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JEE Advanced 2017 Paper - 1 with Solutions


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54 Questions MCQ Test JEE Main & Advanced Mock Test Series | JEE Advanced 2017 Paper - 1 with Solutions

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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 λ0 is produced at point O on the rope. The pulse takes time TOA to reach point A. If the wave pulse of wavelength λ0 is produced at point A (Pulse 2) without disturbing the position of M it takes time TAO to reach point O. Which of the following options is/are correct ?.

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


(A) Speed of wave is property of medium so time taken to cross the string will be equal
(B) Speeds are same but velocity is vector, has opposite directions

(D) Velocity of any pulse is  and it is property of medium.
 

*Multiple options can be correct
JEE Advanced 2017 Paper - 1 with Solutions - Question 2

A human body has a surface area of approximately 1 m2. The normal body temperature is 10 K above the surrounding room temperature T0. Take the room temperature to be T0 = 300 K. For T0 = 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

Assumption : e = 1 (Black body radiation)








(C) Surface area decrease ⇒ Energy radiation decreases

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







Net emf will be difference of emfs in both loops because their polarities are opposite.

*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 = V0 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 ?

Detailed Solution for JEE Advanced 2017 Paper - 1 with Solutions - Question 7

  






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

131I 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 131I is injected into the blood of a person. The activity of the amount of 131I injected was 2.4 × 105 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




120 Bq is the activity of 2.5 ml
∴ 2.4 * 10Bq is the activity of 
∴ Total volume of blood = 5 litres

*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 ni to another with quantum number nf. Vi and Vf are respectively the initial and final potential energies of the electron. then the smallest possible nf 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 nm = n – mΔn, where nm is the refractive index of the mth slab and Δn = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m - 1)th and mth 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

Applying snell's law between entry & exit surfaces, n sin θ = µ sin (π/2)

*Answer can only contain numeric values
JEE Advanced 2017 Paper - 1 with Solutions - Question 12

A stationary source emits sound of frequency f0 = 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

Frequency of sound as received by large car approaching the source.

This car now acts as source for reflected sound wave

frequency of sound received by source,


= 6 Hz

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 E0, B0 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


For particle to move in straight line with constant velocity, 

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 E0, B0 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

For path to be helix with axis along +ve z-direction, particle should experience a centripetal acceleration in x-y plane.
For the given set of options only option (C) satisfy the condition. Path is helical with increasing pitch.

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 E0, B0 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

For particle to move in -ve y-direction, either its velocity must be in –ve y-direction (if initial velocity  0) & force should be parallel to velocity or it must experience a net force in –ve y-direction only (if initial velocity = 0)

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

Work (Column-I), process (Column-II) & corresponding graph (Column-III) are in this sequence.

Only "B" option follow the sequence.

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

Only option "A" follow the sequence.

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

It is for an adiabatic process.

*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


 IUPAC Name- "Toluene" is accepted by IUPAC as a name of parent carbon chain.
 So it can also be named as 4-chlorotoluene.

*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

 

 
(ii)  
(O) and (P) are enantiomers
Explanation of 4 options : (A) (M) and (O) are distereomers of each other.
(N) and (P) are distereomers of each other.
(B) Addition of Br2 on alkene follows non-classical carbocation mechanism. It is anti or trans addition.
(C) (O) and (P) are enantiomers
(D) (M) and (N) are identical and (O) and (P) are enantiomers.
 (M and O) are distereomers and (N and P) are distereomers.

*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 MCl2 . 6H2O (X) and NH4Cl 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



(A) Hyridisation of (Y) is d2sp3 as NH3 is strong field ligand  
(B) [COCl4]2- have sp3 hybridisation  as Cl- is weak field ligand 


When ice is added to the solution the equilibrium shifts right hence pink colour will remain predominant So, correct answer is (A,B& D)

*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 xL and xM 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 (p1 , V1 , T1) to (p2 , V2 , T2) 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, HClO4 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 X2 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

Halogens are coloured due to HOMO-LUMO transition of electrons.

On moving down the group HOMO-LUMO energy gap decreases so transition of electrons become easier  therefore colour intensify.

JEE Advanced 2017 Paper - 1 with Solutions - Question 26

Among H2, He+2, Li2, Be2, B2, C2, N2, 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





If existence of Be2 is considered in atomic form or very weak bonded higher energetic species having zero bond order then it is diamagnetic , then answer will be 6. But if existence of molecular form of Be2 is not considered then magnetic property can't be predicted then answer will be 5

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


Cyclooctatetraene ; non aromatic
Due to nonplanarity of ring the π-electrons are not delocalised.
 
Cyclopropcnyl anion : Anti aromatic 4π-electrons delocalised.

Cyclopropenyl cation ; Aromatic 2π-clcctrons delocalised.

Cyclohexadiene : Non-aromatic.

Tropylium ion : Arom atic 6π-electrons delocalised.

Cyclo pentadienyl cation . Anti-aromatic 4π-electrons delocalised.

Cyclo pentadienyl anion ; Aromatic 6π-electrons delocalised.

