JEE Advanced 2018 Paper 1 Question Paper

Question 1

For a non-zero complex number z, let arg(z) denote the principal argument with $-\pi < \arg(z) \le \pi$. Then, which of the following statement(s) is (are) FALSE ?

Accepted Answer

(A) $\arg(-1-i) = \frac{\pi}{4}$, where $i = \sqrt{-1}$

Accepted Answer

(B) The function $f : R 	o (-\pi, \pi]$, defined by $f(t) = \arg(-1+it)$ for all $t \in R$, is continuous at all points of R, where $i = \sqrt{-1}$

Accepted Answer

(D) For any three given distinct complex numbers $z_{1}$, $z_{2}$ and $z_{3}$, the locus of the point z satisfying the condition $\arg\left(\frac{(z-z_{1})(z_{2}-z_{3})}{(z-z_{3})(z_{2}-z_{1})}\right) = \pi$, lies on a straight line

Answer

(C) For any two non-zero complex numbers $z_{1}$ and $z_{2}$, $\arg\left(\frac{z_{1}}{z_{2}}\right) - \arg(z_{1}) + \arg(z_{2})$ is an integer multiple of $2\pi$

Question 2

In a triangle PQR, let $\angle PQR = 30^{\circ}$ and the sides PQ and QR have lengths $10\sqrt{3}$ and 10, respectively. Then, which of the following statement(s) is (are) TRUE ?

Accepted Answer

(B) The area of the triangle PQR is $25\sqrt{3}$ and $\angle QRP = 120^{\circ}$

Accepted Answer

(C) The radius of the incircle of the triangle PQR is $10\sqrt{3} - 15$

Accepted Answer

(D) The area of the circumcircle of the triangle PQR is $100\pi$

Answer

(A) $\angle QPR = 45^{\circ}$

Question 3

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 ?

Accepted Answer

(C) The acute angle between $P_{1}$ and $P_{2}$ is $60^{\circ}$

Accepted Answer

(D) If $P_{3}$ is the plane passing through the point $(4, 2, -2)$ and perpendicular to the line of intersection of $P_{1}$ and $P_{2}$, then the distance of the point $(2, 1, 1)$ from the plane $P_{3}$ is $\frac{2}{\sqrt{3}}$

Answer

(A) The line of intersection of $P_{1}$ and $P_{2}$ has direction ratios 1, 2, $-1$

Answer

(B) The line $\frac{3x-4}{9} = \frac{1-3y}{9} = \frac{z}{3}$ is perpendicular to the line of intersection of $P_{1}$ and $P_{2}$

Question 4

For every twice differentiable function $f : R 	o [-2, 2]$ with $(f(0))^{2} + (f'(0))^{2} = 85$, which of the following statement(s) is (are) TRUE ?

Accepted Answer

(A) There exist r, s $\in$ R, where $r < s$, such that f is one-one on the open interval (r, s)

Accepted Answer

(B) There exists $x_{0} \in (-4, 0)$ such that $|f'(x_{0})| \le 1$

Accepted Answer

(D) There exist $\alpha \in (-4, 4)$ such that $f(\alpha) + f''(\alpha) = 0$ and $f'(\alpha) 
e 0$

Answer

(C) $\lim_{x 	o \infty} f(x) = 1$

Question 5

Let $f : R 	o R$ and $g : R 	o R$ be two non-constant differentiable functions. If
$f'(x) = \left(e^{(f(x)-g(x))}ight) g'(x)$ for all $x \in R$,
and $f(1) = g(2) = 1$, then which of the following statement(s) is (are) TRUE ?

Accepted Answer

(B) $f(2) > 1 - \log_{e} 2$

Accepted Answer

(C) $g(1) > 1 - \log_{e} 2$

Answer

(A) $f(2) < 1 - \log_{e} 2$

Answer

(D) $g(1) < 1 - \log_{e} 2$

Question 6

Let $f : [0, \infty) 	o R$ be a continuous function such that
$f(x) = 1 - 2x + \int_{0}^{x} e^{x-t} f(t) dt$
for all $x \in [0, \infty)$. Then, which of the following statement(s) is (are) TRUE ?

