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This mock test of VITEEE PCME Mock Test - 10 for JEE helps you for every JEE entrance exam.
This contains 125 Multiple Choice Questions for JEE VITEEE PCME Mock Test - 10 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The maximum value of logx/x in (2, ∞) is

Solution:

QUESTION: 2

The area in square units of the region bounded by the curves x^{2} = 4y, the line x = 2 and the x-axis is

Solution:

The required area

QUESTION: 3

The polar form of the complex number (i^{25} )^{3} is

Solution:

QUESTION: 4

If [(1+i)/(1-i)]^{m} = 1, the least value of m is

Solution:

QUESTION: 5

Solution:

QUESTION: 6

Let [ ] denote the greatest integer function and *f(x)* = [*tan ^{2}x*]. Then

Solution:

QUESTION: 7

The area bounded by two curves y^{2}=4ax and x^{2}=4ay is

Solution:

QUESTION: 8

Solution:

QUESTION: 9

Consider f (x) = x^{2}/| x | , x ≠ 0, f(x) = 0, x = 0

Solution:

QUESTION: 10

The differential equation of the family of curves y^{2}=4a (x+a) is

Solution:

QUESTION: 11

The solution of the equation (1+x^{2})(1+y)dy+(1+x)(1+y^{2})dx=0 is

Solution:

QUESTION: 12

Which equation has the solution, y = 4sin3x?

Solution:

QUESTION: 13

Let A = { x ∈ R : x ≠ 0, − 4 ≤ x ≤ 4 } and f : A → R is defined by f (x) = | x |/x for x ∈ A . Then the range of *f* is

Solution:

QUESTION: 14

The solution of (x + y + 1) dy/dx = 1 is

Solution:

⇒ z - log(z + 1) = x + c ⇒ x + y + 1 = log(x + y + 2) + x + c ⇒ y = log(x + y + 2) + log c

⇒ e^{y} = (x + y + z)c ⇒ x + y + 2 = ce^{y}

QUESTION: 15

∫tan^{-1}[(2x)/(1-x^{2})]dx=

Solution:

QUESTION: 16

∫[(3x^{3}-2√x)/(x)] dx =

Solution:

QUESTION: 17

The derivative of

Solution:

QUESTION: 18

tan[(1/2)cos^{-1}(√5/3)]=

Solution:

QUESTION: 19

What is the value of

Solution:

QUESTION: 20

if f(m) = 3, f^{'}(m) = 2, g(m) = - 1 and g'(m) = 2 is

Solution:

QUESTION: 21

Which of the following is not a statement ?

Solution:

QUESTION: 22

All diagonal elements of skew symmetric matrix are

Solution:

QUESTION: 23

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: 24

If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3, is

Solution:

QUESTION: 25

If A and B are square matrices of the same order, then

Solution:

QUESTION: 26

If *A* and *B* are two events such that *P(A) = p*, *P(B) = q*, P (A ∩ B) = r , then the probability that *A* occurs but *B* does not occur, is

Solution:

QUESTION: 27

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: 28

In Δ A B C , If a^{2} + b^{2} + c^{2} = 8 R^{2} , then the triangle is

Solution:

QUESTION: 29

If b + c, c + a, a + b are in H.P., then a^{2}, b^{2}, c^{2} will be in

Solution:

QUESTION: 30

Mode is approximately given by

Solution:

QUESTION: 31

The S.D. of 5 scores 1,2,3,4,5 is

Solution:

QUESTION: 32

The condition for the roots of the equation (c^{2}-ab)x^{2}-2(a^{2}-bc)x+(b^{2}-ac)=d are equal, is

Solution:

QUESTION: 33

If α,β are the roots of equation x+1=λx(1-λx) and two values of λ can be determined from the equation (α/β)+(β/α)=π-2, then (λ₁^{2}/λ₂^{2})+(λ₂^{2}/λ₁^{2})+2=

Solution:

QUESTION: 34

The general value of θ which satisfies tanθ=-1 and cosθ=(1/√2) the equations is

Solution:

QUESTION: 35

The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 is

Solution:

QUESTION: 36

The slope of the tangent at the point (h, h) of the circle x^{2} + y^{2} = a^{2 }is

Solution:

QUESTION: 37

The distance of the point (2, 1, -1) from the plane x - 2y + 4z = 9 is

Solution:

QUESTION: 38

The equation y^{2} - x^{2} + 2x - 1 = 0 represents

Solution:

QUESTION: 39

The angle between the vectors 3i+j+2k and 2i-2j+4k is

Solution:

QUESTION: 40

If |a+b|=|a-b|, then the angle between a and b is

Solution:

QUESTION: 41

An ideal transformer has 500 and 5000 turns in primary and secondary windings respectively. If the primary voltage is connected to a 6V battery then the secondary voltage is

Solution:

QUESTION: 42

X - rays are

Solution:

QUESTION: 43

To a charged particle, which is moving with a constant initial velocity $\overrightarrow{V}$, a uniform magnetic field is applied in the direction of velocity; then

Solution:

QUESTION: 44

A parallel plate capacitor is charged. If the plates are pulled apart

Solution:

QUESTION: 45

In short wave communication waves of which of the following frequencies will be reflected back by the ionospheric layer having electron density 10^{11} per m^{-3}?

