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JEE Advanced 2017 Paper - 1 with Solutions - Question 1

A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength λ_{0} is produced at point O on the rope. The pulse takes time TOA to reach point A. If the wave pulse of wavelength λ_{0} is produced at point A (Pulse 2) without disturbing the position of M it takes time T_{AO} to reach point O. Which of the following options is/are correct ?.

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 1

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 2

A human body has a surface area of approximately 1 m^{2.} The normal body temperature is 10 K above the surrounding room temperature T_{0}. Take the room temperature to be T_{0 }= 300 K. For T_{0} = 300 K, the value of (where σ is the Stefan-Boltzmann constant). Which of the following options is/are correct ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 2

JEE Advanced 2017 Paper - 1 with Solutions - Question 3

A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x = 0, in a co-ordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following options is/are correct ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 3

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 4

A circular insulated copper wire loop is twisted to form two loops of area A and 2A as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field points into the plane of the paper.

At t = 0, the loop starts rotating about the common diameter as axis with a constant angular velocity ω in the magnetic field. Which of the following options is/are correct?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 4

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 5

For an isosceles prism of angle A and refractive index µ, it is found that the angle of minimum deviation . Which of the following options is/are correct ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 5

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 6

In the circuit shown, L = 1 µH, C = 1 µF and R = 1 kΩ. They are connected in series with an a.c. source V = V_{0} sin ωt as shown. Which of the following options is/are correct ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 6

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 7

A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true ?

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JEE Advanced 2017 Paper - 1 with Solutions - Question 8

A drop of liquid of radius R = 10^{–2} m having surface tension divides itself into K identical drops. In this process the total change in the surface energy then the value of α is

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 8

JEE Advanced 2017 Paper - 1 with Solutions - Question 9

^{131}I is an isotope of Iodine that β decays to an isotope of Xenon with a half-life of 8 days. A small amount of a serum labelled with ^{131}I is injected into the blood of a person. The activity of the amount of ^{131}I injected was 2.4 × 10^{5} Becquerel (Bq). It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After 11.5 hours, 2.5 ml of blood is drawn from the person's body, and gives an activity of 115 Bq. The total volume of blood in the person's body, in liters is approximately

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 9

*Answer can only contain numeric values

JEE Advanced 2017 Paper - 1 with Solutions - Question 10

An electron in a hydrogen atom undergoes a transition from an orbit with quantum number n_{i} to another with quantum number n_{f}. V_{i} and V_{f} are respectively the initial and final potential energies of the electron. then the smallest possible n_{f }is.

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 10

*Answer can only contain numeric values

JEE Advanced 2017 Paper - 1 with Solutions - Question 11

A monochromatic light is travelling in a medium of refractive index n = 1.6. It enters a stack of glass layers from the bottom side at an angle θ = 30°. The interfaces of the glass layers are parallel to each other.

The refractive indices of different glass layers are monotonically decreasing as n_{m} = n – mΔn, where n_{m} is the refractive index of the m^{th} slab and Δn = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m - 1)^{th} and m^{th} slabs from the right side of the stack. What is the value of m ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 11

*Answer can only contain numeric values

JEE Advanced 2017 Paper - 1 with Solutions - Question 12

A stationary source emits sound of frequency f_{0} = 492 Hz. The sound is reflected by a large car approaching the source with a speed of 2 ms^{–1}. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz ? (Given that the speed of sound in air is 330 ms^{–1} and the car reflects the sound at the frequency it has received).

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 12

JEE Advanced 2017 Paper - 1 with Solutions - Question 13

(Direction) Q.13, Q.14 and Q.15 by appropriately matching the information given in the three columns of the following table.

A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity . A uniform electric field and a uniform magnetic field exist everywhere. The velocity , electric field and magnetic field are given in column 1, 2 and 3, respectively. The quantities E_{0}, B_{0} are positive in magnitude.

**Column-1 ** **Column-2 ** **Column-3**

**Q. In which case will the particle move in a straight line with constant velocity ?**

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 13

JEE Advanced 2017 Paper - 1 with Solutions - Question 14

A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity . A uniform electric field and a uniform magnetic field exist everywhere. The velocity , electric field and magnetic field are given in column 1, 2 and 3, respectively. The quantities E_{0}, B_{0} are positive in magnitude.

**Column-1 ** **Column-2 ** **Column-3**

**Q. In which case will the particle describe a helical path with axis along the positive z-direction ?**

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 14

JEE Advanced 2017 Paper - 1 with Solutions - Question 15

A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity . A uniform electric field and a uniform magnetic field exist everywhere. The velocity , electric field and magnetic field are given in column 1, 2 and 3, respectively. The quantities E_{0}, B_{0} are positive in magnitude.

