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JEE Main Practice Test- 1 - Question 1

The self inductance of an electric fan motor is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of

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JEE Main Practice Test- 1 - Question 2

A car of mass 800 kg moves on a circular track of radius 40 m. If the coefficient of friction is 0.5, then the maximum velocity with which the car can move is

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JEE Main Practice Test- 1 - Question 3

Directions: This question has two statements, Statement 1 and Statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.

**Statement 1:** Davisson-Germer experiment proved the wave nature of electrons.

**Statement 2:** If electrons have wave nature, then they can interfere and show diffraction.

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JEE Main Practice Test- 1 - Question 4

A semi circular wire of radius 'r' is charged uniformly with a charge 'Q' as shown in the figure. Then, the force experienced by a charge 'q' kept at its centre is

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JEE Main Practice Test- 1 - Question 5

A shell is fired from a cannon with a speed of 100 ms^{-1} at an angle 30° with the vertical (y-direction). At the highest point of its trajectory, the shell explodes into two fragments of masses in the ratio 1 : 2. The lighter fragment moves vertically upwards with an initial speed of 200 ms-1. What is the speed of the heavier fragment at the time of explosion?

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JEE Main Practice Test- 1 - Question 6

Consider a solid sphere of mass M and radius R. The energy released in forming this solid sphere is

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JEE Main Practice Test- 1 - Question 7

A block of mass m is placed on a surface with a vertical cross-section given by y = x^{3}/6. If the coefficient of friction is 0.5, then the maximum height above the ground at which the block can be placed without slipping is

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JEE Main Practice Test- 1 - Question 8

The logic gate circuit shown in the figure realises which of the following functions?

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JEE Main Practice Test- 1 - Question 9

A horizontal force of 10 N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is 0.2. The weight of the block is-

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JEE Main Practice Test- 1 - Question 10

The magnetism of a magnet is due to which of the following?

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JEE Main Practice Test- 1 - Question 11

The resistance of the rod is 1 Ω. It is bent in form of a square. What is the resistance across adjacent corners?

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JEE Main Practice Test- 1 - Question 12

Figure shows the vertical cross-section of a vessel filled with a liquid of density ρ. The normal thrust per unit area on the walls of the vessel at point P, as shown will be

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JEE Main Practice Test- 1 - Question 13

A conducting ring of mass 2 kg and radius 0.5 m is placed on a smooth horizontal plane. The ring carries a current i = 4 A. A horizontal magnetic field B = 10 T is switched on at time t = 0 as shown in the figure. The initial angular acceleration of the ring will be

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JEE Main Practice Test- 1 - Question 14

A stone is dropped from a height of 45 m on a horizontal level ground. There is the horizontal wind blowing due to which horizontal acceleration of the stone becomes 10 m s^{−2}. (Take g = 10 m s^{−2}). The time taken (t)t by stone to reach the ground and the net horizontal displacement (x) of the stone from the time it is dropped and till it reaches the ground are respectively

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JEE Main Practice Test- 1 - Question 15

The current (I) in the inductance is varying with time according to the plot shown in the figure.

The correct variation of voltage with time in the coil is

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JEE Main Practice Test- 1 - Question 16

Two charges q_{1} and q_{2} are placed 30 cm apart, as shown in the figure. A third charge q_{3} is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is where k is

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JEE Main Practice Test- 1 - Question 17

A point source of heat of power P is placed at the centre of a spherical shell of mean radius R. The material of the shell has thermal conductivity K. Calculate the thickness of the shell if the temperature difference between the outer and inner surfaces of the shell in steady-state is T.

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JEE Main Practice Test- 1 - Question 18

Two condensers, one of capacity C and other of capacity C/2 are connected to a V - volt battery, as shown in the figure. The work done in charging fully both the condensers is

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JEE Main Practice Test- 1 - Question 19

Two radio antennas radiating waves in phase are located at points A and B, 200 m apart (Figure). The radio waves have a frequency of 6 MHz. A radio receiver is moved out from point BB along a line perpendicular to the line connecting A and B (line BC as shown in the figure). At what distances from B will there be destructive interference?

