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

The area formed by triangular shaped region bounded by the curves y = sinx, y = cos x and x = 0 is

Solution:

QUESTION: 2

Solution:

QUESTION: 3

The coordinates of the pole of the line lx+my+n=0 with respect to the circle x^{2}+y^{2}=1 are

Solution:

QUESTION: 4

For solving dy/dx=4x+y+1 suitable substitution is

Solution:

QUESTION: 5

The complex numbers z₁,z₂,z₃ satisfying (z₁-z₃)/(z₂-z₃) = 1-(i√3/2) then triangle is

Solution:

(z_{1}-z_{2})/(z_{2}-z_{3})= cos(-60)+sin(-60)=e-i60

taking mode on both sides

Absolute value of(z_{1}-z_{2}/z_{2}-z_{3})=1

Therefore |z_{1}-z_{2}|=|z_{2}-z_{3}|

Also angle between z_{1}-z_{2} & z_{2}-z_{3} is 60

So given triangle is equilateral triangle.

QUESTION: 6

i^{2} + i^{4} + i^{6} + ... + upto (2n + 1) =

Solution:

QUESTION: 7

Integrating factor of dy/dx+y/x = x^{3}-3 is

Solution:

QUESTION: 8

Solution:

QUESTION: 9

If is continuous at *x* = 0, then *k* =

Solution:

QUESTION: 10

The foci of an ellipse are and minor axis is of unit length. Then the equation of the ellipse is

Solution:

QUESTION: 11

If y=cot⁻^{1}[(1+x)/(1-x)], (dy/dx)=

Solution:

QUESTION: 12

Which statement is logically equivalent to "If Yoda cannot use a lightsaber, then he cannot help Luke win the battle."

Solution:

A statement is logically equivalent to its contrapositive.

To form the contrapositive, switch the "If" and "then" sections

of the statement AND insert "NOTs" into each section.

Notice in this situation, that inserting

"NOTs" turns the thoughts positive (you are negating negative thoughts).

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): If

Reason(R) : When

Solution:

QUESTION: 14

If f : ℝ → ℝ is defined by

Solution:

QUESTION: 15

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):

Reason (R): If

Solution:

QUESTION: 16

In the following questions, 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 sum of the series

Reason (R): The numbers A_{1}, A_{2}, ....., A_{n} are said to be the n arithmetic means between two given numbers a and b if a, A_{1}, A_{2}, ...., A_{n}, b are in A.P.

Solution:

QUESTION: 17

If A and B are two matrices such that A + B and AB are both defined, then

Solution:

Since A+B is defined, A and B are matrices of the same type,

say m×n; Also, AB is defined.

So, the number of columns in A must be equal to the number of rowsin B ie. n=m.

Hence, A and B are square matrices of the same order.

QUESTION: 18

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-

Let the vectors represent the sides of a regular hexagon.

Statement-1:

.

Statement-2:

Solution:

QUESTION: 19

Let

Then the global minimum value of the function is

Solution:

f ′ (x) = 4 So, for 0 ≤ x < 1, we get f ′ x < 0, i . e . , f x is m.d. and for 1 < x ≤ 2 we get f ′ (x) > 0, i . e . , f (x) is m.i .

∴ min f (x) =

QUESTION: 20

The mean of distribution is 22.2 and its mode is 23.3. The median is

Solution:

QUESTION: 21

The parabola y^{2}=4x passes thro' the point (2,-6), then the length of its latus rectum is

Solution:

It is given that the parabola passes through the point (2,-6)

Length of its latus rectum is 4a

y^{2 }= 4ax

i.e.

(-6)^{2 }= 4a(2)

⇒a = 9/2

∴ Length of the latus rectum is 4 x 9/2 = 18

QUESTION: 22

If ^{n}P_{r}=840, ^{n}C_{r}=35, then n=

Solution:

We know that ,

1) ^{n}P_{r}. = n!/( n - r )!

2) ^{n}C_{r} = n!/ [ ( n - r )! r ! ]

3) r! = ( ^{n}P_{r} )/ ^{n}C_{r }

It is given that ,

nPr = 840 ---( 1 )

nCr = 35 ---( 2 )

r! = ( nPr )/ ( nCr )

= 840/35

= 24

r! = 4 × 3 × 2 × 1

r ! = 4!

