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This mock test of JEE Main Mock Test 10 for JEE helps you for every JEE entrance exam.
This contains 90 Multiple Choice Questions for JEE JEE Main Mock Test 10 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The complex number lies in

Solution:

QUESTION: 2

The area contained between the curve x y = a^{2} , the vertical line *x = a, x = 4a (a > 0) *and *x* -axis is

Solution:

QUESTION: 3

Solution:

QUESTION: 4

The equation of the circle whose centre lies on x+2y-3=0 and passes through the intersection of x^{2}+y^{2}-2x-4y+1=0 and x^{2}+y^{2}-4x-2y+4=0 is

Solution:

QUESTION: 5

The coefficient of the middle term in the binomial expansion in powers of x of (1+Î±x)^{4} and (1-Î±x)^{6} is the same, if Î± equals

Solution:

QUESTION: 6

If f(x) = is continuous at , then *a* =

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QUESTION: 7

The interval in which y=x^{2}e^{x} is increasing with respect to x, is

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QUESTION: 8

The differential equation of family of lines which passes (1,-1) is

Solution:

QUESTION: 9

Integrating factor of differential equation cos x dy/dx+y sin x = 1 is

Solution:

QUESTION: 10

The equation of the ellipse whose focus is (1,-1), directrix is the line x - y - 3 = 0 and eccentricity is 1/2 is

Solution:

QUESTION: 11

Let *f(x)* be a function satisfying f ′ x = f x with *f(0)* = 1 and *g(x)* be a function that satisfies *f(x) + g(x) = x*^{2}, then value of integral

*dx* is equal to

Solution:

QUESTION: 12

If f^{'}(2) = 4 and f^{'} (1) = 2 then

Solution:

QUESTION: 13

"If Deb and Sam go to the mall, then it is snowing."

Which statement below is logically equivalent?

Which statement below is logically equivalent?

Solution:
A statement is logically equivalent to its contrapositive.

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 tangent and normal at any point P on the ellipse bisect the external and internal angles between the focal distances of P.

Reason(R): The straight line joining the foci of the ellipse subtends a right angle at P.

Assertion(A): The tangent and normal at any point P on the ellipse bisect the external and internal angles between the focal distances of P.

Reason(R): The straight line joining the foci of the ellipse subtends a right angle at P.

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): The equation x^{2} + 2ax - b^{2} = 0 can have repeated roots, where a,b are real numbers.

Reason(R): The equation Ax^{2} + Bx + C = 0 will have repeated roots when the determinant becomes zero.

Solution:

QUESTION: 16

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 expression is a zero vector .

Reason(R): If be three vectors is known as vector triple product, given

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): The vector equation of the plane passing through the points (1, -2, 5), (0, -5, -1), (-3, 5, 0) is

Reason (R): The vector equation of the plane passing through the points

Solution:

QUESTION: 18

The point (3, 2) is reflected in the y-axis and then moved a distance of 5 units towards the negative side y-axis. the co-ordinates of the point thus obtained are

Solution:

QUESTION: 19

Mean deviation is minimum when deviations are taken from:

Solution:

QUESTION: 20

The number of values of *x* where f (x) = cosx + cos√2 x attains its maximum value is

Solution:

QUESTION: 21

Five seats are vacant in a railway compartment, then in how many ways can three passengers be seated on these seats?

Solution:

QUESTION: 22

The equation of the tangent to the parabola y^{2}=16x which is ⊥ to the line y=3x+7 is

Solution:

QUESTION: 23

Box *A* contains 2 black and 3 red balls, while box *B* contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box *A* is double that of box *B*. If a red ball is drawn from the selected box then the probability that it has come from box *B* is

Solution:

QUESTION: 24

pth term of an A.P. is q and qth term is P,its rth term is

Solution:

QUESTION: 25

If f(x) = (x - 1)/(x + 1), then f (1/f(x)) equals

Solution:

QUESTION: 26

The mcan and standard deviation of a binomial variate *X* are 4 and √3 respectively. Then P (X ≥ 1) =

Solution:

QUESTION: 27

A tetrahedron has vertices at O (0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C (-1, 1, 2). Then the angle between the faces OAB and ABC will be

Solution:

QUESTION: 28

Given that θ is a acute and that sin θ =3/5. Let x,y be positive real numbers such that 3(x-y) =1, then one set of solutions for x and y expressed in terms of θ is given by

Solution:

QUESTION: 29

If the vectors and

are coplanar, then the value of

Solution:

QUESTION: 30

If a=i+j-k, b=-i+2j+k and c=-i+2j-k, the unit vector perpendicular to a+b and b+c is

Solution:

QUESTION: 31

Composition of brown ring is

Solution:

QUESTION: 32

If the value of principal quantum number is 3, the total possible values for magnetic quantum number will be

Solution:

QUESTION: 33

Which of the following reagent will convert glycerol to acrolein?

