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This mock test of VITEEE PCME Mock Test - 7 for JEE helps you for every JEE entrance exam.
This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 7 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. The rate at which the area increases, when the side is 10 cm is

Solution:

QUESTION: 2

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

Solution:

QUESTION: 3

Solution:

QUESTION: 4

The argument and modulus of [(1+i)/(1-i)] are respectively

Solution:

QUESTION: 5

If *a* is real number such that | z − a i | = | z + a i | , then the locus of *z* is

Solution:

QUESTION: 6

for x ≠ 0, f 0 = 0, then f(x) at x = 0 is

Solution:

QUESTION: 7

If - 9 is the root of the equation , then other two roots are

Solution:

QUESTION: 8

Solution:

QUESTION: 9

Let f(x) = log |x - 1|, x ≠ 1. The value of f ′(1/2) is

Solution:

QUESTION: 10

The order and degree of the differential equation (1 + 3dy/dx)^{2/3} = 4d^{3}y/dx^{3} are

Solution:

QUESTION: 11

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

Solution:

QUESTION: 12

The general solution of the differential equation is given by

Solution:

QUESTION: 13

The differential equation of all circles which pass through (0,0) and having centre on y-axis, is

Solution:

QUESTION: 14

Solution:

QUESTION: 15

then f'(1) is ?

Solution:

QUESTION: 16

∫tan^{-1}x dx =

Solution:

QUESTION: 17

∫ tan^{5}θ dθ =

Solution:

QUESTION: 18

The domain of sin^{-1}*x* is

Solution:

QUESTION: 19

If f'(2) = 4 and f ' (1) = 2 then

Solution:

QUESTION: 20

The value of

Solution:

QUESTION: 21

If A and B are 2 x 2 matrices then (A+B)^{2}=

Solution:

QUESTION: 22

If A is singular matrix of order n, then a (adj A) equals,

Solution:

QUESTION: 23

Reena says "The number I am thinking is divisible by 2 or it is divisible by 3". This statement is false if the number Reena is thinking of is

Solution:

This sentence contains the word "or" (disjunction).

A disjunction is only false if BOTH conditions are false.

The only number that is not divisble by 2 and is not divisible by 3 is 11.

QUESTION: 24

Box *A* contains 2 black and 3 red balls, while box *B* contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box *A* is double that of box *B*. If a red ball is drawn from the selected box then the probability that it has come from box *B* is

Solution:

QUESTION: 25

In an examination there are three objective questions and in each question there are 4 options. The number of ways in which any candidate may not give correct answers to all questions is

Solution:

QUESTION: 26

If *A* and *B* are two events such that P(A) = 1/4 , P(B) = 1/2 , P(A ∪ B) = 5/8 then P(A ∩ B) =

Solution:

QUESTION: 27

A card is taken out of a pack of 52 cards numbered 2 to 53. The probability that the number on the card is a prime number less than 20 is

Solution:

QUESTION: 28

In ∆ABC, if cotA,cotB,cotC are in A.P., then a^{2},b^{2},c^{2} are in

Solution:

QUESTION: 29

The most stable measure of central tendency is

Solution:

QUESTION: 30

The harmonic mean of 4,8,16 is

Solution:

QUESTION: 31

If the sum of first n terms of an A.P. is pn + qn^{2} where p and q are constants, then common difference of A.P. will be

Solution:

For the A.P.

S_{n} = pn + qn^{2}

Now S_{1} = p x 1 + q(1)^{2}

S_{1} = p x q ⇒ T_{1} = p + q

Also S_{2} = p x 2 + q(2)^{2}

= 2p + 4q

We have T_{1} + T_{2} = 2p + 4q

or T_{2} = 2p + 4q - T_{1}

or T_{2} = 2p + 4q - (p + q)

or T_{2} = p + 3q

Hence common difference = T_{2} - T_{1}

= p + 3q - (p + q)

= p + 3q - p - q = 2q

QUESTION: 32

The solution of the equation x+(1/x)=2 is

Solution:

QUESTION: 33

If the roots of x^{2}+x+a=0 are greater than a, then

Solution:

QUESTION: 34

The points (5,-4,2),(4,-3,1),(7,-6,4),(8,-7,5) are vertices of a

Solution:

QUESTION: 35

If the planes x+2y+Kz=0 and 2x+y-2z=0 are at right angles, then the value of K is

Solution:

QUESTION: 36

If α is a root of 25cos^{2}θ + 5cosθ - 12 = 0, (π/2)<α<π, then sin2α is equal to

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

The equation of the parabola whose focus is (5, 3) and directrix is 3x - 4y + 1 = 0 is

Solution:

QUESTION: 39

If the position vectors of C and B with respect to B and A are i+j, i-j respectively, the position vector of C with respect to A is

Solution:

QUESTION: 40

A force of magnitude 5 units acting along the vector 2 î - 2 ĵ + k̂ displaces the point of application from (1, 2, 3) to (5, 3, 7), then the work done is

Solution:

QUESTION: 41

The power factor of LCR circuit at resonance is

Solution:

QUESTION: 42

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: 43

The penetrating power of X - rays increases with the

Solution:

QUESTION: 44

Three different capacitors are connected in series. Then:

Solution:

QUESTION: 45

The internal resistance of a primary cell is 4 Ω. It generates a current of 0.2 A in an external resistance of 21 Ω. The rate at which chemical energy is consumed in providing the current is

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

A 100 W, 200 V bulb is connected to a 160 volts supply. The actual power consumption would be

Solution:

QUESTION: 48

An ammeter with internal resistance 90â„¦ reads 1.85 A when connected in a circuit containing a battery and two resistors 700â„¦ and 410â„¦ in series. Actual current will be

Solution:

QUESTION: 49

A wire of length L is drawn such that its diameter is reduced to half of its original diameter. If the initial resistance of the wire were 10Ω, its new resistance would be

Solution:

QUESTION: 50

Keeping the length of the conductor constant, if the radius of the conductor is doubled, then its resistance becomes

Solution:

QUESTION: 51

What will be the ratio of de Broglie wavelengths of proton and α-particle of same energy

Solution:

We know , m_{α} = 2 m_{p}

QUESTION: 52

The working of a dynamo is based on principle of

Solution:

QUESTION: 53

Which of the following does not obey the phenomenon of mutual induction?

Solution:

QUESTION: 54

The number of turns in the primary coil of a transformer is 200 and the number of turns in secondary coil is 10. If 240 V a.c. is applied to the primary, the output from secondary will be

Solution:

QUESTION: 55

The ozone layer absorbs

Solution:

QUESTION: 56

A charge is placed at the centre of a cube, the flux emitted through its one face is

Solution:

QUESTION: 57

An electron of charge e coulomb passes through a potential difference of V volt. Its energy in joule will be

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

A conducting sphere of radius 10 cm is charged with 10 Î¼C. Another uncharged sphere of radius 20 cm in allowed to touch it for some time. If both the spheres are separated, then surface density of charges on the spheres will be in the ratio of

Solution:

QUESTION: 60

A parallel plate capacitor is first charged and then a dielectric slab is introduced between the plates. The quantity that remains unchanged is

Solution:

QUESTION: 61

A dielectric of thickness 5 cm and dielectric constant 10 is introduced in between the plates of a parallel plate capacitor having plate area 500 sq.cm and separation between plates 10 cm. The capacitance of the capacitor is ∈_{o} = 8.8x10^{-12} SI unit

Solution:

QUESTION: 62

A straight wire of length 0.5 meter and carrying a current of 1.2 ampere is placed in a uniform magnetic field of induction 2 telsa. The magnetic field is perpendicular to the length of the wire. The force on the wire is

Solution:

QUESTION: 63

A chain reaction is fission of uranium is possible because

Solution:

QUESTION: 64

The half life of a radioactive material depends on

Solution:

QUESTION: 65

The element which does not exhibit radioactivity is

Solution:

QUESTION: 66

The photoelectric work function for a metal surface is 4.125 eV. The cut off wavelength for this surface is

Solution:

Work function W_{0} = hc/λ

∴ λ = hc/W_{o} = 12400/4.125 = 3000 Å

QUESTION: 67

Which of the following is not dependent on the intensity of incident radiation in a photoelectric experiment ?

Solution:

QUESTION: 68

A man runs towards a mirror with a speed of 15 m-s^{-1}. What is the speed of his image?

Solution:

QUESTION: 69

Which of the following forms a perfect image free from all aberrations?

Solution:

QUESTION: 70

A p-n junction is used as a/an

Solution:

QUESTION: 71

A zener diode works on the principle of

Solution:

QUESTION: 72

An *n-p-n* transistor having a.c. current gain of 50 is to be used to make an amplifier of power gain of 300. What will be the voltage gain of the amplifier?

Solution:

QUESTION: 73

In a good conductor the energy gap between the conduction band and the valence band is

Solution:

QUESTION: 74

In an n-type semiconductor, which of the following is true?

Solution:

QUESTION: 75

When a semiconductor is heated, its resistance

Solution:

QUESTION: 76

Wave optics is based on wave theory of light put forward by Huygen and modified later by

Solution:

QUESTION: 77

The sun is rotating about is own axis. The spectral lines emitted from the two ends of its equator, for an observer on the earth, will show

Solution:

QUESTION: 78

In a semiconductor, separation of energy gap between conduction and valence bands is of the order of

Solution:

QUESTION: 79

The golden view of sea shell is due to

Solution:

QUESTION: 80

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

Solution:

QUESTION: 81

Which of the following does not give red ppt. with Fehling solution?

Solution:

QUESTION: 82

Which of the following statements is correct regarding ease of dehydration?

Solution:

QUESTION: 83

An aldehyde on oxidation gives

Solution:

QUESTION: 84

The reaction/method that does not give an alkane is

Solution:

QUESTION: 85

Which of the following compounds does not react with NaHSO₃?

Solution:

QUESTION: 86

1-Butene may be converted to butane by reaction with

Solution:

QUESTION: 87

Scurvy is caused due to the deficiency of vitamin

Solution:

QUESTION: 88

The set of numerical coefficients that balances the chamical equation K₂CrO₄ + HCl → K₂Cr₂O₇ + KCl + H₂O

Solution:

QUESTION: 89

Irrespective of the source, pure sample of water always yields 88.89% mass of oxygen and 11.11% mass of hydrogen. This is explained by the law of

Solution:

QUESTION: 90

phospholipids are esters of glycerol with

Solution:

QUESTION: 91

Enzymes, in the living systems

Solution:

QUESTION: 92

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

Solution:

QUESTION: 93

Formic acid when treated with H₂SO₄ gives

Solution:

QUESTION: 94

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

Solution:

QUESTION: 95

Vinegar made from cane sugar, now-a-days synthetically contains

Solution:

QUESTION: 96

The rate, at which a substance reacts at constant temperature, depends upon its

Solution:

QUESTION: 97

A liquid is in equilibrium with its vapour at its boiling point. The molecules in these two phases will have equal

Solution:

QUESTION: 98

Which of the following is not correct?

Solution:

QUESTION: 99

In which one the following reactions does the heat change represents the heat of formation of water

Solution:

QUESTION: 100

Which of the following Fischer's projection formula is identical to D-glyceraldehyde ?

Solution:

QUESTION: 101

The propellants in which fuel and oxidiser are allowed to combine at the time of combustion are

Solution:

QUESTION: 102

If the pressure on a NaCl structure is increased, then its co-ordination number will

Solution:

QUESTION: 103

The IUPAC name of [Cr(NH₃)₆]^{3+ }is

Solution:

QUESTION: 104

Alkyl cyanides are

Solution:

QUESTION: 105

The colour of p-aminoazobenzene is

Solution:

QUESTION: 106

If hydrogen electrode dipped into solution of pH = 3 and pH = 6 and salt bridge is connected the e.m.f. of resulting cell is

Solution:

QUESTION: 107

The standard oxidation no. of the most electronegative element in the products of the reaction BaO_{2} and dil. H_{2}SO_{4} is-

Solution:

Reaction between BaO_{2} and H_{2}SO_{4} is

BaO_{2} + H_{2}SO_{4} → BaSO_{4} + H_{2}O_{2}

The most electron negative element in products is oxygen

Oxidation no. of O in BaSO_{4} and H_{2}O_{2} is -2 and -1 respectively

QUESTION: 108

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

Solution:

QUESTION: 109

Standard electrode potentials are

Fe^{2+}/Fe (E^{o} = -0.44 V)

Fe^{3+}/Fe^{2+} (E^{o} = - 0.77 V)

Fe^{2+},Fe^{3+ }and Fe blocks are kept together,then

Solution:

QUESTION: 110

The rate of diffusion of methane at a given temperature is twice that of a gas X. The molecular weight of X is

Solution:

QUESTION: 111

Nickel is purified by thermal decomposition of its

Solution:

QUESTION: 112

Sodium hexametaphosphate is known as

Solution:

QUESTION: 113

In the chemical reaction Ag₂O + H₂O + 2e^{-} → 2Ag + 2OH^{-}

Solution:

QUESTION: 114

Silicon is an important constituent of

Solution:

QUESTION: 115

What is the catalyst used during the manufacture of nitric acid by Ostwald's method ?

Solution:

QUESTION: 116

The 8 : 8 type of packing is present in

Solution:

QUESTION: 117

Number of optically active isomers of tartaric acid

Solution:

QUESTION: 118

Bonding in ferric chloride is

Solution:

QUESTION: 119

Which of the following is a hydrophilic colloidal sol?

Solution:

QUESTION: 120

The metal which is not ferromagnetic is

Solution:

QUESTION: 121

Find the antonym of BASE

Solution:

QUESTION: 122

Fill in the blank with appropriate word.

The man is so ill that he can.........walk.

Solution:

QUESTION: 123

Find the synonym of AUDACIOUS

Solution:

QUESTION: 124

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

He cannot MAKE BOTH ENDS MEET.

Solution:

QUESTION: 125

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

When the solider returned home after the war was over, his wife received him WITH OPEN HANDS.

Solution:

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