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This mock test of JEE Main Mock - 13 (Previous Pattern) for JEE helps you for every JEE entrance exam.
This contains 90 Multiple Choice Questions for JEE JEE Main Mock - 13 (Previous Pattern) (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The area bounded by the curve y = x^{3}, x-axis and two ordinates x = 1 to x = 2 is equal to

Solution:

QUESTION: 2

If x is so small that x^{3} and higher power of x may be neglected, then [(1+x)^{3/2} - [1+(1/2)x]^{3}] / [(1-x)^{1/2}] may be approximated as

Solution:

QUESTION: 3

Solution:

QUESTION: 4

*i*^{243} =

Solution:

QUESTION: 5

If f x and if *f* is continuous at *x* = 1 then *f*(1) =

Solution:

QUESTION: 6

Circle x^{2}+y^{2}+4x-4y+4=0 touches

Solution:

QUESTION: 7

The solution of differential equation (dy/dx)=[((1+x)y)/((y-1)x)] is

Solution:

QUESTION: 8

Area of the triangle in the Argand diagram formed by the complex numbers *z, iz* and *z + iz* is

Solution:

QUESTION: 9

The solution of the equation (1-x^{2})dy+xydx=xy^{2}dx is

Solution:

QUESTION: 10

f(x)=x^{3}-27x+5 is increasing when

Solution:

QUESTION: 11

The eccentricity of the ellipse 9x^{2} + 5y^{2} - 30y = 0 is

Solution:

QUESTION: 12

The negation of the statement ' he is rich and happy' is given by

Solution:

QUESTION: 13

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): is discontinuous for integral values of x.

Reason(R): f(x) is not defined for integral values of x.

Solution:

QUESTION: 14

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): The function f (x) ≡ x^{5} − 5x^{3} − 20x + 7 attains its maximum at x = − 1 .

Reason(R) : f ′ (−1) = 0

Solution:

QUESTION: 15

Solution:

QUESTION: 16

In the following question, a Statement-1 is given followed by a corresponding Statement-2 just below it. Read the statements carefully and mark the correct answer-

Tangents are drawn from the point (17,7) to the circle x^{2}+y^{2}=169.

Statement-1:

The tangents are mutually perpendicular.

Statement-2:

The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^{2}+y^{2}=338.

Solution:

QUESTION: 17

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): If the 21st and 22nd terms in the expansion of (1+x)^{44} are equal, then the value of x is 7/8.

Reason(R): In the expansion of (x+y)^{n}, (r+1)th term , T_{r+1} = ^{n}C_{r+1}x^{n-r+1} y^{r+1}.

Solution:

QUESTION: 18

The number of solutions of 2x + y = 4, x - 2 y = 2, 3x + 5y = 6 is

Solution:

QUESTION: 19

The maximum value of *x*^{-x} is

Solution:

QUESTION: 20

The mean annual salary of all employees in a company is Rs.25,000. The mean salaries of male and female employees are Rs.27,000 and Rs.17,000 respectively, the percentage of males and females employees by the company is

Solution:

QUESTION: 21

The focus of the parabola (y-2)^{2}=20(x+3) is

Solution:

QUESTION: 22

Everybody in a room shakes hand with every body else. The total number of hand-shakes is 66.The number of persons in the room is

Solution:

QUESTION: 23

If A and B are events such that P(A)>0 and P(B)≠1, then P(A̅/B̅) is equal to

Solution:

QUESTION: 24

If x is a positive real number different from 1, then the number 1/1 + √x, 1/1 - x , 1/1 - √x, .... are in

Solution:

QUESTION: 25

Let A = {a,b,c}, B = {b,c,d}, C = {a,b,d,e}, then A ∩ (B ∪ C) is

Solution:

QUESTION: 26

For a binomial distribution

Solution:

QUESTION: 27

The distance of the point (2,3,4) from the plane 3x-6y+2z+11=0 is

Solution:

QUESTION: 28

The value of cos 20ºcos40ºcos60ºcos80º is equal to

Solution:

QUESTION: 29

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

Solution:

QUESTION: 30

A force of magnitude 5 units acting along the vector 2 î - 2 ĵ + k̂ displaces the point of application from (1, 2, 3) to (5, 3, 7), then the work done is

Solution:

QUESTION: 31

The compound obtained by the reaction of ethene with diborane followed by hydrolysis with alkaline hydrogen peroxide is

Solution:

QUESTION: 32

Which of the following forms a hydroxide highly soluble in water?

Solution:

QUESTION: 33

Spectrum of Li^{2+} is similar to that of

Solution:

Number of electrons in Li^{2+} is one similar to the hydrogen atom. One electron system shows similar king of spectra. Many electron system spectra is complex due to inter-electronic repulsions

QUESTION: 34

Reference proteins are those obtained from

Solution:

QUESTION: 35

Which bond angle θ would result in the maximum dipole moment for triatomic molecule XY_{2} as shown below?

Solution:

The dipole moment of two dipoles inclined at an angle θ is given by equation

cos 90 = 0. Since the angle increase from 98-180, the value of cos θ becomes more and more negative and hence resultant decreases. Thus, dipole moment is maximum when θ = 90º.

QUESTION: 36

In graphite, the electrons are

Solution:

QUESTION: 37

Which of the following involve sp^{2} hybridisation?

Solution:

Only SO_{2} has sp^{2} hybridisation while all the remaining molecules i.e., CO_{2}, N_{2}O and CO has sp-hybridisation.

QUESTION: 38

The geometric form of crystals is the result of orderly arrangement of

Solution:

QUESTION: 39

The heat required to raise the temperature of a body by 1K is called

Solution:

QUESTION: 40

The equilibrium constant for the following reaction will be 3 A + 2 B → C

Solution:

The correct answer is k= [C]/[A]^{3}.[B]^{2}

QUESTION: 41

A chemical reaction is catalysed by X. Hence X

Solution:

QUESTION: 42

Which relation is correct?

Solution:

QUESTION: 43

Work done during the compression of a gas from a volume of 6dm^{3} to 4 dm^{3} against a constant external pressure of 3 atm is (1atm-litre=101.32J)

Solution:

QUESTION: 44

The IUPAC name of (CH₃)₃ C - CH = CH₂ is

Solution:

QUESTION: 45

Eka-aluminium and eka-silicon are known as

Solution:

Gallium and Germanium were unknown at the time when Mendeleev's periodic table was formulated. But Mendeleev's predicted the properties of these elements and named them eka-aluminium and eka-silicon. Later when these elements were discovered, their properties were found to be similar to those of aluminium and silicon.

QUESTION: 46

In a closed insulated container a liquid is stirred with a paddle to increase the temperature. Which of the following is true

Solution:

QUESTION: 47

Which of the following is not isoelectronic?

Solution:

Isoelectronic species: a group of ions, atoms, or molecules that have the same number of electrons.

Number of electrons in Na^{+} = 10

Number of electrons in Mg^{2+} = 10

Number of electrons in O^{2 − } = 10

Number of electrons in Cl^{ − } = 18

QUESTION: 48

Which of the complexes is expected to have lowest Δ_{0} value?

Solution:

The magnitude of Δ_{0} varies from stronger to weaker ligands. According to spectro-chemical series F^{−} is weaker while NH_{3} is a stronger ligand. Stronger ligand gives a larger value of Δ_{0}

QUESTION: 49

Which of the following belongs to the actinide series?

Solution:

QUESTION: 50

Which of the following is the use of electrolysis?

Solution:

QUESTION: 51

The property of hydrogen which distinguishes it from other alkali metals is

Solution:

QUESTION: 52

A sample of gas has a volume of 0.2 lit. measured at 1 atm. pressure and 0ºC . At the same pressure but at 273ºC its volume will become

Solution:

QUESTION: 53

Which of the following reacts with chloroform and base to form phenyl isocyanide?

Solution:

QUESTION: 54

Which one of the following compounds is a Lewis acid ?

Solution:

QUESTION: 55

Maximum number of active hydrogens are present in

Solution:

QUESTION: 56

The standard reduction potential at 298 *K* for the following half cell reaction are given below

Which one is the strongest reducing agent?

Solution:

QUESTION: 57

Ethynic hydrogen is released most easily in :

Solution:

QUESTION: 58

Phenol is

Solution:

QUESTION: 59

Among the following, the optically inactive compound is

Solution:

QUESTION: 60

Ether is :

Solution:

QUESTION: 61

Which of th following transitions in a hydrogen atom emits the photon of highest frequency?

Solution:

QUESTION: 62

A nucleus with Z = 92 emits the following in a sequence: α,β⁻,β⁻,α,α,α,α,α,β⁻,β⁻,α,β⁺,β⁺,α. The atomic no. of the resulting nuclues is

Solution:

QUESTION: 63

Uniform wire 16 Ω resistance is made in the form of a square. Two opposite corners of the square are connected by a wire of resistance of 16 Ω . The effective resistance between the other two opposite corners is

Solution:

QUESTION: 64

Three similar cells, each of e.m.f. 2V and internal resistance r Ω send the same current through an external resistance of 2 Ω, when connected in series or in parallel. The strength of the current flowing through the external resistance is

Solution:

QUESTION: 65

Uncertainty in position of the electron is of the order of de-Broglie wavelength. Making use of Heisenberg's uncertainty principle, it will be found that uncertainty in velocity ν is of the order of

Solution:

QUESTION: 66

If momentum of a particle is doubled, then its de-Broglie's wavelength will

Solution:

QUESTION: 67

Radio wave diffract around building although light waves do not. The reason is that radio waves:

Solution:

QUESTION: 68

Five equal capacitors connected in series have a resultant capacitance of 4 μF. The total energy stored in these, when these are connected in parallel and charged to 400V is

Solution:

QUESTION: 69

A 20F capacitor is charged to 5V and isolated. It is then connected in parallel with an uncharged 30F capacitor. The decrease in the energy of the system will be

Solution:

QUESTION: 70

Taking that earth revolves round the sun in a circular orbit of radius 15 x 10^{10} m, with a time period of 1 year, the time taken by another planet, which is a distance of 540 x 10^{10} m, to revolve round the sun in circular orbit once, will be

Solution:

QUESTION: 71

The periodic time of a communication satellite is

Solution:

QUESTION: 72

The energy spectrum of a black body exhibits a maximum around a wavelength λ₀. The temperature of a black body is now changed such that the energy is maximum around a wavelength 0.75 λ₀. The power radiated by the black body will now increase by a factor of

Solution:

QUESTION: 73

A liquid cools down from 70ºC to 60ºC in 5 minutes. The time taken to cool it from 60ºC to 50ºC will be

Solution:

QUESTION: 74

If a particle covers half the circle of radius R with constant speed, then

Solution:

QUESTION: 75

A wire of length L metre, carrying a current I ampere is bent in the form of a circle. its magnitude of magnetic moment will be

Solution:

QUESTION: 76

A particle is moving eastwards with a velocity of 5 m − s⁻^{1}. In 10 s, the velocity changes to 5 m − s⁻1 northwards. The average acceleration in this time is

Solution:

QUESTION: 77

A particle is viberating in a simple harmonic motion with an amplitude of 4 cm. At what displacement from the equilibrium position, is its energy half potential and kinetic ?

Solution:

QUESTION: 78

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): Due to opposition offered by self-inductance, work is done by external agent in establishing current in circuit. This work done is stored as potential energy.

Reason(R): Self-inductance of a coil depends on the geometry of coils and medium.

Solution:

QUESTION: 79

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): Both heat energy and charge are carried by the free electrons in pure metals.

Reason(R) : For pure metals, the electrical conductivity σ is directly related to the thermal conductivity K.

Solution:

QUESTION: 80

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-

Assertion(A): Costly wrist watches and other instruments are enclosed in a soft-iron case to protect it from external field.

Reason(R): Iron-case is used as magnetic screening or shielding.

Solution:

QUESTION: 81

If 'S' is stress and 'Y' is Young's modulus of material of a wire, then the energy stored in the wire per unit volume is

Solution:

QUESTION: 82

The density of ice is 9.0 g/c.c. and that of sea water is 1.1 g/c.c. An ice berg of volume V is floating in sea water. The fraction of ice berg above water level is

Solution:

QUESTION: 83

A light ray passed through an equilateral prism. If the angles of incidence and emergence are 45°45° and 55°55°respectively, the angle of deviation is

Solution:

QUESTION: 84

A constant torque of 314 N-m is exerted on a pivoted wheel. If angular acceleration of wheel is 4π rad-s⁻², then the moment of inertia of the wheel is

Solution:

QUESTION: 85

Two bodies M and N of equal masses are suspended from two separate massless springsof force constants K₁ and K₂ respectively. If the two bodies oscillate vertically such that their maximum velocities are eqaul, the ratio of the amplitude of M to that of N is

Solution:

QUESTION: 86

A stretched string is in unison with a tuning fork of frequency 392 Hz. If the length of the string is decreased by 2%, the number of beats heard per second is

Solution:

QUESTION: 87

During the adiabatic process, the pressure of gas is found to be proportional to the cube of its absolute temperature. The ratio CP/CV for gas is

Solution:

QUESTION: 88

A given system undergoes a change, in which work done by a system equal to decrease in its internal energy. The system must have undergone an

Solution:

QUESTION: 89

Which of the following is not a unit of energy

Solution:

QUESTION: 90

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

Solution:

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