Therefore,

r = 4

Substitute r value in equation ( 1 ),

We get

n!/ ( n - 4 ) ! = 840

n( n - 1 )( n - 2 )( n - 3 ) = 840

n( n - 1 )( n - 2 )( n - 3 ) = 7× 6 × 5 × 4

Therefore ,

n = 7

QUESTION: 23

In a Binomial distribution, the probability of getting a success is 1/4 and standard deviation is 3. Then its mean is

Solution:

QUESTION: 24

If a, b, c are in H.P., then straight line x/a + y/b + 1/c = 0 always passes thro' a fixed point and that point is

Solution:

Since a, b and c are in HP therefore

.

QUESTION: 25

If 4 sin⁻^{1}x + cos⁻^{1}x = π, then x is equal to

Solution:

QUESTION: 26

The probability distribution of a random variable *X* is given below. Then its mean is

X = x_{i } 1 2 3

Solution:

QUESTION: 27

The angle between the line (x - 2)/2 = (y + 1)/-1 = (z - 3)/2 and the plane 3x + 6y - 2z + 5 = 0 is

Solution:

QUESTION: 28

If A-B=π/4, then (1+tan A)(1-tanB) is equal to

Solution:

A-B=π/4

Which implies A=B+π/4

Taking tan on both sides

tanA=tan(B+π/4)

tanA=(tanB + tan(π\4))/(1- tanB.tan(π/4))

tanA=(tanB+1)/(1-tanB)

Substituting the value of tanA in

(1+tanA).(1-tanB) we get

(1+(tanB+1)/(1-tanB)).(1-tanB)

= (1-tanB+tanB+1)/(1-tanB).(1-tanB)

=2

QUESTION: 29

If |a|=3, |b|=4, |c|=5 and a+b+c=0, the angle between a and b is

Solution:

QUESTION: 30

If a,b,c are any three vectors, the statement is true

Solution:

QUESTION: 31

The stablest among the following is

Solution:

QUESTION: 32

Addition of a solution of oxalate to an aqueous solution of mixture of Ba^{2}⁺, Sr^{2}⁺ and Ca^{2}⁺ will precipitate

Solution:

QUESTION: 33

What is the lowest energy of the spectral line emitted by the hydrogen atom in the Lyman series ? (*h* = Planck constant; *c* = Velocity of light; *R* = Rydberg constant).

Solution:

QUESTION: 34

The nodal plane in the π-bond of ethene is located in

Solution:

Formation of a π - bond occurs by the sideways overlap of p-orbitals of two C-atoms.The molecular plane does not have any π - electron density since the p-orbitals are perpendicular to the plane containing the ethene molecule.The nodal plane in the π-bond of ethene is located in the molecular plane.

QUESTION: 35

The compound with carbon uses only its *sp ^{3}* hybrid orbitals for bond formation is

Solution:

QUESTION: 36

The hydrolysis of fats and oils in the body produces

Solution:

**Fats and oils **

1. Fats and oils are a concentrated source of energy.

2. Fats and oils are essential for the transport and storage of fat-soluble vitamins in the body.

3. Fats and oils are tri- esters formed from the condensation of glycerol (propane1,2,3-triol) and three carboxylic acid molecules.

4. The hydrolysis products of a fat or oil can be identified from the structure of the fat or oil.

QUESTION: 37

Identify the least stable among the following?

Solution:

Outer electronic configuration of Li^-1 (2s^{2} most stable)

Be ^{–} ( 2s^{2} 2p^{1} less stable) than Be (2s^{2} most stable)

B ^{–} (2s^{2} 2p^{2 }stable) ; C ^{–} (2s^{2} 2p^{3} most stable)

As Be ^{–} is formed from highly stable configuration it tries to loose electron and form Be.

QUESTION: 38

The common features among the species CN⁻, CO and NO⁺ are

Solution:

According to Molecular Orbital theory,

CN^{−},CO and NO^{+} are isoelectronic (14e^{−}) and bond order is 3.

QUESTION: 39

Heat exchanged in a chemical reaction, at constant temperature and pressure, is called

Solution:

Define all the terms to find the correct answer:

(a) Entropy : It is the measurement of randomness or disorder of system.

(b) Enthalpy : It is the total heat content of system or it is the heat which is exchanged in a chemical reaction at constant temperature andpressure.

(c) Free energy : It is the energy of system which can be converted into useful work.

(d) Internal energy : It is the energy stored within a substance.

QUESTION: 40

The equilibrium constant in a reversible chemical reaction at a given temperature

Solution:

Equilibrium constant is independent of original concentration of reactant.

QUESTION: 41

For a reaction 2N₂O₅ → 4NO₂ + O₂ rate and rate constant are 1.02 x 10^{-4} mol L⁻^{1} s⁻^{1} and 3.4 x 10^{-5} sec⁻1. The conc. of N₂O₅ at that time will be

Solution:

QUESTION: 42

A Carnot engine, working between 500 K to 300 K has a work output of 800 J-cycle⁻^{1}. What is the amount of heat energy supplied to the engine from the source per cycle?

Solution:

QUESTION: 43

An ideal gas heat engine operates in Carnot cycle between 227ºC and 127ºC. It absorbs 6 x 10^{4} cals of heat at higher temp. Amount of heat converted into work is

Solution:

QUESTION: 44

The densities of graphite and diamond at 298 K are 2.25 and 3.31 g-cm^{-3} respectively. If the standard free energy difference (ΔGº)is equal to 1895 J-mol^{-1}, then pressure at which graphite will be transformed into diamond at 298 K is

Solution:

QUESTION: 45

Increasing order of stability among the three main conformations(i.e.,Eclipse,Anti,Gauche) of 2-fluorethanol is

Solution:

The anticonformation is most stable in which F and OH groups are far apart as possible and minimum repulsion between two groups occurs.

In fully eclipsed conformation F and OH groups are so close that the steric strain is maximum .

Hence this conformation is most unstable.

The order of stability of these conformations is anti > gauche > partially eclipsed > fully eclipsed.

Hence a is the correct answer.

QUESTION: 46

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: 47

The first ionisation potential of *Li* will be

Solution:

As we move from left to right in a period, the ionisation potential increases with increasing atomic number and the ionisation potential keeps on decreasing regularly as we move down a group. Thus the first ionisation potential of Li is less than Be and higher than Na.

QUESTION: 48

The CFSE (Crystal Field Stabilisation Energy) for a high spin octahedral complex having d^{1} configuration is __

Solution:

CFSE = [− 0.4p + 0.6q]Δ_{0}

= [− 4p + 6q]Dq

p = electrons in e_{g} orbitals

q = electrons in t_{2g} orbitals

For d_{1} (high spin) configuration

CFSE = [- 0.4 x + 0.6 x 0]Δ_{0}

=[−0.40 + 0]Δ_{0} = − 0.4 Δ

= 4Dq.

(Configuration of d^{1} in high spin or low spin is same).

QUESTION: 49

An aqueous solution of CoCl₂ on addition of excess of concentrated HCl, turns blue due to the formation of

Solution:

CoCl_{2} is a weak Lewis acid, reacting with chloride ion to produce salt containing the tetrahedral [CoCl_{4}]^{2-} ion. CoCl_{2} is blue when anhydrous, and a deep magneta colour when hydrated, for this reason it is widely used as an indicator for water.

QUESTION: 50

The oxidation no. of nitrogen in HNO₃ is

Solution:

Oxidation state of N in HNO3 is +5---

OS of H= +1, & O = -2

H = +1

O x 3 = -2 x 3

= -6

net charge on molecule = 0

So +1 -6 +N = 0

=> N = 0+6-1

= +5

QUESTION: 51

At cathode ,the electrolysis of aqueous Na₂SO₄ gives

Solution:

QUESTION: 52

Density ratio of O₂ and H₂ molecules is 16:1.The ratio of their r.m.s. velocities will be

Solution:

QUESTION: 53

The structure of white phosphorus is

Solution:

The structure of white phosphorus (P_{4}) is tetrahedral.

QUESTION: 54

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

Solution:

Hydrogen is a non-metal while all other members of group 1 (alkali metals) are metals.

QUESTION: 55

Isopropyl chloride undergoes hydrolysis by

Solution:

Secondary, primary allylic and primary benzylic halides may react predominantly either by S_{N}1 or S_{N}2 mechanism or by both the mechanisms without much preference, depending upon the nature of the nuclephile and the solvent.

QUESTION: 56

An organic compound A reacts with methyl magnesium iodide to form an addition product which on hydrolysis forms the compound B. Compound B gives blue colour salt in Victor Meyer's test. The compounds A and B are respectively.