Accepted Answer

(B) The curve $y = f(x)$ passes through the point $(2, -1)$

Accepted Answer

(C) The area of the region $\{(x, y) \in [0, 1] 	imes R : f(x) \le y \le \sqrt{1-x^{2}}\}$ is $\frac{\pi-2}{4}$

Answer

(A) The curve $y = f(x)$ passes through the point $(1, 2)$

Answer

(D) The area of the region $\{(x, y) \in [0, 1] 	imes R : f(x) \le y \le \sqrt{1-x^{2}}\}$ is $\frac{\pi-1}{4}$

Question 7

The value of $\left(\left(\log_{2} 9ight)^{2}ight)^{\frac{1}{\log_{2}\left(\log_{2} 9ight)}} 	imes \left(\sqrt{7}ight)^{\frac{1}{\log_{4} 7}}$ is ______ .

Accepted Answer

8

Question 8

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 ______ .

Accepted Answer

625

Question 9

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 arithmetic progression 9, 16, 23, ….. . Then, the number of elements in the set $X \cup Y$ is ______ .

Accepted Answer

3748

Question 10

The number of real solutions of the equation
$\sin^{-1}\left(\sum_{i=1}^{\infty} x^{i+1} - x \sum_{i=1}^{\infty}\left(\frac{x}{2}\right)^{i}\right) = \frac{\pi}{2} - \cos^{-1}\left(\sum_{i=1}^{\infty}\left(-\frac{x}{2}\right)^{i} - \sum_{i=1}^{\infty}(-x)^{i}\right)$
lying in the interval $\left(-\frac{1}{2}, \frac{1}{2}\right)$ is ______ .
(Here, the inverse trigonometric functions $\sin^{-1}x$ and $\cos^{-1}x$ assume values in $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ and $[0, \pi]$, respectively.)

Accepted Answer

2

Question 11

For each positive integer n, let
$y_{n} = \frac{1}{n}\left((n+1)(n+2)....(n+n)ight)^{1/n}$.
For $x \in R$, let [x] be the greatest integer less than or equal to x. If $\lim_{n 	o \infty} y_{n} = L$, then the value of [L] is ______ .

Accepted Answer

1

Question 12

Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that $\vec{a} \cdot \vec{b} = 0$. For some x, y $\in$ R, let $\vec{c} = x\vec{a} + y\vec{b} + \left(\vec{a} 	imes \vec{b}ight)$. If $|\vec{c}| = 2$ and the vector $\vec{c}$ is inclined at the same angle $\alpha$ to both $\vec{a}$ and $\vec{b}$, then the value of $8\cos^{2}\alpha$ is ______ .

Accepted Answer

3

Question 13

Let a, b, c be three non-zero real numbers such that the equation
$\sqrt{3}a \cos x + 2b \sin x = c$, $x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$,
has two distinct real roots $\alpha$ and $\beta$ with $\alpha + \beta = \frac{\pi}{3}$. Then, the value of $\frac{b}{a}$ is ______ .

Accepted Answer

0.5

Question 14

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 $\Delta$PQR, then the value of n is ______ .

