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This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 5 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The rate of change of the volume of a sphere w.r.t. its surface area, when the radius is 2cm, is

Solution:

QUESTION: 2

A real value of x will satisfy the equation

[((3 - 4 i x)/( 3 + 4i x))] = α - iβ ( α ,β real),if

Solution:

QUESTION: 3

Solution:

QUESTION: 4

The area bounded by the curve y = (x + 1)^{2}, y = (x - 1)^{2} and the line y = 1/4 is

Solution:

Given curves are

(x + 1)^{2} = y .....(1)

and (x - 1)^{2} = y .....(2)

Axis of parabola (1) is x = - 1 and vertex is (- 1, 0) and it meets y-axis at (0,1)

Axis of parabola (2) is x = 1 and vertex is (1, 0) and it cuts y - axis at (0, 1)

When y = 1/4

from (2), x - 1 = 1/2

∴ x = 1/2 , 3/2

∴ C ≡ ( 1/2 , 1/4 )

Required area = 2 area BACB

QUESTION: 5

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: 6

All the roots of the equation z^{n} cos θ_{o} + z^{n − 1} cos θ_{1} + … + cos θ_{n} = 2 , where θ_{o} , θ_{1} , θ_{2} , … , θ_{n} ∈ R will satisfy

Solution:

QUESTION: 7

, then the value of *x* is

Solution:

QUESTION: 8

If f(x) = tanx/x , x ≠ 0 ; f x = 1, x = 0 , then the function at *x* = 0 is

Solution:

QUESTION: 9

Solution:

Multiply R_{1}, R_{2}, R_{3} by a, b, c respectively and divide by abc

Take abc common from C_{3} so that C_{1}, C_{3} are identical

QUESTION: 10

A solution of the differential equation x (dy/dx)^{2} + (y-x) dy/dx - y = 0 is

Solution:

QUESTION: 11

y = A e^{x} + B e^{2x} + C e^{3x }satisfies the diferential equation

Solution:

QUESTION: 12

The solution of differential equation (dy/dx)=[(1+y^{2})/(1+x^{2})] is

Solution:

QUESTION: 13

Which equation has the solution y=A sinx+B cosx?

Solution:

QUESTION: 14

If y=log logx, e^{y}(dy/dx)=

Solution:

QUESTION: 15

If f : A → B is a bijective function then f^{-1} ο f=

Solution:

QUESTION: 16

∫ [sin(logx) + cos(logx)] dx =

Solution:

QUESTION: 17

∫x cos x dx =

Solution:

QUESTION: 18

If tan^{-1} x + tan^{-1} y + tan^{-1} z = π/2 , then 1 - xy - yz - zx =

Solution:

Let tan^{-1} x = A, tan^{-1} y = B, tan^{-1} z = C,

Then x = tan A, y = tan B, z = tan C, A + B + C = π/2

A + B + C = π/2

⇒ tan (A + B + C) is not defined

⇒ 1 - S_{2} = 0

⇒ 1 - tan A tan B - tan B tan C - tan C tan A = 0

⇒ 1 - xy - yz - zx = 0

QUESTION: 19

Solution:

QUESTION: 20

Solution:

QUESTION: 21

A and B are square matrices of the same order. Which is correct?

Solution:

QUESTION: 22

"It has two pairs of opposite sides parallel." Which of the following make this open sentence true?

Solution:

Parallelograms and rectangles have two pairs (sets) of parallel sides. A trapezoid has one pair (set) of parallel sides.

QUESTION: 23

If A,B,C are matrices of order nxn then (ABC)'=

Solution:

QUESTION: 24

A parallelogram is cut by two sets of m lines parallel to the sides, the number of parallelogram thus formed is

Solution:

QUESTION: 25

The chance of throwing a total of 7 or 12 with 2 dice, is

Solution:

QUESTION: 26

From a box containing 10 cards, numbered 1, 2,3,......,10. Four cards are drawn together, what is the probability of their sum is even ?

Solution:

QUESTION: 27

The probabilities that three men hit a target are 1/6 , 1/4 , 1/3 respectively. Each shoots once the target what is the probability that exactly one of the them hits the target?

Solution:

QUESTION: 28

Solution:

QUESTION: 29

In the expansion of (1 + x)^{n},coefficients of 2nd ,3rd and 4th terms are in A.P.Then n is equal to

Solution:

QUESTION: 30

The mean deviation of the numbers 3, 4, 5, 6, 7 is

Solution:

QUESTION: 31

The mean age of a combined group of men and women is 30 years. If the means of the age of men and women are respectively 32 and 27, then the percentage of women in the group is

Solution:

QUESTION: 32

If equations x = cy + bz, y = az + cx and z = bx + ay have any solution except x = 0, y = 0, z = 0, then the relation between a, b and c is

Solution:

The system of homogeneous equations-

x − cy − bz = 0......(i)

cx − y - bz = 0

bx - ay − z = 0

has non-trivial solution (since x, y, z are not all zero)

QUESTION: 33

The value of x^{2} + 2bx + c is positive if

Solution:

The given expression be

x^{2} + 2bx + c

Comparing it with Ax^{2} + Bx + c, we get

A = 1, B = 2b, C = c

Also A = 1 > 0

x^{2} + 2bx + c will be positive i.e.

will be of the same sign as that of A,

if B^{2} - 4AC < 0

4b^{2} - 4(1) (c) < 0

or b^{2} < c

QUESTION: 34

The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = -5 and perpendicular to the plane 5x + 3y + 6z + 8 = 0 is

Solution:

QUESTION: 35

The radius of the sphere which passes thro' the points (0,0,0),(1,0,0),(0,1,0) and (0,0,1) is

Solution:

QUESTION: 36

If 2sec2α = tanβ + cotβ, then one of the value of (α+β) is

Solution:

QUESTION: 37

The number of tangents to the circle x^{2} + y^{2} - 2x + 4y = 0 through the point (-1, 2) is

Solution:

QUESTION: 38

If a circle passes through the point (a, b) and cuts the cirlce x^{2}+ y^{2} = p^{2} orthogonally, then the equation of the locus of its centre is

Solution:

QUESTION: 39

If vectors i-3j+2k, -i+2j represent the diagonals of a parallelogram, then its area is

Solution:

QUESTION: 40

are three non coplanar vectors, then the value of the expression

Solution:

QUESTION: 41

An A.C. source is connected to a resistance circuit. Then

Solution:

QUESTION: 42

To a charged particle, which is moving with a constant initial velocity $\stackrel{\xe2\u2020\u2019}{V}$, a uniform magnetic field is applied in the direction of velocity; then

Solution:

QUESTION: 43

Light of wave length λ and photon energy 2eV falling on a metal surface produces photoelectrons of maximum velocity V. If the λ is decreased by 25% and the maximum velocity of electron is doubled, the work function of the metal is (in eV)

Solution:

QUESTION: 44

Of the following, the one that does not make use of chemical effect of electric current is

Solution:

QUESTION: 45

Consider telecommunication through optical fibres. Which of the following statements is not correct

Solution:

QUESTION: 46

An insulator plate is passed between the plates of a capacitor. Then current

Solution:

QUESTION: 47

Four identical cells each having an electromotive force (e.m.f.) of 12V, are connected in parallel. The resultant electromotive force (e.m.f.) of the combination is

Solution:

QUESTION: 48

An electrical meter of internal resistance 20$\mathrm{\xe2\u201e\xa6}$ gives a full scale deflection when one milliampere current flows through it. The maximum current, that can be measured by using three resistors of resistance 12$\mathrm{\xe2\u201e\xa6}$ each, in milliamperes is

Solution:

QUESTION: 49

Two identical cells of the same e.m.f. and same internal resistance give the same current through an external resistance 2 â„¦, regardless of whether they are connected in series or parallel. The internal resistance of the cell is

Solution:

QUESTION: 50

Two wires of the same material are given. The first wire is twice as long as the second and has twice the diameter of the second. The resistance of the first will be

Solution:

QUESTION: 51

Which of the following is true for photon

Solution:

QUESTION: 52

A choke coil has

Solution:

QUESTION: 53

In an ideal inductor, L =4 H and Ï‰=100 rad/s. The power developed is

Solution:

QUESTION: 54

The energy stored in coil carrying current I s U. If current is halved, then energy stored in the coil will be

Solution:

QUESTION: 55

Which is having minimum wavelength:

Solution:

QUESTION: 56

If the electric flux entering and leaving an enclosed surface respectively is φ_{1} and φ_{2} , the electric charge inside the surface will be

Solution:

QUESTION: 57

Two charges -10 C and + 10 C are placed 10cm apart. Potential at the centre of the line joining two charges is

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

In C.G.S system the capacity of a spherical conductor is numerically equal to its

Solution:

QUESTION: 60

A coil of *n* number of turns is wound tightly in the form of a spiral with inner and outer radii *a* and *b* respectively. When a current of strength *I* is passed through the coil, the magnetic field at its centre is

Solution:

QUESTION: 61

If 1000 droplets each of charge q and radius r are mixed to form a big drop, then the potential of big drop, as compared to small droplet will be

Solution:

If the value of potential on each small drop be V and potential on each small drop be V ^{'}

V ^{'} = n ^{2/3} V

⇒ V ^{'} = 1000 ^{2/3} V

QUESTION: 62

The masses of neutron, proton and deuteron in a.m.u are 1.00893 1.00813 and 2.01473 respectively. The packing fraction of the deuteron in a.m.u is

Solution:

Packing fraction = (M - A)/A , where M is the atomic mass and A is the mass number.

P = M - A/A = (2.01473 - 2) /2 = 73.6 x 10^{-4}

QUESTION: 63

The nucleus finally formed in fusion of protons in proton-proton cycle is

Solution:

QUESTION: 64

Which is not electromagnetic wave in the following?

Solution:

QUESTION: 65

Graph of maximum kinetic energy of the photoelectrons against Î½, the frequency of the incident radiation on the metal, is a straight line of slope equal to

Solution:

QUESTION: 66

Light of wavelength 4000â„« is incident on a sodium surface for which the threshold wave length of photo-electrons is 5420â„«. The work function of sodium is

Solution:

QUESTION: 67

Capacitance of a capacitor becomes 7/6 times its original value if a dielectric slab of thickness, t = 2/3 d is introduced in between the plates. 'd' is the separation between the plates. The dielectric constant of the dielectric slab is

Solution:

QUESTION: 68

A ray of light is incident on a plane mirror at an angle of 60^{0} . The angle of deviation produced by the mirror is

Solution:

QUESTION: 69

In order to increase the angular magnification of a simple microscope, one should increase

Solution:

QUESTION: 70

In forward bias, in a *p* - *n* junction the potential barrier

Solution:

QUESTION: 71

Transistor can be used as

Solution:

QUESTION: 72

For a transistor the parameter β = 99. The value of the parameter α is

Solution:

QUESTION: 73

In extrinsic semiconductors

Solution:

QUESTION: 74

Bonding in a germanium crystal (semiconductor) is

Solution:

QUESTION: 75

The cause of the potential barrier in a p-n diode is

Solution:

QUESTION: 76

At 0^{0}K, fermi level for metals

Solution:

QUESTION: 77

In Young's double slit experiment, the width of the fringes obtained with light of wavelength 6000 Angstrom is 2.0mm. The fringe width, if the entire apparatus is immersed in a liquid of refractive index 1.33, will be

Solution:

Fringe width in Young's double slit experiment β = Dλ/d

When apparatus is immersed in liquid, only wavelength of light (λ) changes

Wavelength of light is liquid,

λ' = λ/n , where n = refractive index of medium

Initial fringe width, β = Dλ/d .....(i)

Fringe width in liquid, β' = Dλ'/d .....(ii)

Dividing Equation (ii) by Equation (i), we get

β/ β = λ'/λ

or β'/β = λ n/λ = 1/n

or β' = β/n

The new fringe width, β' = 2.0/1.33 mm = 1.5 mm

QUESTION: 78

What is the effect on the interference fringes in a Young's double slit experiment, if the monochromatic source is replaced by another monochromatic source of shorter wavelength?

Solution:

QUESTION: 79

In the propagation of light waves, the angle between the direction of vibration and plane of polarisation is

Solution:

QUESTION: 80

Both light and sound waves produce diffraction. It is more difficult to observe the diffraction with light waves because

Solution:

QUESTION: 81

Acetaldehyde reacts with

Solution:

QUESTION: 82

Glycerol on heating with potassium bisulphate yields

Solution:

QUESTION: 83

In Cannizzaro's reaction

Solution:

QUESTION: 84

Which of the following method is most appropriate for the manufacture of methane?

Solution:

QUESTION: 85

Which of the following does not turn Schiff's reagent to pink?

Solution:

QUESTION: 86

Ozonolysis of C₇H₁₄ gave 2-methyl-3-pentanone toluene. The alkene is

Solution:

QUESTION: 87

Which of the following is an electrophilic reagent?

Solution:

QUESTION: 88

The reaction, CH₂ = CH-CH₃ + HBr → CH₃CHBr - CH₃ is

Solution:

QUESTION: 89

The energy stored in the cells of a living body is in the form of

Solution:

QUESTION: 90

Enzymes are made up of

Solution:

QUESTION: 91

Which of the following substance when boiled with caustic soda evolve ammonia ?

Solution:

QUESTION: 92

To become a carbohydrate a compound must contain at least

Solution:

QUESTION: 93

The acid showing salt like character in aqueous solutions is

Solution:

QUESTION: 94

Which salt can be produced by the reaction of carbon monoxide and caustic soda (NaOH)?

Solution:

QUESTION: 95

A chemical reaction is catalyzed by a catalyst X. Hence X

Solution:

QUESTION: 96

A glass bulb is filled with NO₂ gas and immersed in an ice bath at 0^{o}C which becomes colourless after some time . This colourless gas will be

Solution:

QUESTION: 97

Plants and living beings are the examples of

Solution:

QUESTION: 98

Medicine which is an antibiotic is

Solution:

QUESTION: 99

In a closed insulated container a liquid is stirred with a paddle to increase the temperature. Which of the following is true

Solution:

QUESTION: 100

The compound having highest dipole moment is

Solution:

QUESTION: 101

Identify the reaction in which the heat liberated corresponds to the heat of formation ( Δ H )

Solution:

QUESTION: 102

[Cr(H₂O)₆]Cl₃(at no. of Cr=24) has a magnetic moment of 3.83 BM. The correct distribution of 3d electrons in the Chromium of the complex is

Solution:

QUESTION: 103

Which of the following is produced by reaction of RCN in sodium and alcohol ?

Solution:

QUESTION: 104

The indicator that is obtained by coupling the diazonium salt of sulphanilic acid with N,N-dimethylaniline is

Solution:

QUESTION: 105

The correct structure of Fe(CO)₅ is (Z = 26 for Fe)

Solution:

QUESTION: 106

The cell potential of the following cell at 25 ^{0}C (in volts) is

Pt , H_{2} (1 atm) | H^{+} 0.01 M ∥ Cu^{2+} (0.1 M) | Cu (E^{o} Cu^{2+} ∕ Cu = + 0.337 V)

Solution:

QUESTION: 107

A smuggler could not carry gold by chemically depositing iron on the gold surface since

Solution:

QUESTION: 108

The oxidation no. of nitrogen in NaNO₂ is

Solution:

The formal oxidation state of the nitrogen atom in a nitrite is +3. This means that it is can be either oxidised to oxidation states +4 and +5 or reduced to oxidation states as low as -3.

QUESTION: 109

Microcosmic salt is

Solution:

QUESTION: 110

Ether which is liquid at room temperature is

Solution:

QUESTION: 111

A container contains 1 mole of a gas at 1 atm pressure and 27^{o}C, and its volume is 24.6 ltres. If pressure is 10 atm and temperature 327^{o}C, then new volume is approximately

Solution:

QUESTION: 112

Percentage of lead in lead pencil is

Solution:

QUESTION: 113

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: 114

Oxidation state of Fe in Fe₃O₄ is

Solution:

QUESTION: 115

Pick up the correct statement

Solution:

QUESTION: 116

Which of the following is least basic ?

Solution:

QUESTION: 117

The isomers are

Solution:

QUESTION: 118

The catalytic activity of the transition metals and their compounds is ascribed to

Solution:

QUESTION: 119

The separation of colloidal particles from those of molecular dimensions is called

Solution:

QUESTION: 120

The brown ring complex compounds is formulated as [*Fe*(*H*_{2}*O*)_{5}*NO*] *SO*_{4}. The oxidation state of iron is

Solution:

QUESTION: 121

Find the Antonym of TIMID

Solution:

QUESTION: 122

Find the Syonym of AFFLUENT

Solution:

QUESTION: 123

Fill in the blank with appropriate word.

The Hubble Space Telescope will search for planets around other stars, a key to the..........for extra terrestrial life, and examine interstellar dust gases out of which stars are born.

Solution:

QUESTION: 124

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

The staff have felt ON EDGE since they heard the rumour about retrenchment.

Solution:

QUESTION: 125

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

It was indeed a shock for her, but she has LATER recovered from it.

Solution:

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