JEE Main Mock Test - 20 (31-03-2023)

In Coolidge tube experiment, if applied voltage is increased to three times, the short wavelength limit of continuous X - ray spectrum shifts by 20 pm. What is the initial voltage applied to the tube ?

A washer is made of metal having resistivity 10^–7 Ωm. The washer has inner radius 1 cm, outer radius 3 cm and thickness 1 mm. A magnetic field, oriented normal to the plane of the washer, has the time dependent magnitude B = (2t) tesla/sec. Find the current (in ampere) around the washer

Ends of two wires A and B having resistivity  and  of same cross section area joined in series together to from a single wire. If the resistance of the joined wire does not change with temperature, then find the ratio of their lengths  given that temperature coefficient of resistivity of wire A and B is 

α_A= 4 ×10^–5/ °C and α_B = –6 × 10^–6/°C. Assume that mechanical dimensions do not change with temperature

A cone of radius = height = r is under a liquid of density d. Its base is parallel to the free surface of the liquid at a depth H from it as shown in the figure. What is the net force due to liquid on its curved surface? (neglect atmospheric pressure)

A spherical black body has a radius R and steady surface temperature T, heat sources ensure the heat evolution at a constant rate and distributed uniformly over its volume. What would be the new steady surface temperature of the object if the radius is decreased by half? Assume surrounding to be at absolute zero and heat evolution rate through unit volume remain same.

The smallest length scale known in physics is the Planck length. It is an important ingredient in some current cosmological theories. Which of the following expressions could represent this Planck length? (Symbols has usual meaning)

In the figure shown two motors P₁ & P₂ fixed on a plank which is hanging with light string passing over fixed Pulley P. If the motors start winding the thread with angular velocity ω1 & ω2 then velocity of plank V is (here R₁ & R₂ are the radii of motor rotor respectively) [Given: ω1 = 2 rad/s, R₁ = 2m, ω2 = 2 rad/s, R₂ = 3m]

Five identical balls each of mass m and radius r are strung like beads at random and at rest along a smooth, rigid horizontal thin road of length L, mounted between immovable supports. Assume 10r < L and that the collision between balls or between balls and supports are elastic. If one ball is struck horizontally so as to acquire a speed v, the average force felt by the support is

A double star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses m and 2m and let their separation be l. Their time period of rotation about their centre of mass will be proportional to

If white light is used in a Young’s double – slit experiment. Point C represents centre of a screen

Consider a thermodynamic cycle in a PV diagram shown in the figure performed by one mole of a monoatomic gas. The temperature at A is T₀ and volume at A and B are related as V_B = V_C = 2V_A. Choose the correct option(s) form the following

If the plank’s constant would be double the present value, in the Bohr’s model for hydrogen atom

In 1906, Robert Millikan devised an experiment that allowed him to determine the charge of an electron. A schematic of Millikan’s set – up is shown below:
Two metal plates are connected by a series of batteries to form a capacitor. There is an electric field between the plates. The metal plates are inside an insulated cylindrical container.
Oil drops are introduced into the container through a small hole in the top. The oil drops acquire a negative charge as they pass through the nozzle of the oil can. Some of the drops fall through a hole in the upper plate. By adjusting the voltage between the plates, certain drops can be suspended between them. The relationship between the electric field between the plates and the voltage across the plates is ∆V = EL
Where E is the electric field and L is the plate separation.
Millikan chose oil because of its relatively low vapour pressure and high charge holding ability. (To answer the following question assume oil drops as to be non-conducting tiny spheres)

In order for an oil drop of mass m, radius r and volume charge density ρ, to be suspended between the plates, the magnitude and direction of the electric field must be:

In 1906, Robert Millikan devised an experiment that allowed him to determine the charge of an electron. A schematic of Millikan’s set – up is shown below:
Two metal plates are connected by a series of batteries to form a capacitor. There is an electric field between the plates. The metal plates are inside an insulated cylindrical container.
Oil drops are introduced into the container through a small hole in the top. The oil drops acquire a negative charge as they pass through the nozzle of the oil can. Some of the drops fall through a hole in the upper plate. By adjusting the voltage between the plates, certain drops can be suspended between them. The relationship between the electric field between the plates and the voltage across the plates is ∆V = EL
Where E is the electric field and L is the plate separation.
Millikan chose oil because of its relatively low vapour pressure and high charge holding ability. (To answer the following question assume oil drops as to be non-conducting tiny spheres)

Suppose the original oil droplet were replaced with a positively charged one that had twice the charge and three times the mass of the original droplet, how would the magnitude of the electric field have to be changed in order for the drop to remain suspended?

In a hypothetical atom, a negatively charged particle having a charge of magnitude 3e and mass 3m revolves around a proton. Here, e is the electronic charge and m is the electronic mass. Mass of proton may be assumed to be much larger than that of the negatively charged particle, thus the proton is at rest. This “atom” obeys Bohr’s postulate of quantization of angular momentum, that is  It is given that for the first Bohr orbit of hydrogen atom: radius of orbit is r₀ speed of electron is V₀, and total energy is –E_0. Now answer the following questions.
Speed of the revolving particle is, in the first Bohr orbit.