**Column-1 ** **Column-2 ** **Column-3**

**Q. In which case would the particle move in a straight line along the negative direction of y-axis (i.e., move along - ) ?**

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 15

JEE Advanced 2017 Paper - 1 with Solutions - Question 16

(Direction) Q.16, Q.17 and Q.18 by appropriately matching the information given in the three columns of the following table.

An ideal gas is undergoing a cyclic thermodynamics process in different ways as shown in the corresponding P–V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamics processes. Here g is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n.

**Q. Which of the following options is the only correct representation of a process in which ΔU = ΔQ - PΔV?**

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 16

JEE Advanced 2017 Paper - 1 with Solutions - Question 17

An ideal gas is undergoing a cyclic thermodynamics process in different ways as shown in the corresponding P–V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamics processes. Here g is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n.

**Q. Which one of the following options is the correct combination ?**

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 17

JEE Advanced 2017 Paper - 1 with Solutions - Question 18

An ideal gas is undergoing a cyclic thermodynamics process in different ways as shown in the corresponding P–V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamics processes. Here g is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n.

**Q. Which one of the following options correctly represents a thermodynamics process that is used as a correction in the determination of the speed of sound in an ideals gas ?**

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 18

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 19

The IUPAC name(s) of the following compound is (are)

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 19

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 20

The correct statement(s) for the following addition reactions is(are)

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 20

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 21

Addition of excess aqueous ammonia to a pink coloured aqueous solution of MCl_{2} . 6H_{2}O (X) and NH_{4}Cl gives an octahedral complex Y in the presence of air. In aqueous solution, complex Y behaves as 1 : 3 electrolyte. The reaction of X with excess HCl at room temperature results in the formation of a blue coloured complex Z. The calculated spin only magnetic moment of X and Z is 3.87 B.M., whereas it is zero for complex Y.

**Q. Among the following options, which statment is (are) ?**

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 21

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 22

For a solution formed by mixing liquids L and M, the vapour pressure of L plotted against the mole fraction of M in solution is shown in the following figure, Here x_{L} and x_{M} represent mole fractions of L and M, respectively, in the solution. the correct statement(s) applicable to this system is(are) -

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 22

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 23

An ideal gas is expanded from (p_{1} , V_{1} , T_{1}) to (p_{2} , V_{2} , T_{2}) under different conditions. The correct statement(s) among the following is(are)

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 23

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 24

The correct statements(s) about the oxoacids, HClO_{4} and HClO, is (are) -

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 24

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 25

The colour of the X_{2} molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to -

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 25

JEE Advanced 2017 Paper - 1 with Solutions - Question 26

Among H_{2}, He^{+}_{2}, Li_{2}, Be_{2}, B_{2}, C_{2}, N_{2}, O^{-}_{2}, the number of diamagnetic species is -( Atomic number) : H =1, He = 2, Li = 3, Be = 4, B = 5, C = 6, N = 7,I = 8, F = 9)

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 26

JEE Advanced 2017 Paper - 1 with Solutions - Question 27

Among the following, the number of aromatic compound (s) is-

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 27

JEE Advanced 2017 Paper - 1 with Solutions - Question 28

The conductance of a 0.0015 M aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized Pt electrodes. The distance between the electrodes is 120 cm with an area of cross section of 1 cm^{2}. The conductance of this solution was found to be 5 × 10^{–7}S. The pH of the solution is 4. The value of limiting molar conductivity of this weak monobasic acid in aquence solution is

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 28

JEE Advanced 2017 Paper - 1 with Solutions - Question 29

The metal used to recover copper from a solution of copper sulphate is

JEE Advanced 2017 Paper - 1 with Solutions - Question 30

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8g cm^{–3}, then the number of atoms present in 256g of the crystal is N × 10^{24}. The value of N is

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 30

JEE Advanced 2017 Paper - 1 with Solutions - Question 31

(Direction) Q.31, Q.32 and Q.33 by appropriately matching the information given in the three columns of the following table.

The wave function is a mathematical function whose value depends upon spherical polar coordinates (r,θ,φ) of the electron and characterized by the quantum numbers n, l and m_{1}. Here r is distance from nucleus, θ is colatitude and φ is azimuth. In the mathematical functions given in the Table, Z is atomic number a_{0} is Bohr radius.

