JEE Advanced 2019 Paper 1 Question Paper

Question 1

Let $M = \begin{bmatrix} \sin^4	heta & -1-\sin^2	heta \ 1+\cos^2	heta & \cos^4	heta \end{bmatrix} = \alpha I + \beta M^{-1}$, where $\alpha = \alpha(	heta)$ and $\beta = \beta(	heta)$ are real numbers, and I is the $2 	imes 2$ identity matrix. If $\alpha^*$ is the minimum of the set $\{\alpha(	heta) : 	heta \in [0, 2\pi)\}$ and $\beta^*$ is the minimum of the set $\{\beta(	heta) : 	heta \in [0, 2\pi)\}$, then the value of $\alpha^* + \beta^*$ is

Accepted Answer

(D) $-\frac{29}{16}$

Answer

(A) $-\frac{37}{16}$

Answer

(B) $-\frac{31}{16}$

Answer

(C) $-\frac{17}{16}$

Question 2

The area of the region $\{(x, y) : xy \le 8, 1 \le y \le x^2\}$ is

Accepted Answer

(C) $16\log_e 2 - \frac{14}{3}$

Answer

(A) $16\log_e 2 - 6$

Answer

(B) $8\log_e 2 - \frac{14}{3}$

Answer

(D) $8\log_e 2 - \frac{7}{3}$

Question 3

Let S be the set of all complex numbers z satisfying $|z - 2 + i| \ge \sqrt{5}$. If the complex number $z_0$ is such that $\frac{1}{|z_0 - 1|}$ is the maximum of the set $\left\{ \frac{1}{|z - 1|} : z \in S \right\}$, then the principal argument of $\frac{4 - z_0 - \overline{z_0}}{z_0 - \overline{z_0} + 2i}$ is

Accepted Answer

(C) $-\frac{\pi}{2}$

Answer

(A) $\frac{3\pi}{4}$

Answer

(B) $\frac{\pi}{4}$

Answer

(D) $\frac{\pi}{2}$

Question 4

A line $y = mx + 1$ intersects the circle $(x - 3)^2 + (y + 2)^2 = 25$ at the points P and Q. If the midpoint of the line segment PQ has x-coordinate $-\frac{3}{5}$, then which one of the following options is correct?

Accepted Answer

(C) $2 \le m < 4$

Answer

(A) $4 \le m < 6$

Answer

(B) $-3 \le m < -1$

Answer

(D) $6 \le m < 8$

Question 5

Let $\alpha$ and $\beta$ be the roots of $x^2 - x - 1 = 0$, with $\alpha > \beta$. For all positive integers n, define $a_n = \frac{\alpha^n - \beta^n}{\alpha - \beta}$, $n \ge 1$, $b_1 = 1$ and $b_n = a_{n-1} + a_{n+1}$, $n \ge 2$. Then which of the following options is/are correct?

Accepted Answer

(B) $b_n = \alpha^n + \beta^n$ for all $n \ge 1$

Accepted Answer

(C) $a_1 + a_2 + a_3 + ..... + a_n = a_{n+2} - 1$ for all $n \ge 1$

Accepted Answer

(D) $\sum_{n=1}^{\infty} \frac{a_n}{10^n} = \frac{10}{89}$

Answer

(A) $\sum_{n=1}^{\infty} \frac{b_n}{10^n} = \frac{8}{89}$

Question 6

In a non-right-angled triangle $\Delta PQR$, let p, q, r denote the lengths of the sides opposite to the angles at P, Q, R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and PE intersect at O. If $p = \sqrt{3}$, $q = 1$, and the radius of the circumcircle of the $\Delta PQR$ equals 1, then which of the following options is/are correct?

Accepted Answer

(A) length of $OE = \frac{1}{6}$

Accepted Answer

(B) Radius of incircle of $\Delta PQR = \frac{\sqrt{3}}{2}\left(2 - \sqrt{3}\right)$

Accepted Answer

(C) Length of $RS = \frac{\sqrt{7}}{2}$

Answer

(D) Are of $\Delta SOE = \frac{\sqrt{3}}{12}$

Question 7

Let $\Gamma$ denote a curve $y = y(x)$ which is in the first quadrant and let the point (1, 0) lie on it. Let the tangent to $\Gamma$ at a point P intersect the y-axis at $Y_P$. If $PY_P$ has length 1 for each point P on $\Gamma$, then which of the following option is/are correct?