In a hypothetical atom, a negatively charged particle having a charge of magnitude 3e and mass 3m revolves around a proton. Here, e is the electronic charge and m is the electronic mass. Mass of proton may be assumed to be much larger than that of the negatively charged particle, thus the proton is at rest. This “atom” obeys Bohr’s postulate of quantization of angular momentum, that is  It is given that for the first Bohr orbit of hydrogen atom: radius of orbit is r₀ speed of electron is V₀, and total energy is –E_0. Now answer the following questions.
Radius of hypothetical atom is

In a hypothetical atom, a negatively charged particle having a charge of magnitude 3e and mass 3m revolves around a proton. Here, e is the electronic charge and m is the electronic mass. Mass of proton may be assumed to be much larger than that of the negatively charged particle, thus the proton is at rest. This “atom” obeys Bohr’s postulate of quantization of angular momentum, that is  It is given that for the first Bohr orbit of hydrogen atom: radius of orbit is r₀ speed of electron is V₀, and total energy is –E_0. Now answer the following questions.
The momentum of an emitted photon when it makes a transition from the second excited state to ground state, is

The given figure shows a plot of the time dependent force x F acting on a particle in motion along the x-axis. What is the total impulse (in kg-m/s) delivered by this force to the particle from time t = 0 to t = 2 second?

In the figure shown a small block B of mass m is released from the top of a smooth movable wedge A of the same mass m. The height of wedge A shown in figure is h = 16 cm. B ascends another movable smooth wedge C of the same mass. Neglecting friction anywhere find the maximum height (in cm) attained by block B on wedge C.

Mass 2m is kept on a smooth circular track (R = 9 meters) of mass m which is kept on a smooth horizontal surface. The circular track is given a horizontal velocity  towards left and released. Find the maximum height reached by 2m in meters.

Two blocks of masses m₁ and m₂ are connected by spring of constant K such that m₂/m₁=9. The spring is initially compressed and the system is released from rest at t = 0 second. The work done by spring on the blocks m₁ and m₂ be ω₁ and ω₂ respectively by time t. The speeds of both the blocks at time ‘t’ are non-zero. Then find the value of ω₁/ω₂.

Two simple pendulums of length 5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed .... oscillations.

Copper reduces  into NO and NO₂ depending upon concentration of HNO₃ in solution. Assuming  [Cu²⁺] = 0.1M, and P_NO = P_NO2 = 10^–3 bar. At which concentration of HNO₃, thermodynamic tendency for reduction of  into NO and NO₂ by copper is same?

A radioactive material (t_1/2 = 30 days) gets spilled over the floor of a room. If initial activity is ten times the permissible value, after how many days will it be safe to enter the room

 A mixture of all possible stereoisomers from the above structure is subjected to fractional distillation, which of the following statements is correct

Which of the following about SF₄, SOF₄ and COF₂ molecules is correct?

B₂O₃ substitutes nonmetal oxides from several metal salts because

Which of these is most stable?

The correct statement regarding various types of molecular speeds are

The compounds that should be used to prepare glycine and β – alanine by Gabriel phthalimide synthesis are

In which of these compounds, Nitrogen can be estimated by Duma’s method?

A black mineral (A) in solid state is fused with KOH and KNO₃ and the mixture extracted with water to get a green coloured solution (B). On passing CO₂ gas through the solution the colour changes to pink with a black residue (C). Which of the following is/are correct

A is

Formation of “B” through the attack of first two reagents involve respectively

Product “C” is

A white substance (A) reacts with dilute H₂SO₄ to produce a colourless gas (B) and a colourless solution (C). The reaction between (B) and acidified K₂Cr₂O₇ solution produces a green solution and a slightly coloured precipitate (D). The substance (D) burns in air to produce a gas (E), which reacts with (B) to yield (D) and a colourless liquid. Anhydrous copper sulphate is turned blue on addition of this colourless liquid. Addition of aqueous NH₃ or NaOH to (C) produces first a precipitate which dissolves in the excess of the respective reagent to produce a clear solution in each case
(B) and (D) are respectively

A white substance (A) reacts with dilute H₂SO₄ to produce a colourless gas (B) and a colourless solution (C). The reaction between (B) and acidified K₂Cr₂O₇ solution produces a green solution and a slightly coloured precipitate (D). The substance (D) burns in air to produce a gas (E), which reacts with (B) to yield (D) and a colourless liquid. Anhydrous copper sulphate is turned blue on addition of this colourless liquid. Addition of aqueous NH₃ or NaOH to (C) produces first a precipitate which dissolves in the excess of the respective reagent to produce a clear solution in each case
The precipitate obtained by addition of aqueous NH₃ or NaOH to (C) initially is _____ which dissolves in excess reagent to produce ________

Which of the following is correct regarding solutions of sodium metal in liquid ammonia.