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JEE Main Practice Test- 1 - Question 20

With the assumption of no slipping, determine the mass mm of the block which must be placed on the top of a 6 kg cart in order that the system period is 0.75 s. What is the minimum coefficient of static friction μS for which the block will not slip relative to the cart if the cart is displaced m50 mm from the equilibrium positions and released? Take (g = 9.8 m s^{-2}).

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JEE Main Practice Test- 1 - Question 21

In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1 kW. The voltage of the electric main is 220 V. The minimum capacity of the main fuse of the building will be (Key in the integral value, in Amperes)

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JEE Main Practice Test- 1 - Question 22

The resistance of a wire is 5 ohm at 50°C and 6 ohm at 100°C. The resistance of the wire at 0°C will be (in ohm)

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JEE Main Practice Test- 1 - Question 23

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75°C. T (in °C) is given by:

(Given: room temperature = 30°C, specific heat of copper = 0.1 cal/gm°C)

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JEE Main Practice Test- 1 - Question 24

The circuit contains two diodes each with a forward resistance of 50 Ω and with infinite reverse resistance. If the battery voltage is,6 V, the current through the 120 Ω resistance is mA.

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JEE Main Practice Test- 1 - Question 25

The impulse imparted to a ball of mass m, when it strikes a rigid wall with a speed u and rebounds with the same speed is −αmu, what is the value of α?

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JEE Main Practice Test- 1 - Question 26

If 5.08 g of a cupric salt is dissolved in water and excess of KI is added to the solution, and the liberated I_{2} requires 25 ml of M/5 Na_{2}S_{2}O_{3}, where it gets converted into S_{4}O_{6}^{2-}, then find the weight percentage of copper in the salt.

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JEE Main Practice Test- 1 - Question 29

A cell utilises the reaction Zn (s) + 2H^{+} (aq) Zn^{2+} (aq) + H_{2} (g). Addition of H_{2}SO_{4} to the cathode compartment will

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JEE Main Practice Test- 1 - Question 30

Which of the following series of reactions correctly represents the chemical relations related to iron and its compound?

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JEE Main Practice Test- 1 - Question 31

Which of the following is formed when NaCl is heated with conc. H_{2}SO_{4} and solid K_{2}Cr_{2}O_{7}?

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JEE Main Practice Test- 1 - Question 33

Which of the following alkenes will react faster with H_{2} under catalytic hydrogenation conditions?

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JEE Main Practice Test- 1 - Question 34

When m-chlorobenzaldehyde is treated with 50% KOH solution, the product(s) obtained is/are

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JEE Main Practice Test- 1 - Question 35

Among cellulose, poly(vinylchloride), nylon and natural rubber, the polymer in which the intermolecular force of attraction is the weakest is

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JEE Main Practice Test- 1 - Question 36

Name the end product in the following series of reactions

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JEE Main Practice Test- 1 - Question 37

Which of the following does not illustrate the anomalous properties of lithium?

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JEE Main Practice Test- 1 - Question 38

The vapour of Hg absorb some electrons accelerated by a potential difference of 4.5 volts from rest as a result of which light is emitted. If the full energy of a single incident electron is supposed to be converted into light emitted by electron in a single Hg atom, find the wave number (1/λ) of the light

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JEE Main Practice Test- 1 - Question 40

A crystalline hydrated salt on being heated loses 45.6% of its weight. Percentage composition of anhydrous salt is Al - 10.5 %, K - 15.1 %, S - 24.8 %, O - 49.6 %. Find molecular formula of salt (hydrated) (M = 948 g/mol for hydrated salt).

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JEE Main Practice Test- 1 - Question 41

Which one of the following ores is best concentrated by froth flotation method?

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JEE Main Practice Test- 1 - Question 43

At 500 K, the half life period of a gaseous reaction at an initial pressure of 80 kPa is 350 s350 s. When the pressure is 40 kPa, the half life period is 175 s; the order of the reaction is :

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JEE Main Practice Test- 1 - Question 44

Consider the following three halides :

(1) CH_{3} − CH_{2} − ClCH_{3} - CH_{2} - Cl

(2) CH_{2} = CH − ClCH_{2} = CH - Cl

(3) C_{6}H_{5} − ClC_{6}H_{5} - Cl

Arrange C − Cl bond length of these compounds in decreasing order -

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JEE Main Practice Test- 1 - Question 45

Ratio of ΔT_{b}/K_{b} of 10 g AB_{2} and 14 g A_{2}B per 100 g of solvent in their respective, solution (AB_{2} and A_{2}B both are non-electroytes) is 1 mol/kg in both cases. Hence, atomic weight of A and B are respectively :

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JEE Main Practice Test- 1 - Question 46

Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is

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JEE Main Practice Test- 1 - Question 47

The pH of a 0.01 M solution of a weak acid having degree of dissociation 12.5% is ____. (Answer up to 1 decimal place)

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JEE Main Practice Test- 1 - Question 48

For the reaction A → C + D, the initial concentration of A was 0.01 M. After 100 s, the concentration of A becomes 0.001 M. The rate constant of the reaction has the numerical value 9.0. The order of reaction is

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JEE Main Practice Test- 1 - Question 49

The number of stereo isomers possible for a compound of the molecular formula is CH_{3}−CH=CH−CH(NH_{2})−CH_{3} is

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JEE Main Practice Test- 1 - Question 50

Total number of optically inactive stereoisomers of tartaric acid is/are

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JEE Main Practice Test- 1 - Question 53

If the normal at the point (bt_{1}^{2}, 2bt_{1}) on a parabola meets the parabola again at the point (bt_{2}^{2}, 2bt_{2}), then

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JEE Main Practice Test- 1 - Question 55

The differential equation whose solution is Ax^{2} + By^{2} = 1, where A and B are arbitrary constants, is of

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JEE Main Practice Test- 1 - Question 56

The volume of a parallelepiped whose sides are given by = 2i - 3j, = i + j - k, = 3i - k is

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JEE Main Practice Test- 1 - Question 57

In an experiment with 15 observations on x, the following results were available.

∑x^{2} = 2830, ∑x = 170

One observation, which was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance was

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JEE Main Practice Test- 1 - Question 58

The general solution of sin x - 3 sin 2x + sin 3x = cos x - 3 cos 2x + cos 3x is

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JEE Main Practice Test- 1 - Question 59

If the p^{th} term of an A.P. be q and q^{th} term is p, then its r^{th} term will be

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JEE Main Practice Test- 1 - Question 61

For a random variable X, if E(X) = 5 and Var(X) = 6, then E(X^{2}) is equal to

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JEE Main Practice Test- 1 - Question 63

The area bounded by y = xe^{|x|} and the lines |x| = 1, y = 0 is

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JEE Main Practice Test- 1 - Question 64

The integral is equal to (where [.]. denotes the greatest integer function)

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JEE Main Practice Test- 1 - Question 66

A plane passes through (1, 2, 2) and is perpendicular to two planes 2x – 2y + z = 0 and x – y + 2z = 4. Square of the distance of the plane from the point (52, 53, 57) is

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JEE Main Practice Test- 1 - Question 70

If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B are

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JEE Main Practice Test- 1 - Question 72

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is p/q, then p is equal to

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JEE Main Practice Test- 1 - Question 73

^{20}C_{4} + 2.^{20}C_{3} + ^{20}C_{18} - ^{22}C_{18} is equal to

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JEE Main Practice Test- 1 - Question 74

If coefficient of variation of a distribution is 60% and its standard deviation is 18, then its arithmetic mean is

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