Accepted Answer

4

Question 15

PARAGRAPH "X"
Let S be the circle in the x-y plane defined by the equation $x^{2} + y^{2} = 4$.
(There are two questions based on PARAGRAPH "X", the question given below is one of them)

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 $E_{1}$ and $E_{2}$ meet at $E_{3}$, the tangents to S at $F_{1}$ and $F_{2}$ meet at $F_{3}$, and the tangents to S at $G_{1}$ and $G_{2}$ meet at $G_{3}$. Then, the points $E_{3}$, $F_{3}$, and $G_{3}$ lie on the curve

Accepted Answer

(A) $x + y = 4$

Answer

(B) $(x-4)^{2} + (y-4)^{2} = 16$

Answer

(C) $(x-4)(y-4) = 4$

Answer

(D) $xy = 4$

Question 16

PARAGRAPH "X"
Let S be the circle in the x-y plane defined by the equation $x^{2} + y^{2} = 4$.
(There are two questions based on PARAGRAPH "X", the question given below is one of them)

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

Accepted Answer

(D) $x^{2} + y^{2} = x^{2}y^{2}$

Answer

(A) $(x+y)^{2} = 3xy$

Answer

(B) $x^{2/3} + y^{2/3} = 2^{4/3}$

Answer

(C) $x^{2} + y^{2} = 2xy$

Question 17

PARAGRAPH "A"
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 $R_{1}$, $R_{2}$, $R_{3}$, $R_{4}$ and $R_{5}$ 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.
(There are two questions based on PARAGRAPH "A", the question given below is one of them)

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

Accepted Answer

(A) $\frac{3}{40}$

Answer

(B) $\frac{1}{8}$

Answer

(C) $\frac{7}{40}$

Answer

(D) $\frac{1}{5}$

Question 18

PARAGRAPH "A"
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 $R_{1}$, $R_{2}$, $R_{3}$, $R_{4}$ and $R_{5}$ 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.
(There are two questions based on PARAGRAPH "A", the question given below is one of them)

For $i = 1, 2, 3, 4$, let $T_{i}$ denote the event that the students $S_{i}$ and $S_{i+1}$ do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event $T_{1} \cap T_{2} \cap T_{3} \cap T_{4}$ is

Accepted Answer

(C) $\frac{7}{60}$

Answer

(A) $\frac{1}{15}$

Answer

(B) $\frac{1}{10}$

Answer

(D) $\frac{1}{5}$

Question 19

The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V(r) = kr^{2}/2$, where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $R$ about the point $O$. If $v$ is the speed of the particle and $L$ is the magnitude of its angular momentum about $O$, which of the following statements is (are) true?

Accepted Answer

(B) $v = \sqrt{\frac{k}{m}}\,R$

Accepted Answer

(C) $L = \sqrt{mk}\,R^{2}$

Answer

(A) $v = \sqrt{\frac{k}{2m}}\,R$

Answer

(D) $L = \sqrt{\frac{mk}{2}}\,R^{2}$

Question 20

Consider a body of mass $1.0\ kg$ at rest at the origin at time $t = 0$. A force $\vec{F} = \left(\alpha t\,\hat{i} + \beta\,\hat{j}ight)$ is applied on the body, where $\alpha = 1.0\,Ns^{-1}$ and $\beta = 1.0\,N$. The torque acting on the body about the origin at time $t = 1.0\ s$ is $\vec{	au}$. Which of the following statements is (are) true?

Accepted Answer

(A) $\left|\vec{	au}ight| = \frac{1}{3}\,Nm$

Accepted Answer

(C) The velocity of the body at $t = 1s$ is $\vec{v} = \frac{1}{2}\left(\hat{i} + 2\hat{j}\right)ms^{-1}$

Answer

(B) The torque $\vec{	au}$ is in the direction of the unit vector $+\ \hat{k}$

Answer

(D) The magnitude of displacement of the body at $t = 1\ s$ is $\frac{1}{6}\,m$

Question 21

A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $\sigma$. The angle of contact between water and the wall of the capillary tube is $	heta$. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

Accepted Answer

(A) For a given material of the capillary tube, h decreases with increase in $r$

Accepted Answer

(C) If this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases

Answer

(B) For a given material of the capillary tube, h is independent of $\sigma$

Answer

(D) $h$ is proportional to contact angle $	heta$

Question 22

In the figure below, the switches $S_{1}$ and $S_{2}$ are closed simultaneously at $t = 0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current $I$ in the middle wire reaches its maximum magnitude $I_{max}$ at time $t = 	au$. Which of the following statements is (are) true?