Solution:

QUESTION: 34

Which of the following is the strongest nucleophile?

Solution:

A negatively charged nucleophile is always stronger than a neutral one

QUESTION: 35

Enzyme trypsin converts

Solution:

QUESTION: 36

The types of bonds present in CuSO₄.5H₂O are

Solution:

QUESTION: 37

Homolytic fission of C - C bond in ethane (CH₃ - CH₃) gives an intermediate in which carbon atom is

Solution:

QUESTION: 38

KF combines with HF to form KHF₂. The compound contains the species

Solution:

In aqueous solutions, HF dissociates and gives the difluoride ion (HF_{2}^{−}) instead of F^{−} ions. This is because F^{−} forms H-bond with HF. Therfore, the species [H.....F−H]^{−} or HF_{2}^{−} exists.

QUESTION: 39

The heat of formation of the compound in the following reaction is

H₂(g) + Cl(g)→ 2HCl(g)+44 Kcal

Solution:

QUESTION: 40

A reversible reaction is said to have attained equilibrium, when

Solution:

QUESTION: 41

A solution of 500ml of 2*M* Postassium hydroxide is added to 500ml of 2*M* hydrochloric acid and mixture is well stirred. The rise in temperature '*T _{1}*' is recorded. The experiment is then repeated using 250ml of each solution and the rise in temperature '

Solution:

QUESTION: 42

What will be the order of the reaction if doubling of the concentration of a reactant increases the rate by a factor of 4 and tripling the concentration of the reactant by a factor of 9?

Solution:

QUESTION: 43

For an ideal gas, the relation between the enthalpy change and internal energy change at constant temperature is given by

Solution:

QUESTION: 44

Evaporation of water is

Solution:

QUESTION: 45

Which of the following is the most stable ?

Solution:

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

Low spin octahedral complexes are maximum distorted in which of the following state?

Solution:

whenever e_{g} orbitals unsymmetrical, i.e., contain 1,2 or 3 electons in low spin complex strong distortion occurs leading to tetrgonal or square planer complexes. Since the direction of the e_{g} orbitals of the central metals ion correspond with the directions of the ligands disposed octahedrally around the metal ion, the octahedral arrangement of the ligands is likely to be more severely distorted by the dissymmetry of the e_{g} orbitals than that of the t_{2g} orbitals.

QUESTION: 48

Which of the following has the highest electronegativity?

Solution:

Electronegativity of an element is the tendency of its atom to attract the shared pair of electrons towards itself in a covalent bond. The elements of highest electronegativity in the periodic table are:

F (4.0) > O (3.5) > Cl (3.0) = N (3.0) .

QUESTION: 49

The standard reduction potentials of Li⁺/Li,Ba^{2}⁺/Ba,Na⁺/Na and Mg^{2}⁺/Mg are -3.05, - 2.73, - 2.71 and -2.37 volts respectively.Which one of the following is strongest oxidising agent ?

Solution:

QUESTION: 50

The actinides have

Solution:

QUESTION: 51

Both oxidation and reduction takes place in which of the following reaction?

Solution:

QUESTION: 52

To express the concentration of hydrogen peroxide, the term 10 volume hydrogen peroxide refers

Solution:

QUESTION: 53

Phosphine is not obtained by the reation when

Solution:

QUESTION: 54

At its melting point ice is lighter than water because

Solution:

QUESTION: 55

Which of the following compounds will be most easily attacked by an electrophile ?

Solution:

QUESTION: 56

Which of the following compounds will be optically active?

Solution:

QUESTION: 57

Out of the following E1 reaction is favoured in the following case:

Solution:

QUESTION: 58

In the following conjugated system

CH_{3}CH ═ CHCH ═ CHCH_{3} addition is considered at the :

Solution:

QUESTION: 59

Phenol is

Solution:

QUESTION: 60

The Fisher projections shown to the right are

Solution:

QUESTION: 61

A gamma ray photon creates an electron-positron pair. If the rest mass energy of an electron is 0.5 MeV and the total K.E of the electron-positron pair is 0.78 MeV, then the energy of the gamma ray photon must be

Solution:

QUESTION: 62

Which of the following spectral series in hydrogen atom give spectral line of 4860 Å

Solution:

QUESTION: 63

A 220 V, 1000 W bulb is connected across a 110 V mains supply. The power consumed will be

Solution:

QUESTION: 64

We have a galvanometer of resistance 25 Ω. It is shunted by a 2.5 Ω wire. The part of total current that flows through the galvanometer is given as

Solution:

QUESTION: 65

Cathode rays are produced when the pressure is of the order of

Solution:

QUESTION: 66

Light appears to travel in a straight line because

Solution:

QUESTION: 67

Which of the following rays has minimum frequency?

Solution:

QUESTION: 68

Three point charges 1C, 2C, − 2C are placed at the vertices of an equilateral triangle of side one metre. The work done by an external force to increase the separation of the charges to 2 metres in joules is( ∈ 0 is permittivity of air.

Solution:

Initially and finally the net force is zero.

i.e. work done by the external force is zero

QUESTION: 69

Capacitance of a capacitor becomes 7/6 times its original value if a dielectric slab of thickness, t = 2/3 d is introduced in between the plates. 'd' is the separation between the plates. The dielectric constant of the dielectric slab is

Solution:

QUESTION: 70

A space ship is launched into a circular orbit of radius *R* close to surface of earth. The additional velocity to be imparted to the space ship in the orbit to overcome the earth's gravitational pull is [*g* - acceleration due to gravity]

Solution:

QUESTION: 71

The mass of the moon is 1/81 of the earth but the gravitational pull is 1/6 of the earth. It is due to the fact that

Solution:

QUESTION: 72

The radiant energy from the sun incident normally at the surface of earth is 20 kcal/m^{2} min. What would have been the radiant energy incident normally on the earth, if the sun had a temperature twice of the present one

Solution:

QUESTION: 73

A black body, at a temperature of 227ºC, radiates heat at a rate of 84 J-m⁻^{2}-s⁻^{1}. When its temperature is raised to 727ºC, the heat radiated by it in J-m⁻^{2}-s⁻^{1} will be

Solution:

QUESTION: 74

Two balls each of mass 60 g moving in opposite directions with speeds 4 m−s⁻^{1} collide and rebound with the same speed. The change in momentum will be

Solution:

QUESTION: 75

A voltmeter of resistance 20000 Ω reads 5 volt. To make it read 20 volt, the extra resistance required is

Solution:

QUESTION: 76

Thye position x of a particle varies with time, t, as x = at^{2}-bt^{3}. The acceleration of the particle will be zero at time t is equal to

Solution:

QUESTION: 77

A particle is executing simple harmonic motion with an amplitude of 2 cm and angular frequency 100π rad-s⁻^{1}. The maximum acceleration of the particle is

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):When a ball is thrown upwards, its momentum first decreases and then increases.

Reason(R):Law of conservation of momentum is not followed is this process.

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): Pressure in a bubble (σ) in an atmosphere of pressure P_{0} is where r is the radius.

Reason(R): 4σ/r is the excess pressure due to two surfaces exposed to the atmosphere.

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): Gravitational field intensity at the centre of ring is zero.

Reason(R): Net force at the centre of ring is zero.

Solution:

QUESTION: 81

Helium gas is filled in a closed vessel (whose coefficient of thermal expansion is negligible). When it is heated from 300 K to 600 K, then average kinetic energy of helium atoms will be

Solution:

QUESTION: 82

A soap bubble (S.T.30 dyne/cm) has radius of 1 cm. The work done is doubling its radius would be

Solution:

QUESTION: 83

A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of combination is

Solution:

QUESTION: 84

An automobile engine develops 100 kW when rotating at a speed of 1800 rev-min⁻^{1}. What torque does it deliver?

Solution:

QUESTION: 85

The potential energy of a particle with displacement X is U(X). The motion is simple harmonic, when (K is a positive constant)

Solution:

QUESTION: 86

Work done by 0.1 mole of a gas at 27ºC when it expands to double its volume at constant pressure is (assume R=2 cal mole^{-1} K^{-1})

Solution:

QUESTION: 87

A source and an observer move away in opposite directions with speed 10 ms^{-1}, each with respect to ground. Apparent frequency is 1950 Hz. If velocity of sound is 340.5 ms^{-1}, the natural frequency is

Solution:

QUESTION: 88

Length, breadth and thickness of a block of wood are measured and following results are obtained. These are l=(25.12 0.01) cm, b=(20.150.01)cm, t=(15.280.01) cm. The percentage error in the volume of the block is

Solution:

QUESTION: 89

To demonstrate the phenomenon of interference we require two sources which emit radiations of

Solution:

QUESTION: 90

A copper block of mass 4 kg is heated in a furnance to a temperature 425ºC and then placed on a large ice block. The mass of ice that will melt in this process will be (Specific heat of copper=500 J-kg⁻^{1}-ºC⁻^{1} and heat of fusion of ice = 336 kJ-kg⁻^{1}).

Solution:

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