Accepted Answer

(A) $y = \log_e\left(\frac{1 + \sqrt{1 - x^2}}{x}\right) - \sqrt{1 - x^2}$

Accepted Answer

(B) $xy' + \sqrt{1 - x^2} = 0$

Answer

(C) $y = -\log_e\left(\frac{1 + \sqrt{1 - x^2}}{x}\right) + \sqrt{1 - x^2}$

Answer

(D) $xy' - \sqrt{1 - x^2} = 0$

Question 8

Let $M = \begin{bmatrix} 0 & 1 & a \ 1 & 2 & 3 \ 3 & b & 1 \end{bmatrix}$ and adj $M = \begin{bmatrix} -1 & 1 & -1 \ 8 & -6 & 2 \ -5 & 3 & -1 \end{bmatrix}$ where a and b area real numbers. Which of the following options is/are correct?

Accepted Answer

(A) $(\mathrm{adj}\ M)^{-1} + \mathrm{adj}\ M^{-1} = -M$

Accepted Answer

(B) If $M \begin{bmatrix} \alpha \ \beta \ \gamma \end{bmatrix} = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix}$, then $\alpha - \beta + \gamma = 3$

Accepted Answer

(D) $a + b = 3$

Answer

(C) $\det(\mathrm{adj}\ M^2) = 81$

Question 9

Define the collections $\{E_1, E_2, E_3, .......\}$ of ellipses and $\{R_1, R_2, R_3, ...\}$ of rectangles as follows:
$E_1 : \frac{x^2}{9} + \frac{y^2}{4} = 1$;
$R_1$ : rectangle of largest area, with sides parallel to the axes, inscribed in $E_1$;
$E_n$ : ellipse $\frac{x^2}{a_n^2} + \frac{y^2}{b_n^2} = 1$ of largest area inscribed in $R_{n-1}$, $n > 1$;
$R_n$ : rectangle of largest area, with sides parallel to the axes, inscribed in $E_n$, $n > 1$.
Then which of the following options is/are correct?

Accepted Answer

(A) $\sum_{n=1}^{N} \left(	ext{area of } R_night) < 24$, for each positive integer N

Accepted Answer

(D) The length of latus rectum of $E_9$ is $\frac{1}{6}$

Answer

(B) The distance of a focus from the centre in $E_9$ is $\frac{\sqrt{5}}{32}$

Answer

(C) The eccentricities of $E_{18}$ and $E_{19}$ are NOT equal

Question 10

Let $f : R 	o R$ by given by $f(x) = \begin{cases} x^5 + 5x^4 + 10x^3 + 10x^2 + 3x + 1, & x < 0; \ x^2 - x + 1, & 0 \le x < 1; \ \frac{2}{3}x^3 - 4x^2 + 7x - \frac{8}{3}, & 1 \le x < 3; \ (x - 2)\log_e (x - 2) - x + \frac{10}{3}, & x \ge 3. \end{cases}$ Then which of the following options is/are correct?

Accepted Answer

(A) $f'$ has a local maximum at $x = 1$

Accepted Answer

(B) $f'$ is NOT differentiable at $x = 1$

Accepted Answer

(C) f is onto

Answer

(D) f is increasing on $(-\infty, 0)$

Question 11

Let $L_1$ and $L_2$ denote the lines $\vec{r} = \hat{i} + \lambda\left(-\hat{i} + 2\hat{j} + 2\hat{k}\right), \lambda \in R$ and $\vec{r} = \mu\left(2\hat{i} - \hat{j} + 2\hat{k}\right), \mu \in R$ respectively. If $L_3$ is a line which is perpendicular to both $L_1$ and $L_2$ and cuts both of them, then which of the following options describe (s) $L_3$?

Accepted Answer

(A) $\vec{r} = \frac{2}{9}\left(4\hat{i} + \hat{j} + \hat{k}\right) + t\left(2\hat{i} + 2\hat{j} - \hat{k}\right), t \in R$

Accepted Answer

(B) $\vec{r} = \frac{1}{3}\left(2\hat{i} + \hat{k}\right) + t\left(2\hat{i} + 2\hat{j} - \hat{k}\right), t \in R$

Accepted Answer

(C) $\vec{r} = \frac{2}{9}\left(2\hat{i} - \hat{j} + 2\hat{k}\right) + t\left(2\hat{i} + 2\hat{j} - \hat{k}\right), t \in R$

Answer

(D) $\vec{r} = t\left(2\hat{i} + 2\hat{j} - \hat{k}\right), t \in R$

Question 12

There are three bags $B_1$, $B_2$ and $B_3$. The bag $B_1$ contains 5 red and 5 green balls, $B_2$ contains 3 red and 5 green balls and $B_3$ contains 5 red and 3 green balls. Bags $B_1$, $B_2$ and $B_3$ have probabilities $\frac{3}{10}$, $\frac{3}{10}$ and $\frac{4}{10}$ respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?

Accepted Answer

(A) Probability that the chosen ball is green equals $\frac{39}{80}$

Accepted Answer

(B) Probability that the chosen ball is green, given that the selected bag is $B_3$, equals $\frac{3}{8}$

Answer

(C) Probability that the selected bag is $B_3$ and the chosen ball is green equals $\frac{3}{10}$

Answer

(D) Probability that the selected bag is $B_3$, given that the chosen ball is green, equals $\frac{5}{13}$

Question 13

Let $\omega 
e 1$ be a cube root of unity. Then the minimum of the set $\{|a + b\omega + c\omega^2|^2 : a, b, c$ distinct non-zero integers$\}$ equals ____

Accepted Answer

3.00

Question 14

If $I = \frac{2}{\pi} \int_{-\pi/4}^{\pi/4} \frac{dx}{\left(1 + e^{\sin x}\right)\left(2 - \cos 2x\right)}$ then $27 I^2$ equals ____

Accepted Answer

4.00

Question 15

Let S be the sample space of all $3 	imes 3$ matrices with entries from the set $\{0, 1\}$. Let the events $E_1$ and $E_2$ be given by
$E_1 = \{A \in S : \det A = 0\}$ and
$E_2 = \{A \in S :$ sum of entries of A is $7\}$
If a matrix is chosen at random from S, then the conditional probability $P(E_1/E_2)$ equals ____

Accepted Answer

0.50

Question 16

Let the point B be the reflection of the point A(2, 3) with respect to line $8x - 6y - 23 = 0$. Let $\Gamma_A$ and $\Gamma_B$ be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles $\Gamma_A$ and $\Gamma_B$ such that both the circles are on the same side of T. If C is the point of intersection of T and the line passing through A and B, then the length of the line segment AC is ____

Accepted Answer

10.00

Question 17

Let AP(a; d) denote the set of all the terms of an infinite arithmetic progression with first term a and common difference $d > 0$. If $AP(1; 3) \cap AP(2; 5) \cap AP(3; 7) = AP(a; d)$ then $a + d$ equals ____

Accepted Answer

157.00

Question 18

Three lines are given by $\vec{r} = \lambda\hat{i}, \lambda \in R$, $\vec{r} = \mu\left(\hat{i} + \hat{j}\right), \mu \in R$ and $\vec{r} = v\left(\hat{i} + \hat{j} + \hat{k}\right), v \in R$. Let the lines cut the plane $x + y + z = 1$ at the points A, B and C respectively. If the area of the triangle ABC is $\Delta$ then the value of $(6\Delta)^2$ equals

Accepted Answer

0.75

Question 19

Consider a spherical gaseous cloud of mass density ρ(r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K.  The force acting on the particles is their mutual gravitational force. If ρ(r) is constant in time, the particle number density n(r) = ρ(r)/m is
[ G is universal gravitational constant]

Accepted Answer

(B) $\frac{K}{2\pi r^2 m^2 G}$

Answer

(A) $\frac{3K}{\pi r^2 m^2 G}$

Answer

(C) $\frac{K}{6\pi r^2 m^2 G}$

Answer

(D) $\frac{K}{\pi r^2 m^2 G}$

Question 20

A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is $V_0$.  A hole with a small area $\alpha 4\pi R^2 (\alpha << 1)$ is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

Accepted Answer

(C) The ratio of the potential at the center of the shell to that of the point at $\frac{1}{2}$R from center towards the hole will be $\frac{1-\alpha}{1-2\alpha}$

Answer

(A) The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance 2R from the center of the spherical shell will be reduced by $\frac{\alpha V_0}{2R}$

Answer

(B) The magnitude of electric field at the center of the shell is reduced by $\frac{\alpha V_0}{2R}$

Answer

(D) The potential at the center of the shell is reduced by $2\alpha V_0$

Question 21

A current carrying wire heats a metal rod.  The wire provides a constant power (P) to the rod.  The metal rod is enclosed in an insulated container.  It is observed that the temperature (T) in the metal rod changes with time (t) as
$T (t) = T_0 (1 + \beta t^{1/4})$
where β is a constant with appropriate dimension while $T_0$ is a constant with dimension of temperature. The heat capacity of the metal is

Accepted Answer

(D) $\frac{4P(T(t)-T_0)^3}{\beta^4 T_0^4}$

Answer

(A) $\frac{4P(T(t)-T_0)^4}{\beta^4 T_0^5}$

Answer

(B) $\frac{4P(T(t)-T_0)}{\beta^4 T_0^2}$

Answer

(C) $\frac{4P(T(t)-T_0)^2}{\beta^4 T_0^2}$

Question 22

In a radioactive sample $^{40}_{19}$K nuclei either decay into stable $^{40}_{20}$Ca nuclei with decay constant 4.5 × $10^{-10}$ per year or into stable $^{40}_{18}$Ar nuclei with decay constant $0.5 	imes 10^{-10}$ per year. Given that in this sample all the stable $^{40}_{20}$Ca and $^{40}_{18}$Ar nuclei are produced by the $^{40}_{19}$K nuclei only.  In time t × $10^9$ years, if the ratio of the sum of stable $^{40}_{20}$Ca and $^{40}_{18}$Ar nuclei to the radioactive $^{40}_{19}$K nuclei is 99, the value of t will be
[Given : ln10 = 2.3]

Accepted Answer

(C) 9.2

Answer

(A) 1.15

Answer

(B) 4.6

Answer

(D) 2.3

Question 23

A conducting wire of parabolic shape, initially $y = x^2$, is moving with velocity $\vec{V} = V_0\hat{i}$ in a non uniform magnetic field $\vec{B} = B_0\left(1+\left(\frac{y}{L}\right)^{\beta}\right)\hat{k}$, as shown in figure. If $V_0$, $B_0$, L and β are positive constants and Δφ is the potential difference developed between the ends of the wire, then the correct statement(s) is/are:

Accepted Answer

(A) $|\Delta\phi|$ is proportional to the length of the wire projected on the y-axis.

Accepted Answer

(B) $|\Delta\phi|$ remains the same if the parabolic wire is replaced by a straight wire, y = x initially, of length $\sqrt{2}$ L

Accepted Answer

(D) $|\Delta\phi| = \frac{4}{3}B_0V_0L$ for β = 2

Answer

(C) $|\Delta\phi| = \frac{1}{2}B_0V_0L$ for β = 0

Question 24

A thin convex lens is made of two materials with refractive indices $n_1$ and $n_2$, as shown in figure.  The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when $n_1 = n_2 = n$.  The focal length is f + Δf when $n_1$ = n and $n_2$ = n + Δn.  Assuming Δn << (n – 1) and 1 < n < 2.  The correct statement(s) is/are.

Accepted Answer

(B) If $\frac{\Delta n}{n} < 0$ then $\frac{\Delta f}{f} > 0$

Accepted Answer

(C) For n = 1.5, Δn = $10^{-3}$ and f = 20 cm, the value of |Δf| will be 0.02 cm (round off to $2^{nd}$ decimal place).

Accepted Answer

(D) The relation between $\frac{\Delta f}{f}$ and $\frac{\Delta n}{n}$ remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature.

Answer

(A) $\left|\frac{\Delta f}{f}\right| < \left|\frac{\Delta n}{n}\right|$

Question 25

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries $T_1$ and $T_2$ of different materials having water contact angles of $0^0$ and $60^0$, respectively.  The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure.  Which of the following option(s) is (are) correct?
[Surface tension of a water  = 0.075 N/m, density of water = 1000 kg/$m^3$, take g = 10 m/$s^2$]

Accepted Answer

(A) For case I, if the joint is kept at 8 cm above the water surface, the height of water column in the tube will be 7.5 cm.  (Neglect the weight of the water in the meniscus)

Accepted Answer

(C) For case II, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be 3.75 cm. (Neglect the weight of the water in the meniscus)

Accepted Answer

(D) The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus, will be different for both cases.

Answer

(B) For case I, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be more than 8.75 cm.  (Neglect the weight of the water in the meniscus)

Question 26

A charged shell of radius R carries a total charge Q.  Given φ as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell.   Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces.  Which of the following option(s) is/are correct?
[$\varepsilon_0$ is permittivity of free space]

Accepted Answer

(A) If h < 8R/5 and r = 3R/5 then φ = 0

Accepted Answer

(B) If h > 2R and r > R then φ = Q/$\varepsilon_0$

Accepted Answer

(D) If h > 2R and r = 3R/5 then φ = Q/$5\varepsilon_0$

Answer

(C) If h > 2R and r = 4R/5 then φ = Q/$5\varepsilon_0$

Question 27

Let us consider a system of units in which mass and angular momentum are dimensionless.  If length has dimension of L, which of the following statement(s) is/are correct?

Accepted Answer

(A) The dimension of energy is $L^{-2}$

Accepted Answer

(B) The dimension of force is $L^{-3}$

Accepted Answer

(D) The dimension of linear momentum is $L^{-1}$

Answer

(C) The dimension of power is $L^{-5}$

Question 28

In the circuit shown, initially there is no charge on capacitors and keys $S_1$ and $S_2$ are open. The values of the capacitors are $C_1$ = 10 μF, $C_2$ = 30 μF and $C_3$ = $C_4$ = 80 μF.  Which of the statement(s) is/are correct?

Accepted Answer

(B) If key $S_1$ is kept closed for long time such that capacitors are fully charged, the voltage across the capacitor $C_1$ will be 4V.

Accepted Answer

(C) At time t = 0, the key $S_1$ is closed, the instantaneous current in the closed circuit will be 25 mA

Answer

(A) The key $S_1$ is kept closed for long time such that capacitors are fully charged.  Now key $S_2$ is closed, at this time, the instantaneous current across 30Ω resistor (between points P and Q) will be 0.2 A (round off to $1^{st}$ decimal place).

Answer

(D) If key $S_1$ is kept closed for long time such that capacitors are fully charged, the voltage difference between points P and Q will be 10 V.

Question 29

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V – T) diagram. The correct statement(s) is/are:
[R is the gas constant]

Accepted Answer

(A) Work done in this thermodynamic cycle (1 → 2 → 3 → 4 → 1) is $|W| = \frac{1}{2}RT_0$

Accepted Answer

(B) The ratio of heat transfer during processes 1 → 2 and 2 → 3 is $\left|\frac{Q_{1	o 2}}{Q_{2	o 3}}ight| = \frac{5}{3}$

Answer

(C) The above thermodynamic cycle exhibits only isochoric and adiabatic processes.

Answer

(D) The ratio of heat transfer during processes 1 → 2 and 3 → 4 is $\left|\frac{Q_{1	o 2}}{Q_{3	o 4}}ight| = \frac{1}{2}$

Question 30

Two identical moving coil galvanometers have 10 Ω resistance and full scale deflection at 2 μA current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with R = 1000 Ω resistor by using an ideal cell. Which of the following statement(s) is/are correct?