Solution:

Compound B is a sec. alcohol since it gives blue colour in Victor-Meyer test and sec alcohol are obtained by the action of CH_{3}MgIon an aldehyde other than formaldehyde.

QUESTION: 57

Low reactivity of vinyl chloride and chlorobenzene is due to :

Solution:

QUESTION: 58

A pyridine derivative (I) reacts with (II), (II) can be a free radical, cation or anion. The structure of the intermediate (III) formed in the reaction is given below, (I) and (II) can be respectively:

Solution:

QUESTION: 59

Bromine water reacts with phenol to form

Solution:

if bromine water is added to a solution of phenol in water.

the bromine water is decolourised and a white precipitate is formed which smells of antiseptic .

The precipitate is 2,4,6- tribromophenol

Notice the multiple substitution around the ring - into all the activated positions.

QUESTION: 60

Consider the following statement:

"In a sample of butane at room temperature, none of the molecules will be in the least stable conformation".

Solution:

The conformations of butane differ in their relative stabiliities. The anti-periplanar has minimum repulsion between the groups attached tetrahedrally to the two carbon atoms. In synclinal (gauche) conformations, methyl groups are so close that they repel each other, as a result is has 3.8 kJmol^{-1} more energy than anti conformation. similarly, syn-periplanar is least stable having energy 18.4 kJ mol^{−1} than anti conformation. Thus, at room temperature, the more stable ones will have larger populations.

QUESTION: 61

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

Solution:

QUESTION: 62

If a H₂ nucleus is completely converted into energy, the energy produced will be around

Solution:

Mass of H2 nucleus =mass of proton =1 amu energy equivalent to 1 amu is 931 MeV so correct option is (b).

QUESTION: 63

A uniform resistance wire of length L and diameter d has a resistance R. Another wire of same material has length 4 L and diameter 2 d, the resistance will be

Solution:

QUESTION: 64

Nichrome or Manganin is widely used in wire bound standard resistors because of their

Solution:

QUESTION: 65

If particles are moving with same velocity, then maximum de-Broglie's wavelength will be for

Solution:

de Broglie wavelength for a particle is given by λ = h/p = h/mv, where m, v and p are the mass, velocity and momentum respectively. it is Planck's constant. Now, since all the particles are moving with same velocity, the particle with least mass will have maximum de-Broglie wavelength. Out of the given four particles (proton, α -particles, i.e. He nucleus and β-particles. i.e. electrons) β-particles has the lowest mass and therefore it has maximum wavelength.

QUESTION: 66

When ultraviolet rays are incident on metal plate, then photoelectric effect does not occurs. It occurs by the incidence of

Solution:

For photoemission to take place from metal the wavelength of incident ray will be less than threshold value. For photoelectric emission from given metal plate, the incident wavelength must be less than that of ultraviolet rays assuming the wavelength of ultraviolet rays as the threshold value. Out of the given radiations, X-rays have wavelength less than that of ultraviolet rays. Thus, X-rays can cause photoelectric emission.

QUESTION: 67

Which rays are not the portion of electro magnetic spectrum?

Solution:

QUESTION: 68

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

Solution:

When you draw the electric field lines for these 2 charges they will starts from the positive charge and end at the negative charge. And when they pass through the Y axis they will be perpendicular to the Y axis, since both the charges are at equal distance and equal in magnitude. The direction of electric field is found by the tangents to the electric field at that point, since the line is parallel to x axis it's slope will also be zero, So the direction of the electric field line will be along the x axis.

QUESTION: 69

If 1000 droplets each of charge q and radius r are mixed to form a big drop, then the potential of big drop, as compared to small droplet will be

Solution:

If the value of potential on each small drop be V and potential on each small drop be V ^{'}

QUESTION: 70

A satellite with kinetic energy E is revolving around the earth in a circular orbit. The minimum additional kinetic energy required to escape it in the outer space is

Solution:

QUESTION: 71

As we go from the equator to the poles, the value of g

Solution:

Since the Earth is flattened at the poles and bulges at the equator, an oblate spheroid the distance from Earth's center to sea level is roughly 21 kilometers (13 miles) greater at the equator than at the poles. Since the value of g varies inversely with the square of the earth's radius, the shorter radius at the pole will result in a greater value of g.

The second reason is that at latitudes nearer the Equator, the outward centrifugal force produced by Earth's rotation is larger than at polar latitudes. This counteracts the Earth's gravity to a small degree – up to a maximum of 0.3% at the Equator – and reduces the value of g at the equator.

