VITEEE PCME Mock Test - 9


125 Questions MCQ Test VITEEE: Subject Wise and Full Length MOCK Tests | VITEEE PCME Mock Test - 9


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This mock test of VITEEE PCME Mock Test - 9 for JEE helps you for every JEE entrance exam. This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 9 (mcq) to study with solutions a complete question bank. The solved questions answers in this VITEEE PCME Mock Test - 9 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this VITEEE PCME Mock Test - 9 exercise for a better result in the exam. You can find other VITEEE PCME Mock Test - 9 extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

For all real x, the minimum value of 1 - x + x2/1 + x + x2 is

Solution:
QUESTION: 2

AOB is the positive quadrant of the ellipse x2/a2 + y2/b2 = 1, where OA = a, OB = b. The area between the arc AB and the chord AB of the ellipse is

Solution:

 

Required area

QUESTION: 3

If |z| = 4 and arg z = (5π/6), then the value of z is

Solution:
QUESTION: 4

If z₁ and z₂ are two non-zero complex numberssuch that |z₁ + z₂| =|z₁| + |z₂|,then arg z₁ -arg z₂ is equal to

Solution:
QUESTION: 5

Solution:
QUESTION: 6

Solution:
QUESTION: 7

where [x] denotes the greatest integer less than or equal to x, is continuous at x = 2, then the value of a is equal to

Solution:
QUESTION: 8

Solution:
QUESTION: 9

The differential equation representing the family of curves y= 2c(x+√c), where c is a positive perimeter, is of

Solution:
QUESTION: 10

The differential equation | dy/dx | + | y | + 3 = 0 admits

Solution:
QUESTION: 11

Solution:

QUESTION: 12

Find the degree of (y2)2  − √ y1  = y3

Solution:
QUESTION: 13

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

Solution:
QUESTION: 14

If the function f(x) = cos2 x + cos2(π/3 + x) - cos x.cos(π/3 + x) is constant, then the value of this constant is

Solution:
QUESTION: 15

( d/dx )(x2 + cos x)4 =

Solution:

d/dx(x2 + cos x)4

= 4.(x2 + cos x)3 x d/dx (x2 + cos x)
= 4(x2 + cos x)3 x (2x - sin x)

QUESTION: 16

Solution:
QUESTION: 17

∫[sin(logx) + cos(logx)] dx =

Solution:
QUESTION: 18

The domain of sin-1 x is

Solution:
QUESTION: 19

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

Solution:
QUESTION: 20

Which of the following is the converse of the statement: "If x > 4, then x + 2 > 5"?

Solution:

To form the CONVERSE of a statement, the "If" and the "then" sections of the statement switch places.

QUESTION: 21

The value of lim 

Solution:

QUESTION: 22

If A and B are two matrices such that AB = B and BA = A, then A2+ B2 =

Solution:
QUESTION: 23

In how many ways can 5 prizes be given to 4 students if any student can receive more than one prize?

Solution:

Required ways = 4 x 4 x 4 x 4 x 4 = 45

QUESTION: 24

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: 25

If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectively

Solution:
QUESTION: 26

From a well shuffled pack of playing cards, two cards drawn one by one with replacement. The probability that both are aces is

Solution:

For the first card drawn , probability of ace is 4/52 .
Then for the second card, after the first ace is drawn, there are only 3 aces left out of 51 cards,
So probability is 3/51 .
The probability of performing two independent activities such as this is actually the product of the probabilities:
( 4/52 ) x ( 3/51 ).
This reduces to ( 1/13 ) x ( 1/17 ) = 1 221

QUESTION: 27

In shuffling a pack of cards 3 are accedentally dropped, then the chance that missing card should be of different suit is

Solution:

We have to find out the probability of 3 cards of different suits out of four suits
The ways of choosing three suits out of four = 4C3
Since, each suit has 13 cards, the ways of choosing 1 card = 13C1 = 13

QUESTION: 28

If b,c and sinB are given such that ∠B is acute and b<c sinB, then

Solution:

When two sides and angle opposite to one of then be given. In this case, the triangle is not always uniquely determined. It is quite possible to have no triangle, one triangle and two triangles with this type of data.
So, it is called an ambiguous case.
Let b, c and B are given parts.
When B is acute and b < c sin B, then there is no triangle
By Cosine Law
b2 = c2 + a2 - 2ac cos B
⇒ a2 - 2ac cos B = b2 - c2
⇒ a2 - 2ac cos B + c2 cos2 B
= b2 - c2 + c2 cos2 B
⇒ (a - c cos B)2 = b2 - c2 (1 - cos2 B)
= b2 - c2 sin2 B


This equation helps us to determine a, when b, c and B are being given. We observe that:
When b < c sin B, then a is imaginary and so there is no 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 mean of 5 observations is 4.4 and their variance is 8.24. If three observations are 1, 2 and 6, the other two observations are

Solution:
QUESTION: 31

The mode of the following items is 0,1,6,7,2,3,7,6,6,2,6,0,5,6,0, is

Solution:
QUESTION: 32

p and q are the roots of x2 + ax + b = 0, then equation whose roots are p2q, q2p is

Solution:

p + q = - a, p.q = b
Now, p2 q + q2 p = pq(p + q)
= b(-a) = - ab
p2q . q2p = (pq)3 = b3
The required equation is
x2 - (p2q + q2p) x+ (p2q . q2p) = 0
x2 + abx + b3 = 0

QUESTION: 33

If the roots of the equation x2+2mx+m2-2m+6=0 are equal, then the value of m is

Solution:
QUESTION: 34

The locus of x2+y2+z=0 is

Solution:
QUESTION: 35

The angle between the lines 2x=3y=-z and 6x=-y=-4z, is

Solution:
QUESTION: 36

The equation sinx+cosx=2 has

Solution:
QUESTION: 37

If the pair of lines ax2+ 2hxy + by2 + 2gx + 2fy + c = 0 intersect on the y-axis then

Solution:
QUESTION: 38

If |a|=3, |b|=4, |c|=5 and a+b+c=0, the angle between a and b is

Solution:
QUESTION: 39

 

is equal to

Solution:
QUESTION: 40

The point on the axis of y which is equidistant from (-1, 2) and (3, 4) is

Solution:
QUESTION: 41
The ratio of secondary to the primary turns in a transformer is 3:2. If the power output be P, then the input power neglecting all loses must be equal to
Solution:
QUESTION: 42
In photoelectric effect, the photoelectric current
Solution: Higher photocurrent implies, higher no. of electrons emitted/sec which in turn implies higher no. of photons incident per sec per unit area of higher intensity.
Moreover by increasing frequency, energy of incident photon gets changed but not their number
QUESTION: 43
The penetrating power of X - rays increases with the
Solution:
QUESTION: 44

A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitors becomes

Solution:

On removing the oil, the capacitance of the capacitor will become.
C ′ = C/K = C/2

QUESTION: 45

A steady current of 1.5 A flows through a copper voltameter for 10 min. If the electrochemical equivalent of copper is 30 x 10-5  g C-1 , the mass of copper deposited on the electrode will be

Solution:
QUESTION: 46
A laser beam is used for carrying out surgery because it
Solution: As the laser beam is highly monochromatic, directional and coherent, it can be sharply focussed.
Therefore it is used for carrying out surgery
QUESTION: 47
Two wires of same metal have the same length but their cross-sections are in the ratio 3:1. They are joined in series. The resistance of the thicker wire is 10 Ω. The total resistance of the combination will be
Solution:
QUESTION: 48
A galvanometer can be used as a voltmeter by connecting a
Solution:
QUESTION: 49
In a potentiometer experiment, two primary cells are connected in series to support each other and then connected to oppose each other. The balance point are obtained at 4 m and 1 m respectively. The ratio of electromotive forces of the two cells is
Solution:
QUESTION: 50
The resistance of a 10 m long wire is 10 Ω. Its length is increased by 25% by stretching the wire uniformly. The resistance of wire will change to (approximately)
Solution:
QUESTION: 51

The core of a transformer is laminated so that

Solution:
QUESTION: 52
A particle which has zero rest mass and non-zero energy and momentum must travel with a speed
Solution:
QUESTION: 53

The coefficient of mutual inductance, when magnetic flux changes by 2 X 10-2 Wb and current changes by 0.01 A is

