JEE Advanced 2024 Paper 2 Question Paper

Question 1

Considering only the principal values of the inverse trigonometric functions, the value of $	an\left(\sin^{-1}\left(\frac{3}{5}ight) - 2\cos^{-1}\left(\frac{2}{\sqrt{5}}ight)ight)$ is

Accepted Answer

(B) $\frac{-7}{24}$

Answer

(A) $\frac{7}{24}$

Answer

(C) $\frac{-5}{24}$

Answer

(D) $\frac{5}{24}$

Question 2

Let $S = \left\{(x, y) \in \mathbb{R} 	imes \mathbb{R} : x \geq 0, y \geq 0, y^2 \leq 4x, y^2 \leq 12 - 2x 	ext{ and } 3y + \sqrt{8}x \leq 5\sqrt{8}ight\}$. If the area of the region $S$ is $\alpha\sqrt{2}$, then $\alpha$ is equal to

Accepted Answer

(B) $\frac{17}{3}$

Answer

(A) $\frac{17}{2}$

Answer

(C) $\frac{17}{4}$

Answer

(D) $\frac{17}{5}$

Question 3

Let $k \in \mathbb{R}$. If $\lim_{x 	o 0^+} \left(\sin(\sin kx) + \cos x + xight)^{\frac{2}{x}} = e^6$, then the value of $k$ is

Accepted Answer

(B) 2

Answer

(A) 1

Answer

(C) 3

Answer

(D) 4

Question 4

Let $f : \mathbb{R} 	o \mathbb{R}$ be a function defined by
$f(x) = \begin{cases} x^2 \sin\left(\frac{\pi}{x^2}ight) & ; 	ext{ if } x 
eq 0 \ 0 & ; 	ext{ if } x = 0 \end{cases}$
Then which of the following statements is TRUE?

Accepted Answer

(D) f(x) = 0 has more than 25 solutions in the interval $\left(\frac{1}{\pi^2}, \frac{1}{\pi}\right)$

Answer

(A) f(x) = 0 has infinitely many solutions in the interval $\left[\frac{1}{10^{10}}, \infty\right)$

Answer

(B) f(x) = 0 has no solutions in the interval $\left[\frac{1}{\pi}, \infty\right)$

Answer

(C) The set of solutions of f(x) = 0 in the interval $\left(0, \frac{1}{10^{10}}\right)$ is finite

Question 5

Let $S$ be the set of all $(\alpha, \beta) \in \mathbb{R} 	imes \mathbb{R}$ such that
$\lim_{x 	o \infty} \frac{\sin\left(x^2ight)\left(\log_e xight)^{\alpha} \sin\left(\frac{1}{x^2}ight)}{x^{\alpha\beta}\left(\log_e (1+x)ight)^{\beta}} = 0$.
Then which of the following is(are) correct ?

Accepted Answer

(B) $(-1, 1) \in S$

Accepted Answer

(C) $(1, -1) \in S$

Answer

(A) $(-1, 3) \in S$

Answer

(D) $(1, -2) \in S$

Question 6

A straight line drawn from the point P(1, 3, 2), parallel to the line $\frac{x-2}{1} = \frac{y-4}{2} = \frac{z-6}{1}$ intersects the plane $L_1 : x - y + 3z = 6$ at the point Q. Another straight line which passes through Q and is perpendicular to the plane $L_1$ intersects the plane $L_2 : 2x - y + z = -4$ at the point R. then which of the following statements is(are) TRUE?

Accepted Answer

(A) The length of the line segment PQ is $\sqrt{6}$

Accepted Answer

(C) The centroid of the triangle PQR is $\left(\frac{4}{3}, \frac{14}{3}, \frac{5}{3}\right)$

Answer

(B) The coordinates of R are (1, 6, 3)

Answer

(D) The perimeter of the triangle PQR is $\sqrt{2} + \sqrt{6} + \sqrt{11}$

Question 7

Let $A_1$, $B_1$, $C_1$ be three points in the xy-plane. Suppose that the lines $A_1C_1$ and $B_1C_1$ are tangents to the curve $y^2 = 8x$ at $A_1$ and $B_1$, respectively. If $O = (0, 0)$ and $C_1 = (-4, 0)$, then which of the following statements is(are) TRUE?

Accepted Answer

(A) The length of the line segment $OA_1$ is $4\sqrt{3}$

Accepted Answer

(C) The orthocenter of the triangle $A_1B_1C_1$ is (0, 0)

Answer

(B) The length of the line segment $A_1B_1$ is 16

Answer

(D) The orthocenter of the triangle $A_1B_1C_1$ is (1, 0)

Question 8

Let $f : \mathbb{R} 	o \mathbb{R}$ be a function such that $f(x + y) = f(x) + f(y)$ for all $x, y \in \mathbb{R}$, and $g : \mathbb{R} 	o (0, \infty)$ be a function such that $g(x + y) = g(x)g(y)$ for all $x, y \in \mathbb{R}$. If $f\left(\frac{-3}{5}ight) = 12$ and $g\left(\frac{-1}{3}ight) = 2$, then the value of $\left(f\left(\frac{1}{4}ight) + g(-2) - 8ight) g(0)$ is ______

Accepted Answer

51

Question 9

A bag contains N balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i = 1, 2, 3$, let $W_i$, $G_i$, and $B_i$ denote the events that the ball drawn in the $i^{th}$ draw is a white ball, green ball, and blue ball, respectively. If the probability $P\left(W_1 \cap G_2 \cap B_3\right) = \frac{2}{5N}$ and the conditional probability $P\left(B_3 \mid W_1 \cap G_2\right) = \frac{2}{9}$, then N equals ______

Accepted Answer

11

Question 10

Let the function $f : \mathbb{R} 	o \mathbb{R}$ be defined by
$f(x) = \frac{\sin x}{e^{\pi x}} \frac{\left(x^{2023} + 2024x + 2025ight)}{\left(x^2 - x + 3ight)} + \frac{2}{e^{\pi x}} \frac{\left(x^{2023} + 2024x + 2025ight)}{\left(x^2 - x + 3ight)}$.
Then the number of solutions of f(x) = 0 in $\mathbb{R}$ is ______

Accepted Answer

1

Question 11

Let $\vec{p} = 2\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{q} = \hat{i} - \hat{j} + \hat{k}$. If for some real numbers $\alpha$, $\beta$, and $\gamma$, we have
$15\hat{i} + 10\hat{j} + 6\hat{k} = \alpha\left(2\vec{p} + \vec{q}ight) + \beta\left(\vec{p} - 2\vec{q}ight) + \gamma\left(\vec{p} 	imes \vec{q}ight)$,
then the value of $\gamma$ is ______

Accepted Answer

2

Question 12

A normal with slope $\frac{1}{\sqrt{6}}$ is drawn from the point $(0, -\alpha)$ to the parabola $x^2 = -4ay$, where $a > 0$.
Let L be the line passing through $(0, -\alpha)$ and parallel to the directrix of the parabola. Suppose that L intersects the parabola at two points A and B. Let r denote the length of the latus rectum and s denote the square of the length of the line segment AB. If $r : s = 1 : 16$, then the value of $24a$ is ______

Accepted Answer

12

Question 13

Let the function $f : [1, \infty) 	o \mathbb{R}$ be defined by
$f(t) = \begin{cases} (-1)^{n+1} 2 & ; 	ext{ if } t = 2n - 1, n \in \mathbb{N} \ \frac{(2n + 1 - t)}{2} f(2n - 1) + \frac{(t - (2n - 1))}{2} f(2n + 1) & ; 	ext{ if } 2n - 1 < t < 2n + 1, n \in \mathbb{N} \end{cases}$.
Define $g(x) = \int_1^x f(t) \, dt$, $x \in (1, \infty)$. Let $\alpha$ denote the number of solutions of the equation g(x) = 0 in the interval $(1, 8]$ and $\beta = \lim_{x 	o 1^+} \frac{g(x)}{x - 1}$. Then the value of $\alpha + \beta$ is equal to ______

Accepted Answer

5

Question 14

Let $S = \{1, 2, 3, 4, 5, 6\}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties:

i. $R$ has exactly 6 elements.
ii. For each $(a, b) \in R$, we have $|a - b| \ge 2$.

