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This mock test of JEE Main Mock Test 13 for JEE helps you for every JEE entrance exam.
This contains 90 Multiple Choice Questions for JEE JEE Main Mock Test 13 (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

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

Solution:

QUESTION: 8

The solution of differential equation (dy/dx)=[((1+x)y)/((y-1)x)] 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)â‰ 1, then P(AÌ…/BÌ…) is equal to

Solution:

QUESTION: 24

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

Solution:

QUESTION: 25

Let A = {a,b,c}, B = {b,c,d}, C = {a,b,d,e}, then A âˆ© (B âˆª 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 iÌ‚ - 2 jÌ‚ + kÌ‚ 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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