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JEE Main Practice Test- 14 - Question 1

Let f(x) be a one-to-one function such that f(1) = 3, f(3) = 1, f '(1) = – 4 and f '(3) = 2. If g = f ^{–1}, then the slope of the tangent line to 1/g at x = 1 is

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JEE Main Practice Test- 14 - Question 3

If g (x^{3} + 1) = x^{6} + x^{3} + 2, then the value of g(x^{2} – 1) is

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JEE Main Practice Test- 14 - Question 4

Suppose that f (0) = 0 and f ' (0) = 2, and let g (x) = f (- x + f (f (x))). The value of g ' (0) is equal to

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JEE Main Practice Test- 14 - Question 6

A line L is perpendicular to the curve at its point P and passes through (10, –1). The coordinates of the point P are

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JEE Main Practice Test- 14 - Question 7

then the sum of the square of reciprocal of all the values of x where f(x) is non-differentiable, is equal to

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JEE Main Practice Test- 14 - Question 8

h(x) = {x},k(x) = 5^{log2 (x + 3)} then in [0, 1], Lagranges Mean Value Theorem is NOT applicable to

[Note : where [x] and {x} denote the greatest integer and fractional part function of x respectively]

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JEE Main Practice Test- 14 - Question 9

If the function f (x) = ax e^{–bx} has a local maximum at the point (2, 10), then

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JEE Main Practice Test- 14 - Question 10

then the value of x satisfying the equation f (x, 10) = f (x, 11), is

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JEE Main Practice Test- 14 - Question 12

Number of integral solutions of the equation

[Note : where [x] denotes the greatest integer less than or equal to x and sgn x denotes signum function of x.]

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JEE Main Practice Test- 14 - Question 13

The area bounded by the curve y = x^{2} + 4x + 5 , the axes of co-ordinates & the minimum ordinate is

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JEE Main Practice Test- 14 - Question 14

The differential equation of all parabolas having their axis of symmetry coinciding with the axis of x has its order and degree respectively

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JEE Main Practice Test- 14 - Question 15

Number of roots of the equation x^{2} –2x–log_{2} |1 – x | = 3 is

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JEE Main Practice Test- 14 - Question 16

Let F(x) be the primitive of w.r.t. x. If F(10) = 60 then the value of F(13), is

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JEE Main Practice Test- 14 - Question 17

is continuous at x = 0, then

[Note : {x} denotes fractional part of x.]

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JEE Main Practice Test- 14 - Question 19

Point 'A' lies on the curve and has the coordinate where x > 0. Point B has the coordinates (x, 0). If 'O' is the origin then the maximum area of the triangle AOB is

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JEE Main Practice Test- 14 - Question 21

**(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)**

If then the value of must be

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JEE Main Practice Test- 14 - Question 22

The sum of all the real roots of the equations

|x − 2|^{2} + |x − 2| − 2 = 0 is …..

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JEE Main Practice Test- 14 - Question 23

If P_{n} = cos^{n} x + sin^{n} x, then 2.P_{6} - 3.P_{4} + 1 = ..

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JEE Main Practice Test- 14 - Question 24

If x = 2 + t^{3}, y = 3t^{2} and is a constant then the value of 343*n* must be

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JEE Main Practice Test- 14 - Question 25

The value of 49A + 5B, where A = 1 - log_{7}2 and B = - log_{5} 4 is

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JEE Main Practice Test- 14 - Question 26

A transverse wave is travelling along a horizontal string. The first picture shows the shape of the string at an instant of time. This picture is superimposed on a coordinate system to help you make any necessary measurements. The second picture is a graph of the vertical displacement of one point along the string as a function of time. How far does this wave travel along the string in one second?

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JEE Main Practice Test- 14 - Question 27

A cyclic process of an enclosed gas of constant mass is represented by volume (V) against absolute temperature (T) as shown. If P represents pressure, the graph representing the same process can be

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JEE Main Practice Test- 14 - Question 28

A closed organ pipe is vibrating in its second overtone. The length of the pipe is 10cm and maximum amplitude of vibration of particles of the air in the pipe is 2mm. Then the amplitude of S.H.M. of the particles at 9cm from the open end is:

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JEE Main Practice Test- 14 - Question 29

A sound source S and observers O_{1}, O_{2} are placed as shown. S is always at rest and O_{1}, O_{2} start moving with velocity v_{0} at t = 0. At any later instant, let f_{1} and f_{2} represent apparent frequencies of sound received by O_{1} and O_{2}, respectively. The ratio f_{1}/f_{2} is

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JEE Main Practice Test- 14 - Question 30

Equal masses of three liquids A, B and C have temperatures 10^{o}C, 25^{o}C and 40^{o}C respectively. If A and B are mixed, the mixture has a temperature of 15^{o}C. If B and C are mixed, the mixture has a temperature of 30^{o}C,. If A and C are mixed the mixture will have a temperature of

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JEE Main Practice Test- 14 - Question 31

A steel rod is 4.000 cm in diameter at 30ºC. A brass ring has an interior diameter of 3.992 cm at 30ºC. In order that the ring just slides onto the steel rod, the common temperature of the two should be nearly (α_{steel }= 11 × 10^{-6}/ºC and α_{brass }= 19 × 10^{-6}/ºC)

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JEE Main Practice Test- 14 - Question 32

A hot liquid is kept in a big room. The logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. The plot will be very nearly.

