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VITEEE PCME Mock Test - 9


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

VITEEE PCME Mock Test - 9 for JEE 2023 is part of VITEEE: Subject Wise and Full Length MOCK Tests preparation. The VITEEE PCME Mock Test - 9 questions and answers have been prepared according to the JEE exam syllabus.The VITEEE PCME Mock Test - 9 MCQs are made for JEE 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for VITEEE PCME Mock Test - 9 below.
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VITEEE PCME Mock Test - 9 - Question 1

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

VITEEE PCME Mock Test - 9 - 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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 2

 

Required area

VITEEE PCME Mock Test - 9 - Question 3

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

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - Question 5

VITEEE PCME Mock Test - 9 - Question 6

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - Question 8

VITEEE PCME Mock Test - 9 - Question 9

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

VITEEE PCME Mock Test - 9 - Question 10

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

VITEEE PCME Mock Test - 9 - Question 11

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 11

VITEEE PCME Mock Test - 9 - Question 12

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

VITEEE PCME Mock Test - 9 - Question 13

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

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - Question 15

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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 15

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)

VITEEE PCME Mock Test - 9 - Question 16

VITEEE PCME Mock Test - 9 - Question 17

∫[sin(logx) + cos(logx)] dx =

VITEEE PCME Mock Test - 9 - Question 18

The domain of sin-1 x is

VITEEE PCME Mock Test - 9 - Question 19

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

VITEEE PCME Mock Test - 9 - Question 20

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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 20

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

VITEEE PCME Mock Test - 9 - Question 21

The value of lim 

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 21

VITEEE PCME Mock Test - 9 - Question 22

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

VITEEE PCME Mock Test - 9 - Question 23

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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 23

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

VITEEE PCME Mock Test - 9 - Question 24

Which of the following statement is false?

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 24

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

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - 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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 26

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

VITEEE PCME Mock Test - 9 - Question 27

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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 27

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

VITEEE PCME Mock Test - 9 - Question 28

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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 28

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.

VITEEE PCME Mock Test - 9 - Question 29

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

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - Question 32

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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 32

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

VITEEE PCME Mock Test - 9 - Question 33

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

VITEEE PCME Mock Test - 9 - Question 34

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

VITEEE PCME Mock Test - 9 - Question 35

The locus of x2+y2+z=0 is

VITEEE PCME Mock Test - 9 - Question 36

The equation sinx+cosx=2 has

VITEEE PCME Mock Test - 9 - Question 37

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

VITEEE PCME Mock Test - 9 - Question 38

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

VITEEE PCME Mock Test - 9 - Question 39

 

is equal to

VITEEE PCME Mock Test - 9 - Question 40

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

VITEEE PCME Mock Test - 9 - 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
VITEEE PCME Mock Test - 9 - Question 42
In photoelectric effect, the photoelectric current
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 42 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
VITEEE PCME Mock Test - 9 - Question 43
The penetrating power of X - rays increases with the
VITEEE PCME Mock Test - 9 - 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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 44

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

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - Question 46
A laser beam is used for carrying out surgery because it
Detailed Solution for VITEEE PCME Mock Test - 9 - Question 46 As the laser beam is highly monochromatic, directional and coherent, it can be sharply focussed.
Therefore it is used for carrying out surgery
VITEEE PCME Mock Test - 9 - 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
VITEEE PCME Mock Test - 9 - Question 48
A galvanometer can be used as a voltmeter by connecting a
VITEEE PCME Mock Test - 9 - 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
VITEEE PCME Mock Test - 9 - 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)
VITEEE PCME Mock Test - 9 - Question 51

The core of a transformer is laminated so that

VITEEE PCME Mock Test - 9 - Question 52
A particle which has zero rest mass and non-zero energy and momentum must travel with a speed
VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - Question 54
The energy stored in a 50 mH inductor carrying a current of 4 A will be
VITEEE PCME Mock Test - 9 - Question 55
Maxwell in his famous equation of electromagnetism introduced the concept of
VITEEE PCME Mock Test - 9 - 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
VITEEE PCME Mock Test - 9 - 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
VITEEE PCME Mock Test - 9 - 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 - 9 - 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
VITEEE PCME Mock Test - 9 - Question 60

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

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - 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)

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 62

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

VITEEE PCME Mock Test - 9 - Question 63
Which shows radioactivity?
VITEEE PCME Mock Test - 9 - Question 64
The nucleus of 56Ba141 contains ---- neutrons
VITEEE PCME Mock Test - 9 - Question 65
Sodium surface is subjected to ultraviolet and infrared radiations separately and the stopping potential of photoelectrons determined. Then the stopping potential is
VITEEE PCME Mock Test - 9 - Question 66
Which is not electromagnetic wave in the following?
VITEEE PCME Mock Test - 9 - Question 67
Which of the following is not dependent on the intensity of incident radiation in a photoelectric experiment ?
VITEEE PCME Mock Test - 9 - Question 68
A glass slab is placed in the path of convergent light. The point of convergence of light
VITEEE PCME Mock Test - 9 - 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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 69

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

VITEEE PCME Mock Test - 9 - 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
VITEEE PCME Mock Test - 9 - Question 71
A rectifier converts
VITEEE PCME Mock Test - 9 - 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
VITEEE PCME Mock Test - 9 - Question 73
Bonding in a germanium crystal (semiconductor) is
VITEEE PCME Mock Test - 9 - Question 74
Depletion layer consists of
VITEEE PCME Mock Test - 9 - Question 75
In an insulator, the forbidden energy gap between the valence band and conduction band is of the order of
VITEEE PCME Mock Test - 9 - Question 76
GaAs is
VITEEE PCME Mock Test - 9 - 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
VITEEE PCME Mock Test - 9 - Question 78
If wavelength of a photon is 6000 Å, then energy of this photon will be
VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - 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 ]

VITEEE PCME Mock Test - 9 - Question 81

Mild oxidation of glycerol with H₂O₂/FeSO₄ gives

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - Question 83

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

VITEEE PCME Mock Test - 9 - Question 84

Propyne on hydrolysis in presence of HCl and HgSO₄ gives

VITEEE PCME Mock Test - 9 - Question 85

Pentene-1 with HCl gives

VITEEE PCME Mock Test - 9 - 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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 86

VITEEE PCME Mock Test - 9 - 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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 87

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.

VITEEE PCME Mock Test - 9 - Question 88

Point out the incorrect statement about resonance?

VITEEE PCME Mock Test - 9 - Question 89

Enzyme trypsin converts

VITEEE PCME Mock Test - 9 - Question 90

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

VITEEE PCME Mock Test - 9 - Question 91

Glucose reacts with acetic anhydride to form

VITEEE PCME Mock Test - 9 - Question 92

Which amino acid has no assymmetric carbon atom?

VITEEE PCME Mock Test - 9 - Question 93

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

VITEEE PCME Mock Test - 9 - Question 94

In the above reaction , product P is

VITEEE PCME Mock Test - 9 - Question 95

A reaction reaches a state of chemical equilibrium only when

VITEEE PCME Mock Test - 9 - Question 96

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

VITEEE PCME Mock Test - 9 - Question 97

The enthalpy change of a reaction does not depend on

VITEEE PCME Mock Test - 9 - Question 98

In an endothermic reaction, the value of ∆H is

VITEEE PCME Mock Test - 9 - Question 99

The minimum energy required by molecules to react is called

VITEEE PCME Mock Test - 9 - Question 100

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

VITEEE PCME Mock Test - 9 - Question 101

Caranalite is a

VITEEE PCME Mock Test - 9 - Question 102

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

VITEEE PCME Mock Test - 9 - Question 103

The colour of p-aminoazobenzene is

VITEEE PCME Mock Test - 9 - Question 104

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

VITEEE PCME Mock Test - 9 - Question 105

Which of the following will exhibits geometrical isomerism ?

VITEEE PCME Mock Test - 9 - Question 106

Structural formula of ethanenitrile is

VITEEE PCME Mock Test - 9 - 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)

VITEEE PCME Mock Test - 9 - Question 108

At cathode, the electrolysis of aqueous Na₂SO₄ gives

VITEEE PCME Mock Test - 9 - Question 109

Galena is an ore of

VITEEE PCME Mock Test - 9 - Question 110

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

VITEEE PCME Mock Test - 9 - Question 111

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

VITEEE PCME Mock Test - 9 - 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

VITEEE PCME Mock Test - 9 - Question 113

C4H4O4 can be:

VITEEE PCME Mock Test - 9 - Question 114

Crystals of covalent compounds always have

VITEEE PCME Mock Test - 9 - Question 115

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

VITEEE PCME Mock Test - 9 - Question 116

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

Detailed Solution for VITEEE PCME Mock Test - 9 - Question 116

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

VITEEE PCME Mock Test - 9 - Question 117

In chemical reaction, catalyst:

VITEEE PCME Mock Test - 9 - Question 118

Which of the following oxides of Nitrogen is anhydride of HNO3

VITEEE PCME Mock Test - 9 - Question 119

Which of the following is a non-transition element?

VITEEE PCME Mock Test - 9 - Question 120

When KI and CuSO₄ solutions are mixed, it gives

VITEEE PCME Mock Test - 9 - Question 121

Find the Antonym of NADIR

VITEEE PCME Mock Test - 9 - Question 122

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

VITEEE PCME Mock Test - 9 - Question 123

Find the Syonym of ACCENTUATED

VITEEE PCME Mock Test - 9 - 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.

VITEEE PCME Mock Test - 9 - 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.

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