Å , then the atomic radius in fcc crystal is

Solution:

QUESTION: 73

In intrinsic semiconductor at room temperature, number of electrons and holes are

Solution:

QUESTION: 74

Silicon is a semiconductor. If a small amount of As is added to it, then its electrical conductivity

Solution:

QUESTION: 75

In forward bias, the width of potential barrier in a p-n junction diode

Solution:

QUESTION: 76

The golden view of sea shell is due to

Solution:

QUESTION: 77

The wave theory of light was given by

Solution:

QUESTION: 78

A wavefront is an imaginary surface where

Solution:

QUESTION: 79

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

Solution:

QUESTION: 80

Phenomenon of electrolysis was first given by

Solution:

QUESTION: 81

Ethyl alcohol is industrially prepared from ethylene by

Solution:

QUESTION: 82

Acetaldehyde cannot exhibit

Solution:

QUESTION: 83

Formalin is an aqueous solution of

Solution:

QUESTION: 84

When ethylbromide and n-propyl bromide is allowed to react with sodium, in ether, they form

Solution:

QUESTION: 85

Tollen's reagent is

Solution:

QUESTION: 86

Which alkene gives the same product by the Markownikoff's and anti-Markownikoff's method

Solution:

QUESTION: 87

The most stable ion is

Solution:

QUESTION: 88

The most stable free radical among the following is

Solution:

QUESTION: 89

The number of molecules of ATP produced in the lipid metabolism of a molecule of palmitic acid is

Solution:

QUESTION: 90

Rearrangement of an oxime to an amide in the presence of strong acid is called

Solution:

QUESTION: 91

The sequence in the structure of nucleic acid is

Solution:

QUESTION: 92

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

Solution:

QUESTION: 93

Which of the following favours the backward reaction in a chemical equilibrium?

Solution:

QUESTION: 94

What is the main reason for the fact that carboxylic acids can undergo ionization?

Solution:

QUESTION: 95

In a reversible reaction, the catalyst

Solution:

QUESTION: 96

A heat engine absorbs heat Q_{1} at temperature T_{1} and heat Q_{2} at temperature T_{2}. Work done by the engine is (Q_{1} + Q_{2}). This data

Solution:

It does not go against first law of thermodynamics .

However it violates the 2nd law of thermodynamics.

QUESTION: 97

For an ideal gas, the relation between the enthalpy change and internal energy change at constant temperature is given by

Solution:

QUESTION: 98

Given the bond energies of N ≡ N , H − H and N − H bonds as 941.5, 433 and 391 *kJ mole ^{-1}* respectively, the enthalpy of reaction N

Solution:

Enthalpy of reaction = ∑ bond energy_{reactant} - ∑ bond energy_{product}

= bond energy (n_{2}) + 3 x (bond energy) (h_{2}) - 2 x (bond energy) (NH_{3})

= 941.5 + (3 x 433) - 2 x 3 x 391

= 2240.5 - 2346 = 105.4 ≅ -105kJ

QUESTION: 99

A drug that is antipyretic as well as analgesic is

Solution:

QUESTION: 100

The prefixes sys and anti are used to denote

Solution:

QUESTION: 101

Which of the following has largest number of isomers? (R is alkyl group, en is ethylediamine)

Solution:

QUESTION: 102

One mole of complex compound Co(NH₃)₅ Cl₃ gives 3 mol of ions on dissolution in water. One mol of same complex reacts with two mol of AgNO₃ solution to form two mol of AgCl(s). The struture of complex is

Solution:

QUESTION: 103

In the presence of acid, the hydrolysis of methyl cyanide gives

Solution:

QUESTION: 104

The hormone which controls the process like burning of fats, proteins and carbohydrates to liberate energy in the body is

Solution:

Thyroxine is a hormone secreted by thyroid gland.

This hormone controls various biochemical reactions involving burning of proteins carbohydrates, fats to release energy.

QUESTION: 105

Diazo coupling is useful to prepare

Solution:

QUESTION: 106

Which of the following shows maximum no. of oxidation states?

Solution:

QUESTION: 107

Electrolytes when dissolved in water dissociate into ions because

Solution:

QUESTION: 108

On passing a current through *KCl* solution 19.5gm of potassium is deposited. If the same quantity of electricity is passed through a solution of aluminium chloride, the amount of Aluminium deposited is

Solution:

QUESTION: 109

The ether that undergoes electrophilic substitution reactions is

Solution:

QUESTION: 110

Which of the following reacts with water at a high rate?

Solution:

QUESTION: 111

Wt. of 22.4 litres of Cl₂ gas at STP is

Solution:

QUESTION: 112

Lead sulphate is souble in

Solution:

QUESTION: 113

Among the trihalides of nitrogen which one is most basic?

Solution:

QUESTION: 114

HNO₂ acts as an/a

Solution:

QUESTION: 115

The interionic distance for cesium chloride cystal will be

Solution:

QUESTION: 116

Oxidation state of Fe in Fe₃O₄ is

Solution:

QUESTION: 117

Alkane, C_{5}H_{12}, in which all H-atoms are equivalent is:

Solution:

QUESTION: 118

The first element in the 3d-transition series is

Solution:

QUESTION: 119

Elements which generally exhibit mutiple oxidation states and whose ions are usually coloured are

Solution:

QUESTION: 120

Collodial solution of silver is prepared by

Solution:

QUESTION: 121

Find the antonym of ALIENATE

Solution:

QUESTION: 122

Fill in the blank with appropriate word.

To nobody else did the story seem..........

Solution:

QUESTION: 123

Find the synonym of RUPTURE

Solution:

QUESTION: 124

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

The old man CUT TO THE QUICK when his rich son refused to recognise him.

Solution:

QUESTION: 125

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

Despite his old age, his movements were as spirited as A YOUNG MAN

Solution:

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