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JEE Main Practice Test- 14 - Question 33

A body cools from 80°C to 50°C in 5 minutes. Calculate the time it takes to cool from 60°C to 30°C.The temperature of the surroundings is 20°C.

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JEE Main Practice Test- 14 - Question 34

A sinusoidal wave (longitudinal or transverse) is propagating through a medium in the direction of -ve x-axis. The parameters of the waves are A, ω and k. The particle at x = λ/4 executes the motion y(t) = A sinωt. Possible equation of the wave is

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JEE Main Practice Test- 14 - Question 35

PV versus T graph of equal masses of H_{2}, He and CO_{2} is shown in figure.

Choose the correct alternative

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JEE Main Practice Test- 14 - Question 36

A monoatomic gas is taken from A to C as shown in the figure. The temperature of gas at B is 27°C, then the change in internal energy of the gas is

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JEE Main Practice Test- 14 - Question 37

A rope hangs from a rigid support. A pulse is set by jiggling the bottom end. We want to design a rope in which velocity v of pulse is independent of z, the distance of the pulse from fixed end of the rope. If the rope is very long the desired function for mass per unit length µ(z) in terms of µ_{0} (mass per unit length of the rope at the top (z = 0), g, v and z is :

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JEE Main Practice Test- 14 - Question 38

In the Pressure versus Volume graph shown, in the process of going from a to b 60 J of heat is added, and in the process of going from b to d 20 J of heat is added. In the process of going from a to c to d, what is the total heat added?

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JEE Main Practice Test- 14 - Question 39

A glass tube of 1.0 meter length is filled with water. The water can be drained out slowly at the bottom of the tube. If a vibrating tuning fork of frequency 500Hz is brought at the upper end of the tube and the velocity of sound is 330m/s then the total number of resonances obtained will be

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JEE Main Practice Test- 14 - Question 40

A body of mass 25 kg is dragged on a rough horizontal floor for one hour with a speed of 2km/h.The coefficient of friction between the body and the surface in contact is 0.5 and half the heat produced is absorbed by the body. If specific heat of body is 0.1 cal g^{–1} (^{0}C)^{–1}, then the rise in temperature of body is

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JEE Main Practice Test- 14 - Question 41

There is a rectangular metal plate in which two cavities in shape of rectangle and circle are made, as shown in figure, with dimensions. P & Q are centres of these cavities. On heating the plate which of the following quantities increases.

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JEE Main Practice Test- 14 - Question 42

A block of wood is floating in water at 0°C. The temperature of only water is slowly raised from 0°C to 10°C. With the rise in temperature of the water the volume of block above water level will be

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JEE Main Practice Test- 14 - Question 43

A rectangular block of lead has dimensions 4 cm × 3 cm × 20 cm. A temperature difference of 100°C can be applied to any pair of opposite faces that we choose.

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JEE Main Practice Test- 14 - Question 44

Two identical solid spheres have the same constant temperature. One of the spheres is cut into two identical pieces. These two hemispheres are then separated. The intact sphere radiates an energy Q during a given time interval at temperature T_{0}. During the same interval, the two hemisphere radiate at total energy Q' at temperature T_{0}. Emissivity of all the surfaces is same. The ratio Q'/Q has value :

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JEE Main Practice Test- 14 - Question 45

A car blowing a horn of frequency 350 Hz is moving normally towards a wall with a speed of 5 m/s. The beat frequency heard by a person standing between the car and the wall is (speed of sound in air = 350 m/s)

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JEE Main Practice Test- 14 - Question 46

**(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)**

When a plane mirror is placed horizontally on ground at a distance of 60 m from the base of a tower, then the top of the tower and its image in the mirror subtend an angle of 90° at the corner of the mirror nearer to the base of tower. The height of the tower (in m) is:

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JEE Main Practice Test- 14 - Question 47

A bar magnet with magnetic moment 2.5 x 103 JT^{-1} is rotating in horizontal plane in the space containing magnetic induction B = 4 x 10^{-5}T. The work done in rotating the magnet slowly from a direction parallel to the field to a direction 45^{0 }from the field, is (in joule, correct to two decimal places)

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JEE Main Practice Test- 14 - Question 48

In figure, find the velocity of m_{1} in ms^{-1} when m_{2} falls by 9m.

