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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.
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QUESTION: 1

For all real x, the minimum value of 1 - x + x^{2}/1 + x + x^{2} is

Solution:

QUESTION: 2

AOB is the positive quadrant of the ellipse x^{2}/a^{2} + y^{2}/b^{2} = 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^{2 }= 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 (y_{2})^{2} − √ y_{1} = y^{3}

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) = cos^{2} x + cos^{2}(π/3 + x) - cos x.cos(π/3 + x) is constant, then the value of this constant is

Solution:

QUESTION: 15

( d/dx )(x^{2} + cos x)^{4} =

Solution:

d/dx(x^{2} + cos x)^{4}

= 4.(x^{2} + cos x)^{3} x d/dx (x^{2} + cos x)

= 4(x^{2} + 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 A^{2}+ B^{2} =

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 = 4^{5}

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 = ^{4}C_{3}

Since, each suit has 13 cards, the ways of choosing 1 card = ^{13}C_{1} = 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

b^{2} = c^{2} + a^{2} - 2ac cos B

⇒ a^{2} - 2ac cos B = b^{2} - c^{2}

⇒ a^{2} - 2ac cos B + c^{2} cos^{2} B

= b^{2} - c^{2} + c^{2} cos^{2} B

⇒ (a - c cos B)^{2} = b^{2} - c^{2} (1 - cos^{2} B)

= b^{2} - c^{2} sin^{2} 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 x^{2} + ax + b = 0, then equation whose roots are p^{2}q, q^{2}p is

Solution:

p + q = - a, p.q = b

Now, p^{2} q + q^{2} p = pq(p + q)

= b(-a) = - ab

p^{2}q . q^{2}p = (pq)^{3} = b^{3}

The required equation is

x^{2} - (p^{2}q + q^{2}p) x+ (p^{2}q . q^{2}p) = 0

x^{2} + abx + b^{3} = 0

QUESTION: 33

If the roots of the equation x^{2}+2mx+m^{2}-2m+6=0 are equal, then the value of m is

Solution:

QUESTION: 34

The locus of x^{2}+y^{2}+z^{2 }=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 ax^{2}+ 2hxy + by^{2} + 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

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

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 â„¦. 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 Î©. 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 Î¼F charged up to 250 volts is connected in parallel with another capacitor of 5 Î¼F 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 10^{6} 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^{-19}C, mp = 1.67 x 10^{-27} kg)

Solution:

v = 10 MHz = 10 x 10^{6} Hz = 10^{7} 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 _{56}Ba^{141} 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 60^{o} on a prism of refracting angle 30^{o} . The emergent ray is at an angle 30^{o} with the incident ray. The value of refractive index of the prism is

Solution:

Angle of prism = 30^{o} = A

Angle of incidence = i_{1} = 60^{o}

Angle of emergence = i_{2} = ?

Angle of devation = D = 30^{o}

∴ i_{2} = A + D - i_{2} = 30 + 30 - 60 = 0^{o}

⇒ r_{2} = 0^{o}

∴ r_{1} = A-r_{2} = 30 - 0 = 30^{o}

∴ μ = sin i 1 sin r 1 = sin 60^{o} /sin 30^{o} = √ 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 50*HZ* 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 4*I* are superimposed, the ratio between maximum and minimum intensities in the resultant beam is

Solution:

QUESTION: 78

If wavelength of a photon is 6000 â„«, 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 l_{2} containing Na_{2}CO_{3} ?

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 C_{7}H_{16} 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 Cd^{2+} and Cu^{2+}, both are dipositive ions but Cu^{2+} has one half of the concentration compared to that of the Cd^{2+}. Thus, the molar amount of the H_{2}S used to precipitate the metals ions Cd^{2+} and Cu^{2+} 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 *H*_{2}*SO*_{4} 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 E^{0}_{red.} values of A,B,C are 0.68V,- 2.54 V,-0.50V respectively.The order of their reducing power is

Solution:

QUESTION: 113

C_{4}H_{4}O_{4} 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

P_{4}O_{10} has short and long P-O bonds. The number of short P-O bonds in this compound is

Solution:

P_{4}O_{10} 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 HNO_{3}

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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