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# VITEEE PCME Mock Test - 14

## 125 Questions MCQ Test VITEEE: Subject Wise and Full Length MOCK Tests | VITEEE PCME Mock Test - 14

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This mock test of VITEEE PCME Mock Test - 14 for JEE helps you for every JEE entrance exam. This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 14 (mcq) to study with solutions a complete question bank. The solved questions answers in this VITEEE PCME Mock Test - 14 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this VITEEE PCME Mock Test - 14 exercise for a better result in the exam. You can find other VITEEE PCME Mock Test - 14 extra questions, long questions & short questions for JEE on EduRev as well by searching above.
QUESTION: 1

Solution:
QUESTION: 2

Solution:
QUESTION: 3

### The roots of the equation Solution:    QUESTION: 4

If A, B, C are represented by 3 + 4i, 5 - 2i, -1 + 16i respectively, then A, B, C are

Solution:
QUESTION: 5

If α , β are two different complex numbers such that | α | = 1, | β | = 1, then the expression | β − α /1 − α β | equals

Solution:
QUESTION: 6 is continuous at π/4 , then a =

Solution:
QUESTION: 7 Solution:
QUESTION: 8

Consider f (x) = x2 /| x | , x ≠ 0, f(x) = 0, x = 0

Solution:
QUESTION: 9

The area bounded by the curve y = x2 - 4x, x-axis and line x = 2 is

Solution: QUESTION: 10

Find the degree of (y2)2 − √y1 = y3

Solution:
QUESTION: 11

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

Solution:
QUESTION: 12

The degree and order of the differential equation of the family of all parabolas whose axis is x-axis are respectively

Solution:
QUESTION: 13

The differential equation of the family of curves y2=4a (x+a) is

Solution:
QUESTION: 14

If x=a(t-sint) and y=a(1-cost), (dy/dx)=

Solution:
QUESTION: 15

If f(x) is an odd periodic function with period 2, then f(4) equals :

Solution:
QUESTION: 16

∫tan-1x dx =

Solution:
QUESTION: 17 Solution: QUESTION: 18

If tan-1x + tan-1y + tan-1z = π, then x+y+z is equal to

Solution:
QUESTION: 19 Solution:
QUESTION: 20

A function f(x) is defined as f (x) = [ 1 − x2 ] , − 1 ≤ x ≤ 1 , where [x] denotes the greatest integer not exceeding x. The function f(x) is discontinuous at x = 0 because

Solution:
QUESTION: 21

The sentence "____ if and only if x + x = 3x" is TRUE.

Solution:

"if and only if" is TRUE when both conditions are the SAME truth value. Since "x + x = 3x" is false, the first condition must also be false. 2x - x = 2x is false.

QUESTION: 22

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

Solution:
QUESTION: 23

If A and B are two matrices such that AB=B and BA=A, then A2+B2=

Solution:
QUESTION: 24

If nPr=840, nCr=35, then n=

Solution:
QUESTION: 25

A biased coin with probability p,0<p<1 of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even, is 2/5, then p equals

Solution:
QUESTION: 26

In two events P(A∪B) = 5/6, P(A) = 5/6, P(B) = 2/3 then A and B are

Solution:
QUESTION: 27

In four schools B₁, B₂, B₃, B₄ the percentage of girls students is 12, 20, 13, 17 respectively. From a school selected at random, one student is picked up at random and it is found that the student is a girl. The probability that the school selected is B₂, is

Solution:
QUESTION: 28

If the side of a triangle are 13, 14, 15, then the radius of the incircle is

Solution:
QUESTION: 29

The fourth ,seventh and tenth of a G.P. are p,q,r respectively then

Solution:
QUESTION: 30

Two numbers within the brackets denote the ranks of 10 students of a class in two subjects - (1, 10), (2, 9), (3, 8), (4, 7), (5, 6), (6, 5), (7, 4), (8, 3), (9, 2), (10, 1), then rank correlation coefficient is

Solution:
QUESTION: 31

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: 32

The one roots of the equation 2x5-14x4+31x3-64x2+19x+130=0 is

Solution:
QUESTION: 33

The equation of the sphere concentric with the sphere x2+y2+z2-4x-6y-8z=0 and which passes thro' (0.1,0) is

Solution:
QUESTION: 34

If α , β , γ are the roots of the equation x3 − 6 x2 + 11 x + 6 = 0, then Σ α2 β + Σ α β2 =

Solution:
QUESTION: 35

The locus of the point of intersection of tangents to the circle x = a cos θ, y = a sin θ at the points, whose parametric angles differ by π/2 is

Solution:
QUESTION: 36

3x (x - 2) + 3y (y + 1) = 4 is

Solution:
QUESTION: 37

In three dimensional space, the equation 3y+4z=0 represents

Solution:
QUESTION: 38

If vectors 2i+j+k and i-4j+λk are perpendicular, then λ=

Solution:
QUESTION: 39

If the solution for θ of cospθ + cosqθ = 0, p > 0, q > 0 are in A.P., then the numerically smallest common difference of A.P. is

Solution:

