General Instructions

1.The test is of 3 hours duration and the maximum marks is 300.

2.The question paper consists of 3 Parts (Part I: Physics, Part II: Chemistry, Part III: Mathematics). Each Part has two sections (Section 1 & Section 2).

3.Section 1 contains 20 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.

4.Section 2 contains 10 Numerical Value Type Questions Out of which ONLY 5 (any) questions have to be attempted.

You will NOT be allowed to attempt the sixth question. If you wish to attempt any other question apart from the five already attempted, then you will have to delete any one response from the five previously answered and then proceed to answer the new one.

The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer. If the answer is a decimal numerical value, then round-off the value to TWO decimal places. If the answer is an Integer value, then do not add zero in the decimal places. (Example: 6, 81, 1.50, 3.25,

0.08)

5.No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. inside the examination room/hall.

6.On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.

Marking Scheme

1.Section – 1: +4 for correct answer, –1 (negative marking) for incorrect answer, 0 for all other cases.

2.Section – 2: +4 for correct answer, 0 for all other cases. There is no negative marking.

Name of the Candidate (In CAPITALS) :

Roll Number :

OMR Bar Code Number :

SECTION-1

This section contains 20 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.

1.A particle is moving in a circle of radius 1m with angular velocity (ω) given as a function of angular

displacement ( θ ) by the relation ω = θ2 + 2θ. The total acceleration of the particle when θ = 1 rad is:

2.An inverted cone is rotating about its vertical axis. A particle is kept on the inner surface of cone and it is at rest relative to the cone at a height of 0.4m above its vertex. The coefficient of friction between the surface of cone and the particle is 0.6 and the apex angle of cone is 90°. The maximum angular velocity of revolution of the cone can be: (take g = 10 / s2 )

3.Magnetic field exists in the region between lines PQ and RS as shown in the figure. A particle having charge to mass ratio of 'a ' enters the magnetic field as shown in the figure with a speed v. Lines PQ and RS are parallel to each other. Find the value of d such that the charged particle exits the magnetic field region with velocity perpendicular to line RS.

4.A satellite is moving around a planet of radius R in a circular orbit of radius r. The speed of the satellite is v. Find the acceleration due to gravity on the surface of the planet.

5.Two infinite line charges having linear charge density λ1 and λ2 are placed along the x and y axis respectively. The electric field at a point ( x1, y1 ) in the first quadrant is inclined at an angle of 60° with the x-axis. Then which of the following relations is correct.

7.An electron moving with a velocity of 2m / s along +ve x-axis at a point in a magnetic field experiences a force of 2N along -ve y-axis. If the electron moves with of a velocity of 2m / s along +ve y-axis at the same point, it experiences a force of 2N along +ve x-axis. Find force that the electron would experience

if it were moving with a velocity of 2m / s along z-axis.

8.Three rods of equal mass having length L, L and 2L are joined to form a triangular frame as shown in the figure. The system is rotating about an axis passing through the vertex of the triangle and perpendicular to the plane of the triangle with an angular velocity ω. Find the angular momentum of the system.

9.The truth table for the circuit given in the figure is :

10.In an imaginary electric field, the electric potential energy of an electron at a distance r from the centre of force field is given by U = kr2 , where k is a positive constant of appropriate dimensions. If the electron is moving in a circular orbit of radius r about the centre, then the orbital time period of the electron is proportional to:

11.A particle of mass 2 kg is moving in the direction of positive x axis. Initial velocity of the particle is 1m / s. The instantaneous power vs time graph of the particle is shown in the figure. Find the velocity of the particle at 7 seconds.

13.A vernier calliper whose 10 vernier scale divisions coincide with 9 main scale divisions is used to take a reading. Each main scale division is 1mm. Before taking the reading it is observed that the 4th division of the vernier scale coincides with the main scale and zero of main scale is behind zero of vernier scale. When the reading is taken using this vernier calliper, the main scale reads 2.5cm and the 7th division of

the vernier scale coincides with the main scale. Find the final value of the measurement.

14.An inductor and a resistor are connected to an ac supply of 120V ,50Hz. The resistance of the resistor is 20Ω. If the voltages leads the current by a phase difference of 45°, find the inductance of the inductor.

15.Two particles start moving from the same point in two different directions. The first particle moves along the positive x-axis with a constant acceleration of 3m / s2 . The second particle moves in a straight line making an angle of 60° with the positive x-axis with a constant speed of 24m / s. Find the time after which the relative velocity of the particles is minimum.

16.A cylindrical metal rod BC of length material and length but having twice

1m and radius 1cm is joint in series to another rod AB of same the radius as shown in the figure.

17.As a train moving with constant speed crosses the platform, the apparent frequency heard by a person standing on the platform during approach and recession differ by 2% of the actual frequency of the horn. If the speed of sound is 330m / s, find the approximate speed of the train.

(A)emits a γ - ray photon of energy 2MeV

(B)captures a γ - ray photon of energy 2MeV

(C)emits a γ - ray photon of energy 3MeV

(D)captures a γ - ray photon of energy 3MeV

19.An electromagnetic wave is represented by the electric field

E = E0nˆ [t + ( y z)]

The direction of propagation of the wave, sˆ is:

20.A fish moving up in water (μ = 4 / 3) with a speed of 4cm/s observes a bird coming directly towards itself with a speed of 12cm / s. Find the actual speed of the bird with respect to a stationary observer on

the ground.

SECTION-2

Section 2 contains 10 Numerical Value Type Questions Out of which ONLY 5 (any) questions have to be attempted. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the

answer. If the answer is a decimal numerical value, then round-off the value to TWO decimal places. If the answer is an Integer value, then do not add zero in the decimal places. In the OMR, do not bubble the sign for positive values. However, for negative values, Θ sign should be bubbled. (Example: 6, 81, 1.50, 3.25, 0.08)

21.12gm of gas occupy a volume of 4 ×10−3 m3 at a temperature of 7°C. After the gas is heated at constant pressure its density becomes 6 ×10−4 gm / cm3. What is the temperature to which the gas was heated (in kelvin)?

22.In a young’s double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved 8cm towards the slits, the change in fringe width is 4 ×10−5 m. If the separation between the slits is 1mm, find the wavelength of light used (in nm).

23.A bucket of height 20cm is placed under a tap such that water flows into the bucket at a constant rate of 100cm3 / s. There is a small hole in the bucket of cross-sectional area of 1cm2 at height of 3cm from the bottom. Area of hole is very small as compared to area of the bucket. Find the maximum height (in cm) above the bottom upto which the water is filled in the bucket. (Take g = 10m / s2 )

24.A wooden wheel having radius of 1m is to be fitted with an iron ring around it. The diameter of the ring is 6mm smaller than the wooden wheel. If the coefficient of linear expansion of iron is 1.2 ×10−5 / °C, then find the minimum increase in temperature (in °C ) to fit the ring on the wheel.

25.A capacitor of capacitance 3μF is charged to a potential difference of 12V. Another identical capacitor, initially uncharged is filled with a dielectric having dielectric constant K and it is connected to the charged capacitor. The final common potential difference across both capacitors is found to be 2V. Find the value of k.

error in its value. Lengths of the air column l1 and l2 are measured as 25.0cm and 80.0cm respectively. Find the absolute error in the speed of sound (in m/s).

27.An inductor of inductance 0.1H and a resistor of resistance 8Ω are connected in series to a battery of emf 1.5V through a switch. Find the initial rate of growth of current when the switch is closed (in A/s).

28.A particle of mass 3kg moving with speed of 3m / s is acted upon by an impulse. As a result, the particle starts moving in a direction 90° to the original direction with a speed of 4m / s. Find the impulse acted upon on the particle in SI units.

29.In the given circuit find the current through the Zener diode in mA.

30.A beam of unpolarized light of intensity I0 is incident on a polaroid A. Then it is passed through another polaroid B. If the intensity of the emergent light is 18% of the original unpolarized light then find the angle (nearest integer in degree) between the principal plane of polaroid A and B.

SECTION-1

This section contains 20 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.

1.The BOD value of two samples of water are 4ppm and 18 ppm, respectively and this indicates:

2.Molality of sulphuric acid solution in which the mole fraction of water is 0.74 is:

3.The increasing order of pkb values of the following compounds is:

4.

Structure of (D) is:

5.Arrange the following solutions in the decreasing order of pH :

6.Among the nitrates of alkaline earth metals, the thermal stability of Mg(NO3 )2 and Sr(NO3 )2

7.For the reaction NH4Cl(g) NH3 (g) + HCl(g)

8.The incorrect statement is:

9.Consider the assertion and reason given below:

Assertion (A) : Buta-1,3 - diene is a monomer of gutta percha.

Reason (R) : Gutta Percha is formed through cationic addition polymerisation Choose the correct answer from the following:

(A)(A) and (R) both are wrong

(B)Both (A) and (R) are correct and (R) is correct explanation of (A)

(C)(A) is wrong but (R) is correct

(D)Both (A) and (R) are correct but (R) is not correct explanation of (A)

10.Which of the following compounds do not show geometrical isomerism?

12.Which of the following is not an example of σ − bonded organometallic complex?

13.The set that contains atomic numbers of only inner transition elements is:

14.Consider the following reactions

15.

Compound D is:

16.The major product obtained from the following reaction is:

17.The Lanthanoid that does not show +2 oxidation states is:

18.The correct statement is:

(A)Magnalium is an alloy of Al and Cu

(B)Bell metal is an alloy of Cu and Sn

(C)Gun metal is an alloy of Cu, Zn and Ni

(D)Chrome steel is an alloy of Cr, Al and Ni

19.The incorrect statement for lyophilic colloids is

(A)Easy to prepare

(B)Viscosity is high and surface tension is low for D.P. (dispersed phase) than D.M. (dispersion medium)

(C)Viscosity and surface tension for D.P. is almost similar to D.M.