Solution:
QUESTION: 54
The energy stored in a 50 mH inductor carrying a current of 4 A will be
Solution:
QUESTION: 55
Maxwell in his famous equation of electromagnetism introduced the concept of
Solution:
QUESTION: 56
A point charge q is placed at a distance a/2 directly above the centre of a square of side a. The electric flux through the square assuming it to be one face of the cube is
Solution:
QUESTION: 57
A charge of 5 C is given a displacement of 0.5 m. The work done in the process is 10 J. The potential difference between the two points will be
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
A capacitor of 10 μF charged up to 250 volts is connected in parallel with another capacitor of 5 μF charged up to 100 volts. The common potential is
Solution:
QUESTION: 60

If an unchanged capacitor is charged by connecting it to a battery, then the amount of energy lost as heat is

Solution:
QUESTION: 61

A charged particle of mass 5 x 10-6  Kg is held stationary in space by placing it in an electric field of strength 106 N C-1 directed vertically downwards. The charge on the particle is g = 10 m s-2

Solution:
QUESTION: 62

A cyclotron oscillator frequency is 10 MHz. If radius of its dees 60 cm, then magnetic field for accelerating the protons is (Given e = 1.6 x 10-19C, mp = 1.67 x 10-27 kg)

Solution:

v = 10 MHz = 10 x 106 Hz = 107 Hz
R = rm = 60 cm = 0.6 m
e = 1.6 x 10-19 C
m = 1.67 x 10-27 kg
resonance v = Be/2πm
or B = 2πmv/e

QUESTION: 63
Which shows radioactivity?
Solution:
QUESTION: 64
The nucleus of 56Ba141 contains ---- neutrons
Solution:
QUESTION: 65
Sodium surface is subjected to ultraviolet and infrared radiations separately and the stopping potential of photoelectrons determined. Then the stopping potential is
Solution:
QUESTION: 66
Which is not electromagnetic wave in the following?
Solution:
QUESTION: 67
Which of the following is not dependent on the intensity of incident radiation in a photoelectric experiment ?
Solution:
QUESTION: 68
A glass slab is placed in the path of convergent light. The point of convergence of light
Solution:
QUESTION: 69

A ray of light is incident at 60o on a prism of refracting angle 30o . The emergent ray is at an angle 30o with the incident ray. The value of refractive index of the prism is

Solution:

Angle of prism = 30o = A
Angle of incidence = i1 = 60o
Angle of emergence = i2 = ?
Angle of devation = D = 30o
∴ i2 = A + D - i2 = 30 + 30 - 60 = 0o
⇒ r2 = 0o
∴ r1 = A-r2 = 30 - 0 = 30o
∴ μ = sin i 1 sin r 1 = sin 60o /sin 30o = √ 3

QUESTION: 70
The current gain for a transistor working as common-base amplifier is 0.96. If the emitter current is 7.2 mA, then the base current is
Solution:
QUESTION: 71
A rectifier converts
Solution:
QUESTION: 72
If a half wave rectifier is used to convert 50HZ a.c into d.c number of pulses present in the rectified output voltage is
Solution:
QUESTION: 73
Bonding in a germanium crystal (semiconductor) is
Solution:
QUESTION: 74
Depletion layer consists of
Solution:
QUESTION: 75
In an insulator, the forbidden energy gap between the valence band and conduction band is of the order of
Solution:
QUESTION: 76
GaAs is
Solution:
QUESTION: 77
When two coherent monochromatic light beams of intensities I and 4I are superimposed, the ratio between maximum and minimum intensities in the resultant beam is
Solution:
QUESTION: 78
If wavelength of a photon is 6000 Å, then energy of this photon will be
Solution:
QUESTION: 79

A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence is

Solution:
QUESTION: 80

For diffraction of light, the condition for nth secondary minimum is that path difference is equal to [Here a is the width of slit, n is the order of diffraction, λ is the wavelength of light and θ n gives the direction of nth secondary minimum ]

Solution:
QUESTION: 81

Mild oxidation of glycerol with H₂O₂/FeSO₄ gives

Solution:
QUESTION: 82

A compound A has a molecular formula C₂Cl₃OH. It reduces Fehling solution and on oxidation produces a monocarboxylic acid B. A can also be obtained by the action of Cl₂ on Ethanol. A is

Solution:
QUESTION: 83

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

Solution:
QUESTION: 84

Propyne on hydrolysis in presence of HCl and HgSO₄ gives

Solution:
QUESTION: 85

Pentene-1 with HCl gives

Solution:
QUESTION: 86

An alkane C7H16 is produced by the reaction of Lithium di (3-pentyl) cuperate with ethyl bromide. The structural formula of product is

Solution:

QUESTION: 87

The ratio of the molar amounts of H₂S needed to precipitate the metal ions from 20 mL each of 1M Cd(NO₃)₂ and 0.5 M CuSO₄ is

Solution:

As Cd2+ and Cu2+, both are dipositive ions but Cu2+ has one half of the concentration compared to that of the Cd2+. Thus, the molar amount of the H2S used to precipitate the metals ions Cd2+ and Cu2+ is 2 : 1.