Solution:

N max = 10^{11} per m^{-3}

QUESTION: 46

The masses of three wires of copper are in ratio 1 : 2 : 3 and their length are in the ratio 3 : 2 : 1. The ratio of their resistances is

Solution:

QUESTION: 47

If 96500 C of electricity liberates one gram equivalent of any substance, the time taken for a current of 0.15 A to deposit 20 mg of copper from a solution of copper sulphate is (chemical equivalent of copper = 32)

Solution:

QUESTION: 48

A microammeter has a resistance of 100 Ω and full scale range of 50 μA. It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combination

Solution:

QUESTION: 49

When a wire of resistance R is stretched and its radius becomes r/2, then the new resistance will be

Solution:

QUESTION: 50

The resistance of a galvanometer coil is R. What is the shunt resistance required to convert it into an ammeter of range 4 times

Solution:

QUESTION: 51

Photoelectric effect proves the

Solution:

QUESTION: 52

What is self inductance of a which produces 5 V, when current in it changes from 3 A to 2 A in one millisecond ?

Solution:

QUESTION: 53

The core of a transformer is laminated so that

Solution:

QUESTION: 54

A step up transformer operates on a 230 volt line and supplies 2 amp to a load. The ratio of primary and secondary windings is 1:25. Determine the primary current .

Solution:

QUESTION: 55

An accelerated electron would produce

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 = $\frac{{q}_{\mathrm{}}}{{\in}_{0}}$

Hence the electric flux through the given small cube = $\frac{{q}_{\mathrm{}}}{{\mathrm{8\in}}_{0}}$

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 = $\frac{{q}_{\mathrm{}}}{{\in}_{0}}$

Hence the electric flux through the given small cube = $\frac{{q}_{\mathrm{}}}{{\mathrm{8\in}}_{0}}$

QUESTION: 57

Two charges -10 C and + 10 C are placed 10cm apart. Potential at the centre of the line joining two charges is

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

Figure shows an electric line of force which curves along a circular arc. The magnitude of electric field intensity is same at all points on this curve and is equal to *E*. If the potential at *A* is *V*, then the potential at *B* is:

Solution:
V = - ∫ E - dr

⇒ V_{B} - V_{A} = - ERθ

V_{B} = V - ERθ

⇒ V

V

QUESTION: 60

At a point A, there is an electric field of 500 V-m⁻� and potential difference of 3000 V. The distance between the point charge and the point A is

Solution:

QUESTION: 61

Two charges 'Q' and 'Q' are kept at a distance 'd' .The charge 'q' is kept at the midpoint of line joining the charges. The magnitude of 'q' to keep the system in equilibrium is

Solution:

QUESTION: 62

A straight wire of diameter 0.5 mm carrying a current of 1 A is replaced by another wire of 1 mm diameter carrying the same current. The strength of magnetic field far away is

Solution:

QUESTION: 63

The function of the moderator in a nuclear reactor is

Solution:

QUESTION: 64

In a fission of U^{235} nucleus on average ----- neutrons are released.

Solution:
When U^{235} is bombarded by a neutron, it splits into barium,

Krypton and 2 or 3, so average__2.5__ neutrons per fission

Krypton and 2 or 3, so average

QUESTION: 65

A heavy nucleus at rest breaks into two fragments which fly off with velocities 8:1. The ratio of radii of the fragments is

Solution:

QUESTION: 66

The minimum energy required to remove an electron is called

Solution:

QUESTION: 67

The maximum energy received by the earth from the sun is in the form of

Solution:

QUESTION: 68

The threshold wavelength is 2000 Å. The work function is

Solution:

QUESTION: 69

The eye-piece used in biological microscope is

Solution:

QUESTION: 70

In an n-p-n transistor, p-acts as a/an

Solution:

QUESTION: 71

Pick out the incorrect statement regarding reverse saturation current in a *p* - *n* junction diode.

Solution:

QUESTION: 72

In an intrinsic - semiconductor the charge carriers responsible for electrical conduction are

Solution:

QUESTION: 73

In a P-type semiconductor, germanium is doped with

Solution:

QUESTION: 74

The most commonly used material for making transistor is

Solution:

QUESTION: 75

When a semiconductor is continuously heated the value of its resistance

Solution:

QUESTION: 76

In N-type semiconductors, majority charge carriers are

Solution:

QUESTION: 77

In a biprism expt., by using light of wavelength 5000 Å, 5 mm wide fringes are obtained on a screen 1.0 m away from coherent sources. The separation between two coherent sources is

Solution:

QUESTION: 78

For the constructive interference the path difference between the two interfering waves must be equal to

Solution:

QUESTION: 79

A train is approaching a platform with a velocity ν. The frequency heard by an observer standing at the station is

Solution:

QUESTION: 80

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

Solution:

QUESTION: 81

Final product formed on reduction of glycerol by hydriodic acid is

Solution:

QUESTION: 82

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: 83

In Cannizzaro's reaction

Solution:

QUESTION: 84

Which of the following method is most appropriate for the manufacture of methane?

