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

Solution:
Plot the graph of 1-|x| to plot it first you know graph of |x| then taking x-axis as the mirror take image of |x| then shift the the graph 1 unit upward that will be your final graph the 3 vertices of the triangle so formed will be (-1,0) ,(0,1), (1,0) then find the area it will be 1.

QUESTION: 2

For the curve x = t^{2} - 1, y = t^{2} - t tangent is parallel to x-axis where

Solution:

QUESTION: 3

If ω is a complex cube root of unity ,then the value of ω ^{99} + ω ^{100} + ω^{101} is

Solution:
1+w+wÂ²=0

divide w powers by 3 and put remainders as powers then you will get 0

divide w powers by 3 and put remainders as powers then you will get 0

QUESTION: 4

If |(z-1)/(z-i)| = 1, then the locus of z is

Solution:

QUESTION: 5

Solution:

QUESTION: 6

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

Solution:

QUESTION: 7

Solution:

QUESTION: 8

Solution:

QUESTION: 9

If *a, b, c* are different

Solution:

QUESTION: 10

and A_{1} , B_{1} , C_{1} etc are cofactors of a 1 , b 1 , c 1 , then

Solution:

QUESTION: 11

The solution of the equation (2y-1) dx-(2x+3) dy=0 is

Solution:

QUESTION: 12

The solution of is

Solution:
2xydy/dx = 1 + yÂ²

2 ydy/1 + yÂ² = dx/x

Integrating

log(1 + yÂ²) = logx + c

log(1 + yÂ²/x) = c

1 + yÂ²/x = e^c(new constant) = câ€²

1 + yÂ² = cx

2 ydy/1 + yÂ² = dx/x

Integrating

log(1 + yÂ²) = logx + c

log(1 + yÂ²/x) = c

1 + yÂ²/x = e^c(new constant) = câ€²

1 + yÂ² = cx

QUESTION: 13

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

Solution:
Let

y = x^6

z = xÂ³

To find : dy/dz

dy/dx = 6x^5

dz/dx = 3xÂ²

dy/dx Ã— dx/dz = 6x^5/3xÂ²

= 2xÂ³

y = x^6

z = xÂ³

To find : dy/dz

dy/dx = 6x^5

dz/dx = 3xÂ²

dy/dx Ã— dx/dz = 6x^5/3xÂ²

= 2xÂ³

QUESTION: 14

If *c* is parameter then the differential equation whose solution is y = c^{2} + c/x is

Solution:

QUESTION: 15

The minimum value of sinx + cosx is

Solution:

QUESTION: 16

What is the value of

Solution:

QUESTION: 17

Solution:

QUESTION: 18

If cot^{-1}[(cos α)^{1/2}] - tan^{-1}[(cot α)^{1/2}] = x, then sin x =

Solution:

QUESTION: 19

where [x] denotes the greatest integer not exceeding x, then

Solution:

QUESTION: 20

Solution:

QUESTION: 21

Which statement represents the inverse of the statement "If it is snowing, then Skeeter wears a sweater."?

Solution:

To form the INVERSE of a statement, insert "NOT" into the "If" and the "then" sections of the sentence.

QUESTION: 22

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

Solution:

QUESTION: 23

If |A| represents the determinant of a square matrix of order 3 then (-2A)=

Solution:

QUESTION: 24

From a box containing 10 cards, numbered 1, 2,3,......,10. Four cards are drawn together, what is the probability of their sum is even ?

Solution:

QUESTION: 25

The number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that the committee contains atleast 3 ladies is

Solution:

A committee of 6 members is to formed from 8 gentlemen and 4 ladies by taking

(i) 3 lady out of 4 and 3 gentlemen out of 8

(ii) 4 lady out of 4 and 2 gentlemen out of 8

In case (i) the number of ways = ^{4}c_{3} x ^{8}c_{3}

= 4 x 56 = 224

In case (ii) the number of ways = ^{4}c_{4} x ^{8}c_{2}

= 1 x 28 = 28

Hence, the required number of ways = 224 + 28 = 252

QUESTION: 26

The probabilites of solving a problem by three students *A, B, C* independently are 1/3 , 1/4 , 1/5 . The probability that the problem will be solved is

Solution:

QUESTION: 27

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: 28

The harmonic mean of the roots of the equation (5 + √2)x^{2} - (4 + √5)s + 8 + 2√5 = 0 is

Solution:

QUESTION: 29

The average of values 0, 2, 4, 6, 8, ...., 2n is

Solution:

QUESTION: 30

In ΔABC, if cot A/2 = (b + c)/a , then the triangle is

Solution:

⇒ cos (A/2) = cos [(B - C)/2]

⇒ A/2 = (B - C)/2

⇒ A = B - C

⇒ A + C = B

⇒ B = 90^{0}.