Accepted Answer

(A) The measured value of R will be 978 Ω < R < 982 Ω

Accepted Answer

(D) The resistance of the Ammeter will be 0.02Ω (round off to $2^{nd}$ decimal place)

Answer

(B) The resistance of the Voltmeter will be 100 kΩ

Answer

(C) If the ideal cell is replaced by a cell having internal resistance of 5Ω then the measured value of R will be more than 1000 Ω

Question 31

A block of weight 100 N is suspended by copper and steel wires of same cross sectional area 0.5 $cm^2$ and, length $\sqrt{3}$ m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30° and 60°, respectively. If elongation in copper wire is $\left(\Delta\ell_C\right)$ and elongation in steel wire is $\left(\Delta\ell_S\right)$, then the ratio $\frac{\Delta\ell_C}{\Delta\ell_S}$ is ______
[Young's modulus for copper and steel are 1 × $10^{11}$ N/$m^2$ and 2 × $10^{11}$ N/$m^2$, respectively.]

Accepted Answer

2.00

Question 32

A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force $\vec{F} = \left(\alpha y\hat{i} + 2\alpha x\hat{j}\right) N$, where x and y are in meter and α = – 1 $Nm^{-1}$. The work done on the particle by this force $\vec{F}$ will be ________ Joule.

Accepted Answer

0.75

Question 33

A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is ______.
[Speed of the sound = 330 m/s]

Accepted Answer

8.12 or 8.13

Question 34

A liquid at 30°C is poured very slowly into a Calorimeter that is at temperature of 110°C. The boiling temperature of the liquid is 80°C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be 50°C. The ratio of the Latent heat of the liquid to its specific heat will be ______ °C.
[Neglect the heat exchange with surrounding]

Accepted Answer

270.00

Question 35

A planar structure of length L and width W is made of two different optical media of refractive indices $n_1$ = 1.5 and $n_2$ = 1.44 as shown in figure. If L >> W, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For L = 9.6 m, if the incident angle θ is varied, the maximum time taken by a ray to exit the plane CD is t × $10^{-9}$ s, where t is ______.
[Speed of light c = 3 × $10^8$ m/s]

Accepted Answer

50.00

Question 36

A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness $\delta = \frac{d}{N}$. The dielectric constant of the $m^{th}$ layer is $K_m = K\left(1+\frac{m}{N}\right)$. For a very large $N\left(>10^3\right)$, the capacitance C is $\alpha\left(\frac{K\varepsilon_0 A}{d \ln 2}\right)$. The value of α will be ______.
[$\varepsilon_0$ is the permittivity of free space]

Accepted Answer

1.00

Question 37

The green colour produced in the borax bead test of a chromium(III) salt is due to

Accepted Answer

(D) Cr(BO$_{2}$)$_{3}$

Answer

(A) CrB

Answer

(B) Cr$_{2}$O$_{3}$

Answer

(C) Cr$_{2}$(B$_{4}$O$_{7}$)$_{3}$

Question 38

Molar conductivity ($\Lambda_{m}$) of aqueous solution of sodium stearate, which behaves as a strong electrolyte, is recorded at varying concentrations (c) of sodium stearate. Which one of the following plots provides the correct representation of micelle formation in the solution?
(critical micelle concentration (CMC) is marked with an arrow in the figures

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 39

Calamine, malachite, magnetite and cryolite, respectively, are

Accepted Answer

(B) ZnCO$_{3}$, CuCO$_{3}$.Cu(OH)$_{2}$, Fe$_{3}$O$_{4}$, Na$_{3}$AlF$_{6}$

Answer

(A) ZnSO$_{4}$, Cu(OH)$_{2}$, Fe$_{3}$O$_{4}$, Na$_{3}$AlF$_{6}$

Answer

(C) ZnSO$_{4}$, CuCO$_{3}$, Fe$_{2}$O$_{3}$, AlF$_{3}$

Answer

(D) ZnCO$_{3}$, CuCO$_{3}$, Fe$_{2}$O$_{3}$, Na$_{3}$AlF$_{6}$

Question 40

The correct order of acid strength of the following carboxylic acids is

Accepted Answer

(C) I > II > III > IV

Answer

(A) I > III > II > IV

Answer

(B) III > II > I > IV

Answer

(D) II > I > IV > III

Question 41

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

Accepted Answer

(B) The two six-membered cyclic hemiacetal forms of D-(+)-glucose are called anomers