Given m_{1} = m; m_{2} = 2m (take g = 10 ms^{-2})

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JEE Main Practice Test- 14 - Question 49

The figure shows three particles A, B and C on the x-axis. They are given velocities v_{1} = 3 m/s, v_{2} = 2 m/s and v3 = 5 m/s, respectively, in the direction shown. The position of centre of mass of *A, B* and* C *at time* t = 1 s *will be x = k (m), where k is:

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JEE Main Practice Test- 14 - Question 50

Four bricks, each of length *l,* are put on the top of one another as in the figure in such a way that a part of each extends beyond the one beneath. For the largest equilibrium extensions, the TOTAL overhanging length on the edge of the bottom brick is n *l*, where n is:

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JEE Main Practice Test- 14 - Question 51

During the process of electrolytic refining of Copper which of the following may obtained as a anode mud?

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JEE Main Practice Test- 14 - Question 52

How many moles of KOH are required per mole of R–NH_{2} in the balanced reaction?

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JEE Main Practice Test- 14 - Question 53

An ionic solid 'AB' (M_{w} = 120 g/mol) has NaCl type structure. The shortest distance between cation and anion is 500 pm. If there is a schottky defect of 2% then the density of crystal in g / cm^{3} will be : (N_{A} = 6 ×10^{23})

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JEE Main Practice Test- 14 - Question 54

Which of the following metal is not commercially extracted by self reduction method from their corresponding ore?

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JEE Main Practice Test- 14 - Question 55

What is the major product of the given reaction sequence?

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JEE Main Practice Test- 14 - Question 56

At 27°C, the vapour pressure of an aqueous solution of urea is equal to the osmotic pressure of 5 × 10^{–3} M aqueous solution of glucose. If vapour pressure of pure water at 27°C is 114 torr then the mole fraction of urea in its solution is - [Given : R = 0.08 L-atm/mol-K]

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JEE Main Practice Test- 14 - Question 57

Select incorrect statement regarding silver extraction -

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JEE Main Practice Test- 14 - Question 58

What is the colour of the dye formed in the given reaction?

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JEE Main Practice Test- 14 - Question 59

In a solid compound, X-particles are present in ccp position, Y-particle are in all octahedral voids and Z-particles are in alternate tetrahedral voids. If all void- particles along one of the body-diagonal are removed then the formula of compound will be given as -

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JEE Main Practice Test- 14 - Question 60

During the extraction process of Copper, Silica is added to roasted ore, in order to remove.

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JEE Main Practice Test- 14 - Question 61

Find the incorrect combination of reaction and reaction name.

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JEE Main Practice Test- 14 - Question 62

For a 1^{st} order reaction, the correct graph showing variation of half-life (t_{1/2}) with inverse of Kelvintemperature (1/T) will be -

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JEE Main Practice Test- 14 - Question 63

During Froath Floatation process, use of depressant is :

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JEE Main Practice Test- 14 - Question 65

Due to non-stoichiometric defect, a sample of cuprous oxide is found to have a composition Cu_{1.8}O.The mole % of Cu^{2+} in total copper content of the crystal will be -

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JEE Main Practice Test- 14 - Question 66

A salt impart red colour to the borax bead in reducing flame, what could be the colour of the bead in oxidisingflame.

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JEE Main Practice Test- 14 - Question 68

The abnormal molecular mass of CH_{3}COOH when dissolved in benzene is found to be 80 g/mol. The percentage of CH_{3}COOH present in dimeric form in solution is -

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JEE Main Practice Test- 14 - Question 69

Which of the following pair of cations can be separated by using excess NH_{3} solution?

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JEE Main Practice Test- 14 - Question 71

**(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)**

Number of pπ –pπ double bond in given compound CN–CH = CH–CN is _____ .

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JEE Main Practice Test- 14 - Question 72

A compound H_{2}X with molar weight of 80 g is dissolved in a solvent having density of 0.4 g ml^{–1}. Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is

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JEE Main Practice Test- 14 - Question 73

The number of correct options is

a. P_{2}O_{5} > ZnO > MgO > Na_{2}O_{2} (acidic strength)

b. Tl_{2}O_{3} > Tl_{2}O > Ga_{2}O_{3} > Al_{2}O_{3} (basic strength)

c. MnO > P_{2}O_{5} > CrO_{3} > Mn_{2}O_{7} (ionic character)

d. H_{2}O > HF > NH_{3} (melting point)

e. H_{2}O > HF > NH_{3} (boiling point)

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JEE Main Practice Test- 14 - Question 74

A single electron orbits around a stationary nucleus of charge +Ze, where Z is a constant and e is the magnitude of electronic charge, It requires 47.2 eV to excite the electron from the second Bohr orbit to the third Bohr orbit. Find the ionisation energy of above electron system in electronvolt.

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JEE Main Practice Test- 14 - Question 75

The number of sp^{3} and sp^{2} hybridisation of underlined atoms in following molecule is *x* and *y* respectively then xyxy is

__A__ICl_{4}^{–}, Cl_{2}__O__, __N__H_{2}^{–}, ^{⊕}__C__H_{3}, __B__F_{4}^{–}

__P__Cl_{4}^{+}, __C__lO_{2}^{–}, H_{3}__O__^{+}, H_{2}__C__O, __B___{2}H_{6}

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