QUESTION: 31

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: 32

If the roots of the equation x^{2}+2mx+m^{2 }-2m+6=0 are equal, then the value of m is

Solution:

QUESTION: 33

If there is a multiple root of order 3 for the equation x^{4} − 2x^{3} + 2 x − a = 0 , then the other roots is

Solution:

QUESTION: 34

The ratio in which the line joining (2,4,5), (3,5,-9) is divided by the YZ-plane is

Solution:

QUESTION: 35

The line (p + 2q) x + (p - 3q) y = p - q for different values of p and q passes through the fixed point

Solution:

QUESTION: 36

In a three dimensional space, the equation 3x - 4y = 0 represents

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

Solution:

QUESTION: 39

If sin(x-y) = cos(x+y) = 1/2, the value of x and y lying between 0^{0} and 180^{0}, are given by

Solution:

QUESTION: 40

If A(-1,2,3),B(1,1,1) and C(2,-1,3) are points in a plane, the unit vector perpendicular to the plane AB is

Solution:

QUESTION: 41

In a transformer, current and e.m.f. in the output is 10 A and is 220 V respectively. If ratio of no. of turns in secondary and primary coil 50:10, then current in the primary coil is

Solution:

QUESTION: 42

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:
At closest approach K.E = P.E

I.e. 1/2mv2= 1/4Ï€â‚¬0Ã—( ZeÃ—2e)/r here r is distance of closest approach

r is inversely proportional to square of velocity

r1/r2=(v2/v1)^2=(3v/v)^2=9

X/r2=9. r2=X/9

I.e. 1/2mv2= 1/4Ï€â‚¬0Ã—( ZeÃ—2e)/r here r is distance of closest approach

r is inversely proportional to square of velocity

r1/r2=(v2/v1)^2=(3v/v)^2=9

X/r2=9. r2=X/9

QUESTION: 43

A charged particale accelerated through a P.D. of 100 volt passes throught the uniform electric and magnetic fields so as to experience no deflection. If E = 15 x 10^{6} V m^{-1} and B = 5 x10^{3} T , then the specific charge of the particle is

Solution:

QUESTION: 44

A parallel plate capacitor of plate area A and the plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates and work done by the system in question, in the process of inserting the slab, then select the incorrect relation from the following :

Solution:

QUESTION: 45

The relation between Faraday constant F, electron charge e, and Avogardo Number N is

Solution:

QUESTION: 46

Consider telecommunication through optical fibres. Which of the following statements is not correct

Solution:

QUESTION: 47

Two wires of same material have length L and 2L and cross-sectional areas 4A and A respectively. The ratio of their specific resistance would be

Solution:

QUESTION: 48

Two non-ideal batteries are connected in parallel. Consider the following statements.

(i)The equivalent *emf* is smaller than either of the two *emfs*.

(ii)The equivalent internal resistance is smaller than either of the two internal resistances.

Solution:

QUESTION: 49

There are three voltmeters of the same range but of resistances 10000 Ω, 8000 Ω and 4000 Ω respectively. The best voltmeter among these is the one whose resistance is

Solution:

QUESTION: 50

Quantum theory of light gives concept of

Solution:

QUESTION: 51

Choke coil works on the principle of

Solution:

QUESTION: 52

In a *H* - atom an electron makes 6.6x10^{15} rev/sec around the nucleus. Then its equivalent current is

Solution:

QUESTION: 53

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: 54

Infra-red radiations are detected by

Solution:

QUESTION: 55

The core of transformer is laminated to reduce the effect of

Solution:

QUESTION: 56

On moving a charge of 20 C by 2 cm, 2 joule of work is done, then the potential difference between the points is

Solution:

W = QV

∴ V = W/Q = 2/20 = 0.1 volt

QUESTION: 57

A loop of area 0.1 m^{2} rotates with a speed of 60 rps perpendicualr to a magnetic field of 0.4 T. If there are 100 turns in the loop, maximum voltage induced in the loop is

Solution:

QUESTION: 58

The time in seconds required to produce a potential diference of 20V across a capacitor of 1000 μ F when it is charged at the steady rate of 200 μ C/s is

Solution:

QUESTION: 59

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

Solution:

QUESTION: 60

Two point charges *+q *and *-q* are held fixed at (-d,0) and (d,0) respectively of a x-y coordinate system. Then

Solution:

QUESTION: 61

When two deuterium nuclei fuse together, in addition to tritium, we get a

Solution:

QUESTION: 62

Current is flowing in two long parallel conductors in the same direction. The conductors

Solution:

QUESTION: 63

The radius of an electron orbit in a hydrogen atom is of the order of

Solution:

QUESTION: 64

The decay constant of a radio active substance is λ . Its half life is

Solution:

QUESTION: 65

Stopping potential for photoelectrons

Solution:

QUESTION: 66

A parallel plate air condenser has certain capacity. When 2/3 of the distance between the plates is filled with a dielectric, the capacity is found to increase by a factor of 2.25. The dielectric constant is

Solution:

QUESTION: 67

Two radiations containing photons of energy twice and five times the work function of the metal are incident successively on the metal surface. The ratio of the maximum velocities of the emitted electrons in the two cases will be

Solution:

QUESTION: 68

The far point of a myopic eye is 1.5 m. To correct this defect of the eye, the power of lens is

Solution:

QUESTION: 69

A plano convex lens is made refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is

Solution:

QUESTION: 70

The function of base layer in a transistor is similar to that --- in a vacuum triode.

Solution:

QUESTION: 71

The electric circuit used to get smooth d.c. output from a rectifier circuit is called

Solution:

QUESTION: 72

At 0 K intrinsic semiconductors behaves as

Solution:

QUESTION: 73

The ratio of work function and temperatures of two emitters are 1:2, then the ratio of current densities obtained by them will be

Solution:

QUESTION: 74

P-N junction is said to be forward biased, when

Solution:

QUESTION: 75

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

Solution:

QUESTION: 76

Ga As is

Solution:

QUESTION: 77

Two waves of intensities I and 4 I superimpose, then maximum and minimum intensities are

Solution:

QUESTION: 78

If a star is moving towards earth, then the lines are shifted towards

Solution:

QUESTION: 79

In Huygen's wave theory, the locus of all points oscillating in the same phase is called a

Solution:

QUESTION: 80

A wave front travels

Solution:

QUESTION: 81

Rectified spirit is a mixture of

Solution:

QUESTION: 82

Carbonyl compounds undergo nucleophilic addition because of

Solution:
Carbonyl carbon acquires positive charge,thus nucleophile can attack on it easily. Hence aldehydes and ketones show nucleophilic addition reactions easily. Due to electromaric effect oxygen atom acquired negative charge and carbon acquired positive charge.

QUESTION: 83

The cyanohydrin of a compound X on hydrolysis gives lactic acid; The X is

Solution:

QUESTION: 84

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

Solution:

QUESTION: 85

Which of the following reactions can be used for the synthesis of an alkene

Solution:

QUESTION: 86

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

Solution:

QUESTION: 87

The significant figures in 3400 are

Solution:

QUESTION: 88

The hormone which controls the processes of burning of fats, proteins and carbohydrates to librates energy in the body is

Solution:

QUESTION: 89

The α-amino acids, usually, exist in the form of zwitter ions. It means they consist of

Solution:

QUESTION: 90

On heating with conc. HNO₃, proteins give yellow colour. This test is called

Solution:
The xanthoproteic reaction is a method that can be used to determine the amount of protein soluble in a solution, using concentrated nitric acid. The test gives a positive result in amino acids carrying aromatic groups, especially in the presence of tyrosine.

QUESTION: 91

Calcium acetate when dry distilled gives

Solution:

QUESTION: 92

Which of the following does not contain a carboxyl group?

Solution:

QUESTION: 93

Toluic acid on reaction with Br₂ + Fe gives

Solution:

QUESTION: 94

The reaction,SO₂ + Cl₂ → SO₂Cl₂ is exothermic and reversible.A mixture of SO₂(g),Cl₂(g) and SO₂Cl₂ (l) is at equilibrium in a closed container.Now a certain quantity of extra SO₂ is introduced into the container , the volume remaining the same.which of the following is/are true ?

Solution:

QUESTION: 95

when a catalyst is added to a reversible reaction in equilibrium state, the value of equilibrium constant

Solution:

QUESTION: 96

Heat of combustion ΔH for C(s), H_{2}(g) and CH_{4}(g) are -94, -68 and -213 cal/mol. Then ΔH for C(s) + 2H_{2}(g) → CH_{4}(g) is

Solution:

CH_{4} + 2O_{2} = CO_{2} + 2H_{2}O

ΔH = -213 cal/mol .....(1)

C + O_{2} = CO_{2}

ΔH = - 94 cal/mol .....(2)

H_{2} + (1/2) O_{2} = H_{2}O

ΔH = - 68 cal/mol .....(3)

ΔH for C(s) + 2H_{2}(g) → CH_{4}(g)

= 2(eq 3) + (eq 2) - (eq 1)

= (- 68x2) + (- 94) - (- 213) = -17Kcal

QUESTION: 97

Internal energy of a substance/system is a

Solution:

QUESTION: 98

Given C(s) + O₂(g) → CO₂(g) ; ∆H = −395kJ, S(s) + O₂(g) → SO₂(g);∆H = −295kJ , CS₂(l) + 3O₂(g) → CO₂(g) + 2SO₂(g) ; ∆H = −1110kJ. The heat of formation of CS₂(l) is

Solution:

QUESTION: 99

Detergents are prepared by the action of H₂SO₄ followed by neutralization by starting with

Solution:

QUESTION: 100

The IUPAC name of (CH₃)₂CHCH₃ is

Solution:

QUESTION: 101

In which of the following complex ion, the central metal ion is in a state of sp^{3} d^{2} hybridisation?

Solution:

QUESTION: 102

The reaction takes place with

Solution:

QUESTION: 103

Acetaldoxime reacts with P₂O₅ to give

Solution:

QUESTION: 104

Dye test can be used to distinguish between

Solution:

QUESTION: 105

Corrosion can be prevented by

Solution:

QUESTION: 106

During the electrolysis of a solution of AgNO₃, 9650 C of charge passes through the electroplating bath, the mass of silver deposited on the cathode will be

Solution:

QUESTION: 107

The standard reduction potentials of 4 elements are given below.Which of the following will be the most suitable reducing agent?

I = -3.04 V, II = -1.90 V, III =0 V, IV = 1.90 V

Solution:

QUESTION: 108

Which of the following is simple ether ?

Solution:

QUESTION: 109

The internal energy of one mole of an ideal gas is given by

Solution:

QUESTION: 110

The most common alum is

Solution:

QUESTION: 111

Which of the following is used in the preparation of aerated water (soda)?

Solution:

QUESTION: 112

Which of the following compound is not known

Solution:

QUESTION: 113

Which of the following contains a coordinate covalent bond ?

Solution:

QUESTION: 114

In the conversion Br₂ → BrO₃^{-} the oxidation state of bromine changes from

Solution:

QUESTION: 115

The blue complex formed on addition of conc. NH₄OH solution to a Cu^{2+} salt solution has the structure?

Solution:

QUESTION: 116

Solution:

QUESTION: 117

Which among the following statements is false?

Solution:

QUESTION: 118

Space lattice of CaF₂ is

Solution:

QUESTION: 119

Two moles of an aldehyde react with concentrated solution of sodium hydroxide and produce one mole of acid and one mole of alcohol. The aldehyde is

Solution:

QUESTION: 120

During extraction of silver, which of the following is formed ?

Solution:

QUESTION: 121

Find the antonym of CELIBATE

Solution:

QUESTION: 122

Fill in the blank with appropriate word.

The miser gazed.........at the pile of gold coins in front of him.

Solution:

QUESTION: 123

Find the synonym of AMENDABLE

Solution:

QUESTION: 124

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

He does not like to be friendly with Sarita; he always GIVES HER A COLD SHOULDER.

Solution:

QUESTION: 125

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

No one could explain how a calm and balanced person like him could PENETRATE such a mindless act on his friends.

Solution:

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