Accepted Answer

(B) $I_{max} = \frac{V}{4R}$

Accepted Answer

(D) $	au = \frac{2L}{R}\ln 2$

Answer

(A) $I_{max} = \frac{V}{2R}$

Answer

(C) $	au = \frac{L}{R}\ln 2$

Question 23

Two infinitely long straight wires lie in the $xy$-plane along the lines $x = \pm R$. The wire located at $x = +R$ carries a constant current $I_{1}$ and the wire located at $x = -R$ carries a constant current $I_{2}$. A circular loop of radius $R$ is suspended with its centre at $(0, 0, \sqrt{3}R)$ and in a plane parallel to the $xy$-plane. This loop carries a constant current $I$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $+\hat{j}$ direction. Which of the following statements regarding the magnetic field $\vec{B}$ is (are) true?

Accepted Answer

(A) If $I_{1} = I_{2}$, then $\vec{B}$ cannot be equal to zero at the origin $(0, 0, 0)$

Accepted Answer

(B) If $I_{1} > 0$, and $I_{2} < 0$, then $\vec{B}$ can be equal to zero at the origin $(0, 0, 0)$

Accepted Answer

(D) If $I_{1} = I_{2}$, then the $z$-component of the magnetic field at the centre of the loop is $\left(-\frac{\mu_{0}I}{2R}\right)$

Answer

(C) If $I_{1} < 0$, and $I_{2} > 0$, then $\vec{B}$ can be equal to zero at the origin $(0, 0, 0)$

Question 24

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?

Accepted Answer

(B) In process II, gas absorbs heat

Accepted Answer

(C) In process IV, gas releases heat

Accepted Answer

(D) Processes I and III are not isobaric

Answer

(A) Process I is an isochoric process

Question 25

Two vectors $\vec{A}$ and $\vec{B}$ are defined as $\vec{A} = a\hat{i}$ and $\vec{B} = a\left(\cos\omega t\,\hat{i} + \sin\omega t\,\hat{j}ight)$, where $a$ is a constant and $\omega = \pi/6\ rad\ s^{-1}$. If $\left|\vec{A} + \vec{B}ight| = \sqrt{3}\left|\vec{A} - \vec{B}ight|$ at time $t = 	au$ for the first time, the value of $	au$, in seconds, is ______.

Accepted Answer

2.00

Question 26

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed $1.0\ ms^{-1}$ and the man behind walks at a speed $2.0\ ms^{-1}$. A third man is standing at a height $12\ m$ above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency $1430\ Hz$. The speed of sound in air is $330\ ms^{-1}$. At the instant, when the moving men are $10\ m$ apart, the stationary man is equidistant from them. The frequency of beats in $Hz$, heard by the stationary man at this instant, is __________.

Accepted Answer

5.00

Question 27

A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle $60^{\circ}$ with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is $(2 - \sqrt{3})/\sqrt{10}\ s$, then the height of the top of the inclined plane, in metres, is __________. Take $g = 10\ ms^{-2}$.

Accepted Answer

0.75

Question 28

A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0\ N\,m^{-1}$ and the mass of the block is $2.0\ kg$. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass $1.0\ kg$ moving with a speed of $2.0\ m\ s^{-1}$ collides elastically with the first block. The collision is such that the $2.0\ kg$ block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time is __________.

Accepted Answer

2.09

Question 29

Three identical capacitors $C_{1}$, $C_{2}$ and $C_{3}$ have a capacitance of $1.0\ \mu F$ each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C_{1}$ is then filled completely with a dielectric material of relative permittivity $\in_{r}$. The cell electromotive force (emf) $V_{0} = 8V$. First the switch $S_{1}$ is closed while the switch $S_{2}$ is kept open. When the capacitor $C_{3}$ is fully charged, $S_{1}$ is opened and $S_{2}$ is closed simultaneously. When all the capacitors reach equilibrium, the charge on $C_{3}$ is found to be $5\mu C$. The value of $\in_{r} = $__________.