For the given reaction the correct statement is

Choose the correct option

For the cell (at 1 bar H₂ pressure) Pt/H₂(g) H X (m₁), NaX(m₂), NaCl(m₃)/AgCl/Ag/Pt it is found that the value of E

 approaches 0.2490 in the limit of zero concentration. Calculate  for the acid HX at 27°C. (R = 8.3 Jmole^–1K^–1, F = 96500C)

During the titration of 100 ml of a weak monobasic acid solution using 0.1 M NaOH, the solution became neutral at 40 mL addition of NaOH and equivalence point was obtained at 50 mL NaOH addition. The K_a of the acid is (log 2 = 0.3)

The sum of no of cyclic transition states and intermediates in the above reaction during the formation of product is/are....

How many carbon atoms (In A, B and (c) changed their hybridization till the formation of D? (Consider each reaction and do not consider stereoisomerism)

No of stereoisomers possible for X is

Index of hydrogen of the major product is….

No of 1° carbons in product is …..

Let a, b and c be positive constants. The value of ‘a’ in terms of ‘c’ if the value of integral   is independent of ‘b’ equals

Let  are three vectors along the adjacent edges of a tetrahedron,  if  and  then volume of tetrahedron is

Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r₁, r₂ and r₃ are the numbers obtained on the die, then the probability that 

A ray of light travels along a line y = 4 and strikes the surface of a curves y² = 4 (x + y), then equations of the line along which reflected ray travel is

A triangle ABC having vertices A (5, 1), B (–1, –7) and C (1, 4) respectively. If L1 be the line mirror passing through C and parallel to AB, a light ray emanating from point A and goes along the direction of internal bisector of the angle A, which meets the mirror at E and BC at D. Then sum of the area of ΔACE and ΔABC is

The number of different ways in which the persons A, B, C having 6 one rupee coins, 7 one rupee coins, 8 one rupee coins respectively donate 10 one rupee coins collectively is equal

Let a = cos^–1 (cos 20), b = cos^–1 (cos 30) and c = sin^–1 sin (a + b) then maximum value of sin (2 (a+b+c) x) + cos² ((a+b+c) x) is

If ‘A₁’ is the area bounded by |x – aiai| + |y| = bibi, i ∈ N, where  and  then

A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. Let the position of the vertex A remains unchanged and C₁ is the new position of C.
The distance of C₁ from A is equal to

A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. Let the position of the vertex A remains unchanged and C₁ is the new position of C.
If ∠∠ABC₁ = θ, then cos θ is equal to

A square ABCD of diagonal 2a is folded along the diagonal AC so that the planes DAC and BAC are at right angle. The shortest distance between DC and AB is

Family of curves which makes an angle of π/4 with the family of hyperbola xy = a, is (a > 0, and a is a parameter)

Let position vector of the orthocenter of ΔABC be  Then, which of the following statement(s) is/are correct (Given position vector of points A, B, C are 

Let f (x) = x³ + 2x² – x + 1, then which of the following statement(s) is/are correct

 where b ∈ R. The value of ‘I’ can be

The equations of AB, BC, AC, the three sides of ΔABC are –x + y –1 = 0, x + y –1 = 0 and x = –4. If (α, 0) and (0, β) lie inside the triangle where α, β ∈ Z, then

a, b ∈ I satisfies equation a(b – l) = 3 + b – b², then a + b is equal to

Let  be a sequence of sets defined by a_n = (n² - 1)/n. Then,

A right angle triangle ABC, right angle at A is inscribed in hyperbola xy = c² (c > 0) such that slope of BC is 2. If distance of point A from centre of xy = c² is √10, then which of the following is/are correct for xy = c²

Let P(a, b) be a variable point satisfying  Let R be the complete region represented in x-y plane in which P can lie.
Area of region R is

Let z₁, z₂, z₃ be complex numbers such that |z₁| = |z₂| = |z₃| = 3&(z₁ ≠ z₃). Then find the value of  

Let z represents a variable point in complex plane such that z − z₁ is real, where z₁ is a fixed point in the same plane? Let “m” be the number of “z” values such that |z| = λ, where λ >|Im(z₁)| & let “n” be the number of “z” values such that |z| = λ, where λ = |Im(z₁)| then value of m + n =__________

The least possible degree of a polynomial equation, with real coefficients having 2ω², 3 + 4ω, 3 + 4ω², 5 − ω − ω² as roots is ________ 
(ω, ω² are non-real cube roots of 1).

A curve is defined as  Two spiders, one male and other female were moving together along the curve. The female spider suddenly realizes that the male spider is a rogue spider and immediately tries to get away as far as possible from it. Hence it moved onto the another point on the curve. The maximum distance between two final points when both spiders try out all possibilities, is k. Then the value of  __________[.] Greatest integer function

If α,β,γ are the roots of x³ − 3x² + 3x + 7 = 0 and w is a non-real cube root of 1, and the value of  then number of ordered pairs (p, q) such that p + q = 15 is _______