So as we move from equator to pole value of g will increase. Hence option C is the correct.

QUESTION: 72

On a cold morning, a metal surface will feel colder to touch than a wooden surface because

Solution:

Due to higher thermal conductivity of metal than wood, heat begins to flow readily from our body to the metal surface and so we feel colder.

QUESTION: 73

A black body at a temperature of 1640 K has the wavelength corresponding to maximum emission equal to 1.75μ. Assuming the moon to be a perfectly black body, the temperature of the moon, if the wavelength corresponding to maximum emission is 14.35 μ is

Solution:

QUESTION: 74

A man weighs 80 kg. He stands on a weighing scale in a lift, which is moving upwards with a uniform acceleration of 5 m−s⁻^{2}. What would be the reading on the scale?(Take g = 10 m−s⁻^{2})

Solution:

The reading on scale would be

w= M (g+a)

w=80 ( 10+ 5)

w=1200

QUESTION: 75

If a car covers 2/5th of the total distance with ν₁ speed and 3/5th distance with ν₂ then average speed is

Solution:

QUESTION: 76

A current passing through a circular coil of two produces a magnetic field of 8 T at its centre. The coil is then rewound, so as to have four turns and current is passed through it is doubled. Now magnetic field at the centre of the coil will be

Solution:

QUESTION: 77

A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. what is the maximum angular displacement of the pendulum of the string with respect to the vertical ?

Solution:

Tension at mean position,

mg+

(i) and if the body displaces by angle q with the vertical then v =

(ii) Comparing (i) and (ii),

cosθ = 0 Þ θ = 90º

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):A falling ball is attracted by the earth, because of which velocity of the ball goes on increasing in the downward direction. The ball also attracts the earth with same force but velocity developed in earth is negligible.

Reason(R):Momentum of ball and earth system is conserved.

Solution:

Since the mass of the earth is infinitely large compared to that of the ball, hence velocity developed in the earth is negligible

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): A thin hollow cylindrical shell of radius 0.5 m has a mass of 2 kg. Its moment of inertia about its own axis is 0.5 kgm^{2}.

Reason(R) : Moment of inertia of a cylindrical shell about its axis I = MR^{2}.

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):Air is thrown on a sail attached to a boat from an electric fan placed on the boat, because of which some movement is caused in the boat.

Reason(R):When the fan pushes the sail by the air, then air also pushes the fan in the opposite direction, causing motion.

Solution:

QUESTION: 81

A force 10^{3} newton stretches the length of a hanging wire by 1 millimetre. The force required to stretch a wire of same material and length but having four times the diameter by 1 millimeter is

Solution:

(Y,l and L are constant) If diameter is made four times then force required will be 16 times. i.e. 16 x 10^{3} N

QUESTION: 82

A cylindrical vessel is filled with water up to height H. A hole is bored in the wall at a depth h from the free surface of water. For maximum range, h is equal to

Solution:

QUESTION: 83

The eye-piece used in biological microscope is

Solution:

QUESTION: 84

A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be

Solution:

QUESTION: 85

We consider a thermodynamic system. If ∆U represents the increase in its internal energy and W the work done by the system, which of the following statements is true

Solution:

Explanation: In an adiabatic process,

∆Q=0

∆U=∆Q-∆W=0-W=-W.

QUESTION: 86

A body of mass 5 g is executing S.H.M. with amplitude 10 cm. Its maximum velocity is 100 cm/s. Its velocity will be 50 cm/s at a displacement from the mean position equal to

Solution:

QUESTION: 87

The golden view of sea shell is due to

Solution:

When a ray of light falls on sea shell, then its small amount first gets refracted (slightly polarised) and then almost gets reflected back (fully polarised). That is why, view of sea shell is golden due to polarisation.

QUESTION: 88

The maximum speed of a body vibrating under simple harmonic motion with a time period of π/4 sec and amplitude of 7 cm is

Solution:

QUESTION: 89

Calcorimeters are made of which of the following

Solution:

Calorimeters are made up of metal only because they are good conductor of heat and hence the heat exchange is quick which the basic requirement for the working of calorimeter.

QUESTION: 90

The position of a particle at time *'t'* is given by the equation Where *V _{0}* is constant and A > 0. Dimensions of

Solution:

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