Accepted Answer

1.50

Question 30

In the $xy$-plane, the region $y > 0$ has a uniform magnetic field $B_{1}\hat{k}$ and the region $y < 0$ has another uniform magnetic field $B_{2}\hat{k}$. A positively charged particle is projected from the origin along the positive $y$-axis with speed $v_{0} = \pi\ m\ s^{-1}$ at $t = 0$, as shown in the figure. Neglect gravity in this problem. Let $t = T$ be the time when the particle crosses the $x$-axis from below for the first time. If $B_{2} = 4B_{1}$, the average speed of the particle, in $ms^{-1}$, along the $x$-axis in the time interval $T$ is __________.

Accepted Answer

2.00

Question 31

Sunlight of intensity $1.3\ \mathrm{kWm}^{-2}$ is incident normally on a thin convex lens of focal length $20\ cm$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in $kW\ m^{-2}$, at a distance $22\ cm$ from the lens on the other side is __________.

Accepted Answer

130.00

Question 32

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_{1} = 300\ K$ and $T_{2} = 100\ K$, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K_{1}$ and $K_{2}$ respectively. If the temperature at the junction of the two cylinders in the steady state is $200\ K$, then $K_{1}/K_{2} = $__________.

Accepted Answer

4.00

Question 33

PARAGRAPH "X"

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fields respectively, while $[\in_{0}]$ and $[\mu_{0}]$ stand for dimensions of the permittivity and permeability of free space respectively. $[L]$ and $[T]$ are dimensions of length and time respectively. All the quantities are given in SI units.

(There are two questions based on PARAGRAPH "X", the question given below is one of them)

The relation between $[E]$ and $[B]$ is

Accepted Answer

(C) $[E] = [B]\,[L]\,[T]^{-1}$

Answer

(A) $[E] = [B]\,[L]\,[T]$

Answer

(B) $[E] = [B]\,[L]^{-1}\,[T]$

Answer

(D) $[E] = [B]\,[L]^{-1}\,[T]^{-1}$

Question 34

PARAGRAPH "X"

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fields respectively, while $[\in_{0}]$ and $[\mu_{0}]$ stand for dimensions of the permittivity and permeability of free space respectively. $[L]$ and $[T]$ are dimensions of length and time respectively. All the quantities are given in SI units.

(There are two questions based on PARAGRAPH "X", the question given below is one of them)

The relation between $[\in_{0}]$ and $[\mu_{0}]$ is

Accepted Answer

(D) $[\mu_{0}] = [\in_{0}]^{-1}\,[L]^{-2}\,[T]^{2}$

Answer

(A) $[\mu_{0}] = [\in_{0}]\,[L]^{2}\,[T]^{-2}$

Answer

(B) $[\mu_{0}] = [\in_{0}]\,[L]^{-2}\,[T]^{2}$

Answer

(C) $[\mu_{0}] = [\in_{0}]^{-1}\,[L]^{2}\,[T]^{-2}$

Question 35

PARAGRAPH "A"

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation $z = x/y$. If the errors in $x, y$ and $z$ are $\Delta x$, $\Delta y$ and $\Delta z$, respectively, then

$z \pm \Delta z = \frac{x \pm \Delta x}{y \pm \Delta y} = \frac{x}{y}\left(1 \pm \frac{\Delta x}{x}\right)\left(1 \pm \frac{\Delta y}{y}\right)^{-1}.$

The series expansion for $\left(1 \pm \frac{\Delta y}{y}\right)^{-1}$, to first power in $\Delta y/y$, is $1 \mp (\Delta y/y)$. The relative errors in independent variables are always added. So the error in $z$ will be

$\Delta z = z\left(\frac{\Delta x}{x} + \frac{\Delta y}{y}\right).$

The above derivation makes the assumption that $\Delta x/x \ll 1$, $\Delta y/y \ll 1$. Therefore, the higher powers of these quantities are neglected.

