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This mock test of VITEEE PCME Mock Test - 13 for JEE helps you for every JEE entrance exam.
This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 13 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If the slope of the normal to the curve x^{3} = 8a^{2}y, a > 0, at a point in the first quadrant is - 2/3, then the point is

Solution:

QUESTION: 2

Area bounded by parabola y^{2} = x and st.line 2 y = x is

Solution:

QUESTION: 3

If ω is a cube of unity and equation has one root . Then

Solution:

⇒ x = 0

∵ x^{2} + 5 = 0. Not possible ∀ x ∈ R

QUESTION: 4

If 1 + i is the conjugate of (x+iy)(1-2i), then

Solution:

QUESTION: 5

Let y = | x | + | x − 2 | . Then dy/dx at x = 2 is

Solution:

QUESTION: 6

If | z_{1} − 1 | < 1 , | z_{2} − 2 | < 2 , | z_{3} − 3 | < 3 then | z_{1} + z_{2} + z_{3} |

Solution:

QUESTION: 7

If *f*: R → R defined by is continuous function, then

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QUESTION: 8

The value of

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QUESTION: 9

The order of the differential equation y(dy/dx)=x/(dy/dx)+(dy/dx)^{3} is

Solution:

QUESTION: 10

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QUESTION: 11

The solution of differential equation (xdy/dx) = y+x^{2} is

Solution:

QUESTION: 12

The solution of the equation xdy-ydx=0 is

Solution:

QUESTION: 13

The order of differential equation (d^{2}y/dx^{2})^{2 }= (1+dy/dx)^{1/2} is

Solution:

QUESTION: 14

If f x = x − x^{2} + x^{3} − x^{4} + … ∞ , | x | < 1, then f′(x) =

Solution:

QUESTION: 15

If f(x) = log (1 + x/1 - x), then f(2x/1 + x^{2}) is equal to

Solution:

QUESTION: 16

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QUESTION: 17

sin(sin^{-1}(1/2) + cos^{-1}(1/2))=

Solution:

QUESTION: 18

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QUESTION: 19

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QUESTION: 20

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QUESTION: 21

∼ [ p ↔ q ] is

Solution:

QUESTION: 22

m [ − 3,4 ] + n [ 4 − 3 ] = [ 10 − 11 ] ⇒ 3 m + 7 n =

Solution:

QUESTION: 23

All diagonal elements of skew symmetric matrix are

Solution:

QUESTION: 24

In how many ways can 4 boys and 3 girls be seated in a row of 7 chairs if the boys and girls alternate?

Solution:

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

If the mean of a Poisson's Distribution is λ, then its standard deviation is

Solution:

QUESTION: 27

If in a Δ A B C , 3 a = b + c then tanB/2 .tan C/2 is equal to

Solution:

QUESTION: 28

If A and B are two mutually exclusive events such that P(B) = 2P(A) and A ∪ B = S. Then P(A) is equal to

Solution:

QUESTION: 29

If (a, b), (c, d), (e, f) are the verices of a triangle such that a, c, e are in G.P. with common ratio r and b, d, f are in G.P. with common ratio's then the area of the triangle is

Solution:

QUESTION: 30

For a frequency distribution mean deviation from mean is computed by

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

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 two roots of the equation x^{2}-3x+2=0 are equal, roots are

Solution:

QUESTION: 34

The smallest radius of the sphere passing thro'(1,0,0),(0,1,0) and (0,0,1) is

Solution:

Let the sphere be

x^{2} + y^{2} + z^{2} + 2ux + 2vy + 2wz + d' = 0 ...(i)

It passes through the points (1, 0, 0), (0, 1, 0), (0, 0, 1)

∴ 1 + 2y + d' = 0...(ii)

1 + 2v + d' = 0 ...(iii)

1 + 2w + d' = 0 ...(iv)

From (ii), (iii), (iv), we get u = v = w = - d' + 1/2

Let r denote the radius of (i)

∴ r^{2} = u^{2} + v^{2} + w^{2} - d'

= 3 ( d' + 1/2 )^{2} - d'

= 3/4 (d' + 1)^{2} - d'

r will be minimum if d is minimum.

QUESTION: 35

The equation of the sphere with centre (3, 6, -4) and touching the plane

2x - 2y - z - 10 = 0 is

Solution:

As the required sphere touches the plane

2x - 2y - z - 10 = 0 .....(1)

∴ Radius of the required sphere = ⊥ from the center (3, 6, -4) of the required sphere to the plane (1)

∴ The required equation of the sphere is given by

(x - 3)^{2} + (y - 6)^{2} + (z + 4)^{2} = 16 (Central form)

⇒ x^{2} + 9 - 6x + y^{2} + 36 - 12y + z^{2} + 16 + 8z = 16

⇒ x^{2} + y^{2} + z^{2} - 6x - 12y + 8z + 45 = 0

QUESTION: 36

If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=

Solution:

QUESTION: 37

The vertex of the parabola

y^{2 }= 4(a' - a) (x - a) is

Solution:

QUESTION: 38

Two common tangents to the circle x^{2} + y^{2} = 2a^{2} and parabola y^{2} = 8ax are

Solution:

QUESTION: 39

If are unit vectors and then the value of is equal to

Solution:

QUESTION: 40

Consider A, B, C and D with position vectors 7î - 4ĵ + 7k̂, î - 6ĵ + 10k̂, -î -3ĵ + 4k̂ and 5î - ĵ + 5k̂ respectively. Then ABCD is a

Solution:

QUESTION: 41

A step-up transformer is used on a 120V line to provide a potential difference of 2400 V. If the primary coil has 75 turns, the number of turns in the secondary coil is

Solution:

QUESTION: 42

A positron and a proton are accelerated by the same accelerating potential. Then the ratio of the associated wavelengths of positron and proton will be [M = mass of proton; m = mass of positron]

Solution:

Since both proton and positron have the same charge

QUESTION: 43

A particle of mass 0.6 gm and having charge of 25 nC is moving horizontally with a uniform velocity 1.2 x 10^{4} m s^{-1} in a uniform magnetic field, then the value of the magnetic induction is (g = 10 m s^{-2})

Solution:

QUESTION: 44

A condenser is connected across another charged condenser. The energy in the two condensers will be

Solution:

QUESTION: 45

The resistance of a cell does not depend upon

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

The temperature coefficient of resistance for a wire is 0.00125/ ^{o}C. At 300 K its resistance is 1 ohm. The temperature at which the resistance becomes 2 ohm is

Solution:

QUESTION: 48

In a Wheatstone bridge all the four arms have equal resistance R. If the resistance of the galvanometer arm is also R, The equivalent resistance of the combination as seen by the battery is

Solution:

QUESTION: 49

The resistance of an ammeter is 13 Ω and its scale is graduated for a current upto 100*A*. After an additional shunt has been connected to this ammeter it becomes possible to measure currents upto 750*A* by this meter. The value of shunt resistance is

Solution:

QUESTION: 50

The effective resistance of two resistors in parallel is 12/7 Ω. If one of the resistors is disconnected the resistance becomes 4 Ω. The resistance of the other resistor is

Solution:

QUESTION: 51

A caesium photocell, with a steady potential difference of 60V across, is illuminated by a bright point source of light 50cm away. When the same light is placed 1m away the photoelectrons emitted from the cell

Solution:

QUESTION: 52

A choke coil has

Solution:

QUESTION: 53

When current cahnge from + 2 A to -2 A in 0.05 s, an e.m.f. of 8 V is induced in a coil. The coefficient of self inductance of the coil is

Solution:

QUESTION: 54

A coil of wire of radius r has 600 turns and a self inductance of 108 mH. The self inductance of a similar coil of 500 turns will be

Solution:

As L ∝ N^{2}

∴ L = 108 x (500/600)^{2} = 75 mH

QUESTION: 55

Heat radiations propagate with the speed of

Solution:

QUESTION: 56

A charge q is placed at the corner of a cube of side l. The electric flux passing through the cube is

Solution:

Eight cubes, each side l, are required to form a Gaussian surface

So that the charge q at the corner of a small cube appears at the centre of the bigger cube

According to Gauss's law, the electric flux through the bigger cubes = q/∈_{0}

Hence the electric flux through the given small cube =q/8∈_{0}

QUESTION: 57

Consider the situation shown in figure. Work done in carrying a point charge from *k* to *A, B, C* are W_{A} , W_{B} , W_{c }respectively. Which one is true?

Solution:

QUESTION: 58

Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining centre to this point makes an angle θ with the axis of the dipole, then potential at the point P is given by

Solution:

QUESTION: 59

A conducting sphere of radius 10 cm is charged with 10 μC. 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

When a body is connected to the earth, then electron from the earth, flow into the body. It means that the body is

Solution:

QUESTION: 61

Inside a hollow charged spherical conductor, the potential at every point

Solution:

QUESTION: 62

Two wires of equal length are placed perpendicular to the plane of paper at a distance of 5 cm from each other. If the currents flowing in first and second wires are 2 A and 5 A respectively in opposite direction, then the resultant magnetic field at mid-point of both the wires is

Solution:

QUESTION: 63

Out of the following which has no charge?

Solution:

QUESTION: 64

The element which does not exhibit radioactivity is

Solution:

QUESTION: 65

What is the particle *x* in the following nuclear reaction?

Solution:

QUESTION: 66

Find the kinetic energy of the photoelectrons emitted when light of wavelength 4000 Å is incident on a metal of work function 2 eV (find approximately)

Solution:

QUESTION: 67

In photoelectric effect experiment, the stopping potential for incident light of wave-length 4000 Å is 2 volt. If the wavelength is changed to 3000 Å, the stopping potential is

Solution:

QUESTION: 68

The resolving power of a telescope depends on

Solution:

QUESTION: 69

When a glass prism of refracting angle 60^{0} is immersed in a liquid its angle of minimum deviation is 30^{0} . The critical angle of glass with respect to the liquid medium is

Solution:

QUESTION: 70

An *n* - type and *p* - silicon can be obtained by doping pure silicon with:

Solution:

For obtaining ‘n’ type semi conductor V group element is doped with silicon.

Ex: Phosphorus

For obtaining ‘p’ type semiconductor III group element is doped with silicon.

Ex: Indium

QUESTION: 71

On increasing the reverse bias to a large value, in a p-n junction diode, the current

Solution:

QUESTION: 72

In an npn transistor, the emitter current is

Solution:

QUESTION: 73

At OK temperature, a p-type semiconductor

Solution:

QUESTION: 74

Depletion layer consists of

Solution:

QUESTION: 75

The dominant contribution to current comes from holes in case of

Solution:

QUESTION: 76

In intrinsic semiconductor at room temperature, number of electrons and holes are

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

If the phase differenc between light waves from two slits of Young's double slit experiment is π radian, then the central fringe will be

Solution:

QUESTION: 79

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

Solution:

QUESTION: 80

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

Solution:

QUESTION: 81

Ethylene reacts with 1% cold alkaline KMnO₄ to give

Solution:

QUESTION: 82

Which of the following is hypnotic ?

Solution:

QUESTION: 83

Consider the following compounds :

I. HCHO II.CH₃CHO III. CH₃COCH₃

The reactivities of these compounds are such that

Solution:

QUESTION: 84

Which of the following reagent react differently with HCHO and CH₃CHO and CH₃COCH₃

Solution:

QUESTION: 85

12 g of Mg (at. mass 24) on reacting completely with acid gives hydrogen gas, the volume of which at S.T.P would be

Solution:

QUESTION: 86

1-Butene may be converted to butane by reaction with

Solution:

QUESTION: 87

The significant figures of the number 6.0023 are

Solution:

QUESTION: 88

How many monochlorobutanes will be obtained on chlorination of n-butane?

Solution:

QUESTION: 89

Which of the following element is responsible for oxidation of water to O₂ in biological processes?

Solution:

QUESTION: 90

When three different amino acid molecules condense, then how many different tripeptide molecules are formed?

Solution:

When two amino acids condense they form a dipeptide and water. A tripeptide is made up from three amino acids. If the three amino acids are all different then there are six possible ways in which they can combine

QUESTION: 91

Which is correct statement?

Solution:

QUESTION: 92

Melting points are normally the highest for

Solution:

QUESTION: 93

Which of the following compounds on boiling with KMnO₄ and the subsequent acidification will not give benzoic acid ?

Solution:

QUESTION: 94

Hydrolysis of an ester gives a carboxylic acid which on Kolbe's electrolysis yields ethane. The ester is

Solution:

QUESTION: 95

Which one of the following informations can be obtained on the basis of Le Chatelier principle ?

Solution:

QUESTION: 96

Two moles of HI was heated in a sealed tube at 440 ^{o}C till the equilibrium was reached. HI was found to be 22% decomposed. The equilibrium constant for dissociation is

Solution:

QUESTION: 97

In an endothermic reaction, the value of âˆ†H is

Solution:

QUESTION: 98

In which of the following reactions, heat liberated is known as standard heat of formation of *CO _{2}*?

Solution:

QUESTION: 99

Which of the following is antipyretic?

Solution:

QUESTION: 100

Which of the following is an example of intensive property?

Solution:

QUESTION: 101

The number of possible structural isomers of C₄H₁₀O is

Solution:

QUESTION: 102

Which one of the following cyano complexes would exhibit the lowest value of paramagnetic behaviour?

(At. No. : Cr = 24, Mn = 25, Fe = 26, Co = 27)

Solution:

QUESTION: 103

The hydrid state of Ni in Ni(CO)₄ is

Solution:

QUESTION: 104

In the following reaction C₆H₆NH₂ + CHCl₃ + 3NaOH → A + 3B + 3C the product A is

Solution:

QUESTION: 105

When electricity is passed through aqueous solution of aluminium chloride, 13.5 g of Al are deposited. The number of faradays of electricity passed must be

Solution:

QUESTION: 106

Which one of the following is not the correct reaction of aryl diazonium salts?

Solution:

QUESTION: 107

A certain current liberate 0.5 g of hydrogen in 2 h. How many grams of copper can be liberated by the same current flowing for the same time in a copper sulphate solution?

Solution:

QUESTION: 108

If the standard electrode potential of *Cu*^{2+}/*Cu* electrode is 0.34 *V*, what is the electrode potential at 0.01 *M* concentration of *Cu*^{2+}? (*T* = 298*K*)

Solution:

QUESTION: 109

Ethyl chloride is converted into diethyl ether by

Solution:

QUESTION: 110

Cassiterite is concentrated by

Solution:

QUESTION: 111

White P when boiled with strong solution of caustic soda produces

Solution:

QUESTION: 112

The components present in producer gas are

Solution:

QUESTION: 113

Oxygen and cyclopropane at partial pressure of 570 torr and 170 torr respectively are mixed in a gas cylinder. What is the ratio of the number of moles of cyclopropane to the number of moles of oxygen ?

Solution:

QUESTION: 114

In H₂O₂, the oxidation state of oxygen is

Solution:

QUESTION: 115

Which of the following fluorides does not exist ?

Solution:

QUESTION: 116

The edge length of face centred unit cubic cell is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is

Solution:

QUESTION: 117

Which of the following can't be explained by adsorption?

Solution:

QUESTION: 118

Among the following ions in aqueous solution, the ion is likely to be colourless

Solution:

QUESTION: 119

The addition of Br_{2} to E-but-2-ene gives

Solution:

QUESTION: 120

Among the following which is used as an electrolyte in electroplating a baser metal with gold?

Solution:

QUESTION: 121

find the synonym of DELECTABLE

Solution:

QUESTION: 122

Fill in the blank with appropriate word.

Waking at three o'clock, I heard the........of thunder

Solution:

QUESTION: 123

Find the Antonym of SULKY

Solution:

QUESTION: 124

**Choose the alternative which best expresses the meaning of the idiom/phrase.**

To take with a grain of salt

Solution:

QUESTION: 125

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

He should move on to the next point, and not HARP ONE STRING ONLY.

Solution:

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