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# VITEEE PCME Mock Test - 13

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## 125 Questions MCQ Test VITEEE: Subject Wise and Full Length MOCK Tests | VITEEE PCME Mock Test - 13

VITEEE PCME Mock Test - 13 for JEE 2023 is part of VITEEE: Subject Wise and Full Length MOCK Tests preparation. The VITEEE PCME Mock Test - 13 questions and answers have been prepared according to the JEE exam syllabus.The VITEEE PCME Mock Test - 13 MCQs are made for JEE 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for VITEEE PCME Mock Test - 13 below.
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VITEEE PCME Mock Test - 13 - Question 1

### If the slope of the normal to the curve x3 = 8a2y, a > 0, at a point in the first quadrant is - 2/3, then the point is

VITEEE PCME Mock Test - 13 - Question 2

### Area bounded by parabola y2 = x and st.line 2 y = x is

VITEEE PCME Mock Test - 13 - Question 3

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

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 3      ⇒ x = 0
∵ x2 + 5 = 0. Not possible ∀ x ∈ R

VITEEE PCME Mock Test - 13 - Question 4

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

VITEEE PCME Mock Test - 13 - Question 5

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

VITEEE PCME Mock Test - 13 - Question 6

If | z1 − 1 | < 1 , | z2 − 2 | < 2 , | z3 − 3 | < 3 then | z1 + z2 + z3 |

VITEEE PCME Mock Test - 13 - Question 7

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

VITEEE PCME Mock Test - 13 - Question 8

The value of VITEEE PCME Mock Test - 13 - Question 9

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

VITEEE PCME Mock Test - 13 - Question 10 Detailed Solution for VITEEE PCME Mock Test - 13 - Question 10    VITEEE PCME Mock Test - 13 - Question 11

The solution of differential equation (xdy/dx) = y+x2 is

VITEEE PCME Mock Test - 13 - Question 12

The solution of the equation xdy-ydx=0 is

VITEEE PCME Mock Test - 13 - Question 13

The order of differential equation (d2y/dx2)= (1+dy/dx)1/2 is

VITEEE PCME Mock Test - 13 - Question 14

If f x = x − x2 + x3 − x4 + … ∞ , | x | < 1, then f′(x) =

VITEEE PCME Mock Test - 13 - Question 15

If f(x) = log (1 + x/1 - x), then f(2x/1 + x2) is equal to

VITEEE PCME Mock Test - 13 - Question 16 VITEEE PCME Mock Test - 13 - Question 17

sin(sin-1(1/2) + cos-1(1/2))=

VITEEE PCME Mock Test - 13 - Question 18 VITEEE PCME Mock Test - 13 - Question 19 VITEEE PCME Mock Test - 13 - Question 20 VITEEE PCME Mock Test - 13 - Question 21

∼ [ p ↔ q ] is

VITEEE PCME Mock Test - 13 - Question 22

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

VITEEE PCME Mock Test - 13 - Question 23

All diagonal elements of skew symmetric matrix are

VITEEE PCME Mock Test - 13 - 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?

VITEEE PCME Mock Test - 13 - 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 - 13 - Question 26

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

VITEEE PCME Mock Test - 13 - Question 27

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

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 27  VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - Question 30

For a frequency distribution mean deviation from mean is computed by

VITEEE PCME Mock Test - 13 - Question 31

The mode of the following items is 0, 1, 6, 7, 2, 3, 7, 6, 6, 2, 6, 0, 5, 6, 0

VITEEE PCME Mock Test - 13 - 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 - 13 - 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 - 13 - Question 33

If the two roots of the equation x2-3x+2=0 are equal, roots are

VITEEE PCME Mock Test - 13 - Question 34

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

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 34

Let the sphere be
x2 + y2 + z2 + 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)
∴ r2 = u2 + v2 + w2 - d'
= 3 ( d' + 1/2 )2 - d'
= 3/4 (d' + 1)2 - d'
r will be minimum if d is minimum.  VITEEE PCME Mock Test - 13 - Question 35

The equation of the sphere with centre (3, 6, -4) and touching the plane
2x - 2y - z - 10 = 0 is

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 35

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)
⇒ x2 + 9 - 6x + y2 + 36 - 12y + z2 + 16 + 8z = 16
⇒ x2 + y2 + z2 - 6x - 12y + 8z + 45 = 0

VITEEE PCME Mock Test - 13 - Question 36

If cosθ+cos7θ+cos3θ+cos5θ=0, then θ=

VITEEE PCME Mock Test - 13 - Question 37

The vertex of the parabola
y= 4(a' - a) (x - a) is

VITEEE PCME Mock Test - 13 - Question 38

Two common tangents to the circle x2 + y2 = 2a2 and parabola y2 = 8ax are

VITEEE PCME Mock Test - 13 - Question 39

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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - 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]

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 42

Since both proton and positron have the same charge VITEEE PCME Mock Test - 13 - 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 104  m s-1 in a uniform magnetic field, then the value of the magnetic induction is (g = 10 m s-2)

VITEEE PCME Mock Test - 13 - Question 44

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

VITEEE PCME Mock Test - 13 - Question 45

The resistance of a cell does not depend upon

VITEEE PCME Mock Test - 13 - Question 46

A laser beam is used for carrying out surgery because it

Detailed Solution for VITEEE PCME Mock Test - 13 - 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 - 13 - Question 47

The temperature coefficient of resistance for a wire is 0.00125/ oC. At 300 K its resistance is 1 ohm. The temperature at which the resistance becomes 2 ohm is

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - Question 49

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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - Question 52

A choke coil has

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - 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

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 54

As L ∝ N2
∴ L = 108 x (500/600)2 = 75 mH

VITEEE PCME Mock Test - 13 - Question 55

Heat radiations propagate with the speed of

VITEEE PCME Mock Test - 13 - Question 56

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

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 56 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

VITEEE PCME Mock Test - 13 - Question 57

Consider the situation shown in figure. Work done in carrying a point charge from k to A, B, C are WA , WB , Wrespectively. Which one is true? VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - Question 61

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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - Question 63

Out of the following which has no charge?

VITEEE PCME Mock Test - 13 - Question 64

The element which does not exhibit radioactivity is

VITEEE PCME Mock Test - 13 - Question 65

What is the particle x in the following nuclear reaction? VITEEE PCME Mock Test - 13 - 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)

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - Question 68

The resolving power of a telescope depends on

VITEEE PCME Mock Test - 13 - Question 69

When a glass prism of refracting angle 600 is immersed in a liquid its angle of minimum deviation is 300 . The critical angle of glass with respect to the liquid medium is

VITEEE PCME Mock Test - 13 - Question 70

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

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 70

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

VITEEE PCME Mock Test - 13 - Question 71

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

VITEEE PCME Mock Test - 13 - Question 72

In an npn transistor, the emitter current is

VITEEE PCME Mock Test - 13 - Question 73

At OK temperature, a p-type semiconductor

VITEEE PCME Mock Test - 13 - Question 74

Depletion layer consists of

VITEEE PCME Mock Test - 13 - Question 75

The dominant contribution to current comes from holes in case of

VITEEE PCME Mock Test - 13 - Question 76

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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - Question 79

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

VITEEE PCME Mock Test - 13 - Question 80

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

VITEEE PCME Mock Test - 13 - Question 81

Ethylene reacts with 1% cold alkaline KMnO₄ to give

VITEEE PCME Mock Test - 13 - Question 82

Which of the following is hypnotic ?

VITEEE PCME Mock Test - 13 - Question 83

Consider the following compounds :
I. HCHO II.CH₃CHO III. CH₃COCH₃
The reactivities of these compounds are such that

VITEEE PCME Mock Test - 13 - Question 84

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

VITEEE PCME Mock Test - 13 - Question 85

1-Butene may be converted to butane by reaction with

VITEEE PCME Mock Test - 13 - Question 86

The significant figures of the number 6.0023 are

VITEEE PCME Mock Test - 13 - Question 87

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

VITEEE PCME Mock Test - 13 - Question 88

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

VITEEE PCME Mock Test - 13 - Question 89

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

VITEEE PCME Mock Test - 13 - Question 90

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

Detailed Solution for VITEEE PCME Mock Test - 13 - Question 90

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

VITEEE PCME Mock Test - 13 - Question 91

Which is correct statement?

VITEEE PCME Mock Test - 13 - Question 92

Melting points are normally the highest for

VITEEE PCME Mock Test - 13 - Question 93

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

VITEEE PCME Mock Test - 13 - Question 94

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

VITEEE PCME Mock Test - 13 - Question 95

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

VITEEE PCME Mock Test - 13 - Question 96

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

VITEEE PCME Mock Test - 13 - Question 97
In an endothermic reaction, the value of ∆H is
VITEEE PCME Mock Test - 13 - Question 98

In which of the following reactions, heat liberated is known as standard heat of formation of CO2?

VITEEE PCME Mock Test - 13 - Question 99

Which of the following is an example of intensive property?

VITEEE PCME Mock Test - 13 - Question 100

Which of the following is antipyretic?

VITEEE PCME Mock Test - 13 - Question 101

The number of possible structural isomers of C₄H₁₀O is

VITEEE PCME Mock Test - 13 - 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)

VITEEE PCME Mock Test - 13 - Question 103

The hydrid state of Ni in Ni(CO)₄ is

VITEEE PCME Mock Test - 13 - Question 104

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

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - Question 106

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

VITEEE PCME Mock Test - 13 - 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?

VITEEE PCME Mock Test - 13 - Question 108

If the standard electrode potential of Cu2+/Cu electrode is 0.34 V, what is the electrode potential at 0.01 M concentration of Cu2+? (T = 298K)

VITEEE PCME Mock Test - 13 - Question 109

Cassiterite is concentrated by

VITEEE PCME Mock Test - 13 - Question 110

Ethyl chloride is converted into diethyl ether by

VITEEE PCME Mock Test - 13 - Question 111

White P when boiled with strong solution of caustic soda produces

VITEEE PCME Mock Test - 13 - Question 112

The components present in producer gas are

VITEEE PCME Mock Test - 13 - 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 ?

VITEEE PCME Mock Test - 13 - Question 114

In H₂O₂, the oxidation state of oxygen is

VITEEE PCME Mock Test - 13 - Question 115

Which of the following fluorides does not exist ?

VITEEE PCME Mock Test - 13 - 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

VITEEE PCME Mock Test - 13 - Question 117

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

VITEEE PCME Mock Test - 13 - Question 118

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

VITEEE PCME Mock Test - 13 - Question 119

The addition of Br2 to E-but-2-ene gives

VITEEE PCME Mock Test - 13 - Question 120

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

VITEEE PCME Mock Test - 13 - Question 121

find the synonym of DELECTABLE

VITEEE PCME Mock Test - 13 - Question 122

Fill in the blank with appropriate word.
Waking at three o'clock, I heard the........of thunder

VITEEE PCME Mock Test - 13 - Question 123

Find the Antonym of SULKY

VITEEE PCME Mock Test - 13 - Question 124

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

To take with a grain of salt

VITEEE PCME Mock Test - 13 - 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.

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