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# VITEEE PCME Mock Test - 6

## 125 Questions MCQ Test VITEEE: Subject Wise and Full Length MOCK Tests | VITEEE PCME Mock Test - 6

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This mock test of VITEEE PCME Mock Test - 6 for JEE helps you for every JEE entrance exam. This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 6 (mcq) to study with solutions a complete question bank. The solved questions answers in this VITEEE PCME Mock Test - 6 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this VITEEE PCME Mock Test - 6 exercise for a better result in the exam. You can find other VITEEE PCME Mock Test - 6 extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

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QUESTION: 2

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QUESTION: 3

### The area bounded by the parabola x = 4 − y2 and the y-axis, in square units is

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QUESTION: 4

The value of (1 + ω2+2ω)3n - (1+ω+2ω2)3n is

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QUESTION: 5

The area bounded by the curve y=xsinx and x-axis between x=0 and x=2π is

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QUESTION: 6

for x ≠ 1 and if f is continuous at x = 1 then f(1) =

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QUESTION: 7

If x dy = y(dx + y dy), y > 0 and y (1) = 1, then y (-3) is equal to

Solution:
QUESTION: 8

The solution of the differential equation 2xy(dy/dx) = x2+3y2 is (where c is a constant)

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QUESTION: 9

The solution of the equation (1+x2)(1+y)dy+(1+x)(1+y2)dx=0 is

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QUESTION: 10

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QUESTION: 11

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QUESTION: 12

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QUESTION: 13

Integrating factor of dy/dx + y/x = x3-3 is

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QUESTION: 14

If y = sin-1 [(1 - x2)/(1 + x2)], then (dy/dx) =

Solution:
QUESTION: 15

f : R → R is a function defined by f(x)   = 10 x − 7. If g = f -1 then g(x) =

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QUESTION: 16

If ∫[(1)/(1+sinx)] dx = tan((x/2)+(a)) + b, then

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QUESTION: 17

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QUESTION: 18

If tan-1x - tan-1y = tan-1A, then A=

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QUESTION: 19

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QUESTION: 20

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QUESTION: 21

∼ [ p ↔ q ] is

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QUESTION: 22

The inverse of

Solution:
QUESTION: 23

Which of the following statement is false?

Solution:

The determinant of skew-symmetric matrix of odd order is always zero
Therefore the inverse of skew-symmetric matrix does not exist

QUESTION: 24

How many numbers between 3000 and 4000 divisible by 5 can be formed from the digits 3,4,5,6,7,8 if repetition of any digit is not allowed?

Solution:
QUESTION: 25

A card is drawn at random from a well shuffled pack of 52 cards. The probability of getting a heart or diamond is

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QUESTION: 26

Each coefficients in the equation ax2+bx+c=0 is determined by throwing an ordinary die. The probability that the equation will have equal roots is

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QUESTION: 27

Two persons A and B takes turn in throwing a pair of dice. The first person to through 9 from both dice will be avoided the prize. If A throws first, then the probability that B wins the game is

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QUESTION: 28

If the side of a triangle are 13, 14, 15, then the radius of the incircle is

Solution:
QUESTION: 29

The number of terms of the A.P. 3, 7, 11, 15,...to be taken so that the sum is 406 is

Solution:
QUESTION: 30

The Quartile Deviation of the daily wages (in Rs) of 7 persons given below :
12, 7, 15, 10, 17, 19, 25 is

Solution:
QUESTION: 31

If the roots of 5x2 + 13x + k = 0 are reciprocal of each other, then the value of k is____

Solution:

QUESTION: 32

The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be

Solution:

If each item of a data is increased (or decreased) by the same quantity, the standard deviation (and the variance) is not changed.