QUESTION: 88

Point out the incorrect statement about resonance?

Solution:
QUESTION: 89

Enzyme trypsin converts

Solution:
QUESTION: 90

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

Solution:
QUESTION: 91

Glucose reacts with acetic anhydride to form

Solution:
QUESTION: 92

When propanamide reacts with Br₂ and NaOH then which of the following compounds is formed ?

Solution:
QUESTION: 93

Which amino acid has no assymmetric carbon atom?

Solution:
QUESTION: 94

In the above reaction , product P is

Solution:
QUESTION: 95

A reaction reaches a state of chemical equilibrium only when

Solution:
QUESTION: 96

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

Solution:
QUESTION: 97

The enthalpy change of a reaction does not depend on

Solution:
QUESTION: 98

In an endothermic reaction, the value of ∆H is

Solution:
QUESTION: 99

The minimum energy required by molecules to react is called

Solution:
QUESTION: 100

The synthetic product which closely resembles with the natural musk in odour is

Solution:
QUESTION: 101

The colour of p-aminoazobenzene is

Solution:
QUESTION: 102

Caranalite is a

Solution:
QUESTION: 103

The effective atomic number of Cr (at. no. 24) in [(Cr(NH₃)₆] Cl₃ is

Solution:
QUESTION: 104

When dilute H2SO4 is electrolysed at room temperature between Pt electrodes. The substance liberated at anode is

Solution:
QUESTION: 105

Structural formula of ethanenitrile is

Solution:
QUESTION: 106

Which of the following will exhibits geometrical isomerism ?

Solution:
QUESTION: 107

How many litres of O₂ at STP are needed to complete the combustion of 39 g of liquid benzene as per equation given below ?
2C₆H₆(l) + 15O₂(g) →12CO₂(g) + 6H₂O(g)

Solution:
QUESTION: 108

Galena is an ore of

Solution:
QUESTION: 109

tert-Butyl methyl ether on heating with HI of one molar concentration gives

Solution:
QUESTION: 110

The correct order of the mobility of the alkali metal ions in aqueous solution is

Solution:
QUESTION: 111

At cathode, the electrolysis of aqueous Na₂SO₄ gives

Solution:
QUESTION: 112

The standard E0red. values of A,B,C are 0.68V,- 2.54 V,-0.50V respectively.The order of their reducing power is

Solution:
QUESTION: 113

C4H4O4 can be:

Solution:
QUESTION: 114

Crystals of covalent compounds always have

Solution:
QUESTION: 115

If molecular weight of KMnO₄ is M, then its equivalent weight in acidic medium would be

Solution:
QUESTION: 116

P4O10 has short and long P-O bonds. The number of short P-O bonds in this compound is

Solution:

P4O10 has four P = O bonds which are shorter than P-O single bonds.
Each P atom has three P-O single bonds and one P = O bond, i.e.,
a total of four P-O linkages

QUESTION: 117

In chemical reaction, catalyst:

Solution:
QUESTION: 118

Which of the following oxides of Nitrogen is anhydride of HNO3

Solution:
QUESTION: 119

Which of the following is a non-transition element?

Solution:
QUESTION: 120

When KI and CuSO₄ solutions are mixed, it gives

Solution:
QUESTION: 121

Find the Antonym of NADIR

Solution:
QUESTION: 122

Fill in the blank with appropriate word.
Manuring in agricultural fields increases........

Solution:
QUESTION: 123

Find the Syonym of ACCENTUATED

Solution:
QUESTION: 124

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

Being an introvert, he will eat his HEART OUT.

Solution:
QUESTION: 125

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

No one could explain how a calm and balanced person like him could PENETRATE such a mindless act on his friends.

Solution:

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