(There are two questions based on PARAGRAPH "A", the question given below is one of them)

Consider the ratio $r = \frac{(1 - a)}{(1 + a)}$ to be determined by measuring a dimensionless quantity $a$. If the error in the measurement of $a$ is $\Delta a$ $(\Delta a/a \ll 1)$, then what is the error $\Delta r$ in determining $r$ ?

Accepted Answer

(B) $\frac{2\Delta a}{(1 + a)^{2}}$

Answer

(A) $\frac{\Delta a}{(1 + a)^{2}}$

Answer

(C) $\frac{2\Delta a}{(1 - a^{2})}$

Answer

(D) $\frac{2a\Delta a}{(1 - a^{2})}$

Question 36

PARAGRAPH "A"

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation $z = x/y$. If the errors in $x, y$ and $z$ are $\Delta x$, $\Delta y$ and $\Delta z$, respectively, then

$z \pm \Delta z = \frac{x \pm \Delta x}{y \pm \Delta y} = \frac{x}{y}\left(1 \pm \frac{\Delta x}{x}\right)\left(1 \pm \frac{\Delta y}{y}\right)^{-1}.$

The series expansion for $\left(1 \pm \frac{\Delta y}{y}\right)^{-1}$, to first power in $\Delta y/y$, is $1 \mp (\Delta y/y)$. The relative errors in independent variables are always added. So the error in $z$ will be

$\Delta z = z\left(\frac{\Delta x}{x} + \frac{\Delta y}{y}\right).$

The above derivation makes the assumption that $\Delta x/x \ll 1$, $\Delta y/y \ll 1$. Therefore, the higher powers of these quantities are neglected.

(There are two questions based on PARAGRAPH "A", the question given below is one of them)

In an experiment the initial number of radioactive nuclei is 3000. It is found that $1000 \pm 40$ nuclei decayed in the first $1.0s$. For $|x| \ll 1$, $\ln(1 + x) = x$ up to first power in $x$. The error $\Delta\lambda$, in the determination of the decay constant $\lambda$, in $s^{-1}$, is

Accepted Answer

(C) 0.02

Answer

(A) 0.04

Answer

(B) 0.03

Answer

(D) 0.01

Question 37

The compound(s) which generate(s) $N_{2}$ gas upon thermal decomposition below 300°C is (are)

Accepted Answer

(B) $(NH_{4})_{2}Cr_{2}O_{7}$

Accepted Answer

(C) $Ba(N_{3})_{2}$

Answer

(A) $NH_{4}NO_{3}$

Answer

(D) $Mg_{3}N_{2}$

Question 38

The correct statement(s) regarding the binary transition metal carbonyl compounds is (are)
(Atomic numbers: Fe = 26, Ni = 28)

Accepted Answer

(B) These are predominantly low spin in nature

Accepted Answer

(C) Metal–carbon bond strengthens when the oxidation state of the metal is lowered

Answer

(A) Total number of valence shell electrons at metal centre in $Fe(CO)_{5}$ or $Ni(CO)_{4}$ is 16

Answer

(D) The carbonyl C−O bond weakens when the oxidation state of the metal is increased

Question 39

Based on the compounds of group 15 elements, the correct statement(s) is (are)

Accepted Answer

(A) $Bi_{2}O_{5}$ is more basic than $N_{2}O_{5}$

Accepted Answer

(B) $NF_{3}$ is more covalent than $BiF_{3}$

Accepted Answer

(C) $PH_{3}$ boils at lower temperature than $NH_{3}$

Answer

(D) The N−N single bond is stronger than the P−P single bond

Question 40

In the following reaction sequence, the correct structure(s) of X is (are)