Solution:

QUESTION: 85

Formalin is an aqueous solution of

Solution:

QUESTION: 86

Propene is reacted with HBr in presence of peroxide, the product is

Solution:

QUESTION: 87

Which one of the following compounds is not a vitamin?

Solution:

QUESTION: 88

The mass of 112 cm^{3} of CH₄ gas at STP is

Solution:

QUESTION: 89

Sodium ethoxide reacts with ethyl acetate to

Solution:

QUESTION: 90

The reagent which forms crystalline osazone derivative when reacted with glucose is

Solution:

QUESTION: 91

4.4 g of an unknown gas occupies 2.24 L of volume at standard temperature and pressure. The gas may be

Solution:

QUESTION: 92

Scurvy is caused due to deficiency of

Solution:

QUESTION: 93

A cylinder filled with a movable piston contains liquid water in equilibrium with water vapour at 25^{0}C. Which one of the following operations results in a decreace in the equilibrium vapour pressure ?

Solution:

QUESTION: 94

The enthalpy of a solution of *KNO _{3}* is + 35.64

Solution:

QUESTION: 95

Hydrolysis of benzonitrite by dilute HCl yields

Solution:

QUESTION: 96

Hess's law deals with

Solution:

QUESTION: 97

In a reversible reaction, the catalyst

Solution:

QUESTION: 98

The acid showing salt like character in aqueous solutions is

Solution:

QUESTION: 99

Adiabatic process involves

Solution:

QUESTION: 100

In the presence of acid, the hydrolysis of methyl cyanide gives

Solution:

QUESTION: 101

The d-electron configurations of Cr^{2+}, Mn^{2+}, Fe^{2+} and Ni^{2+} are 3d^{4}, 3d^{5, 3d6} and 3d^{8} respectively. Which one of the following aqua complexes will exhibit the minimum paramagnetic behaviour?

(At No. Cr = 24, Mn = 25, Fe = 26, Ni = 28)

Solution:

QUESTION: 102

The ingredient used as vehicle in perfumery is

Solution:

QUESTION: 103

Copper sulphate dissolves in excess of KCN to give

Solution:

QUESTION: 104

The IUPAC name of CH₃-C≡C-CH(CH₃)₂ is

Solution:

QUESTION: 105

Which of the following reagent can be used to convert benzene diazonium chloride into benzene ?

Solution:

QUESTION: 106

At STP,1.12 litre of H₂ is obtained on flowing a current for 965 seconds in a solution.The value of current is

Solution:

QUESTION: 107

Which of the following reactions does not yield an alkyl halide?

Solution:

QUESTION: 108

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

Solution:

QUESTION: 109

The single electrode reactions Cd(s) → Cd + 2(aq) + 2e^{-} E^{0} = 0.403 V

Cu^{+2} (aq) + 2 e^{-} → Cus E^{0} = 0.337 V can be combined to give the cell reaction

. Cd (s) → Cu^{+2} (aq) → Cd^{+2} (aq) + Cu s . The emf of such cell is

Solution:

QUESTION: 110

In which of the following solutions are ions present?

Solution:

QUESTION: 111

When the product of pressure and volume is plotted against pressure for a given amount of the gas, the line obtained is

Solution:

QUESTION: 112

Which of the following halides is the most stable?

Solution:

QUESTION: 113

Among the trihalides of nitrogen which one is most basic?

Solution:

QUESTION: 114

A compound contains atoms of three elements : A,B and C. If the oxidation number of A is + 2, B is + 5 and that of C is -2, the possible formula of the compound is

Solution:

QUESTION: 115

The intermetallic compound LiAg crystallizes in cubic lattice in which both lithium and silver have co-ordination number of eight. The crystal class is

Solution:

QUESTION: 116

The oxide which is the anhydride of orthophosphoric acid is

Solution:

QUESTION: 117

The bleeding on a wound is stopped by the application of ferric chloride due to

Solution:

QUESTION: 118

In the ground state, an element has 13 electrons in its "M-shell". The element is.......

Solution:

QUESTION: 119

The valence shell of transition elements consist of

Solution:

QUESTION: 120

C_{4}H_{4}O_{4} can be:

Solution:

QUESTION: 121

Find the Antonym of GATHERED

Solution:

QUESTION: 122

Fill in the blank with appropriate word.

.........learning does not help the mental growth of a student.

Solution:

QUESTION: 123

Find the synonym of ATTRIBUTE

Solution:

QUESTION: 124

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

Bring forth

Solution:

QUESTION: 125

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

I waited for half an hour for my friend, but the train didn't TURN IN.

Solution:

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