Given cospθ = - cosqθ = cos (π + qθ)
⇒ pθ = 2nπ (π + qθ), n ∈ I
⇒ θ = (2n + 1)π/p - q or (2n - 1)π/p + q , n ∈ I
Angle θ = (2n + 1)π p - q given us an AP with common
difference 2π/p - q and θ = (2n - 1)π/p + q gives also an AP with common difference 2π/p + q
Then, certainly, 2π/p + q < | 2π/p - q |
∴ The smallest common difference is 2π/p + q

QUESTION: 40

The projection of the vector î - 2 ĵ + k̂ on the vector 4 î - 4 ĵ + 7 k̂ is

Solution:
QUESTION: 41

Sodium has body centred packing. Distance between two nearest atoms is 3.7 Å . The lattice parameter is:

Solution:
QUESTION: 42

For series LCR circuit, wrong statement is

Solution:
QUESTION: 43

The closest distance of approach of an α - particle travelling with a velocity 'V' to a certain nucleus is 'x'. The distance of closest approach of α - particle travelling with a velocity 3V to the same nucleus is

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

QUESTION: 47

EMF is most closely related to

Solution:
QUESTION: 48

Three resistors are connected to form the sides of a triangle ABC, the resistance of the sides AB, BC and CA are 40 ohms, 60 ohms and 100 ohms respectively. The effective resistance between the points A and B in ohms will be

Solution:
QUESTION: 49

Taking the internal resistance of the battery as negligible, the steady state current in the 2 Ω resistor shown in the figure will be Solution:
QUESTION: 50

If two identical heaters of 220 V, 1000 W are placed parallel to each other across 220 V lines, then the combined power of the heaters is

Solution:
QUESTION: 51

In a D.C. motor induced e.m.f will be maximum

Solution:
QUESTION: 52

The approximated wavelength of a photon of energy 2.48eV is

Solution:
QUESTION: 53

A 5 cm long solenoid having 10 cm resistance and 5 mH inductance is joined to a 10 V battery. At steady state, current through solenoid is

Solution:

At steady state, inductance is ineffective
I = V/R = 10/10 = 1A

QUESTION: 54

When the current in a coil is changed from 10 A in one direction to 10 A in opposite direction in 0.5 s, an e.m.f. of 1 V is induced in it. Self-inductance of the coil is

Solution:
QUESTION: 55

Out of the folowing statement which is NOT true?

Solution:
QUESTION: 56

If the electric flux entering and leaving an enclosed surface respectively is φ₁ and φ₂, the electric charge inside the surface will be

Solution:
QUESTION: 57

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: 58

Two equal charges, q each are placed at a distance of 2a, and a third charge -2q is placed at the mid point. The potential energy of the system is

Solution:
QUESTION: 59

The capacitance of a parallel plate capacitor becomes 4/3 times its original value if a dielectric slab of thickness t = d/2 is inserted between the plates (where d is separation between the plates). The dielectric constant of the slab 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

The inward and outward electric flux of a closed surface are 8x10C and 4x10C respectively. The net charge inside the closed surface is

Solution:
QUESTION: 62

A 10 A ammeter has a resistance of 0.09 Ω. What resistance of the shunt will enable it to read up to 100 A?

Solution:
QUESTION: 63

The first atomic reactor was constructed by

Solution:
QUESTION: 64

The half life period of radio - active isotope is 5 minutes. The fraction of isotope, that will be remaining after 30 minutes is

Solution:
QUESTION: 65

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:

Solution:
QUESTION: 66

When a metallic surface is illuminated by a monochromatic light of wavelength λ, then the potential difference required to stop the ejection of electrons is 3V₀. When the same surface is illuminated by the light of wavelength 2λ, then the potential difference required to stop the ejection of electrons is V₀. Then for photoelectric effect, the threshold wavelength for the metal surface will be

Solution:
QUESTION: 67

The work function of a metal is 2.8 eV. Its threshold wavelength will be

Solution:
QUESTION: 68

A telescope consists of two thin lenses of focal lengths 0.3 m and 3 cm respectively. It is focused on moon which subtends an angle of 0.50 at the objective. Then, the angle subtended at the eye by the final image will be

Solution:
QUESTION: 69

Ultra-violet rays are detected by

Solution:
QUESTION: 70

In the middle of the depletion layer of a reverse-biased p-n junction, the

Solution:
QUESTION: 71

The method of connecting the negative pole of battery to p - material and positive pole to n - material of a p - n junction is called

Solution:
QUESTION: 72

Rectifier is used to convert

Solution:
QUESTION: 73

The band gap in Germanium and silicon in eV respectively is

Solution:
QUESTION: 74

When germanium atoms is doped with equal no. of antimony atoms, we get a/an

Solution:
QUESTION: 75

Suitable impurities are added to a semiconductor depending on its use. This is done to

Solution:
QUESTION: 76

At room temperature, a p-type semiconductor has

Solution:
QUESTION: 77

In interference pattern, the energy is

Solution:
QUESTION: 78

Young's double slit experiment gives interference fringes of width 0.3mm. A thin glass plate made of material of refractive index 1.5 is kept in the path of light from one of the slits, then the fringe width becomes

Solution:
QUESTION: 79

Which one of the following properties of light does not support wave theory of light?