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 41

The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is(are)

Accepted Answer

(A) (A)

Accepted Answer

(B) (B)

Accepted Answer

(D) (D)

Answer

(C) (C)

Question 42

A reversible cyclic process for an ideal gas is shown below. Here, $P$, $V$, and $T$ are pressure, volume and temperature, respectively. The thermodynamic parameters $q$, $w$, $H$ and $U$ are heat, work, enthalpy and internal energy, respectively.
The correct option(s) is (are)

Accepted Answer

(B) $w_{BC} = P_{2}(V_{2}-V_{1})$ and $q_{BC} = \Delta H_{AC}$

Accepted Answer

(C) $\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{BC}$

Answer

(A) $q_{AC} = \Delta U_{BC}$ and $w_{AB} = P_{2}(V_{2}-V_{1})$

Answer

(D) $q_{BC} = \Delta H_{AC}$ and $\Delta H_{CA} > \Delta U_{CA}$

Question 43

Among the species given below, the total number of diamagnetic species is ___.
H atom, $NO_{2}$ monomer, $O_{2}^{-}$ (superoxide), dimeric sulphur in vapour phase, $Mn_{3}O_{4}$, $(NH_{4})_{2}[FeCl_{4}]$, $(NH_{4})_{2}[NiCl_{4}]$, $K_{2}MnO_{4}$, $K_{2}CrO_{4}$

Accepted Answer

1

Question 44

The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by $NiCl_{2}.6H_{2}O$ to form a stable coordination compound. Assume that both the reactions are 100% complete. If 1584 g of ammonium sulphate and 952 g of $NiCl_{2}.6H_{2}O$ are used in the preparation, the combined weight (in grams) of gypsum and the nickel-ammonia coordination compound thus produced is ___.
(Atomic weights in g $mol^{-1}$ : H = 1, N = 14, O = 16, S = 32, Cl = 35.5, Ca = 40, Ni = 59)

Accepted Answer

2992

Question 45

Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance.
(i) Remove all the anions (X) except the central one
(ii) Replace all the face centered cations (M) by anions (X)
(iii) Remove all the corner cations (M)
(iv) Replace the central anion (X) with cation (M)
The value of $\left(\dfrac{	ext{number of anions}}{	ext{number of cations}}ight)$ in Z is ___.

Accepted Answer

3

Question 46

For the electrochemical cell,
$Mg(s) \mid Mg^{2+} (aq, 1\ M) \parallel Cu^{2+} (aq, 1\ M) \mid Cu(s)$
the standard emf of the cell is 2.70 V at 300 K. When the concentration of $Mg^{2+}$ is changed to $x$ M, the cell potential changes to 2.67 V at 300 K. The value of $x$ is ___.
(given, $\dfrac{F}{R} = 11500$ K $V^{-1}$, where $F$ is the Faraday constant and $R$ is the gas constant, $\ln(10) = 2.30$)

Accepted Answer

10

Question 47

A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume (in $m^{3}$) of the compartment A after the system attains equilibrium is ___.

Accepted Answer

2.22

Question 48

Liquids A and B form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids A and B has vapour pressure 45 Torr. At the same temperature, a new solution of A and B having mole fractions $x_{A}$ and $x_{B}$, respectively, has vapour pressure of 22.5 Torr. The value of $x_{A}/x_{B}$ in the new solution is ___.
(given that the vapour pressure of pure liquid A is 20 Torr at temperature T)

Accepted Answer

19

Question 49

The solubility of a salt of weak acid (AB) at pH 3 is $Y 	imes 10^{-3}$ mol $L^{-1}$. The value of Y is ___.
(Given that the value of solubility product of AB ($K_{sp}$) $= 2 	imes 10^{-10}$ and the value of ionization constant of HB ($K_{a}$) $= 1 	imes 10^{-8}$)

Accepted Answer

4.47

Question 50

The plot given below shows P—T curves (where $P$ is the pressure and $T$ is the temperature) for two solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents.
On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y. Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y, the degree of dimerization in solvent X is ___.