**Q. For the given orbital in column 1, the only CORRECT combination for any hydrogen - like species is :**

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 31

JEE Advanced 2017 Paper - 1 with Solutions - Question 32

The wave function is a mathematical function whose value depends upon spherical polar coordinates(r,θ,φ) of the electron and characterized by the quantum numbers n, l and m_{1}. Here r is distance from nucleus, θ is colatitude and φ is azimuth. In the mathematical functions given in the Table, Z is atomic number a_{0} is Bohr radius.

**Q. For He+ ion, the only INCORRECT combination is **

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 32

JEE Advanced 2017 Paper - 1 with Solutions - Question 33

The wave function is a mathematical function whose value depends upon spherical polar coordinates (r,θ,φ) of the electron and characterized by the quantum numbers n, l and m_{1}. Here r is distance from nucleus, θ is colatitude and φ is azimuth. In the mathematical functions given in the Table, Z is atomic number a_{0} is Bohr radius.

**Q. For hydrogen atom, the only CORRECT combination is**

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 33

JEE Advanced 2017 Paper - 1 with Solutions - Question 34

**Q.**

For the synthesis of benzoic acid, the only CORRECT combination is

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 34

JEE Advanced 2017 Paper - 1 with Solutions - Question 35

**Q.**

The only CORRECT combination in which the reaction proceeds through radical mechanism is

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 35

JEE Advanced 2017 Paper - 1 with Solutions - Question 36

**Q.**

The only CORRECT combination that gives two different carboxylic acids is

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 36

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 37

Which of the following is(are) NOT the square of a 3 × 3 matrix with real entries ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 37

JEE Advanced 2017 Paper - 1 with Solutions - Question 38

If a chord, which is not a tangent, of the parabola y^{2} = 16x has the equation 2x + y = p, and midpoint (h, k), then which of the following is(are) possible value(s) of p, h and k ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 38

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 39

Let a, b, x and y be r eal n um ber s su ch th at a – b = 1 and y ¹ 0 . If t he co mp lex nu mb er z = x + iy satisfies

then which of the following is(are) possible value(s) of x ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 39

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 40

Let X and Y be two events such that and Then

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 40

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 41

Let [x] be the greatest integer less than or equal to x. Then, at which of the following point(s) the function ƒ(x) = xcos(π(x + [x])) is discontinuous ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 41

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 42

If 2x – y + 1 = 0 is tangent to the hyperbola

then which of the following CANNOT be sides of a right angled triangle ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 42

*Multiple options can be correct

JEE Advanced 2017 Paper - 1 with Solutions - Question 43

Let ƒ : R → (0,1) be a continuous function. Then, which of the following function(s) has(have) the value zero at some point in the interval (0, 1)?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 43

JEE Advanced 2017 Paper - 1 with Solutions - Question 44

The sides of the right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 44

JEE Advanced 2017 Paper - 1 with Solutions - Question 45

For how many values of p, the circle x^{2} + y^{2} + 2x + 4y – p = 0 and the coordinate axes have exactly three common points ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 45

JEE Advanced 2017 Paper - 1 with Solutions - Question 46

For a real number a, if the system

of linear equations, has infinitely many solutions, then 1 + α + α^{2} =

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 46

JEE Advanced 2017 Paper - 1 with Solutions - Question 47

Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated; and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, y/9x =

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 47

JEE Advanced 2017 Paper - 1 with Solutions - Question 48

Let f : R → R be a differentiable function such that f(0) = 0, and f'(0) = 1. If

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 48

JEE Advanced 2017 Paper - 1 with Solutions - Question 49

**Q.**

The tangent to a suitable conic (Column 1) at is found to be then which of the following options is the only CORRECT combination ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 49

JEE Advanced 2017 Paper - 1 with Solutions - Question 50

**Q.**

If a tangent to a suitable conic (Column 1) is found to be y = x + 8 and its point of contact is (8,16), then which of the following options is the only CORRECT combination ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 50

JEE Advanced 2017 Paper - 1 with Solutions - Question 51

**Q.**

For a=√2 , if a tangent is drawn to a suitable conic (Column 1) at the point of contact (-1,1), then which of the following options is the only CORRECT combination for obtaining its equation ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 51

JEE Advanced 2017 Paper - 1 with Solutions - Question 52

**Q.**

Which of the following options is the only CORRECT combination ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 52

JEE Advanced 2017 Paper - 1 with Solutions - Question 53

**Q. **Which of the following options is the only CORRECT combination ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 53

JEE Advanced 2017 Paper - 1 with Solutions - Question 54

**Q.**

Which of the following options is the only INCORRECT combination ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 54

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