Solution:
QUESTION: 80

If ratio of amplitude of two waves is 4:3, then ratio of maximum and minimum intensity is

Solution:
QUESTION: 81

Ethyl alcohol can be used for preparation of which of the following?

Solution:
QUESTION: 82

Aldol condensation will not be observed in

Solution:
QUESTION: 83

The base-catalysed aldol condensation will not occur with

Solution:
QUESTION: 84

Which of the following reaction cannot be used for the conversion RCO → RCH₂

Solution:
QUESTION: 85

Tetrabromomethane on treatment with Zn gives

Solution:
QUESTION: 86

The product formed by the action of chlorine on ethene in saturated solution of KBr is/are

Solution:
QUESTION: 87

In the following reaction, which choice has value twice that of the equivalent mass of the oxidising agent SO₂ + H₂O → 3S + 2H₂O

Solution:
QUESTION: 88

Which species represents the electrophile in aromatic nitration?

Solution:
QUESTION: 89

Lipids are

Solution:
QUESTION: 90

Chargaff's rule states that in an organism

Solution:
QUESTION: 91

Ethyl alcohol reacts with acetyl chloride to form

Solution:
QUESTION: 92

A certain compound gives negative test with ninhydrin and positive test with Benedict's solution. The compound is

Solution:
QUESTION: 93

Rancidity of butter is due to the formation of

Solution:
QUESTION: 94

From the following values of dissociation constants of four acids which value represents the strongest acid ?

Solution:
QUESTION: 95

The chemical equilibrium of a reversible reaction is not influenced by

Solution:
QUESTION: 96

In the case of gaseous homogeneous reaction,the active mass of the reactant is obtained by the expression

Solution:
QUESTION: 97

The internal energy of a subtance does not depend upon

Solution:
QUESTION: 98

A compound with molecular formula C₇H₁₆ shows optical isomerism , the compound will be

Solution:
QUESTION: 99

Which of these is a hypnotic?

Solution:
QUESTION: 100

The heat of formation of the compound in the following reaction is H₂(g) + Cl₂(g) → 2HCl(g) + 44 kcal

Solution:
QUESTION: 101

Calculate Δ H in KJ for the following reaction C(s) + O2 g → CO2 g Given that
H2O g + C g → CO g + H2  g , Δ H = + 131 k J
CO g + 1/2 O2  g → CO2  g , Δ H = − 282 k J
H2g + 1/2 O2 g → H2O g , Δ H = − 242 k J

Solution:
QUESTION: 102

The complex CoCl₃.3NH₃ ionises to give

Solution:
QUESTION: 103

The oxidation state of Cr in [ Cr (NH3)4 Cl 2 ] + is :

Solution:
QUESTION: 104

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

Solution:
QUESTION: 105

Diazo coupling is useful to prepare

Solution:
QUESTION: 106

Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by CN⁻ ion towards metal species is

Solution:
QUESTION: 107

Calculate the amount of change flowing in 2 minute in a wire of resistance 10 Ω when a potential difference of 20 V is applied

Solution:
QUESTION: 108

On heating quick lime with coke in an electric furnace, we get

Solution:
QUESTION: 109

Diethyl ether can be decomposed by

Solution:
QUESTION: 110

The standard reduction potential at 298 K for the following half cell reaction are given below
Zn2+ + 2e-  → Zn E0 = − 0.762 V
Cr+3 + 3 e- → Cr E0  = − 0.740 V
2 H+ + 2 e → HE0  = − 0.0 V
Fe+3  + e-  → Fe+2  E0  = − 0.770 V
Which one is the strongest reducing agent?

Solution:
QUESTION: 111

Solution:
QUESTION: 112

The largest bond angle is in

Solution:
QUESTION: 113

If the pressure and absolute temperatre of 2 litres of CO₂ are doubles, the volume of CO₂ would become

Solution:
QUESTION: 114

Which one of the following is pyrophosphoric acid?

Solution:
QUESTION: 115

Which substance is serving as a reducing agent in the following reaction? 14H⁺ + Cr₂O₇2- + 3Ni → 2Cr+3 + 7H₂O + 3Ni+2

Solution:
QUESTION: 116

Following compounds are respectively ... geometrical isomers

Solution:
QUESTION: 117

A face-centred cubic element has a edge length of 400 pm. What is its density? At. weight of element= 60)

Solution:
QUESTION: 118

Solution:
QUESTION: 119

Colourless solutions of the following four salts are placed separately in four different test tubes and a strip of copper is dipped in each one of these. Which solution will turn blue ?

Solution:
QUESTION: 120

Highest oxidation state of transition element is

Solution:
QUESTION: 121

Find the antonym of CORPULENT

Solution:
QUESTION: 122

Fill in the blank with appropriate word.
You will have to face some practical problems when you start.........this plan.

Solution:
QUESTION: 123

Find the Synonym of LANGUISHING

Solution:
QUESTION: 124

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

To be under a cloud

Solution:
QUESTION: 125

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

He has very good command ON English.

Solution: