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This mock test of VITEEE PCME Mock Test - 3 for JEE helps you for every JEE entrance exam.
This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 3 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The perimeter of a sector is p. the area of the sector is maximum when its radius is

Solution:

QUESTION: 2

Let z,w be complex numbers such that z̅ + iw ̅ = 0 and arg zw = π.Then arg z equals

Solution:

QUESTION: 3

The area, in square unit, bounded by the curves * y = x ^{3}, y = x^{2}* and the ordinates

Solution:

QUESTION: 4

If (a+ib)(c+id)(e+if)(g+ih) = A+iB, then (a^{2}+b^{2})(c^{2}+d^{2})(c^{2}+f^{2})(g^{2}+h^{2}) =

Solution:

QUESTION: 5

for x ≠ 5 and *f* is continuous at *x* = 5 then *f*(5) =

Solution:

QUESTION: 6

Solution:

Put sin^{2}x = t

Then sin2x dx = d t ; x = 0, π/2 ⇒ t = 0,1

QUESTION: 7

Solution:

QUESTION: 8

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

Solution:

QUESTION: 9

The solution of the equation (x-y^{2}x)dx=(y-x^{2}y)dy is

Solution:

QUESTION: 10

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: 11

The solution of dy/dx + 1 = e^{X+Y} is

Solution:

QUESTION: 12

The order of the differential equation

Solution:

QUESTION: 13

Integrating factor of

Solution:

QUESTION: 14

Differential of x^{6} w.r. to x^{3} is equal to

Solution:

QUESTION: 15

Two functions f : R → R , g : R → R are defined as follows :

Solution:

QUESTION: 16

If ∫(sin 2x - cos 2x)dx = (1/√2) sin (2x-a) + b

Solution:

QUESTION: 17

What is the value of the integral ∫ e^{x} [ f'x + f x ] dx ?

Solution:

QUESTION: 18

sin[(1/2)cos^{-1}(4/5)] is equal to

Solution:

QUESTION: 19

What is the value of

Solution:

QUESTION: 20

True statement for

lim _{x → 0} 1 + x − 1 − x^{2} + 3x − 2 − 3 x is

Solution:

QUESTION: 21

The statement "If x is divisible by 8, then it is divisible by 6" is false if x equals

Solution:

A sentence in "If....then..." form is called an implication. The only time when an implication is false is when the "If" part of the sentence is true and the "then" part of the sentence is false. The number 32 makes the first part of the statement true and the second part of the statement false.

QUESTION: 22

The system of equation

*2x + y = 5*

*x - 3y = -1*

*3x + 4y = k*

is consistent, when *k* is

Solution:

QUESTION: 23

If A is a singular matrix then Adj A is

Solution:

QUESTION: 24

Five digit number divisible by 3 is formed using the digits 0, 1 , 2, 3, 4 and 5 without repetition. Total number of such numbers is

Solution:

A number is divisible by 3 if and only if the sum of its digits are divisible by 3

Notice that 1 + 2 + 3 + 4 + 5 = 15, which is divisible by 3

The only other way we can have a sum of 5 digits divisible by 3 is to replace the 3 by the 0 making the sum 3 less:

1 + 2 + 0 + 4 + 5 = 12, which is divisible by 3

No other choice of 5 digits can have a sum divisible by 3, because there is no other way to make the sum 12 or 15, and we certainly can't have a sum of 9 or 18

So the number of 5-digit numbers that can be formed from the digits {1,2,3,4,5} is

Number of ways = 1 x 2 x 3 x 4 x 5 = 120

And the number of 5-digit numbers that can be formed from the digits {1, 2, 0, 4, 5} is figured this way

Number of ways = 1 x 2 x 3 x 4 x 4 = 96

Total Number of ways = 120 + 96 = 216

QUESTION: 25

For a B.D., the parameters n and p are 16 and 1/2 respectively. Then its S.D.Ïƒ is equal to

Solution:

QUESTION: 26

If *A* and *B* are two events such that P(A ∪ B) = 0 .65, P(A ∩ B) = 0.15 then

Solution:

QUESTION: 27

You are given a box with 20 cards in it. 10 of these cards have the letter 1 printed on them. The other ten have the letter T printed on them. If you pick up 3 cards at random and keep them in the same order, the probability of making the word IIT is

Solution:

QUESTION: 28

If to form a ΔABC it is given that a=5, b=7, sinA=( 3/4 ), then possible triangles are

Solution:

Given a = 5, b = 7 and sin A = 3/4

∴ b sin A = 7 x ( 3/4 ) = 21/4 > a (= 5),

Thus is this case no triangle in possible

QUESTION: 29

If the A.M. and G.M, of the roots of a quadratic equation in x are p and q respectively, then its equation is

Solution:

QUESTION: 30

If v is the variance and σ is the standard deviation, then

Solution:

QUESTION: 31

Coefficients of correlation between observations (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) is

Solution:

QUESTION: 32

The condition that one root of the equation (1+m^{2}) x^{2} + 2 cmx + (c^{2} - a^{2}) = 0 is reciprocal of the other is____

Solution:

Let the roots of the equation

(1+m^{2}) x^{2} + 2 cmx + (c^{2} - a^{2}) = 0

are α and 1/α .

QUESTION: 33

If | x + 1 | − | x | + 3 | x − 1 || x − 2 | = x + 2 , then solution for − 1 ≤ x ≤ 0 is ___

Solution:

When − 1 ≤ x < 0

(x + 1) − (− x) + 3 (− x + 1)( − x + 2) = x + 2

⇒ 3 x^{2} − 8 x + 5 = 0

⇒ 3 x^{2} − 3 x − 5 x + 5 = 0

⇒ 3 x − 5 x − 1 = 0

⇒ x = 1 , x = 5 ∕ 3

− 1 ≤ x < 0

Hence, given equation has no solution in − 1 ≤ x < 0. .

QUESTION: 34

If cos α, cos β, cos γ are the d.c. of a line, then value of sinα^{2 }+ sin^{2}β + sin^{2}γ is

Solution:

QUESTION: 35

The Cartesian equation of the plane perpendicular to the line (x - 1)/2 = (y - 3)/-1 = (z - 4)/2 and passing through the origin is

Solution:

QUESTION: 36

If sin2x+sin4x=2sin3x, then x=

Solution:

QUESTION: 37

Let p be a variable point on the ellipse [(x^{2}/a^{2}) + (y^{2}/b^{2})] = 1 with foci F_{1} and F_{2}. If A is area of triangle PF_{1}F_{2}, then the maximum value of A is

Solution:

QUESTION: 38

The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x^{2} + y^{2} = 9 is

Solution:

QUESTION: 39

If a,b,c are three non-coplanar vectors, then [a+b,b+c,c+a]=-

Solution:

QUESTION: 40

i x (a x i)+j x (a x j)+k x (a x k)=

Solution:

QUESTION: 41

In a circuit containing an inductance of zero resistance, the emf of the applied A.C. voltage leads the current by

Solution:

QUESTION: 42

In photo electric effect the stopping potential is

Solution:

In the photoelectric effect is that the stopping potential is a function of the frequency of the incident light. As shown in Figure, there is even a cutoff frequency ν_{0} below which there is no photoelectric effect occurs, regardless of the intensity of the light.

A plot of stopping potential vs. frequency of incident light (Cathode: Sodium ; Cutoff frequency νo =4.39x 10^{14} Hz

Hence option (A) is correct.

QUESTION: 43

Which of the following metal thermionically emit an electron at a relatively lowest temperature among them?

Solution:

QUESTION: 44

A metal foil of negligible thickness is introduced between two plates of a capacitor of capacitance *C* at the centre. The new capacitance of the capacitor will be

Solution:

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} gC^{-1}, the mass of copper deposited on the electrode will be

Solution:

QUESTION: 46

If sky wave with a frequency of 50 MHz is incident on D-region at an angle of 30^{0} then angle of refraction is

Solution:

QUESTION: 47

In a metre bridge, the balancing length from the left end (standard resistance of one ohm is in the right gap) is found to be 20 cm. The value of the unknown resistance is

Solution:

QUESTION: 48

In a Wheatstone's bridge, all the four arms have equal resistance R. If resistance of the galvanometer arm is also R, then equivalent resistance of the combination is

Solution:

QUESTION: 49

Four two *ohm* resistors are connecte together along the edges of a square. A 10*V* battery of negligible internal resistance is connected across a pair of the diagonally opposite corners of the square. The power dissipated in the circuit is

Solution:

QUESTION: 50

Which of the following does not obey the ohm's law?

Solution:

QUESTION: 51

Particle nature and wave nature of electromagnetic waves and electrons be shown by

Solution:

QUESTION: 52

A choke coil has

Solution:

QUESTION: 53

*R*, *L* and *C* represent the physical quantities resistance, inductance and capacitance respectively. Which one of the following combinations has dimension of frequency?

Solution:

QUESTION: 54

A metal disc of radius 100 cm is rotated at a constant angular speed of 60 rad/s in a plane at right angles to an external field of magnetic induction 0.05 Wb/m^{2}. The emf induced between the centre and a point on the rim will be

Solution:

QUESTION: 55

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: 56

Electromagnetic radiation of highest frequency is

Solution:

QUESTION: 57

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: 58

Equal charges are given to two spheres of different radii. The potential will be

Solution:

QUESTION: 59

Two equal and unlike charges places 3 cm apart in air, attract each other with a force of 40 N. The magnitude of each charge in micro coulomb is

Solution:

QUESTION: 60

The figure shows a charge *q* placed inside a cavity in an uncharged conductor. Now if an external electric field is switched on:

Solution:

QUESTION: 61

A 2 μ F condenser is charged to 500V and then its plates are joined through of consistance. The heat produced in the resistance in joules is

Solution:

QUESTION: 62

A straight wire carrying current I is turned into a circular loop. If the magnitude of magnetic moment associated with it in M.K.S. unit is M, the length of wire will be

Solution:

QUESTION: 63

Which of the following is more effective in inducing nuclear fission

Solution:

QUESTION: 64

A radioactive element has a half life of 15 years. The fraction that will decay in 30 years is

Solution:

QUESTION: 65

The photoelectric threshold of a certain metal is 30 Å. If the radiation of 2000 Å is incident on the metal

Solution:

QUESTION: 66

Mass - energy equation was proposed by

Solution:

QUESTION: 67

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

Solution:

QUESTION: 68

A glass slab is placed in the path of convergent light. The point of convergence of light

Solution:

QUESTION: 69

The image formed by an objective of a compound microscope is

Solution:

QUESTION: 70

Application of a forward bias to a p-n junction

Solution:

QUESTION: 71

The element that can be used as acceptor impurity to dope silicon is

Solution:

QUESTION: 72

In a common-base amplifier, the phase difference between the input signal voltage and output voltage is

Solution:

A common-emitter amplifier is shown in the figure (A).

In this Circuit , the output signal is an amplified version of the input signal and is 180 degrees out of phase with the input signal.

Common emitter Amplifier

Common Base Amplifier

Figure (B) is a common-base amplifier. In this circuit the output signal is an amplified version of the input signal and is in phase with the input signal. In both of these circuits, the output signal is controlled by the base-to-emitter bias. As this bias changes (because of the input signal) the current through the transistor changes.

QUESTION: 73

A half-wave rectifier is being used to rectify an alternating voltage of frequency 50 Hz. The number of pulses of rectified current obtained in one second is

Solution:

QUESTION: 74

The intrinsic semiconductor becomes an insulator at

Solution:

QUESTION: 75

The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the

Solution:

QUESTION: 76

The bond that exists in a semiconductor is

Solution:

QUESTION: 77

A wave front travels

Solution:

QUESTION: 78

Which of the following property of light waves is not observed in sound waves?

Solution:

QUESTION: 79

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: 80

Bubble's of colourless soap solution appear coloured in sun light. This is due to

Solution:

QUESTION: 81

The reagent required to convert propene to 1-Propanol is

Solution:

QUESTION: 82

In nucleophilic substitution reactions, the reactivity of carbonyl compounds follows the order

Solution:

QUESTION: 83

The most reactive compound towards formation of cyanohydrin on treatment with KCN followed by acidification is

Solution:

QUESTION: 84

In which of the following reactions, both oxidised and reduced forms of the same compound are obtained?

Solution:

QUESTION: 85

Wurtz reaction involves the interaction of alkyl halides in dry ether with

Solution:

QUESTION: 86

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

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

The enzyme present in saliva is

Solution:

QUESTION: 89

The volume in litres of CO_{2} liberated at STP when 10 grams of 90% pure limestone is heated completely is

Solution:

Limestone (CaCO_{3}) has a molar mass of = 100 g/mol

So, 10 gm of 100% pure CaCO_{3} would = 10 gm of CaCO_{3}

90% pure CaCO_{3} means, each 10 gm of sample will have, = ( 90/100 ) x 10 = 9 gm CaCO_{3}

So, number of moles of CaCO_{3} = given mass/ molar mass = 9/100 = 0.09

Now, we have the reaction,

CaCO_{3} → CaO + CO_{2}

When 1 mole of CaCO_{3} yields 1 moles of CO_{2}

0.09 moles of CaCO_{3} will yield 0.09 moles of CO_{2}

1 mole of CO_{2} = 22.4 liters (at STP)

So, total volume = 22.4 x 0.09 = 2.016 liters

QUESTION: 90

Which of the following biomolecule is insoluble in water?

Solution:

QUESTION: 91

Pick out the one which does not belong to family of enzymes.

Solution:

QUESTION: 92

Acetyl chloride can not be obtained by treating acetic acid with

Solution:

QUESTION: 93

A colourless liquid at room temperature reacts with soda lime to form sodium salt of carboxylic acid and ammonia gas.The liquid is

Solution:

QUESTION: 94

Rancidity of butter is due to the formation of

Solution:

QUESTION: 95

In a reversible reaction, the catalyst

Solution:

QUESTION: 96

Chemical equilibrium is dynamic in nature, because

Solution:

The two opposite processes, forward reaction and reverse reaction, keep on occurring in it all the time but at exactly equal rates (or equal speeds)

A chemical reaction does not stop after reaching the equilibrium state, only the rate of the forward and the reverse reactions become equal at the equilibrium state

QUESTION: 97

Latent heat of vaporisation of a liquid at 500 K and 1 atm pressure is 10.0 kcal/mol. What will be the change in internal energy (ΔE) of 3 mol of liquid at same temperature?

Solution:

Vaporization of 3 moles of H_{2}O vapors is:

3H_{2}O(l) → 3H_{2}O(g)

Δn = 3 - 0 = 3

Therefore,

ΔU = ΔH - ΔnRT

= (3 x10) - 3 (0.002) (500) = 27

change in internal energy is:

ΔU = 27 Kcal

QUESTION: 98

The minimum energy required by molecules to react is called

Solution:

QUESTION: 99

Given that

2C s + 2O_{2 } g → 2CO_{2} g , Δ H = − 787 k J

H_{2} g + 12O_{2} g → H_{2}O l , Δ H = − 286 k J

C_{2}H_{2} g + 2 1/2 O_{2} g → 2CO_{2} + H_{2}O l , Δ H = − 1301 k J

Heat of formation of acetylene is

Solution:

QUESTION: 100

The primary and secondary valencies of chromium in the complex ion, dichlorodioxalatochromium (III) are respectively

Solution:

QUESTION: 101

Structurally biodegradable detergent should contain

Solution:

QUESTION: 102

Which one is false in the following statements ?

Solution:

QUESTION: 103

In which of the following complex the oxidation number of the central metal atom is zero?

Solution:

QUESTION: 104

In the diazotisation of aniline with sodium nitrite and hydrochloric acid, the excess of hydrochloric acid is used primarily to

Solution:

QUESTION: 105

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

Solution:

QUESTION: 106

The *pH* of aqueous *KCl* solution is 7.0. This solution was electrolysed for a few seconds using *Pt* electrodes. Which of the following is correct?

Solution:

QUESTION: 107

In a galvanic cell, the electrons flow from

Solution:

QUESTION: 108

What is the standard cell potential for the cell? Zn ; Zn^{2+}(1M) ∥ Cu^{2+}(1M) ; Cu (E^{0} for Zn^{2+}∕Zn = −0.76 ; E^{0}for Cu^{2}⁺∕Cu = +0.34)

Solution:

QUESTION: 109

When diethyl ether is treated with excess of Cl₂ in the presence of sunlight, then the product formed is

Solution:

QUESTION: 110

When the densities of the ore particles and gangue particles are different, then the ore is concentrated by

Solution:

QUESTION: 111

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

Solution:

QUESTION: 112

Gun metal is an alloy of

Solution:

QUESTION: 113

Maximum enolisation takes place of:

Solution:

QUESTION: 114

When iron or zinc is added to CuSO₄ solution, copper is precipitated. It is due to

Solution:

QUESTION: 115

The most stable hydride is

Solution:

QUESTION: 116

When concentrated H₂SO₄ is heated with dry KNO₃, brown fumes evolve. These fumes are due to

Solution:

QUESTION: 117

The ratio of cationic radius to anionic radius in an ionic crystal is greater than 0.732. Its co-ordination number is

Solution:

QUESTION: 118

The separation of colloidal particles from those of molecular dimensions is known as

Solution:

QUESTION: 119

When calomel reacts with ammonium hydroxide, we get

Solution:

QUESTION: 120

Finely divided iron combines with CO to give

Solution:

QUESTION: 121

Find the antonym of CALLOUS

Solution:

QUESTION: 122

Fill in the blank with appropriate word.

Soft minded individuals are........to embrace all kinds of superstitions.

Solution:

QUESTION: 123

Find the Synonym of COLOSSUS

Solution:

QUESTION: 124

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

Poor Tom LAID in the shade of a tree before he could walk further.

Solution:

QUESTION: 125

**Fill in the blanks with the most suitable idiom/phrase.**

Let us now _____ and work for the advancement of the country .

Solution:

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