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 cm2. The conductance of this solution was found to be 5 × 10–7S. 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

For weak acid [H+

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 × 1024. The value of N is

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

Formula of density = 
For FCC unit cell Z = 4
Edge length a = 4 * 10-8 cm



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 m1. 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 a0 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

(A) (IV) (iv) (R) ⇒ incorrect, because, dz2   has no nodal plane.
(B) (II) (ii) (P)  ⇒ correct, because 2s orbtial has 1 radial node.

(C) (III) (iii)  (P) ⇒ incorrect, because probability density for 2p at nucleus is zero.
(D) (I) (ii) (S)  ⇒ incorrect, because 1s orbital has no radial node.

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 m1. 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 a0 is  Bohr radius.

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

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

The option (D) is incorrect because in the wave function of 1s orbital , no angular function should be present.

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 m1. 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 a0 is  Bohr radius.

Q. For hydrogen atom, the only CORRECT combination is

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

We have to select only correct combination hence, the option (D) is correct.


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

(D). (II)(i)(S)

(A)

(B)

(C)

(D)

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

Ans. [A](I)(ii)(R)

mechanism involved is free radical substitution

(B)

(C)

(D)

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

Ans. (B)

*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

Ans. (A,B)

JEE Advanced 2017 Paper - 1 with Solutions - Question 38

If a chord, which is not a tangent, of the parabola y2 = 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

Ans. (D)

Equation of chord with mid point (h, k) :

⇒ 8x – ky + k2 – 8h = 0

Comparing with 2x + y – p = 0, we get k = –4; 2h – p = 4 only (D) satisfies above relation.

*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

Ans. (A,D)

*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

Ans. (A,D)

from this information, we get

*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

Ans. (A,C,D)

Discontinuous at all integers except zero.

*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

Ans. (B,C,D)

The line y= mx + c is tangent to the hyperbola 

c2 = a2m2 - b2

*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

Ans. (B,D)

For option (A),

⇒ g(x) is strictly incrasing function.
Also, g(0) = 1

∴ option (A) is not possible.
For option (B), let 

⇒ k(0). k(1) < 0
So, option(B) is correct.
For option (C), let

so, option(C) is not possible.
For option (D),

⇒ M(0). M(1) < 0
∴ option (D) is correct.

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

Ans. 6

where d > 0, a > 0
⇒ length of smallest side = a - d
Now (a + d)2 = a2 + (a - d)2
⇒  a(a - 4d) = 0

∴ a = 4d ...(1)  
(As a = 0 is rejected)

Also,

a(a – d) = 48 ...(2)

∴ From (1) and (2),
we get a = 8, d = 2
Hence, length of smallest side
(a - d) = (8 - 2) = 6

option d

JEE Advanced 2017 Paper - 1 with Solutions - Question 45

For how many values of p, the circle x2 + y2 + 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

Ans. 2

We shall consider 3 cases.
Case I : When p = 0 (i.e. circle passes through origin) Now, equation of circle becomes x2 + y2 + 2x + 4y = 0

Case II : When circle intersects x-axis at 2 distinct points and touches y-axis
Now (g2 – c) > 0        &   ƒ2 – c = 0

⇒ 1 - (- p) > 0 & 4 - (- p) = 0
⇒ p = - 4  ⇒ p > -1

∴  Not possible.

Case III : When circle intersects y-axis at 2 distinct points & touches x-axis.
Now, g2 – c = 0 & ƒ2 – c > 0
⇒ 1 – (–p) = 0 & 4 – (–p) > 0
⇒ p = –1   ⇒  p > –4

∴ p = – 1 is possible.

∴ Finally we conclude that p = 0, –1
⇒ Two possible values of p.

Option 3

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 + α2 =

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

αns. 1

Δ = 0 ⇒  1(1 - α2) - α(α - α3) + α22 - α2) = 0
(1 – α2) - α2 + α4 = 0
2 - 1)2 = 0   ⇒   α = ±1
but αt α = 1 No solution so rejected αt α = -1 αll three equαtion become x - y + z = 1 (coincident plαnes)  

∴1 + α + α2 = 1

Hence Option.  b

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

Ans. 5

x = 10!

Hence option.  c

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

Ans. 2

Hence Option. c

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

Ans. (D)

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

Ans. (A)

Sol. y = x + 8 is tangent ⇒ m = 1; P(8, 16)

Comparing tangent with (i) of column 2, m = 1 satisfied and a = 8 obtained which matches for point of contact (P) of column 3 and (III) of column I.

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

Ans. (D)

For a=√2 and point (-1,1) only I of column -1 satisfies. Hence equaiton of tangent is - x + y = 2 or y = x + 2

⇒  m = 1 which matches with (ii) of column 2 and also with Q of column 3

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

Ans. (D)

(I) ƒ(1) ƒ(e2) < 0 so true
(II) ƒ'(1) ƒ'(e) < 0 so true
(III) Graph of ƒ'(x) so (III) is false
(IV) Is false

Alternate :

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

Ans. (D)

(I) ƒ(1) ƒ(e2) < 0 so true
(II) ƒ'(1) ƒ'(e) < 0 so true
(III) Graph of ƒ'(x) so (III) is false
(IV) Is false

Alternate :

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

Ans. (D)

(I) ƒ(1) ƒ(e2) < 0 so true
(II) ƒ'(1) ƒ'(e) < 0 so true
(III) Graph of ƒ'(x) so (III) is false
(IV) Is false

Alternate :

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