Accepted Answer

0.05

Question 51

PARAGRAPH "X"
Treatment of benzene with CO/HCl in the presence of anhydrous $AlCl_{3}$/CuCl followed by reaction with $Ac_{2}O$/NaOAc gives compound X as the major product. Compound X upon reaction with $Br_{2}$/$Na_{2}CO_{3}$, followed by heating at 473 K with moist KOH furnishes Y as the major product. Reaction of X with $H_{2}$/Pd-C, followed by $H_{3}PO_{4}$ treatment gives Z as the major product.
(There are two questions based on PARAGRAPH "X", the question given below is one of them)

The compound Y is

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 52

PARAGRAPH "X"
Treatment of benzene with CO/HCl in the presence of anhydrous $AlCl_{3}$/CuCl followed by reaction with $Ac_{2}O$/NaOAc gives compound X as the major product. Compound X upon reaction with $Br_{2}$/$Na_{2}CO_{3}$, followed by heating at 473 K with moist KOH furnishes Y as the major product. Reaction of X with $H_{2}$/Pd-C, followed by $H_{3}PO_{4}$ treatment gives Z as the major product.
(There are two questions based on PARAGRAPH "X", the question given below is one of them)

The compound Z is

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 53

PARAGRAPH "A"
An organic acid P ($C_{11}H_{12}O_{2}$) can easily be oxidized to a dibasic acid which reacts with ethylene glycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic ketone as one of the products. P undergoes the following reaction sequences to furnish R via Q. The compound P also undergoes another set of reactions to produce S.
S $\xleftarrow{}$ [1) $H_{2}$/Pd−C, 2) $NH_{3}$/$\Delta$, 3) $Br_{2}$/NaOH, 4) $CHCl_{3}$, KOH, $\Delta$, 5) $H_{2}$/Pd−C] P $\xrightarrow{}$ [1) $H_{2}$/Pd−C, 2) $SOCl_{2}$, 3) MeMgBr, $CdCl_{2}$, 4) $NaBH_{4}$] Q $\xrightarrow{}$ [1) HCl, 2) Mg/$Et_{2}O$, 3) $CO_{2}$ (dry ice), 4) $H_{3}O^{+}$] R
(There are two questions based on PARAGRAH 'A', the question given below is one of them)

The compound R is

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 54

PARAGRAPH "A"
An organic acid P ($C_{11}H_{12}O_{2}$) can easily be oxidized to a dibasic acid which reacts with ethylene glycol to produce a polymer dacron. Upon ozonolysis, P gives an aliphatic ketone as one of the products. P undergoes the following reaction sequences to furnish R via Q. The compound P also undergoes another set of reactions to produce S.
S $\xleftarrow{}$ [1) $H_{2}$/Pd−C, 2) $NH_{3}$/$\Delta$, 3) $Br_{2}$/NaOH, 4) $CHCl_{3}$, KOH, $\Delta$, 5) $H_{2}$/Pd−C] P $\xrightarrow{}$ [1) $H_{2}$/Pd−C, 2) $SOCl_{2}$, 3) MeMgBr, $CdCl_{2}$, 4) $NaBH_{4}$] Q $\xrightarrow{}$ [1) HCl, 2) Mg/$Et_{2}O$, 3) $CO_{2}$ (dry ice), 4) $H_{3}O^{+}$] R
(There are two questions based on PARAGRAPH "A", the question given below is one of them)

The compound S is

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

JEE Advanced 2018 Paper 1 Question Paper with Answers

Physics — JEE Advanced 2018 Paper 1

Chemistry — JEE Advanced 2018 Paper 1

Mathematics — JEE Advanced 2018 Paper 1

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Attempt JEE Advanced 2018 Paper 1 under exam timing.