QUESTION: 33

If α,β are the roots of the equation x- 2x + 4 = 0 then α+ β5=

Solution:
QUESTION: 34

If a line makes angles α,β,γ with the +ve direction of x,y and z axis respectively, then cos2α + cos2β + cos2γ

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QUESTION: 35

The line (x - 2)/3 = (y - 3)/4 = (z - 4)/5 is parallel to the plane

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QUESTION: 36

If √3 cos θ − sin θ = 1 then θ =

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QUESTION: 37

The pair of lines represented by 3ax2+ 5xy + (a2 - 2) y= 0 and at right angles to each other for

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QUESTION: 38

A force  acts at a point A whose position vector is . If point of application of F moves from A to the point B with position vector , then work done by F is

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QUESTION: 39

If P is any point on the hyperbola [(x - 1)2/9 - (y + 1)2/16] = 1 and S1, S2 are its foci, then |s1 P - S2 P |

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QUESTION: 40

If a = i + 2 j + 3k, b = - i + 2 j + k and c = 3 i + j and a + tb is perpendicular to c, the value of t is

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QUESTION: 41
The armature of D.C. motor has 20 Ω resistance. It draws current of 1.5 ampere when run by 220 volts D.C. supply. The value of back e.m.f. induced in it will be
Solution:
QUESTION: 42

If two atoms have their atomic numbers as z1 and z2 , the ratio of the wavelengths λ1 and λ2  corresponding to their Kα lines is

Solution:
QUESTION: 43

The de-Broglie wavelength of a particle moving with a velocity 2.25 x 108  m s-1  is equal to the wavelength of a photon. The ratio of kinetic energy of the particle to the energy of the photon is [ velocity of light = 3 x 108  m s-1]

Solution:

From Compton effect
λ = h/p = c/v [From de-Broglie wavelength]
c p = h v

QUESTION: 44
Increasing the charge on the plates of a capacitor means
Solution: C is fixed for a given capacitor.
Charge Q increases the potential V as V = Q/C
QUESTION: 45
In electrolysis, the amount of mass deposited or liberated at an electrode is directly propotional to
Solution:
QUESTION: 46
Consider telecommunication through optical fibres. Which of the following statements is not correct
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QUESTION: 47
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: 48
Two wires of the same metal have same length, but their cross-sectional areas are in the ratio 3 : 1. If resistance of the thicker wire is 10 Ω, then total resistance of the wires in series combination will be
Solution:
QUESTION: 49
Potential difference across the terminals of a battery is 50 V, when 11 A current is drawn. And it is 60 V, when 1 A current is drawn. The e.m.f. and internal resistance of battery is
Solution: e = v + Ir
e = emf
V = potential difference
r = internal resistance
Here e = 50 + 11r .....(1)
and e = 60 + 1r .....(2)
Solving these equations (1) and (2) for e and r we get
e = 61V and r = 1 Ω
QUESTION: 50
A cell of internal resistance 3 ohm and emf 10 volt is connected to a uniform wire of length 500 cm and resistance 3 ohm. The potential gradient in the wire is
Solution:
QUESTION: 51

An electron having charge e and mass m is moving in a uniform electric field E. Its acceleration will be

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QUESTION: 52
A transformer is employed to
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QUESTION: 53

A rectangular, a square, a circular and an elliptical loop, all in the (x - y) plane, are moving out of a uniform magnetic field with a constant velocity, V = vî . The magnetic field is directed along the negative z axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for:

Solution:
QUESTION: 54
Two coils have mutual inductance of 1.5 H. If current in primary circuit is raised to 5 A in one millisecond after closing the circuit, then e.m.f. induced in the secondary circuit is
Solution:
QUESTION: 55
Which one of the following electromagnetic radiations have the smallest wavelength?
Solution:
QUESTION: 56
If the electric flux entering and leaving an enclosed surface respectively is φ₁ and φ₂, the electric charge inside the surface will be
Solution:
QUESTION: 57

Two equal print charges are fixed at x = -a and x = +a on the X axis. Another point charge Q is placed at the origin. The change in electrical potential energy of Q, when it is displaced by a small distance x along the X-axis is approximately proportional to

Solution:
QUESTION: 58
A hollow metal sphere of radious 10 cm is charged such that the potential on its surface is 80V. The potential at the centre of the sphere is
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QUESTION: 59
Figure shows a solid hemisphere with a charge of 5nC distributed uniformly through its volume. The hemisphere lies on a plane and point P is located on the plane, along a radial line from the centre of curvature at distance 15cm. The electric potential at point P due to the hemisphere is:
Solution:
QUESTION: 60
When a body is connected to the earth, then electron from the earth, flow into the body. It means that the body is
Solution:
QUESTION: 61

Two point charges each equal to 2μC are 0.5 m apart. If both of them exist inside vaccum, then electrostatic force between them is

Solution:

QUESTION: 62
A galvanometer of resistance 20 Ω is to be converted into an ammeter of range 1 ampere. If a current of 1 mA produces full scale deflection, the shunt required for the purpose is
Solution:
QUESTION: 63
Among electron, proton, neutron and $\alpha$ - particle the maximum penetration capacity is for
Solution:
QUESTION: 64
Which is not electromagnetic wave in the following?
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QUESTION: 65

The size of the nucleus varies as ----- power of the atomic number

Solution:
QUESTION: 66
The work function of oxide coated tungsten emitter will be
Solution:
QUESTION: 67
The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately
Solution:
QUESTION: 68
A palne mirror produces a magnification of
Solution:
QUESTION: 69
A convex lens will become less convergent in
Solution:
QUESTION: 70
In a transistor, the emitter-base junction and the collector-base junction are
Solution:
QUESTION: 71
For a transistor amplifier, the voltage gain
Solution:
QUESTION: 72
When a p - n junction diode is reverse biased, the thickness of the depletion layer
Solution:
QUESTION: 73
A P-type semiconductor can be obtained by adding
Solution:
QUESTION: 74
The forbidden gap in the energy bands of germanium at room temperature is about
Solution:
QUESTION: 75
P-N junction diode can be used as
Solution:
QUESTION: 76
In a semiconductor crystal if current flows due to breakage of crystal bonds, then the semiconductor is called
Solution:
QUESTION: 77
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: 78
Huygen's wave theory of light can not explain
Solution:
QUESTION: 79

If the two slits in Young's experiment have width ratio 1:4, the ratio of intensity at maxima and minima in the interference pattern in

Solution:

QUESTION: 80
When exposed to sunlight, thin films of oil on water often exhibit brilliant colours due to the phenomenon of
Solution:
QUESTION: 81

When ethanol is refluxed with conc. sulphuric acid at 160o it gives

Solution:
QUESTION: 82

Which of the following gives iodoform on heating with a solution of l2 containing Na2CO3 ?

Solution:
QUESTION: 83

Trioxane is trimer of

Solution:
QUESTION: 84

How many monochlorobutanes will be obtained on chlorination of n-butane?

Solution:

QUESTION: 85

Which of the following reactions can be used for the synthesis of an alkene

Solution:
QUESTION: 86

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

Solution:
QUESTION: 87

The reaction in which sodium cyanide is used is

Solution:
QUESTION: 88

One mole of CO₂ contains

Solution:
QUESTION: 89

The protein which maintains blood sugar level is

Solution:
QUESTION: 90

Acetamide and NaOBr/OH⁻ produce

Solution:
QUESTION: 91

Which one of the following proteins transports oxygen in the blood stream?

Solution:
QUESTION: 92

In a reaction involving ring substitution of C6H5Y, the major product is meta isomer. The group Y can be

Solution:

Electron withdrawing groups favour meta substitution
- COOH group is metadirecting group

QUESTION: 93

The end product of protein digestion is

Solution:
QUESTION: 94

The equilibrium constant in a reversible chemical reaction at a given temperature

Solution:
QUESTION: 95

C + O2 → CO2 , Δ H = − 94 K cals ,
CO + 1/2O2 → CO2 , Δ H = − 67.7 K . cal.

On the basis of above data, the heat of formation of CO is

Solution:
QUESTION: 96

Formic acid when treated with H₂SO₄ gives

Solution:
QUESTION: 97

For the melting of a solid at 250C, the fusion process requires energy equivalent to 2906 Joules to be added to system considering the process to be reversible at fusion point, the entropy change of the process is

Solution:
QUESTION: 98

Heat of combustion of carbon is 96k cal mol-1. When some quantity of carbon is burnt in oxygen, 48 k cal of heat is liberated. What is the volume (in lit) of oxygen at STP reacted with this carbon?

Solution:

∵ 96 k cal heat is produced by 1 mol of carbon.
∴ 48 k cal heat is produced by 0.5 mol of carbon.
As 1 mol carbon reacts with 1 mol of oxygen, which has 22.4 litre volume at NTP.
∴ The volume of O2 at NTP reacts with 0.5 mol carbon = 22.4/2 = 11.2 litre.

QUESTION: 99

The rate, at which a substance reacts at constant temperature, depends upon its

Solution:
QUESTION: 100

One of the oxidants used with liquid propellants is

Solution:
QUESTION: 101

Which one of the following is an example of octahedral complex?

Solution:
QUESTION: 102

Name of the following compound is

Solution:
QUESTION: 103

Which one of the following will not show geometrical isomerism?

Solution:
QUESTION: 104

Dye test can be used to distinguish between

Solution:
QUESTION: 105

Hydrolysis of benzonitrile gives

Solution:
QUESTION: 106

Out of Cu, Ag, Fe and Zn, the metal which can displace all others from their salt solutions is

Solution:
QUESTION: 107

The electrode potentials of half-cell reactions are: Zn → Zn2+ + 2e⁻ ; E = -0.76 V and Fe → Fe2+ + 2e⁻ ; E=0.41 V. The e.m.f. of the cell Fe2+ + Zn → Zn2+ + Fe is

Solution:
QUESTION: 108

Molten CuCl2 is electrolysed using platinum electrodes. The reaction occuring at anode is .......

Solution:
QUESTION: 109

Absolute ethyl alcohol can be converted to diethyl ether by heating it to 410 K in the presence of

Solution:
QUESTION: 110

The most electropositive metals are isolated from their ores by

Solution:
QUESTION: 111

50 mL of hydrogen diffuses out through a small hole of a vessel, in 20 minutes. The time taken by 40 mL of oxygen to diffuse out is

Solution:
QUESTION: 112

Solution:
QUESTION: 113

Orthophosphoric acid is

Solution:
QUESTION: 114

The basicity of phosphorous acid is

Solution:
QUESTION: 115

A crystal lattice with alternate positive and negative ions has radius ratio 0.524. Its coordination number is

Solution:

Radius ratio of the given crystal lattice is in the range of 0.414 - 0.732. So the coordination number is 6.

QUESTION: 116

Zn2+(aq) + 2e- → Zn(s). This is

Solution:
QUESTION: 117

In the following structure

Solution:
QUESTION: 118

One of the following is false for Hg ?

Solution:
QUESTION: 119

A colloidal system in which gas bubbles are dispersed in liquid is known as

Solution:
QUESTION: 120

Bell metal is an alloy of

Solution:
QUESTION: 121

Fill in the blank with appropriate word.
I am given to.......that you are going abroad.

Solution:
QUESTION: 122

Find the Antonym of SUAVITY

Solution:
QUESTION: 123

find the synonym of OSTENTATION

Solution:
QUESTION: 124

Choose the alternative which best expresses the meaning of the idiom/phrase.

Bring forth

Solution:
QUESTION: 125

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

ANY ABLE BODIED MAN eligible for the job.

Solution: