Be Paitent While your exam is being loaded

View Solution

Participate to compete with other aspirants at an all India level.

Attempt Mock Test

Participate to compete with other aspirants at an all India level.

General Instructions

Choose Your Default Language

Please read the instructions carefully

General Instructions:

- Total duration of is 180 min.
The clock will be set at the server. The countdown timer in the top right corner of screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You will not be required to end or submit your examination.
The Questions Palette displayed on the right side of screen will show the status of each question using one of the following symbols:
1. You have not visited the question yet.
2. You have not answered the question.
3. You have answered the question.
4. You have NOT answered the question, but have marked the question for review.
5. The question(s) "Answered and Marked for Review" will be considered for evalution.
You can click on the ">" arrow which apperes to the left of question palette to collapse the question palette thereby maximizing the question window. To view the question palette again, you can click on "<" which appears on the right side of question window.
You can click on your "Profile" image on top right corner of your screen to change the language during the exam for entire question paper. On clicking of Profile image you will get a drop-down to change the question content to the desired language.
You can click on to navigate to the bottom and to navigate to top of the question are, without scrolling.

Navigating to a Question:

To answer a question, do the following:
1. Click on the question number in the Question Palette at the right of your screen to go to that numbered question directly. Note that using this option does NOT save your answer to the current question.
2. Click on Save & Next to save your answer for the current question and then go to the next question.
3. Click on Mark for Review & Next to save your answer for the current question, mark it for review, and then go to the next question.

Answering a Question:

Procedure for answering a multiple choice type question:
1. To select you answer, click on the button of one of the options.
2. To deselect your chosen answer, click on the button of the chosen option again or click on the Clear Response button
3. To change your chosen answer, click on the button of another option
4. To save your answer, you MUST click on the Save & Next button.
5. To mark the question for review, click on the Mark for Review & Next button.
To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question.

Navigating through sections:

Sections in this question paper are displayed on the top bar of the screen. Questions in a section can be viewed by click on the section name. The section you are currently viewing is highlighted.
After click the Save & Next button on the last question for a section, you will automatically be taken to the first question of the next section.
You can shuffle between sections and questions anything during the examination as per your convenience only during the time stipulated.
Candidate can view the corresponding section summery as part of the legend that appears in every section above the question palette.

Please note all questions will appear in your default language. This language can be changed for a particular question later on.

I have read and understood the instructions. All computer hardware allotted to me are in proper working condition. I declare that I am not in possession of / not wearing / not carrying any prohibited gadget like mobile phone, bluetooth devices etc. /any prohibited material with me into the Examination Hall.I agree that in case of not adhering to the instructions, I shall be liable to be debarred from this Test and/or to disciplinary action, which may include ban from future Tests / Examinations

Proceed

Category: IIT-JEE 2018 Physics Paper 2

Question 1:

A particle of mass ݉m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as ݀dK / dt = yt, where y is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

(A)	The force applied on the particle is constant
(B)	The speed of the particle is proportional to time
(C)	The distance of the particle from the origin increases linearly with time
(D)	The force is conservative

A,D and C

A,B and C

A,B and D

None of there

Category: IIT-JEE 2018 Physics Paper 2

Question 2:

An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge density

λ

.It pierces a thin non-conducting spherical shell of radius ܴ in such a way that the arc ܲܳPQ subtends an angle 120° at the centre ܱ0 of the spherical shell, as shown in the figure. The permittivity of free space is

\in_{0}

. Which of the following statements is (are) true?

(A)	The electric flux through the shell is $\sqrt{3} R λ / ε_{0}$
(B)	The z-component of the electric field is zero at all the points on the surface of the shell
(C)	The electric flux through the shell is $\sqrt{2} R λ / ε_{0}$
(D)	The electric field is normal to the surface of the shell at all points

A and B

B and C

A and D

B and D

Category: IIT-JEE 2018 Physics Paper 2

Question 3:

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length ݂

f

, as shown in the figure. Which of the figures shown in the four options qualitatively represent (s) the shape of the image of the bent wire? (These figures are not to scale.)

Category: IIT-JEE 2018 Physics Paper 2

Question 4:

In a radioactive decay chain,

T_{90}^{232} h

nucleus decays to

P_{82}^{212} b

nucleus. Let ܰ

N_{a}

and

N_{β}

be the number of

α

and

β^{-}

particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

(A)	$N_{a} = 5$	(B)	$N_{a} = 6$
(C)	$N_{β} = 2$	(D)	$N_{β} = 4$

A and B

A and C

C and D

All of these

Category: IIT-JEE 2018 Physics Paper 2

Question 5:

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 ܿ݉cm and 83.9 ܿ݉cm Which of the following statements is (are) true?

(A)	The speed of sound determined from this experiment is 332 $m s^{- 1}$
(B)	The end correction in this experiment is 0.9 ܿcm
(C)	The wavelength of the sound wave is 66.4 ܿcm
(D)	The resonance at 50.7 ܿ݉ corresponds to the fundamental harmonic

A and D

B and D

C and A

D and A

Category: IIT-JEE 2018 Physics Paper 2

Question 6:

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass ݉m=0.4 ݇݃ is at rest on this surface. An impulse of 1.0 ܰ N s is applied to the block at time t = 0 so that it starts moving along the x-axis with a velocity

v (t) = v_{0} e^{- t / τ}

, where

v_{0}

is a constant and

τ = 4 s

.The displacement of the block, in ݉݁metres, at t=

τ

__________. Take ݁

e^{- 1}

0.37.

5.30

4.30

7.30

6.30

Category: IIT-JEE 2018 Physics Paper 2

Question 7:

A ball is projected from the ground at an angle of 45° with the horizontal surface. It reaches a maximum height of 120 ݉m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of 30° with the horizontal surface. The maximum height it reaches after the bounce, in ݉݁metres, is ___________.

10.00

30.00

20.00

none of there

Category: IIT-JEE 2018 Physics Paper 2

Question 8:

A particle, of mass

10^{- 3} k g

and charge 1.0 C,is initially at rest. At time

t = 0

, the particle comes under the influence of an electric field

\vec{E} (t) = E_{0} \sin ω t \hat{ι}

where

E_{0}

and

ω = 10^{3} r a d s^{- 1}

. Consider the effect of only the electrical force on the particle. Then the maximum speed, in ݉

m s^{- 1}

, attained by the particle at subsequent times is ____________.

2.00

1.75

2.25

1.25

Category: IIT-JEE 2018 Physics Paper 2

Question 9:

A moving coil galvanometer has 50 turns and each turn has an area

2 \times 10^{- 4} m^{2}

. The magnetic field produced by the magnet inside the galvanometer is 0.02 T ܶ. The torsional constant of the suspension wire is

10^{- 4} N m r a d^{- 1}

When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad .݀ܽThe resistance of the coil of the galvanometer is 50

Ω

.This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 - 1.0 A .For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms ,is __________.

5.34/5.46

5.46/5.34

5.56/5.55

5.55/5.56

Category: IIT-JEE 2018 Physics Paper 2

Question 10:

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100 k and the universal gas constant ܴ

R = 8.0 j m o l^{- 1} k^{- 1}

, the decrease in its internal energy, in joule ,݈݁ is__________.

900.00

800.00

700.00

None of there

Category: IIT-JEE 2018 Physics Paper 2

Question 11:

In a photoelectric experiment a parallel beam of monochromatic light with power of 200 W is incident on a perfectly absorbing cathode of work function 6.25 eV ܸ݁. The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of 500 ܸ is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force F=

n \times 10^{- 4} N

due to the impact of the electrons. The value of ݊ is __________. Mass of the electron

m_{e} = 9 \times 10^{- 31} k g a n d 1.0 e v = 1.6 \times 10^{- 19} j

23.00

22.00

24.00

25.00

Category: IIT-JEE 2018 Physics Paper 2

Question 12:

Consider a hydrogen-like ionized atom with atomic number Z ܼ with a single electron. In the emission spectrum of this atom, the photon emitted in the n=2 to n=1 transition has energy 74.8 ܸ݁eV higher than the photon emitted in the ݊n = 3 to n = 2 transition. The ionization energy of the hydrogen atom is 13.6 ܸ݁eV The value of ܼ Z is __________.

3.50

3.00

4.00

4.50

Category: IIT-JEE 2018 Physics Paper 2

Question 13:

The electric field ܧ is measured at a point P(0,0,d) generated due to various charge distributions and the dependence of ܧ on ݀ is found to be different for different charge distributions. List-I contains different relations between E and ݀. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.

	LIST–I		LIST–II
P.	E is independent of ݀ d	1.	A point charge Q at the origin
Q.	$E \infty \frac{1}{d}$	2.	A small dipole with point charges Q at (0,0,l) and -Q at (0,0,l). Take 2l << d
R.	$E \infty \frac{1}{d^{2}}$	3.	An infinite line charge coincident with the x-axis, with uniform linear charge density $λ$
S.	$E \infty \frac{1}{d^{3}}$	4.	Two infinite wires carrying uniform linear charge density parallel to the x -axis. The one along (y = 0, z = l) has a charge density $+ λ$ and the one along (y = 0, z = -l) has a charge density – $λ$ .Take 2݈l ≪ ݀d
		5.	Infinite plane charge coincident with the xy-plane with uniform surface charge density

(A)	$P \to 5; Q \to 3, 4; R \to 1; S \to 2$
(B)	$P \to 5; Q \to 3; R \to 1, 4; S \to 2$
(C)	$P \to 5; Q \to 3; R \to 1, 2; S \to 4$
(D)	$P \to 4; Q \to 2, 3; R \to 1; S \to 5$

Category: IIT-JEE 2018 Physics Paper 2

Question 14:

A planet of mass M ,has two natural satellites with masses ݉

m_{1}

and ݉

m_{2}

. The radii of their circular orbits are

R_{1}

and

R_{2}

ܴ respectively. Ignore the gravitational force between the satellites. Define

v_{1}, L_{1}, K_{1} a n d T_{1}

to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and

v_{2}

L_{2}

K_{2}

and ܶ

T_{2}

to be the corresponding quantities of satellite 2. Given ݉

m_{1} / m_{2} = 2 a n d R_{1} / R_{2} = 1 / 4

, match the ratios in List-I to the numbers in List-II.

	LIST–I		LIST–II
P.	$\frac{v_{1}}{v_{2}}$	1.	$\frac{1}{8}$
Q.	$\frac{L_{1}}{L_{2}}$	2.	1
R.	$\frac{K_{1}}{K_{2}}$	3.	2
S.	$\frac{T_{1}}{T_{2}}$	4.	8

Category: IIT-JEE 2018 Physics Paper 2

Question 15:

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the PV-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

	LIST–I		LIST–II
P.	In process I	1.	Work done by the gas is zero
Q.	In process II	2.	Temperature of the gas remains unchanged
R.	In process III	3.	No heat is exchanged between the gas and its surroundings
S.	In process IV	4.	Work done by the gas is $6 P_{0} V_{0}$

(A)	$P \to 4; Q \to 3; R \to 1; S \to 2$
(B)	$P \to 1; Q \to 3; R \to 2; S \to 4$
(C)	$P \to 3; Q \to 4; R \to 1; S \to 2$
(D)	$P \to 3; Q \to 4; R \to 2; S \to 1$

Category: IIT-JEE 2018 Physics Paper 2

Question 16:

In the List-I below, four different paths of a particle are given as functions of time. In these functions,

a

and

β

are positive constants of appropriate dimensions and

α \neq β

.In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned:

\vec{p}

Ԧis the linear momentum,

\vec{L}

is the angular momentum about the origin, K is the kinetic energy, ܷ U is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path.

	LIST–I		LIST–II
P.	$\vec{r} (t) = a t \hat{ι} + β t \hat{j}$	1.	$\vec{p}$
Q.	$\vec{r} (t) = a \cos ω t \hat{ι} + β \sin ω t \hat{j}$	2.	$\vec{L}$
R.	$\vec{r} (t) = a (\cos ω t \hat{ι} + β \sin ω t \hat{j})$	3.	K
S.	$\vec{r} (t) = a t \hat{ι} + \frac{β}{2} t^{2} \hat{j}$	4.	U
		5.	E

(A)	$P \to 1, 2, 3, 4, 5; Q \to 2, 5; R \to 2, 3, 4, 5; S \to 5$
(B)	$P \to 1, 2, 3, 4, 5; Q \to 3, 5; R \to 2, 3, 4, 5; S \to 2, 5$
(C)	$P \to 2, 3, 4; Q \to 5; R \to 1, 2, 4; S \to 2, 5$
(D)	$P \to 1, 2, 3, 4, 5; Q \to 2, 5; R \to 2, 3, 4, 5; S \to 2, 5$

Category: IIT-JEE 2018 Physics Paper 2

Question 17:

Consider a thin square plate floating on a viscous liquid in a large tank. The height ݄ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity

u_{o}

Which of the following statements is (are) true?

(A)	The resistive force of liquid on the plate is inversely proportional to h
(B)	The resistive force of liquid on the plate is independent of the area of the plate
(C)	The tangential (shear) stress on the floor of the tank increases with $u_{o}$
(D)	The tangential (shear) stress on the plate varies linearly with the viscosity $η$ of the liquid

A,D and C

B,C and D

C, B and A

D,B and A

Category: IIT-JEE 2018 Physics Paper 2

Question 18:

A steel wire of diameter 0.5 mm ݉݉and Young’s modulus

2 \times 10^{11} N m^{- 2}

carries a load of mass M. The length of the wire with the load is 1.0 ݉m . A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 ݉݉, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 ݇݃, the vernier scale division which coincides with a main scale division is __________. Take ݃

g = 10 m s^{- 2} a n d π = 3.2

2.00

3.50

3.00

None of these

Category: IIT-JEE 2018 Chemistry Paper 2

Question 19:

The correct option(s) regarding the complex

[C o (e n) {(N H_{3})}_{3} {(H_{2} O)}^{3 +} (e n = H_{2} N C H_{2} C H_{2} N H_{2})

is (are)

(A)	It has two geometrical isomers
(B)	It will have three geometrical isomers if bidentate ‘en’ is replaced by two cyanide ligands
(C)	It is paramagnetic
(D)	It absorbs light at longer wavelength as compared to

A,B and C

A,D and C

A,B and D

None of these

Category: IIT-JEE 2018 Chemistry Paper 2

Question 20:

The correct option(s) to distinguish nitrate salts of

M n^{2 +}

and

C u^{2 +}

taken separately is (are)

(A)	$M n^{2 +}$ shows the characteristic green colour in the flame test
(B)	Only $C u^{2 +}$ shows the formation of precipitate by passing $H_{2} S$ in acidic medium
(C)	Only $M n^{2 +}$ shows the formation of precipitate by passing $H_{2} S$ in faintly basic medium
(D)	$C u^{2 +}$ /Cu has higher reduction potential than $M n^{2 +}$ /Mn (measured under similar conditions)

A and B

A and C

B and C

B and D

Category: IIT-JEE 2018 Chemistry Paper 2

Question 21:

Aniline reacts with mixed acid (conc.

H N O_{3}

and conc.

H_{2} S O_{4}

at 288 K to give P (51 %), Q (47%) and R (2%). The major product(s) of the following reaction sequence is (are)

R \to_{\begin{matrix} 3) H_{3} O^{+} \\ 4) N a N O_{2}, H C I / 273 - 278 k \\ 5) E t O H, ∆ \end{matrix}}^{\begin{matrix} 1) A c_{2} O, p y r i d i n e \\ 2) B r_{2}, C H_{3} C O_{2} H \end{matrix}} S \to_{\begin{matrix} 3) N a n o_{2}, H C V 273 - 278 K \\ 4) H_{3} P o_{2} \end{matrix}}^{\begin{matrix} 1) S n / H C I \\ 2) B_{2} / H_{2} O (e x c e s s) \end{matrix}}

major product(s)

Category: IIT-JEE 2018 Chemistry Paper 2

Question 22:

The Fischer presentation of D-glucose is given below.

The correct structure(s) of β-L-glucopyranose is (are)

Category: IIT-JEE 2018 Chemistry Paper 2

Question 23:

For a first order reaction A(g) → 2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (t = 0) and at time t are ܲ

P_{0}

and

P_{t}

, respectively. Initially, only A is present with concentration

{[A]}_{0}

, and

t_{1 / 3}

is the time required for the partial pressure of A to reach

1 / 3^{r d}

of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

A and C

A and D

B and D

B and C

Category: IIT-JEE 2018 Chemistry Paper 2

Question 24:

For a reaction, A ⇌ P, the plots of [A] and [P] with time at temperatures

T_{1}

and

T_{2}

are given below.

If ܶ

T_{2} > T_{1}

, the correct statement(s) is (are) (Assume

∆ H^{θ}

and

∆ S^{θ}

are independent of temperature and ratio of lnK at ܶ

T_{1}

to lnK at ܶ

T_{2}

is greater than ܶ

\frac{T_{2}}{T_{1}}

. Here H, S, G and K are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)

(A)	$∆ H^{θ} < 0, ∆ S^{θ} < 0$
(B)	$∆ G^{θ} < 0, ∆ H^{θ} < 0$
(C)	$∆ G^{θ} < 0, ∆ S^{θ} < 0$
(D)	$∆ G^{θ} < 0, ∆ S^{θ} < 0$

A and B

A and D

A and C

Category: IIT-JEE 2018 Chemistry Paper 2

Question 25:

The total number of compounds having at least one bridging oxo group among the molecules given below is ____.

N_{2} O_{3}, N_{2} O_{5}, P_{4} O_{6}, P_{4} O_{7}, H_{4} P_{2} O_{10}, H_{2} S_{2} O_{3}, H_{2} S_{2} O_{5}

6.5

Category: IIT-JEE 2018 Chemistry Paper 2

Question 26:

Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of air is stopped, but the heating is continued in a closed furnace such that the contents undergo self-reduction. The weight (in kg) of Pb produced per kg of

O_{2}

consumed is ____. (Atomic weights in g

m o l^{- 1}

: O = 16, S = 32, Pb = 207)

6.66

6.47

6.77

None of these

Category: IIT-JEE 2018 Chemistry Paper 2

Question 27:

To measure the quantity of

M n C I_{2}

dissolved in an aqueous solution, it was completely converted to

K M n O_{4}

using the reaction,

M n C I_{2} + K_{2} S_{2} O_{8} + H_{2} 0 \to K M n O_{4} + H_{2} S O_{4} + H C I

(equation not balanced). Few drops of concentrated HCl were added to this solution and gently warmed. Further, oxalic acid (225 mg) was added in portions till the colour of the permanganate ion disappeared. The quantity of MnCl2 (in mg) present in the initial solution is ____. (Atomic weights in g

m o l^{- 1}

: Mn = 55, Cl = 35.5)

122

125

130

126

Category: IIT-JEE 2018 Chemistry Paper 2

Question 28:

For the given compound X, the total number of optically active stereoisomers is ____.

This type of bond indicates that the configuration at the specific carbon and the geometry of the bond is fixed

This type of bond indicates that the configuration at the specific carbon and the geometry of the double bond is not Fixed

Category: IIT-JEE 2018 Chemistry Paper 2

Question 29:

In the following reaction sequence, the amount of D (in g) formed from 10 moles of acetophenone is ____. (Atomic weights in g

m o l^{- 1}

: H = 1, C = 12, N = 14, O = 16, Br = 80. The yield (%) corresponding to the product in each step is given in the parenthesis)

475

495

465

None of these

Category: IIT-JEE 2018 Chemistry Paper 2

Question 30:

The surface of copper gets tarnished by the formation of copper oxide.

N_{2}

gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the

N_{2}

gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below:

2 C u (s) + H_{2} O (g) \to C u_{2} O (S) + H_{2} (g)

p_{H_{2}}

is the minimum partial pressure of H2 (in bar) needed to prevent the oxidation at 1250 K. The value of

I n ({p_{H}}_{2})

is ____. (Given: total pressure = 1 bar, R (universal gas constant) = 8 J

K^{- 1} m o l^{- 1}

, ln(10) = 2.3. Cu(s) and

C u_{2} O (s)

are mutually immiscible. At 1250 K: 2Cu(s)+

\frac{1}{2} O_{2} (g) \to C u_{2} O (s); ∆ G^{θ} = - 78, 000 j m o l^{- 1}

H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O (g); ∆ G^{θ} = - 1, 78, 000 J m o l^{- 1}; G i s t h e G i b b s e n e r g y)

-14.6

-16.2

-18.4

-14.8

Category: IIT-JEE 2018 Chemistry Paper 2

Question 31:

Consider the following reversible reaction, A(g) + B(g) ⇌ AB(g). The activation energy of the backward reaction exceeds that of the forward reaction by 2ܴܶRT (in J

m o l^{- 1}

). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of ∆

G^{θ}

(in J

m o I^{- 1}

) for the reaction at 300 K is ____. (Given; ln(2) = 0.7, ܴܶ = 2500 J

m o l^{- 1}

at 300 K and G is the Gibbs energy)

8200

8500

8000

7500

Category: IIT-JEE 2018 Chemistry Paper 2

Question 32:

Consider an electrochemical cell: A(s) |

A^{n +}

(aq, 2 M) ||

B^{2 n +}

(aq, 1 M) | B(s). The value of

∆ H^{θ}

for the cell reaction is twice that of

∆ G^{θ}

at 300 K. If the emf of the cell is zero, the

∆ S^{θ}

(in J

K^{- 1} m o l^{- 1}

) of the cell reaction per mole of B formed at 300 K is ____. (Given: ln(2) = 0.7, ܴ (universal gas constant) = 8.3 J

K^{- 1}

m o l^{- 1}

. H, S and G are enthalpy, entropy and Gibbs energy, respectively.)

-12.66

-12.87

11.62

-11.62

Category: IIT-JEE 2018 Chemistry Paper 2

Question 33:

Match each set of hybrid orbitals from LIST–I with complex(es) given in LIST–II.

	LIST–I		LIST–I
P.	$d s p^{2}$	1.	${[F e F_{6}]}^{4 -}$
Q.	$s p^{3}$	2.	$[T i {(H_{2} O)}_{3} C I_{3}]$
R.	$s p^{3} d^{2}$	3.	$[C r {(N H_{3})}_{6}]^{3 +}$
S.	$d^{2} s p^{3}$	4.	${[F e C l_{4}]}^{2 -}$
		5.	$N i {(C O)}_{4}$
		6.	$[N i {(C N)}_{4}]^{2 -}$

The correct option is

(A)	$P \to 5; Q \to 4, 6; R \to 2, 3; S \to 1$
(B)	$P \to 5, 6; Q \to 4, 5; R \to 1; S \to 2, 3$
(C)	$P \to 6; Q \to 4, 5; R \to 1; S \to 2, 3$
(D)	$P \to 4, 6; Q \to 5, 6; R \to 1, 2; S \to 3$

Category: IIT-JEE 2018 Chemistry Paper 2

Question 34:

The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II. (given, order of migratory aptitude: aryl > alkyl > hydrogen)

	List-I			List-II
P.		$+ H_{2} S O_{4}$	1.	$I_{2}, N a O H$
Q.		$+ H N O_{2}$	2.	$[A g {(N H_{3})}_{2}] O H$
R.		$+ H_{2} S O_{4}$	3.	Fehling solution
S.		$+ A g N O_{3}$	4.	HCHO, NaOH
			5.	NaOBr

The correct option is

(A)	$P \to 1 : Q \to 2, 3; R \to 1, 4; S \to 2, 4$
(B)	$P \to 1, 5; Q \to 3, 4; R \to 4, 5; S \to 3$
(C)	$P \to 1, 5; Q \to 3, 4; R \to 5; S \to 2, 4$
(D)	$P \to 1, 5 Q \to 2, 3; R \to 1, 5; S \to 2, 3$

Category: IIT-JEE 2018 Chemistry Paper 2

Question 35:

LIST-I contains reactions and LIST-II contains major products.

	List-I			List-II
p.		$\to$	1.
Q.		+ HBr $\to$	2.
R.		+ NaOMe $\to$	3.
S.		+ MeBr $\to$	4.
			5.

Match each reaction in LIST-I with one or more products in LIST-II and choose the correct option.

(A)	$P \to 1, 5; Q \to 2; R \to 3; S \to 4$
(B)	$P \to 1, 4; Q \to 2; R \to 4; S \to 3$
(C)	$P \to 1, 4; Q \to 1, 2; R \to 3, 4; S \to 4$
(D)	$P \to 4, 5; Q \to 4; R \to 4; S \to 3, 4$

Category: IIT-JEE 2018 Chemistry Paper 2

Question 36:

Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on [

H^{+}

] are given in LIST-II. (Note: Degree of dissociation (a) of weak acid and weak base is << 1; degree of hydrolysis of salt <<1; [

H^{+}

] represents the concentration of

H^{+}

ions)

	LIST–I		LIST–II
P.	(10 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 60 mL	1.	the value of [ $H^{+}$ ] does not change on dilution
Q.	(20 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 80 mL	2.	the value of [ $H^{+}$ ] changes to half of its initial value on dilution
R.	(20 mL of 0.1 M HCl + 20 mL of 0.1 M ammonia solution) diluted to 80 mL	3.	the value of [ $H^{+}$ ] changes to two times of its initial value on dilution
S.	10 mL saturated solution of $N i {(O H)}_{2}$ in equilibrium with excess solid $N i {(O H)}_{2}$ is diluted to 20 mL (solid $N i {(O H)}_{2}$ is still present after dilution).	4.	the value of [ $H^{+}$ ] changes to $\frac{1}{\sqrt{2}}$ times of its initial value on dilution
		5.	the value of [ $H^{+}$ ] changes to $\sqrt{2}$ times of its initial value on dilution

Match each process given in LIST-I with one or more effect(s) in LIST-II. The correct option is

(A)	$P \to 4; Q \to 2; R \to 3; S \to 1$
(B)	$P \to 4; Q \to 3; R \to 2; S \to 3$
(C)	$P \to 1; Q \to 4; R \to 5; S \to 3$
(D)	$P \to 1; Q \to 5; R \to 4; S \to 1$

Category: IIT-JEE 2018 Math Paper 1

Question 37:

For a non-zero complex number 𝑧, let arg(𝑧) denote the principal argument with

- π < \arg (z) \leq π

Then, which of the following statement(s) is (are) FALSE?

A	$a r g (- 1 - i) = \frac{π}{4} =, w h e r e i = \sqrt{1}$	B	The function 𝑓: ℝ $(- π, π] defined by f (t) = \arg (- 1 + it)$ for all 𝑡∈ℝ, is continuous at all points of ℝ, where $i = \sqrt{- 1}$
C	For any two non-zero complex numbers $Z_{1} a n d Z_{2}$ $a r g (\frac{Z_{1}}{Z_{2}}) - a r g (Z_{1}) + a r g (Z_{2})$ is an integer multiple of 2𝜋	D	For any three given distinct complex numbers $Z_{1}, Z_{2} a n d Z_{3}$ the locus of the point 𝑧 satisfying the condition $a r g (\frac{(z - z_{1}) (z_{2} - z_{3})}{(z - z_{3}) (z_{2} - z_{1})})$ = 𝜋, lies on a straight line

A,D and C

A,B and D

A,B and C

None of these

Category: IIT-JEE 2018 Math Paper 1

Question 38:

In a triangle 𝑃𝑄𝑅, let

< P Q R = 30 °

and the sides 𝑃𝑄 and 𝑄𝑅 have lengths and 10

\sqrt{3}

, respectively. Then, which of the following statement(s) is (are) TRUE?

A	$< Q P R = 45 °$	B	The area of the triangle 𝑃𝑄𝑅 is 25 $\sqrt{3}$ and $< Q R P = 120 °$
C	The radius of the incircle of the triangle 𝑃𝑄𝑅 is $10 \sqrt{3} - 15$	D	The area of the circumcircle of the triangle $P Q R i s 100 π$

A,B and C

B,C and D

C,D and A

Category: IIT-JEE 2018 Math Paper 1

Question 39:

Let

P_{1}

: 2𝑥+𝑦−𝑧=3 and

P_{2}

: 𝑥+2𝑦+𝑧=2 be two planes. Then, which of the following statement(s) is (are) TRUE?A

A	The line of intersection of $p_{1} a n d p_{2}$ has direction ratios 1,2,−1.	B	The line $\frac{3 x - 4}{9} = \frac{1 - 3 y}{9} = \frac{z}{3}$
C	The acute angle between $p_{1} a n d p_{2} i s 60 °$	D	If $p_{3}$ is the plane passing through the point (4,2,−2) and perpendicular to the line of intersection of $p_{1} a n d p_{2}$ , then the distance of the point (2,1,1) from the plane $p_{3} i s \frac{2}{\sqrt{3}}$

A and B

B and C

C and D

D and A

Category: IIT-JEE 2018 Math Paper 1

Question 40:

For every twice differentiable function 𝑓: ℝ→[−2,2] with

{(f (0))}^{2} + {(f' (0))}^{2}

=85, which of the following statement(s) is (are) TRUE?

A	There exist 𝑟,𝑠∈ℝ, where 𝑟<𝑠, such that 𝑓 is one-one on the open interval (𝑟,𝑠)	B	There exists 𝑥0∈ $x_{0} \in (- 4, 0)$ such that $f' (o x) \leq 1$
C	$\lim_{x \to \infty} f (x) = 1$	D	There exists 𝛼∈(−4,4) such that 𝑓(𝛼)+𝑓′′(𝛼) = 0 and 𝑓′(𝛼)≠0

A,B and D

B, C and D

C,B and D

None of these

Category: IIT-JEE 2018 Math Paper 1

Question 41:

Let 𝑓:ℝ→ℝ and 𝑔:ℝ→ℝ be two non-constant differentiable functions. If

f' (x) = (e^{(f (x) - g (x))}) g' (x)

for all 𝑥∈ℝ, and 𝑓(1)=𝑔(2)=1, then which of the following statement(s) is (are) TRUE?

A	$f (2) < 1 - \log_{e} 2$	B	$f (2) > 1 - \log_{e} 2$
C	$g (1) > 1 - \log_{e} 2$	D	$g (1) < 1 - \log_{e} 2$

A and B

B and C

C and A

D and A

Category: IIT-JEE 2018 Math Paper 1

Question 42:

Let 𝑓:[0,∞)→ℝ be a continuous function such that

f (x) = 1 - 2 x + \int_{0}^{x} e^{x - t} f (t) d t

for all 𝑥∈[0,∞). Then, which of the following statement(s) is (are) TRUE?

A	for all 𝑥∈[0,∞). Then, which of the following statement(s) is (are) TRUE?	B	The curve 𝑦=𝑓(𝑥) passes through the point (2,−1)
C	The area of the region ${(x, y) \in [0, 1] x ℝ : f (x) \leq y \leq \sqrt{1 - x^{2}}} i s \frac{π - 2}{4}$	D	The area of the region ${(x, y) \in [0, 1] x ℝ : f (x) \leq y \leq \sqrt{1 - x^{2}}} i s \frac{π - 1}{4}$

A and B

B and A

C and B

D and A

Category: IIT-JEE 2018 Math Paper 1

Question 43:

The value of

({(\log_{2} 9)}^{2}) \frac{1}{\log_{2} (\log_{2} 9) x (\sqrt{7})} \frac{1}{\log_{4} 7}

is ______ .

Category: IIT-JEE 2018 Math Paper 1

Question 44:

The number of 5 digit numbers which are divisible by 4, with digits from the set {1,2,3,4,5} and the repetition of digits is allowed, is _____ .

625

650

600

675

Category: IIT-JEE 2018 Math Paper 1

Question 45:

Let 𝑋 be the set consisting of the first 2018 terms of the arithmetic progression 1,6,11,… , and 𝑌 be the set consisting of the first 2018 terms of the arithmetic progression 9,16,23,… . Then, the number of elements in the set 𝑋∪𝑌 is _____.

3746

3748

3747

None of these

Category: IIT-JEE 2018 Math Paper 1

Question 46:

The number of real solutions of the equation

\sin^{- 1} (\sum_{i = 1}^{\infty} i_{x} + 1_{- x} \sum_{i = 1}^{\infty} {(\frac{x}{2})}^{i}) = \frac{π}{2} - \cos^{- 1} (\sum_{i = 1}^{\infty} {(- \frac{x}{2})}^{i} - \sum_{i = 1}^{\infty} {(- x)}^{i})

lying in the interval

(- \frac{1}{2}, \frac{1}{2})

is _____ . (Here, the inverse trigonometric functions

\sin^{- 1}

𝑥 and

\cos^{- 1}

𝑥 assume values in

[- \frac{π}{r}, \frac{π}{r}]

and [0,𝜋], respectively.)

2.1

2.5

2.2

Category: IIT-JEE 2018 Math Paper 1

Question 47:

For each positive integer 𝑛, let

y_{n} = \frac{1}{n} {((n + 1) (n + 2) . . . (n + n))}^{\frac{1}{2}}

For 𝑥∈ℝ, let [𝑥] be the greatest integer less than or equal to 𝑥.if

\lim_{n \to \infty} y_{n} =

𝐿, then the value of [𝐿] is _____ .

0.1

Category: IIT-JEE 2018 Math Paper 1

Question 48:

let

\vec{a} a n d \vec{b}

be two unit vectors such that

\vec{a} . \vec{b}

For some 𝑥,𝑦∈ℝ, let

\vec{c} = x \vec{a} + y \vec{b} + (\vec{a} + \vec{b)}

.If

|\vec{c}|

⃗|=2 and the vector

\vec{c}

is inclined at the same angle 𝛼 to both

\vec{a} a n d \vec{b}

then the value of

\cos^{2}

𝛼 is _____.

Category: IIT-JEE 2018 Math Paper 1

Question 49:

Let 𝑎,𝑏,𝑐 be three non-zero real numbers such that the equation

\sqrt{3}

𝑎cos𝑥+2 𝑏sin𝑥=𝑐, 𝑥

\in [- \frac{π}{2}, \frac{π}{2}],

has two distinct real roots

α a n d β

with 𝛼+𝛽=

\frac{π}{3}

Then, the value of

\frac{b}{a} i s .

_____ .

0.0

0.5

0.3

0.1

Category: IIT-JEE 2018 Math Paper 1

Question 50:

A farmer

F_{1}

has a land in the shape of a triangle with vertices at 𝑃(0,0),𝑄(1,1) and 𝑅(2,0).From this land, a neighbouring farmer

F_{2}

takes away the region which lies between the side 𝑃𝑄 and a curve of the form

y = x^{n} (n > 1)

If the area of the region taken away by the farmer

F_{2}

is exactly 30% of the area of Δ𝑃𝑄𝑅, then the value of 𝑛 is _____ .

Category: IIT-JEE 2018 Math Paper 1

Question 51:

Let 𝑆 be the circle in the 𝑥𝑦-plane defined by the equation

x^{2} + y^{2} = 4

.Let

E_{1} E_{2}

and

F_{1} F_{2}

be the chords of 𝑆 passing through the point

P_{0}

(1,1) and parallel to the x-axis and the y-axis, respectively. Let

G_{1} G_{2}

be the chord of S passing through

P_{0}

and having slope −1.Let the tangents to 𝑆 at

E_{1} a n d E_{2}

meet at

E_{3}

the tangents to 𝑆 at

F_{1} a n d F_{2}

meet at

F_{3}

and the tangents to 𝑆 at

G_{1} a n d G_{2} m e e t a t G_{3}

Then, the points

E_{3} F_{3}

and

G_{3}

.lie on the curve

A	𝑥+𝑦=4	B	( $�� - 4)^{2} + {(�� - 4)}^{2} = 16$
C	(𝑥−4)(𝑦−4)=4	D	𝑥𝑦=4

Category: IIT-JEE 2018 Math Paper 1

Question 52:

Let 𝑆 be the circle in the 𝑥𝑦-plane defined by the equation

x^{2} + y^{2} = 4

Let 𝑃 be a point on the circle 𝑆 with both coordinates being positive. Let the tangent to 𝑆 at 𝑃 intersect the coordinate axes at the points 𝑀 and 𝑁. Then, the mid-point of the line segment 𝑀𝑁 must lie on the curve

A	${(�� + ��)}^{2} = 3 �� $	B	$x^{2 / 3} + y^{2 / 3} = 2^{4 / 3}$
C	$x^{2} + y^{2} = 2 �� $	D	$x^{2} + y^{2} = x^{2} y^{2}$

Category: IIT-JEE 2018 Math Paper 1

Question 53:

There are five students

S_{1} S_{2} S_{3} S_{4}

and

S_{5}

in a music class and for them there are five seats

R_{1} R_{2} R_{3} R_{4} a n d R_{5}

arranged in a row, where initially the seat

R_{i}

is allotted to the student

S_{i}

𝑖=1,2,3,4,5. But, on the examination day, the five students are randomly allotted the five seats. The probability that, on the examination day, the student

s_{1}

gets the previously allotted seat

R_{1}

, and NONE of the remaining students gets the seat previously allotted to him/her is.

A	$\frac{3}{40}$	B	$\frac{1}{8}$
C	$\frac{7}{40}$	D	$\frac{1}{5}$

Category: IIT-JEE 2018 Math Paper 1

Question 54:

There are five students

S_{1} S_{2} S_{3} S_{4}

and

S_{5}

in a music class and for them there are five seats

R_{1} R_{2} R_{3} R_{4} a n d R_{5}

arranged in a row, where initially the seat

R_{i}

is allotted to the student

S_{i}

𝑖=1,2,3,4,5. But, on the examination day, the five students are randomly allotted the five seats. For 𝑖=1,2,3,4, let 𝑇𝑖 denote the event that the students

S_{1} a n d s_{i + 1}

do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event

T_{1} \cap T_{2} \cap T_{3} \cap T_{4} i s

A	$\frac{1}{15}$	B	$\frac{1}{10}$
C	$\frac{7}{60}$	D	$\frac{1}{5}$

⮜ Back Next ⮞

Not Visited	0	Not Answered
Answered	0	Marked for Review
Answered & Marked for Review (will be considered for evaluation)

Question 1:

(A)	The force applied on the particle is constant
(B)	The speed of the particle is proportional to time
(C)	The distance of the particle from the origin increases linearly with time
(D)	The force is conservative

Correct Answer : A,B and D

Question 2:

An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge density

λ

\in_{0}

. Which of the following statements is (are) true?

(A)	The electric flux through the shell is $\sqrt{3} R λ / ε_{0}$
(B)	The z-component of the electric field is zero at all the points on the surface of the shell
(C)	The electric flux through the shell is $\sqrt{2} R λ / ε_{0}$
(D)	The electric field is normal to the surface of the shell at all points

Correct Answer : A and B

Question 3:

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length ݂

f

, as shown in the figure. Which of the figures shown in the four options qualitatively represent (s) the shape of the image of the bent wire? (These figures are not to scale.)

Correct Answer : B

Question 4:

In a radioactive decay chain,

T_{90}^{232} h

nucleus decays to

P_{82}^{212} b

nucleus. Let ܰ

N_{a}

and

N_{β}

be the number of

α

and

β^{-}

particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

(A)	$N_{a} = 5$	(B)	$N_{a} = 6$
(C)	$N_{β} = 2$	(D)	$N_{β} = 4$

Correct Answer : A and C

Question 5:

(A)	The speed of sound determined from this experiment is 332 $m s^{- 1}$
(B)	The end correction in this experiment is 0.9 ܿcm
(C)	The wavelength of the sound wave is 66.4 ܿcm
(D)	The resonance at 50.7 ܿ݉ corresponds to the fundamental harmonic

Correct Answer : C and A

Question 6:

v (t) = v_{0} e^{- t / τ}

, where

v_{0}

is a constant and

τ = 4 s

.The displacement of the block, in ݉݁metres, at t=

τ

__________. Take ݁

e^{- 1}

0.37.

Correct Answer : 6.30

Question 7:

Correct Answer : 30.00

Question 8:

A particle, of mass

10^{- 3} k g

and charge 1.0 C,is initially at rest. At time

t = 0

, the particle comes under the influence of an electric field

\vec{E} (t) = E_{0} \sin ω t \hat{ι}

where

E_{0}

and

ω = 10^{3} r a d s^{- 1}

. Consider the effect of only the electrical force on the particle. Then the maximum speed, in ݉

m s^{- 1}

, attained by the particle at subsequent times is ____________.

Correct Answer : 2.00

Question 9:

A moving coil galvanometer has 50 turns and each turn has an area

2 \times 10^{- 4} m^{2}

. The magnetic field produced by the magnet inside the galvanometer is 0.02 T ܶ. The torsional constant of the suspension wire is

10^{- 4} N m r a d^{- 1}

When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad .݀ܽThe resistance of the coil of the galvanometer is 50

Ω

Correct Answer : 5.55/5.56

Question 10:

R = 8.0 j m o l^{- 1} k^{- 1}

, the decrease in its internal energy, in joule ,݈݁ is__________.

Correct Answer : 900.00

Question 11:

n \times 10^{- 4} N

due to the impact of the electrons. The value of ݊ is __________. Mass of the electron

m_{e} = 9 \times 10^{- 31} k g a n d 1.0 e v = 1.6 \times 10^{- 19} j

Correct Answer : 24.00

Question 12:

Correct Answer : 3.00

Question 13:

	LIST–I		LIST–II
P.	E is independent of ݀ d	1.	A point charge Q at the origin
Q.	$E \infty \frac{1}{d}$	2.	A small dipole with point charges Q at (0,0,l) and -Q at (0,0,l). Take 2l << d
R.	$E \infty \frac{1}{d^{2}}$	3.	An infinite line charge coincident with the x-axis, with uniform linear charge density $λ$
S.	$E \infty \frac{1}{d^{3}}$	4.	Two infinite wires carrying uniform linear charge density parallel to the x -axis. The one along (y = 0, z = l) has a charge density $+ λ$ and the one along (y = 0, z = -l) has a charge density – $λ$ .Take 2݈l ≪ ݀d
		5.	Infinite plane charge coincident with the xy-plane with uniform surface charge density

(A)	$P \to 5; Q \to 3, 4; R \to 1; S \to 2$
(B)	$P \to 5; Q \to 3; R \to 1, 4; S \to 2$
(C)	$P \to 5; Q \to 3; R \to 1, 2; S \to 4$
(D)	$P \to 4; Q \to 2, 3; R \to 1; S \to 5$

Correct Answer : B

Question 14:

A planet of mass M ,has two natural satellites with masses ݉

m_{1}

and ݉

m_{2}

. The radii of their circular orbits are

R_{1}

and

R_{2}

ܴ respectively. Ignore the gravitational force between the satellites. Define

v_{1}, L_{1}, K_{1} a n d T_{1}

to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and

v_{2}

L_{2}

K_{2}

and ܶ

T_{2}

to be the corresponding quantities of satellite 2. Given ݉

m_{1} / m_{2} = 2 a n d R_{1} / R_{2} = 1 / 4

, match the ratios in List-I to the numbers in List-II.

	LIST–I		LIST–II
P.	$\frac{v_{1}}{v_{2}}$	1.	$\frac{1}{8}$
Q.	$\frac{L_{1}}{L_{2}}$	2.	1
R.	$\frac{K_{1}}{K_{2}}$	3.	2
S.	$\frac{T_{1}}{T_{2}}$	4.	8

Correct Answer : B

Question 15:

	LIST–I		LIST–II
P.	In process I	1.	Work done by the gas is zero
Q.	In process II	2.	Temperature of the gas remains unchanged
R.	In process III	3.	No heat is exchanged between the gas and its surroundings
S.	In process IV	4.	Work done by the gas is $6 P_{0} V_{0}$

(A)	$P \to 4; Q \to 3; R \to 1; S \to 2$
(B)	$P \to 1; Q \to 3; R \to 2; S \to 4$
(C)	$P \to 3; Q \to 4; R \to 1; S \to 2$
(D)	$P \to 3; Q \to 4; R \to 2; S \to 1$

Correct Answer : C

Question 16:

In the List-I below, four different paths of a particle are given as functions of time. In these functions,

a

and

β

are positive constants of appropriate dimensions and

α \neq β

.In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned:

\vec{p}

Ԧis the linear momentum,

\vec{L}

	LIST–I		LIST–II
P.	$\vec{r} (t) = a t \hat{ι} + β t \hat{j}$	1.	$\vec{p}$
Q.	$\vec{r} (t) = a \cos ω t \hat{ι} + β \sin ω t \hat{j}$	2.	$\vec{L}$
R.	$\vec{r} (t) = a (\cos ω t \hat{ι} + β \sin ω t \hat{j})$	3.	K
S.	$\vec{r} (t) = a t \hat{ι} + \frac{β}{2} t^{2} \hat{j}$	4.	U
		5.	E

(A)	$P \to 1, 2, 3, 4, 5; Q \to 2, 5; R \to 2, 3, 4, 5; S \to 5$
(B)	$P \to 1, 2, 3, 4, 5; Q \to 3, 5; R \to 2, 3, 4, 5; S \to 2, 5$
(C)	$P \to 2, 3, 4; Q \to 5; R \to 1, 2, 4; S \to 2, 5$
(D)	$P \to 1, 2, 3, 4, 5; Q \to 2, 5; R \to 2, 3, 4, 5; S \to 2, 5$

Correct Answer : A

Question 17:

u_{o}

Which of the following statements is (are) true?

(A)	The resistive force of liquid on the plate is inversely proportional to h
(B)	The resistive force of liquid on the plate is independent of the area of the plate
(C)	The tangential (shear) stress on the floor of the tank increases with $u_{o}$
(D)	The tangential (shear) stress on the plate varies linearly with the viscosity $η$ of the liquid

Correct Answer : A,D and C

Question 18:

A steel wire of diameter 0.5 mm ݉݉and Young’s modulus

2 \times 10^{11} N m^{- 2}

g = 10 m s^{- 2} a n d π = 3.2

Correct Answer : 3.00

Question 19:

The correct option(s) regarding the complex

[C o (e n) {(N H_{3})}_{3} {(H_{2} O)}^{3 +} (e n = H_{2} N C H_{2} C H_{2} N H_{2})

is (are)

(A)	It has two geometrical isomers
(B)	It will have three geometrical isomers if bidentate ‘en’ is replaced by two cyanide ligands
(C)	It is paramagnetic
(D)	It absorbs light at longer wavelength as compared to

Correct Answer : A,B and D

Question 20:

The correct option(s) to distinguish nitrate salts of

M n^{2 +}

and

C u^{2 +}

taken separately is (are)

(A)	$M n^{2 +}$ shows the characteristic green colour in the flame test
(B)	Only $C u^{2 +}$ shows the formation of precipitate by passing $H_{2} S$ in acidic medium
(C)	Only $M n^{2 +}$ shows the formation of precipitate by passing $H_{2} S$ in faintly basic medium
(D)	$C u^{2 +}$ /Cu has higher reduction potential than $M n^{2 +}$ /Mn (measured under similar conditions)

Correct Answer : B and D

Question 21:

Aniline reacts with mixed acid (conc.

H N O_{3}

and conc.

H_{2} S O_{4}

at 288 K to give P (51 %), Q (47%) and R (2%). The major product(s) of the following reaction sequence is (are)

R \to_{\begin{matrix} 3) H_{3} O^{+} \\ 4) N a N O_{2}, H C I / 273 - 278 k \\ 5) E t O H, ∆ \end{matrix}}^{\begin{matrix} 1) A c_{2} O, p y r i d i n e \\ 2) B r_{2}, C H_{3} C O_{2} H \end{matrix}} S \to_{\begin{matrix} 3) N a n o_{2}, H C V 273 - 278 K \\ 4) H_{3} P o_{2} \end{matrix}}^{\begin{matrix} 1) S n / H C I \\ 2) B_{2} / H_{2} O (e x c e s s) \end{matrix}}

major product(s)

Correct Answer : D

Question 22:

The Fischer presentation of D-glucose is given below.

The correct structure(s) of β-L-glucopyranose is (are)

Correct Answer : D

Question 23:

For a first order reaction A(g) → 2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (t = 0) and at time t are ܲ

P_{0}

and

P_{t}

, respectively. Initially, only A is present with concentration

{[A]}_{0}

, and

t_{1 / 3}

is the time required for the partial pressure of A to reach

1 / 3^{r d}

of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

Correct Answer : A and D

Question 24:

For a reaction, A ⇌ P, the plots of [A] and [P] with time at temperatures

T_{1}

and

T_{2}

are given below.

If ܶ

T_{2} > T_{1}

, the correct statement(s) is (are) (Assume

∆ H^{θ}

and

∆ S^{θ}

are independent of temperature and ratio of lnK at ܶ

T_{1}

to lnK at ܶ

T_{2}

is greater than ܶ

\frac{T_{2}}{T_{1}}

. Here H, S, G and K are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)

(A)	$∆ H^{θ} < 0, ∆ S^{θ} < 0$
(B)	$∆ G^{θ} < 0, ∆ H^{θ} < 0$
(C)	$∆ G^{θ} < 0, ∆ S^{θ} < 0$
(D)	$∆ G^{θ} < 0, ∆ S^{θ} < 0$

Correct Answer : A and C

Question 25:

The total number of compounds having at least one bridging oxo group among the molecules given below is ____.

N_{2} O_{3}, N_{2} O_{5}, P_{4} O_{6}, P_{4} O_{7}, H_{4} P_{2} O_{10}, H_{2} S_{2} O_{3}, H_{2} S_{2} O_{5}

Correct Answer : 6

Question 26:

O_{2}

consumed is ____. (Atomic weights in g

m o l^{- 1}

: O = 16, S = 32, Pb = 207)

Correct Answer : 6.47

Question 27:

To measure the quantity of

M n C I_{2}

dissolved in an aqueous solution, it was completely converted to

K M n O_{4}

using the reaction,

M n C I_{2} + K_{2} S_{2} O_{8} + H_{2} 0 \to K M n O_{4} + H_{2} S O_{4} + H C I

m o l^{- 1}

: Mn = 55, Cl = 35.5)

Correct Answer : 126

Question 28:

For the given compound X, the total number of optically active stereoisomers is ____.

This type of bond indicates that the configuration at the specific carbon and the geometry of the bond is fixed

This type of bond indicates that the configuration at the specific carbon and the geometry of the double bond is not Fixed

Correct Answer : 7

Question 29:

In the following reaction sequence, the amount of D (in g) formed from 10 moles of acetophenone is ____. (Atomic weights in g

m o l^{- 1}

: H = 1, C = 12, N = 14, O = 16, Br = 80. The yield (%) corresponding to the product in each step is given in the parenthesis)

Correct Answer : 495

Question 30:

The surface of copper gets tarnished by the formation of copper oxide.

N_{2}

gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the

N_{2}

gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below:

2 C u (s) + H_{2} O (g) \to C u_{2} O (S) + H_{2} (g)

p_{H_{2}}

is the minimum partial pressure of H2 (in bar) needed to prevent the oxidation at 1250 K. The value of

I n ({p_{H}}_{2})

is ____. (Given: total pressure = 1 bar, R (universal gas constant) = 8 J

K^{- 1} m o l^{- 1}

, ln(10) = 2.3. Cu(s) and

C u_{2} O (s)

are mutually immiscible. At 1250 K: 2Cu(s)+

\frac{1}{2} O_{2} (g) \to C u_{2} O (s); ∆ G^{θ} = - 78, 000 j m o l^{- 1}

H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O (g); ∆ G^{θ} = - 1, 78, 000 J m o l^{- 1}; G i s t h e G i b b s e n e r g y)

Correct Answer : -14.6

Question 31:

Consider the following reversible reaction, A(g) + B(g) ⇌ AB(g). The activation energy of the backward reaction exceeds that of the forward reaction by 2ܴܶRT (in J

m o l^{- 1}

). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of ∆

G^{θ}

(in J

m o I^{- 1}

) for the reaction at 300 K is ____. (Given; ln(2) = 0.7, ܴܶ = 2500 J

m o l^{- 1}

at 300 K and G is the Gibbs energy)

Correct Answer : 8500

Question 32:

Consider an electrochemical cell: A(s) |

A^{n +}

(aq, 2 M) ||

B^{2 n +}

(aq, 1 M) | B(s). The value of

∆ H^{θ}

for the cell reaction is twice that of

∆ G^{θ}

at 300 K. If the emf of the cell is zero, the

∆ S^{θ}

(in J

K^{- 1} m o l^{- 1}

) of the cell reaction per mole of B formed at 300 K is ____. (Given: ln(2) = 0.7, ܴ (universal gas constant) = 8.3 J

K^{- 1}

m o l^{- 1}

. H, S and G are enthalpy, entropy and Gibbs energy, respectively.)

Correct Answer : -11.62

Question 33:

Match each set of hybrid orbitals from LIST–I with complex(es) given in LIST–II.

	LIST–I		LIST–I
P.	$d s p^{2}$	1.	${[F e F_{6}]}^{4 -}$
Q.	$s p^{3}$	2.	$[T i {(H_{2} O)}_{3} C I_{3}]$
R.	$s p^{3} d^{2}$	3.	$[C r {(N H_{3})}_{6}]^{3 +}$
S.	$d^{2} s p^{3}$	4.	${[F e C l_{4}]}^{2 -}$
		5.	$N i {(C O)}_{4}$
		6.	$[N i {(C N)}_{4}]^{2 -}$

The correct option is

(A)	$P \to 5; Q \to 4, 6; R \to 2, 3; S \to 1$
(B)	$P \to 5, 6; Q \to 4, 5; R \to 1; S \to 2, 3$
(C)	$P \to 6; Q \to 4, 5; R \to 1; S \to 2, 3$
(D)	$P \to 4, 6; Q \to 5, 6; R \to 1, 2; S \to 3$

Correct Answer : C

Question 34:

	List-I			List-II
P.		$+ H_{2} S O_{4}$	1.	$I_{2}, N a O H$
Q.		$+ H N O_{2}$	2.	$[A g {(N H_{3})}_{2}] O H$
R.		$+ H_{2} S O_{4}$	3.	Fehling solution
S.		$+ A g N O_{3}$	4.	HCHO, NaOH
			5.	NaOBr

The correct option is

(A)	$P \to 1 : Q \to 2, 3; R \to 1, 4; S \to 2, 4$
(B)	$P \to 1, 5; Q \to 3, 4; R \to 4, 5; S \to 3$
(C)	$P \to 1, 5; Q \to 3, 4; R \to 5; S \to 2, 4$
(D)	$P \to 1, 5 Q \to 2, 3; R \to 1, 5; S \to 2, 3$

Correct Answer : D

Question 35:

LIST-I contains reactions and LIST-II contains major products.

	List-I			List-II
p.		$\to$	1.
Q.		+ HBr $\to$	2.
R.		+ NaOMe $\to$	3.
S.		+ MeBr $\to$	4.
			5.

Match each reaction in LIST-I with one or more products in LIST-II and choose the correct option.

(A)	$P \to 1, 5; Q \to 2; R \to 3; S \to 4$
(B)	$P \to 1, 4; Q \to 2; R \to 4; S \to 3$
(C)	$P \to 1, 4; Q \to 1, 2; R \to 3, 4; S \to 4$
(D)	$P \to 4, 5; Q \to 4; R \to 4; S \to 3, 4$

Correct Answer : B

Question 36:

Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on [

H^{+}

] are given in LIST-II. (Note: Degree of dissociation (a) of weak acid and weak base is << 1; degree of hydrolysis of salt <<1; [

H^{+}

] represents the concentration of

H^{+}

ions)

	LIST–I		LIST–II
P.	(10 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 60 mL	1.	the value of [ $H^{+}$ ] does not change on dilution
Q.	(20 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 80 mL	2.	the value of [ $H^{+}$ ] changes to half of its initial value on dilution
R.	(20 mL of 0.1 M HCl + 20 mL of 0.1 M ammonia solution) diluted to 80 mL	3.	the value of [ $H^{+}$ ] changes to two times of its initial value on dilution
S.	10 mL saturated solution of $N i {(O H)}_{2}$ in equilibrium with excess solid $N i {(O H)}_{2}$ is diluted to 20 mL (solid $N i {(O H)}_{2}$ is still present after dilution).	4.	the value of [ $H^{+}$ ] changes to $\frac{1}{\sqrt{2}}$ times of its initial value on dilution
		5.	the value of [ $H^{+}$ ] changes to $\sqrt{2}$ times of its initial value on dilution

Match each process given in LIST-I with one or more effect(s) in LIST-II. The correct option is

(A)	$P \to 4; Q \to 2; R \to 3; S \to 1$
(B)	$P \to 4; Q \to 3; R \to 2; S \to 3$
(C)	$P \to 1; Q \to 4; R \to 5; S \to 3$
(D)	$P \to 1; Q \to 5; R \to 4; S \to 1$

Correct Answer : D

Question 37:

For a non-zero complex number 𝑧, let arg(𝑧) denote the principal argument with

- π < \arg (z) \leq π

Then, which of the following statement(s) is (are) FALSE?

A	$a r g (- 1 - i) = \frac{π}{4} =, w h e r e i = \sqrt{1}$	B	The function 𝑓: ℝ $(- π, π] defined by f (t) = \arg (- 1 + it)$ for all 𝑡∈ℝ, is continuous at all points of ℝ, where $i = \sqrt{- 1}$
C	For any two non-zero complex numbers $Z_{1} a n d Z_{2}$ $a r g (\frac{Z_{1}}{Z_{2}}) - a r g (Z_{1}) + a r g (Z_{2})$ is an integer multiple of 2𝜋	D	For any three given distinct complex numbers $Z_{1}, Z_{2} a n d Z_{3}$ the locus of the point 𝑧 satisfying the condition $a r g (\frac{(z - z_{1}) (z_{2} - z_{3})}{(z - z_{3}) (z_{2} - z_{1})})$ = 𝜋, lies on a straight line

Correct Answer : A,B and D

Question 38:

In a triangle 𝑃𝑄𝑅, let

< P Q R = 30 °

and the sides 𝑃𝑄 and 𝑄𝑅 have lengths and 10

\sqrt{3}

, respectively. Then, which of the following statement(s) is (are) TRUE?

A	$< Q P R = 45 °$	B	The area of the triangle 𝑃𝑄𝑅 is 25 $\sqrt{3}$ and $< Q R P = 120 °$
C	The radius of the incircle of the triangle 𝑃𝑄𝑅 is $10 \sqrt{3} - 15$	D	The area of the circumcircle of the triangle $P Q R i s 100 π$

Correct Answer : B,C and D

Question 39:

Let

P_{1}

: 2𝑥+𝑦−𝑧=3 and

P_{2}

: 𝑥+2𝑦+𝑧=2 be two planes. Then, which of the following statement(s) is (are) TRUE?A

A	The line of intersection of $p_{1} a n d p_{2}$ has direction ratios 1,2,−1.	B	The line $\frac{3 x - 4}{9} = \frac{1 - 3 y}{9} = \frac{z}{3}$
C	The acute angle between $p_{1} a n d p_{2} i s 60 °$	D	If $p_{3}$ is the plane passing through the point (4,2,−2) and perpendicular to the line of intersection of $p_{1} a n d p_{2}$ , then the distance of the point (2,1,1) from the plane $p_{3} i s \frac{2}{\sqrt{3}}$

Correct Answer : C and D

Question 40:

For every twice differentiable function 𝑓: ℝ→[−2,2] with

{(f (0))}^{2} + {(f' (0))}^{2}

=85, which of the following statement(s) is (are) TRUE?

A	There exist 𝑟,𝑠∈ℝ, where 𝑟<𝑠, such that 𝑓 is one-one on the open interval (𝑟,𝑠)	B	There exists 𝑥0∈ $x_{0} \in (- 4, 0)$ such that $f' (o x) \leq 1$
C	$\lim_{x \to \infty} f (x) = 1$	D	There exists 𝛼∈(−4,4) such that 𝑓(𝛼)+𝑓′′(𝛼) = 0 and 𝑓′(𝛼)≠0

Correct Answer : A,B and D

Question 41:

Let 𝑓:ℝ→ℝ and 𝑔:ℝ→ℝ be two non-constant differentiable functions. If

f' (x) = (e^{(f (x) - g (x))}) g' (x)

for all 𝑥∈ℝ, and 𝑓(1)=𝑔(2)=1, then which of the following statement(s) is (are) TRUE?

A	$f (2) < 1 - \log_{e} 2$	B	$f (2) > 1 - \log_{e} 2$
C	$g (1) > 1 - \log_{e} 2$	D	$g (1) < 1 - \log_{e} 2$

Correct Answer : B and C

Question 42:

Let 𝑓:[0,∞)→ℝ be a continuous function such that

f (x) = 1 - 2 x + \int_{0}^{x} e^{x - t} f (t) d t

for all 𝑥∈[0,∞). Then, which of the following statement(s) is (are) TRUE?

A	for all 𝑥∈[0,∞). Then, which of the following statement(s) is (are) TRUE?	B	The curve 𝑦=𝑓(𝑥) passes through the point (2,−1)
C	The area of the region ${(x, y) \in [0, 1] x ℝ : f (x) \leq y \leq \sqrt{1 - x^{2}}} i s \frac{π - 2}{4}$	D	The area of the region ${(x, y) \in [0, 1] x ℝ : f (x) \leq y \leq \sqrt{1 - x^{2}}} i s \frac{π - 1}{4}$

Correct Answer : C and B

Question 43:

The value of

({(\log_{2} 9)}^{2}) \frac{1}{\log_{2} (\log_{2} 9) x (\sqrt{7})} \frac{1}{\log_{4} 7}

is ______ .

Correct Answer : 8

Question 44:

The number of 5 digit numbers which are divisible by 4, with digits from the set {1,2,3,4,5} and the repetition of digits is allowed, is _____ .

Correct Answer : 625

Question 45:

Correct Answer : 3748

Question 46:

The number of real solutions of the equation

\sin^{- 1} (\sum_{i = 1}^{\infty} i_{x} + 1_{- x} \sum_{i = 1}^{\infty} {(\frac{x}{2})}^{i}) = \frac{π}{2} - \cos^{- 1} (\sum_{i = 1}^{\infty} {(- \frac{x}{2})}^{i} - \sum_{i = 1}^{\infty} {(- x)}^{i})

lying in the interval

(- \frac{1}{2}, \frac{1}{2})

is _____ . (Here, the inverse trigonometric functions

\sin^{- 1}

𝑥 and

\cos^{- 1}

𝑥 assume values in

[- \frac{π}{r}, \frac{π}{r}]

and [0,𝜋], respectively.)

Correct Answer : 2

Question 47:

For each positive integer 𝑛, let

y_{n} = \frac{1}{n} {((n + 1) (n + 2) . . . (n + n))}^{\frac{1}{2}}

For 𝑥∈ℝ, let [𝑥] be the greatest integer less than or equal to 𝑥.if

\lim_{n \to \infty} y_{n} =

𝐿, then the value of [𝐿] is _____ .

Correct Answer : 1

Question 48:

let

\vec{a} a n d \vec{b}

be two unit vectors such that

\vec{a} . \vec{b}

For some 𝑥,𝑦∈ℝ, let

\vec{c} = x \vec{a} + y \vec{b} + (\vec{a} + \vec{b)}

.If

|\vec{c}|

⃗|=2 and the vector

\vec{c}

is inclined at the same angle 𝛼 to both

\vec{a} a n d \vec{b}

then the value of

\cos^{2}

𝛼 is _____.

Correct Answer : 3

Question 49:

Let 𝑎,𝑏,𝑐 be three non-zero real numbers such that the equation

\sqrt{3}

𝑎cos𝑥+2 𝑏sin𝑥=𝑐, 𝑥

\in [- \frac{π}{2}, \frac{π}{2}],

has two distinct real roots

α a n d β

with 𝛼+𝛽=

\frac{π}{3}

Then, the value of

\frac{b}{a} i s .

_____ .

Correct Answer : 0.5

Question 50:

A farmer

F_{1}

has a land in the shape of a triangle with vertices at 𝑃(0,0),𝑄(1,1) and 𝑅(2,0).From this land, a neighbouring farmer

F_{2}

takes away the region which lies between the side 𝑃𝑄 and a curve of the form

y = x^{n} (n > 1)

If the area of the region taken away by the farmer

F_{2}

is exactly 30% of the area of Δ𝑃𝑄𝑅, then the value of 𝑛 is _____ .

Correct Answer : 4

Question 51:

Let 𝑆 be the circle in the 𝑥𝑦-plane defined by the equation

x^{2} + y^{2} = 4

.Let

E_{1} E_{2}

and

F_{1} F_{2}

be the chords of 𝑆 passing through the point

P_{0}

(1,1) and parallel to the x-axis and the y-axis, respectively. Let

G_{1} G_{2}

be the chord of S passing through

P_{0}

and having slope −1.Let the tangents to 𝑆 at

E_{1} a n d E_{2}

meet at

E_{3}

the tangents to 𝑆 at

F_{1} a n d F_{2}

meet at

F_{3}

and the tangents to 𝑆 at

G_{1} a n d G_{2} m e e t a t G_{3}

Then, the points

E_{3} F_{3}

and

G_{3}

.lie on the curve

A	𝑥+𝑦=4	B	( $�� - 4)^{2} + {(�� - 4)}^{2} = 16$
C	(𝑥−4)(𝑦−4)=4	D	𝑥𝑦=4

Correct Answer : A

Question 52:

Let 𝑆 be the circle in the 𝑥𝑦-plane defined by the equation

x^{2} + y^{2} = 4

A	${(�� + ��)}^{2} = 3 �� $	B	$x^{2 / 3} + y^{2 / 3} = 2^{4 / 3}$
C	$x^{2} + y^{2} = 2 �� $	D	$x^{2} + y^{2} = x^{2} y^{2}$

Correct Answer : D

Question 53:

There are five students

S_{1} S_{2} S_{3} S_{4}

and

S_{5}

in a music class and for them there are five seats

R_{1} R_{2} R_{3} R_{4} a n d R_{5}

arranged in a row, where initially the seat

R_{i}

is allotted to the student

S_{i}

𝑖=1,2,3,4,5. But, on the examination day, the five students are randomly allotted the five seats. The probability that, on the examination day, the student

s_{1}

gets the previously allotted seat

R_{1}

, and NONE of the remaining students gets the seat previously allotted to him/her is.

A	$\frac{3}{40}$	B	$\frac{1}{8}$
C	$\frac{7}{40}$	D	$\frac{1}{5}$

Correct Answer : A

Question 54:

There are five students

S_{1} S_{2} S_{3} S_{4}

and

S_{5}

in a music class and for them there are five seats

R_{1} R_{2} R_{3} R_{4} a n d R_{5}

arranged in a row, where initially the seat

R_{i}

is allotted to the student

S_{i}

𝑖=1,2,3,4,5. But, on the examination day, the five students are randomly allotted the five seats. For 𝑖=1,2,3,4, let 𝑇𝑖 denote the event that the students

S_{1} a n d s_{i + 1}

do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event

T_{1} \cap T_{2} \cap T_{3} \cap T_{4} i s

A	$\frac{1}{15}$	B	$\frac{1}{10}$
C	$\frac{7}{60}$	D	$\frac{1}{5}$

Correct Answer : C

Back
Scrore Card
Total Question		Total Attempted
Correct Answers		Incorrect Answers
Score

JEE Main 2018 Complete Exam Set 2 With Solution

View Solution

Attempt Mock Test

General Instructions

Please read the instructions carefully

General Instructions:

Navigating to a Question:

Answering a Question:

Navigating through sections:

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7:

Question 8:

Question 9:

Question 10:

Question 11:

Question 12:

Question 13:

Question 14:

Question 15:

Question 16:

Question 17:

Question 18:

Question 19:

Question 20:

Question 21:

Question 22:

Question 23:

Question 24:

Question 25:

Question 26:

Question 27:

Question 28:

Question 29:

Question 30:

Question 31:

Question 32:

Question 33:

Question 34:

Question 35:

Question 36:

Question 37:

Question 38:

Question 39:

Question 40:

Question 41:

Question 42:

Question 43:

Question 44:

Question 45:

Question 46:

Question 47:

Question 48:

Question 49:

Question 50:

Question 51:

Question 52:

Question 53:

Question 54:

Exam Summary

Are you sure you want to submit for final marking? No changes will be allowed after submission.

Thank you, Submitted Successfully.

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7:

Question 8:

Question 9:

Question 10:

Question 11:

Question 12:

Question 13:

Question 14:

Are you sure you want to submit for final marking?
No changes will be allowed after submission.