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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.
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QUESTION: 1

The argument of complex number [(13-5i)/(4-9i)] is

Solution:

QUESTION: 2

Maximum slope of the curve y = -x^{3} + 3x^{2} + 9x − 27 is

Solution:

QUESTION: 3

The area bounded by the parabola x = 4 − y^{2} and the *y*-axis, in square units is

Solution:

QUESTION: 4

The value of (1 + ω^{2}+2ω)^{3n} - (1+ω+2ω^{2})^{3n} is

Solution:

QUESTION: 5

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

Solution:

QUESTION: 6

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

Solution:

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) = x^{2}+3y^{2} is (where c is a constant)

Solution:

QUESTION: 9

The solution of the equation (1+x^{2})(1+y)dy+(1+x)(1+y^{2})dx=0 is

Solution:

QUESTION: 10

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QUESTION: 11

Solution:

QUESTION: 12

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QUESTION: 13

Integrating factor of dy/dx + y/x = x^{3}-3 is

Solution:

QUESTION: 14

If y = sin^{-1} [(1 - x^{2})/(1 + x^{2})], 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) =

Solution:

QUESTION: 16

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

Solution:

QUESTION: 17

Solution:

QUESTION: 18

If tan^{-1}x - tan^{-1}y = tan^{-1}A, then A=

Solution:

QUESTION: 19

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QUESTION: 20

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QUESTION: 21

∼ [ p ↔ q ] is

Solution:

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

Solution:

QUESTION: 26

Each coefficients in the equation ax^{2}+bx+c=0 is determined by throwing an ordinary die. The probability that the equation will have equal roots is

Solution:

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

Solution:

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 5x^{2} + 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^{2 }- 2x + 4 = 0 then α^{5 }+ β^{5}=

Solution:

QUESTION: 34

If a line makes angles α,β,γ with the +ve direction of x,y and z axis respectively, then cos^{2}α + cos^{2}β + cos^{2}γ

Solution:

QUESTION: 35

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

Solution:

QUESTION: 36

If √3 cos θ − sin θ = 1 then θ =

Solution:

QUESTION: 37

The pair of lines represented by 3ax^{2}+ 5xy + (a^{2} - 2) y^{2 }= 0 and at right angles to each other for

Solution:

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

Solution:

QUESTION: 39

If P is any point on the hyperbola [(x - 1)^{2}/9 - (y + 1)^{2}/16] = 1 and S_{1}, S_{2} are its foci, then |s_{1} P - S_{2} P |

Solution:

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

Solution:

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 z_{1} and z_{2} , the ratio of the wavelengths λ_{1} and λ_{2} corresponding to their K_{α } lines is

Solution:

QUESTION: 43

The de-Broglie wavelength of a particle moving with a velocity 2.25 x 10^{8} 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 10^{8} 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

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

Solution:

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

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

Solution:

QUESTION: 52

A transformer is employed to

Solution:

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

Solution:

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?

Solution:

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 160^{o} it gives

Solution:

QUESTION: 82

Which of the following gives iodoform on heating with a solution of l_{2} containing Na_{2}CO_{3} ?

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 C_{6}H_{5}Y, 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 + O_{2} → CO_{2} , Δ H = − 94 K cals ,

CO + 1/2O_{2} → CO_{2} , 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 25^{0}C, 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 96*k cal mol ^{-1}*. When some quantity of carbon is burnt in oxygen, 48

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 O_{2} 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 → Zn^{2+} + 2e⁻ ; E = -0.76 V and Fe → Fe^{2+} + 2e⁻ ; E=0.41 V. The e.m.f. of the cell Fe^{2+} + Zn → Zn^{2+} + Fe is

Solution:

QUESTION: 108

Molten *CuCl*_{2} 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

White lead is

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

Zn^{2+}(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:

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