(D)Stable

20.For a reaction P → Q, the Ea for the forward reaction and backward reaction is 15KJ / mol and 5KJ / mol, respectively, potential energy of P is 8KJ / mol, then the heat of reaction (in kJ) is:

SECTION-2

Section 2 contains 10 Numerical Value Type Questions Out of which ONLY 5 (any) questions have to be attempted. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the

answer. If the answer is a decimal numerical value, then round-off the value to TWO decimal places. If the answer is an Integer value, then do not add zero in the decimal places. In the OMR, do not bubble the sign for positive values. However, for negative values, Θ sign should be bubbled. (Example: 6, 81, 1.50, 3.25, 0.08)

21.In an estimation of sulphur by carius method, 0.25gm of an organic compound gave 0.35gm of BaSO4. The mass percentage of sulphur in the compound is_____. (Molecular weight of BaSO4 = 233 g / mol )

22.How much propyl alcohol must be added to 1.00 lt. of water so the solution will not freeze at −15°C? (Kf of water = 1.86 K Kg mol) [ d(H2O) = 1g/ml and molecular mass of propyl alcohol = 60 g/mol]

23.Calculate the volume occupied by 12.0g of propane gas at 60°C and 740mm of pressure. (Molecular weight of C = 12 g/mol, H = 1 g/mol) [R = 0.082 L atm/mol K]

24.200 ml of 0.5M solution of CuBr2 was electrolysed using Pt as electrodes with a current of 0.965

ampere in one hour, what is the normality of the remaining CuBr2 solution assuming no change in volume?

25.The number of Cl = O bond in Chlorous acid is_____.

26.For how many metals leaching method is used for its concentration of ore Metals: Cu, Zn,Pb, Al, Au, Ag

27.The EAN value of ⎡Ti(σ − C5H5 )2 (π − C5H5 )2 is______.

28.The Number of Species which have square pyramidal shape Species:- XeOF4 , ClF5 , XeF4 ,PCl5 ,XeO3F2 ,SbCl5 ,BrF5 .

29.Consider the following reaction

40°C

CH2 = CH − CH = CH2 + HBr ⎯⎯⎯→ the number of geometrically active products is/are:

30.The number of compounds which do not show Fehling solution test? Compounds:

SECTION-1

This section contains 20 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE CHOICE is correct.

3.From first 100 natural numbers, 3 numbers are selected. If these numbers are in A.P., then the probability that these numbers are even is:

4.The parabola y = x2 − 9 and y = kx2 intersect each other at the points A and B. If the length AB is

equal to 10 units then the value of k is:

(α − 2)12 + (β − 6)12 −1 is:

α12

6.a,b,c are positive integers forming an increasing G.P. whose common ratio is a natural number. b a

10.Coefficient of variation of two distributions are 50% and 60% and their arithmetic means are 30 and

25 respectively. Difference of standard deviation is:

11.The remainder when 52222 is divided by 7 is:

of the foot of perpendicular from origin on the line is:

13.Two teachers are taking 6 students to a zoo. The teachers decide to split up. Each student must choose

one of the teachers, with the condition that each teacher must take at least one student. Number of possible ways of doing this is:

15.Area of the region bounded by x = 0, y = 0, x = 2, y = 2, y ex and y ≥ ln x, is:

18.If z = cos 20° + isin 20, then z + 2z2 + 3z3 + ......... + 18z18 −1 is:

x

tan−1 tdt

20.Let a2 ,b2 ,c2 be three distinct numbers in A.P. If ab + bc + ca = 1 then (b + c),(c + a) and (a + b) are

SECTION-2

Section 2 contains 10 Numerical Value Type Questions Out of which ONLY 5 (any) questions have to be attempted. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the

answer. If the answer is a decimal numerical value, then round-off the value to TWO decimal places. If the answer is an Integer value, then do not add zero in the decimal places. In the OMR, do not bubble the sign for positive values. However, for negative values, Θ sign should be bubbled. (Example: 6, 81, 1.50, 3.25, 0.08)

elements common in A× B and B × A are ______.

23.If x & y are real numbers satisfying the relation x2 + y2 − 6x + 8y + 24 = 0 then minimum value of log2 ( x2 + y2 ) is______.

24.Let f ( x)

then

1

is ______.

amin

25.A vertical pole PS has two marks at Q and R such that portions

α,β,γ respectively at a point on the ground which is at distance x

PQ = 1, PR = 2, PS = 3 and α + β + γ = 180°, then x2 is ______.

PQ, PR and PS subtends angle from the bottom of pole P. If

27.In a hurdle race, a runner has probability p of jumping over a specific hurdle. Given that in 5 trials, the runner succeeded 3 times, the conditional probability that the runner has succeeded in the first trial is ______.

29.Let n ( A) = 4 and n ( B) = 6, then the number of one- one functions from A to B is ______.

   End of Mock JEE Main - 5 | JEE 2021   