Let $Y = \{R \in X : 	ext{The range of } R 	ext{ has exactly one element}\}$ and
$Z = \{R \in X : R 	ext{ is a function from } S 	ext{ to } S\}$.
Let $n(A)$ denote the number of elements in a set $A$.

If $n(X) = {}^{m}C_6$, then the value of m is ______

Accepted Answer

20.00

Question 15

Let $S = \{1, 2, 3, 4, 5, 6\}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties:

i. $R$ has exactly 6 elements.
ii. For each $(a, b) \in R$, we have $|a - b| \ge 2$.

Let $Y = \{R \in X : 	ext{The range of } R 	ext{ has exactly one element}\}$ and
$Z = \{R \in X : R 	ext{ is a function from } S 	ext{ to } S\}$.
Let $n(A)$ denote the number of elements in a set $A$.

If the value of n(Y) + n(Z) is $k^2$, then $|k|$ is ______

Accepted Answer

36.00

Question 16

Let $f : \left[0, \frac{\pi}{2}ight] 	o [0, 1]$ be the function defined by $f(x) = \sin^2 x$ and let $g : \left[0, \frac{\pi}{2}ight] 	o [0, \infty)$ be the function defined by $g = \sqrt{\frac{\pi x}{2} - x^2}$.

The value of $2\int_0^{\frac{\pi}{2}} f(x)g(x) \, dx - \int_0^{\frac{\pi}{2}} g(x) \, dx$ is ______

Accepted Answer

0.00

Question 17

Let $f : \left[0, \frac{\pi}{2}ight] 	o [0, 1]$ be the function defined by $f(x) = \sin^2 x$ and let $g : \left[0, \frac{\pi}{2}ight] 	o [0, \infty)$ be the function defined by $g = \sqrt{\frac{\pi x}{2} - x^2}$.

The value of $\frac{16}{\pi^3} \int_0^{\frac{\pi}{2}} f(x)g(x) \, dx$ is ______

Accepted Answer

0.25

Question 18

A region in the form of an equilateral triangle (in $x-y$ plane) of height L has a uniform magnetic field $\vec{B}$ pointing in the $+z$ -direction. A conducting loop PQR , in the form of an equilateral triangle of the same height L , is placed in the $x-y$ plane with its vertex P at $x = 0$ in the orientation shown in the figure. At $t = 0$ , the loop starts entering the region of the magnetic field with a uniform velocity $\vec{v}$ along the $+x$-direction. The plane of the loop and its orientation remain unchanged throughout its motion.

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 19

A particle of mass m is under the influence of the gravitational field of a body of mass $M(\gg m)$ . The particle is moving in a circular orbit of radius $r_0$ with time period $T_0$ around the mass M . Then, the particle is subjected to an additional central force, corresponding to the potential energy $V_c(r) = m\alpha/r^3$ , where α is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius $r_0$ in the combined gravitational potential due to M and $V_c(r)$ , but with a new time period $T_1$ , then ( $T_1^2 - T_0^2$ / $T_1^2$ is given by [G is the gravitational constant.]

Accepted Answer

(A) $\frac{3\alpha}{GMr_0^2}$

Answer

(B) $\frac{\alpha}{2GMr_0^2}$

Answer

(C) $\frac{\alpha}{GMr_0^2}$

Answer

(D) $\frac{2\alpha}{GMr_0^2}$

Question 20

A metal target with atomic number $Z = 46$ is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio r of the wavelengths of the $K_\alpha$ -line and the cut-off is found to be r = 2 . If the same electron beam bombards another metal target with Z = 41 , the value of r will be

Accepted Answer

(A) 2.53

Answer

(B) 1.27

Answer

(C) 2.24

Answer

(D) 1.58

Question 21

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass m and radius r and it is in a uniform vertical magnetic field $B_0$ , as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity g , on two conducting supports at P and Q . When a current I is passed through the loop, the loop turns about the line PQ by an angle θ given by

Accepted Answer

(A) tan θ $= \pi r l B_0/(mg)$

Answer

(B) tan θ $= 2\pi r l B_0/(mg)$

Answer

(C) tan θ $= \pi r l B_0/(2mg)$

Answer

(D) tan θ $= mg/(\pi r l B_0)$

Question 22

A small electric dipole $\vec{p}_0$ , having a moment of inertia I about its center, is kept at a distance r from the center of a spherical shell of radius R . The surface charge density σ is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle θ as shown in the figure. While staying at a distance r , the dipole is free to rotate about its center. If released from rest, then which of the following statement(s) is(are) correct? [ε₀ is the permittivity of free space.]

Accepted Answer

(B) The dipole will undergo small oscillations at any finite value of r > R .

Accepted Answer

(D) The dipole will undergo small oscillations with an angular frequency $\sqrt{\frac{\sigma p_0}{100\varepsilon_0 I}}$ at r = 10R .

Answer

(A) The dipole will undergo small oscillations at any finite value of r .

Answer

(C) The dipole will undergo small oscillations with an angular frequency of $\sqrt{\frac{2\sigma p_0}{\varepsilon_0 I}}$ at r = 2R .

Question 23

A table tennis ball has radius $(3/2) 	imes 10^{-2}m$ and mass $(22/7) 	imes 10^{-3}kg$ . It is slowly pushed down into a swimming pool to a depth of d = 0.7 m below the water surface and then released from rest. It emerges from the water surface at speed v , without getting wet, and rises up to a height H . Which of the following option(s) is(are) correct? [Given: π = 22/7, g = $10ms^{-2}$ , density of water = $1 	imes 10^3kgm^{-3}$ , viscosity of water = $1 	imes 10^{-3}Pa \cdot s$ .]

Accepted Answer

(A) The work done in pushing the ball to the depth d is 0.077J .

Accepted Answer

(B) If we neglect the viscous force in water, then the speed v = 7m/s .

Accepted Answer

(D) The ratio of the magnitudes of the net force excluding the viscous force to the maximum viscous force in water is 500/9.

Answer

(C) If we neglect the viscous force in water, then the height H = 1.4m .

Question 24

A positive, singly ionized atom of mass number $A_M$ is accelerated from rest by the voltage 192V . Thereafter, it enters a rectangular region of width w with magnetic field $\vec{B}_0 = 0.1\hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance x below its starting trajectory. [Given: Mass of neutron/proton = $(5/3) 	imes 10^{-27}kg$ , charge of the electron = $1.6 	imes 10^{-19}C$ .] Which of the following option(s) is(are) correct?

Accepted Answer

(A) The value of x for $H^+$ ion is 4 cm .

Accepted Answer

(B) The value of x for an ion with $A_M = 144$ is 48cm .

Answer

(C) For detecting ions with $1 \leq A_M \leq 196$ , the minimum height $(x_1 - x_0)$ of the detector is 55cm .

Answer

(D) The minimum width w of the region of the magnetic field for detecting ions with $A_M = 196$ is 56cm .

Question 25

The dimensions of a cone are measured using a scale with a least count of 2mm . The diameter of the base and the height are both measured to be 20.0cm . The maximum percentage error in the determination of the volume is -

Accepted Answer

3

Question 26

A ball is thrown from the location $(x_0, y_0) = (0, 0)$ of a horizontal playground with an initial speed $v_0$ at an angle $	heta_0$ from the +x-direction. The ball is to be hit by a stone, which is thrown at the same time from the location $(x_1, y_1) = (L, 0)$ . The stone is thrown at an angle $(180 - 	heta_1)$ from the +x -direction with a suitable initial speed. For a fixed $v_0$ , when $(	heta_0, 	heta_1) = (45^0, 45^0)$ , the stone hits the ball after time $T_1$ , and when $(	heta_0, 	heta_1) = (60^0, 30^0)$ , it hits the ball after time $T_2$ . In such a case, $(T_1/T_2)^2$ is ________________

Accepted Answer

2

Question 27

A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle θ at P, as shown in the figure. When θ = 30°, then the electric flux through the curved surface of the cylinder is Φ. If θ = 60°, then the electric flux through the curved surface becomes $\frac{\phi}{\sqrt{n}}$, where the value of n is ______

Accepted Answer

3

Question 28

Two equilateral-triangular prisms $P_1$ and $P_2$ are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism $P_1$ at an angle of incidence θ such that the outgoing ray undergoes minimum deviation in prism $P_2$. If the respective refractive indices of $P_1$ and $P_2$ are $\sqrt{\frac{3}{2}}$ and $\sqrt{3}$, then θ = $\sin^{-1}\left[\sqrt{\frac{3}{2}}\sin\left(\frac{\pi}{\beta}\right)\right]$, where the value of β is

Accepted Answer

12

Question 29

An infinitely long thin wire, having a uniform charge density per unit length of 5nC/m, is passing through a spherical shell of radius 1m, as shown in the figure. A 10nC charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points P and R, in Volt, is
[Given: In SI units $\frac{1}{4\pi\varepsilon_0}$ = 9 × $10^9$, ln 2 = 0.7. Ignore the area pierced by the wire.]

Accepted Answer

171

Question 30

A spherical soap bubble inside an air chamber at pressure $P_0$ = $10^5$ Pa has a certain radius so that the excess pressure inside the bubble is ΔP = 144Pa. Now, the chamber pressure is reduced to $8P_0/27$ so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure ΔP in both the cases to be much smaller than the chamber pressure. The new excess pressure ΔP in Pa is

Accepted Answer

96

Question 31

In a Young's double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of 0.8 mm. The distance between the slits at time $t$ is given by $d = (0.8 + 0.04 \sin \omega t)$ mm, where $\omega = 0.08$ rad s$^{-1}$. The distance of the screen from the slits is 1 m and the wavelength of the light used to illuminate the slits is 6000 Å. The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point O.

The $8^{	ext{th}}$ bright fringe above the point O oscillates with time between two extreme positions. The separation between these two extreme positions, in micrometer (μm), is

Accepted Answer

601.50

Question 32

In a Young's double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of 0.8 mm. The distance between the slits at time $t$ is given by $d = (0.8 + 0.04 \sin \omega t)$ mm, where $\omega = 0.08$ rad s$^{-1}$. The distance of the screen from the slits is 1 m and the wavelength of the light used to illuminate the slits is 6000 Å. The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point O.

The maximum speed in μm/s at which the $8^{	ext{th}}$ bright fringe will move is

Accepted Answer

24

Question 33

Two particles, 1 and 2, each of mass $m$, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_0$, are oscillating with amplitude $a$ and angular frequency $\omega$. Thus, their positions at time $t$ are given by $x_1(t) = (x_0 + d) + a \sin \omega t$ and $x_2(t) = (x_0 - d) - a \sin \omega t$, respectively, where $d > 2a$. Particle 3 of mass $m$ moves towards this system with speed $u_0 = a\omega/2$, and undergoes instantaneous elastic collision with particle 2, at time $t_0$. Finally, particles 1 and 2 acquire a center of mass speed $v_{	ext{cm}}$ and oscillate with amplitude $b$ and the same angular frequency $\omega$.

If the collision occurs at time $t_0$ = 0, the value of $v_{	ext{cm}}/(a\omega)$ will be

Accepted Answer

0.75

Question 34

Two particles, 1 and 2, each of mass $m$, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at $x_0$, are oscillating with amplitude $a$ and angular frequency $\omega$. Thus, their positions at time $t$ are given by $x_1(t) = (x_0 + d) + a \sin \omega t$ and $x_2(t) = (x_0 - d) - a \sin \omega t$, respectively, where $d > 2a$. Particle 3 of mass $m$ moves towards this system with speed $u_0 = a\omega/2$, and undergoes instantaneous elastic collision with particle 2, at time $t_0$. Finally, particles 1 and 2 acquire a center of mass speed $v_{	ext{cm}}$ and oscillate with amplitude $b$ and the same angular frequency $\omega$.

If the collision occurs at time $t_0$ = $\pi/(2\omega)$, then the value of $4b^2/a^2$ will be

Accepted Answer

4.25

Question 35

According to Bohr's model, the highest kinetic energy is associated with the electron in the

Accepted Answer

(B) first orbit of He$^{+}$

Answer

(A) first orbit of H atom

Answer

(C) second orbit of He$^{+}$

Answer

(D) second orbit of Li$^{2+}$

Question 36

In a metal deficient oxide sample, $M_xY_2O_4$ ($M$ and $Y$ are metals), $M$ is present in both +2 and +3 oxidation states and $Y$ is in +3 oxidation state. If the fraction of $M^{2+}$ ions present in $M$ is $\frac{1}{3}$, the value of $X$ is______.

Accepted Answer

(D) 0.75

Answer

(A) 0.25

Answer

(B) 0.33

Answer

(C) 0.67

Question 37

In the following reaction sequence, the major product Q is

L − Glucose $\xrightarrow[	ext{ii) } Cr_2O_3	ext{, } 775\ K	ext{, } 10-20	ext{ atm}]{	ext{i) HI, } \Delta}$ P $\xrightarrow[	ext{UV}]{Cl_2	ext{(excess)}}$ Q

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 38

The species formed on fluorination of phosphorus pentachloride in a polar organic solvent are

Accepted Answer

(B) $[PCl_4]^+[PCl_4F_2]^-$ and $[PCl_4]^+[PF_6]^-$

Answer

(A) $[PF_4]^+[PF_6]^-$ and $[PCl_4]^+[PF_6]^-$

Answer

(C) $PF_3$ and $PCl_3$

Answer

(D) $PF_5$ and $PCl_3$

Question 39

An aqueous solution of hydrazine ($N_2H_4$) is electrochemically oxidized by $O_2$, thereby releasing chemical energy in the form of electrical energy. One of the products generated from the electrochemical reaction is $N_2(g)$.
Choose the correct statement(s) about the above process
(A) $OH^-$ ions react with $N_2H_4$ at the anode to form $N_2(g)$ and water, releasing 4 electrons to the anode.
(B) At the cathode, $N_2H_4$ breaks to $N_2(g)$ and nascent hydrogen released at the electrode reacts with oxygen to form water.
(C) At the cathode, molecular oxygen gets converted to $OH^-$.
(D) Oxides of nitrogen are major by-products of the electrochemical process.

Accepted Answer

(A) $OH^-$ ions react with $N_2H_4$ at the anode to form $N_2(g)$ and water, releasing 4 electrons to the anode.

Accepted Answer

(C) At the cathode, molecular oxygen gets converted to $OH^-$.

Answer

(B) At the cathode, $N_2H_4$ breaks to $N_2(g)$ and nascent hydrogen released at the electrode reacts with oxygen to form water.

Answer

(D) Oxides of nitrogen are major by-products of the electrochemical process.

Question 40

The option(s) with correct sequence of reagents for the conversion of P to Q is(are)

Accepted Answer

(C) i) $NaBH_4$; ii) $SnCl_2$/HCl; iii) $H_3O^+$; iv) Lindlar's catalyst, $H_2$;

Accepted Answer

(D) i) Lindlar's catalyst, $H_2$; ii) $NaBH_4$; iii) $SnCl_2$/HCl; iv) $H_3O^+$

Answer

(A) i) Lindlar's catalyst, $H_2$; ii) $SnCl_2$/HCl; iii) $NaBH_4$; iv) $H_3O^+$

Answer

(B) i) Lindlar's catalyst, $H_2$; ii) $H_3O^+$; iii) $SnCl_2$/HCl; iv) $NaBH_4$

Question 41

The compound(s) having peroxide linkage is(are)

Accepted Answer

(B) $H_2S_2O_8$

Accepted Answer

(D) $H_2SO_5$

Answer

(A) $H_2S_2O_7$

Answer

(C) $H_2S_2O_5$

Question 42

To form a complete monolayer of acetic acid on 1g of charcoal, 100 mL of 0.5 M acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 mL of 1 M NaOH solution was required. If each molecule of acetic acid occupies P $	imes 10^{-23}$ m$^{2}$ surface area on charcoal, the value of P is ______.
[Use given data : Surface area of charcoal = $1.5	imes 10^{2}$ m$^{2}$ g$^{-1}$; Avogadro's number ($N_A$) = $6.0	imes 10^{23}$ mol$^{-1}$]

Accepted Answer

2500

Question 43

Vessel-1 contains $w_2$ g of a non-volatile solute X dissolved in $w_1$ g of water. Vessel-2 contains $w_2$ g of another non-volatile solute Y dissolved in $w_1$ g of water. Both the vessels are at the same temperature and pressure. The molar mass of X is 80% of that of Y. The van't Hoff factor for X is 1.2 times of that of Y for their respective concentrations.
The elevation of boiling point for solution in Vessel-1 is ________ % of the solution in Vessel-2.

Accepted Answer

150

Question 44

For a double strand DNA, one strand is given below: The amount of energy required to split the double strand DNA into two single strands is ______ kcal mol$^{-1}$. [Given: Average energy per H-bond for A-T base pair = 1.0 kcal mol$^{-1}$, G-C base pair = 1.5 kcal mol$^{-1}$, and A-U base pair = 1.25 kcal mol$^{-1}$. Ignore electrostatic repulsion between the phosphate groups.]

Accepted Answer

41

Question 45

Among $[Co(CN)_4]^{4-}$, $[Co(CO)_3(NO)]$, $XeF_4$, $[PCl_4]^{+}$, $[PdCl_4]^{2-}$, $[ICl_4]^{-}$, $[Cu(CN)_4]^{3-}$ and $P_4$ the total number of species with tetrahedral geometry is ______.

Accepted Answer

5

Question 46

An organic compound **P** having molecular formula $C_6H_6O_3$ gives ferric chloride test and does not have intramolecular hydrogen bond. The compound **P** reacts with 3 equivalents of $NH_2OH$ to produce oxime **Q**. Treatment of **P** with excess methyl iodide in the presence of KOH produces compound **R** as the major product. Reaction of **R** with excess *iso*-butylmagnesium bromide followed by treatment with $H_3O^{+}$ gives compound **S** as the major product. The total number of methyl ($-CH_3$) group(s) in compound **S** is _____.

Accepted Answer

12

Question 47

An organic compound **P** with molecular formula $C_9H_{18}O_2$ decolorizes bromine water and also shows positive iodoform test. **P** on ozonolysis followed by treatment with $H_2O_2$ gives **Q** and **R**. While compound **Q** shows positive iodoform test, compound **R** does not give positive iodoform test. **Q** and **R** on oxidation with pyridinium chlorochromate (PCC) followed by heating give **S** and **T**, respectively. Both **S** and **T** show positive iodoform test.
Complete copolymerization of 500 moles of **Q** and 500 moles of **R** gives one mole of a single acyclic copolymer **U**.
[Given, atomic mass: H = 1, C = 12, O = 16]

The molecular weight of **U** is ______.

Accepted Answer

93018

Question 48

When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex **P** is formed. In a strong acidic medium, the equilibrium shifts completely towards **P**. Addition of zinc chloride to **P** in a slightly acidic medium results in a sparingly soluble complex **Q**.

The number of moles of potassium iodide required to produce two moles of **P** is ______.

Accepted Answer

2

JEE Advanced 2024 Paper 2 Question Paper with Answers

Physics — JEE Advanced 2024 Paper 2

Chemistry — JEE Advanced 2024 Paper 2

Mathematics — JEE Advanced 2024 Paper 2

Chapters tested in this paper

Attempt JEE Advanced 2024 Paper 2 under exam timing.