Accepted Answer

(C) Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones

Accepted Answer

(D) Hydrolysis of sucrose gives dextrorotatory glucose and laevorotatory fructose

Answer

(A) Oxidation of glucose with bromine water gives glutamic acid

Question 42

Choose the correct option(s) for the following set of reactions

Accepted Answer

(C) (C)

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Question 43

Each of the following options contains a set of four molecules, Identify the option(s) where all four molecules possess permanent dipole moment at room temperature.

Accepted Answer

(A) SO$_{2}$, C$_{6}$H$_{5}$Cl, H$_{2}$Se, BrF$_{5}$

Accepted Answer

(D) NO$_{2}$, NH$_{3}$, POCl$_{3}$, CH$_{3}$Cl

Answer

(B) BeCl$_{2}$, CO$_{2}$, BCl$_{3}$, CHCl$_{3}$

Answer

(C) BF$_{3}$, O$_{3}$, SF$_{6}$, XeF$_{6}$

Question 44

Choose the reaction(s) from the following options, for which the standard enthalpy of reaction is equal to the standard enthalpy of formation.

Accepted Answer

(B) $\frac{3}{2}$O$_{2}$(g) $\longrightarrow$ O$_{3}$(g)

Accepted Answer

(D) $\frac{1}{8}$S$_{8}$(s) + O$_{2}$(g) $\longrightarrow$ SO$_{2}$(g)

Answer

(A) 2C(g) + 3H$_{2}$(g) $\longrightarrow$ C$_{2}$H$_{6}$(g)

Answer

(C) 2H$_{2}$(g) + O$_{2}$(g) $\longrightarrow$ 2H$_{2}$O($\ell$)

Question 45

Fusion of MnO$_{2}$ with KOH in presence of O$_{2}$ produces a salt W. Alkaline solution of W upon electrolytic oxidation yields another salt X. The manganese containing ions present in W and X, respectively, are Y and Z. Correct statement(s) is(are)

Accepted Answer

(A) In aqueous acidic solution, Y undergoes disproportionation reaction to give Z and MnO$_{2}$

Accepted Answer

(B) In both Y and Z, $\pi$-bonding occurs between p-orbitals of oxygen and d-orbitals of manganese

Accepted Answer

(D) Both Y and Z are coloured and have tetrahedral shape

Answer

(C) Y is diamagnetic in nature while Z is paramagnetic

Question 46

Which of the following statement(s) is(are) correct regarding the root mean square speed (U$_{rms}$) and average translational kinetic energy ($\varepsilon_{av}$) of a molecule in a gas at equilibrium ?

Accepted Answer

(A) $\varepsilon_{av}$ at a given temperature does not depend on its molecular mass

Accepted Answer

(B) U$_{rms}$ is doubled when its temperature is increased four times

Accepted Answer

(D) U$_{rms}$ is inversely proportional to the square root of its molecular mass

Answer

(C) $\varepsilon_{av}$ is doubled when its temperature is increased four times

Question 47

A tin chloride Q undergoes the following reactions (not balanced)
Q + Cl$^{-}$ $\longrightarrow$ X
Q + Me$_{3}$N $\longrightarrow$ Y
Q + CuCl$_{2}$ $\longrightarrow$ Z + CuCl
X is a monoanion having pyramidal geometry. Both Y and Z are neutral compounds. Choose the correct option(s)

Accepted Answer

(B) The central atom in X is sp$^{3}$ hybridized

Accepted Answer

(C) There is a coordinate bond in Y

Answer

(A) The central atom in Z has one lone pair of electrons

Answer

(D) The oxidation state of the central atom in Z is +2

Question 48

In the decay sequence,
$^{238}_{92}$U $\xrightarrow{-x_{1}}$ $^{234}_{90}$Th $\xrightarrow{-x_{2}}$ $^{234}_{91}$Pa $\xrightarrow{-x_{3}}$ $^{234}$Z $\xrightarrow{-x_{4}}$ $^{230}_{90}$Th
x$_{1}$, x$_{2}$, x$_{3}$ and x$_{4}$ are particles /radiation emitted by the respective isotopes. The correct option(s) is(are)

Accepted Answer

(B) Z is an isotope of uranium

Accepted Answer

(C) x$_{2}$ is $\beta^{-}$

Accepted Answer

(D) x$_{1}$ will deflect towards negatively charged plate

Answer

(A) x$_{3}$ is $\gamma$-ray

Question 49

Among B$_{2}$H$_{6}$, B$_{3}$N$_{3}$H$_{6}$, N$_{2}$O, N$_{2}$O$_{4}$, H$_{2}$S$_{2}$O$_{3}$ and H$_{2}$S$_{2}$O$_{8}$, the total number of molecules containing covalent bond between two atoms of the same kind is

Accepted Answer

4.00

Question 50

On dissolving 0.5 g of a non-volatile non-ionic solute to 39 g of benzene, its vapour pressure decreases from 650 mm Hg to 640 mm Hg. The depression of freezing point of benzene (in K) upon addition of the solute is
(Given data: Molar mass and the molal freezing point depression constant of benzene are 78 g mol$^{-1}$ and 5.12 K kg mol$^{-1}$, respectively)

Accepted Answer

1.02 or 1.03

Question 51

For the following reaction, the equilibrium constant K$_{c}$ at 298 K is 1.6 $	imes$ 10$^{17}$
Fe$^{2+}$(aq) + S$^{2-}$(aq) $ightleftharpoons$ FeS(s)
When equal volumes of 0.06 M Fe$^{2+}$(aq) and 0.2 M S$^{2-}$(aq) solutions are mixed, the equilibrium concentration of Fe$^{2+}$(aq) is found to be Y $	imes$ 10$^{-17}$ M. The value of Y is ……… .

Accepted Answer

8.92 or 8.93

Question 52

Experiment No. | [A] (mol dm$^{-3}$) | [B] (mol dm$^{-3}$) | [C] (mol dm$^{-3}$) | Rate of reaction (mol dm$^{-3}$s$^{-1}$)
1 | 0.2 | 0.1 | 0.1 | 6.0 $	imes$ 10$^{-5}$
2 | 0.2 | 0.2 | 0.1 | 6.0 $	imes$ 10$^{-5}$
3 | 0.2 | 0.1 | 0.2 | 1.2 $	imes$ 10$^{-4}$
4 | 0.3 | 0.1 | 0.1 | 9.0 $	imes$ 10$^{-5}$
The rate of the reaction for [A] = 0.15 mol dm$^{-3}$, [B] = 0.25 mol dm$^{-3}$ and [C] = 0.15 mol dm$^{-3}$ is found to be Y $	imes$ 10$^{-5}$ mol dm$^{-3}$s$^{-1}$. The value of Y is ……… .

Accepted Answer

6.75

Question 53

Schemes 1 and 2 describe the conversion of P to Q and R to S, respectively. Scheme 3 describes the synthesis of T from Q and S. The total number of Br atoms in a molecule of T is

Accepted Answer

4.00

Question 54

At 143 K, the reaction of XeF$_{4}$ with O$_{2}$F$_{2}$ produces xenon compound Y. The total number of lone Pair(s) of electrons present on the whole molecule of Y is ……… .

Accepted Answer

19.00

JEE Advanced 2019 Paper 1 Question Paper with Answers

Physics — JEE Advanced 2019 Paper 1

Chemistry — JEE Advanced 2019 Paper 1

Mathematics — JEE Advanced 2019 Paper 1

Chapters tested in this paper

Attempt JEE Advanced 2019 Paper 1 under exam timing.