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phy | JEE Adv 2023 Paper 2 | A | 19 | MCQ | Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$, Planck's constant $h$ and the speed of light $c$, as $Y=c^{\alpha} h^{\beta} G^{\gamma}$. Which of the following is the correct option?
(A) $\alpha=7, \beta=-1, \gamma=-2$
(B) $\alpha=-7, \beta=-1, \gamma=-2$
(C) $\alpha=7, \beta=-1, \gamma=2$
(D) $\alpha=-7, \beta=1, \gamma=-2$ |
phy | JEE Adv 2023 Paper 2 | A | 20 | MCQ | A particle of mass $m$ is moving in the $x y$-plane such that its velocity at a point $(x, y)$ is given as $\overrightarrow{\mathrm{v}}=\alpha(y \hat{x}+2 x \hat{y})$, where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?
(A) $\vec{F}=2 m \alpha^{2}(x \hat{x}+y \hat{y})$
(B) $\vec{F}=m \alpha^{2}(y \hat{x}+2 x \hat{y})$
(C) $\vec{F}=2 m \alpha^{2}(y \hat{x}+x \hat{y})$
(D) $\vec{F}=m \alpha^{2}(x \hat{x}+2 y \hat{y})$ |
phy | JEE Adv 2023 Paper 2 | C | 21 | MCQ | An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$. The internal energy of one mole of the gas is $U_{n}$ and the speed of sound in the gas is $\mathrm{v}_{n}$. At a fixed temperature and pressure, which of the following is the correct option?
(A) $v_{3}<v_{6}$ and $U_{3}>U_{6}$
(B) $v_{5}>v_{3}$ and $U_{3}>U_{5}$
(C) $v_{5}>v_{7}$ and $U_{5}<U_{7}$
(D) $v_{6}<v_{7}$ and $U_{6}<U_{7}$ |
phy | JEE Adv 2023 Paper 2 | AD | 24 | MCQ(multiple) | The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec{E}=30(2 \hat{x}+\hat{y}) \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^{7}}{3} z\right)\right] \mathrm{Vm}^{-1}$. Which of the following option(s) is(are) correct?
[Given: The speed of light in vacuum, $c=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$ ]
(A) $B_{x}=-2 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^{7}}{3} z\right)\right] \mathrm{Wb} \mathrm{m}^{-2}$.
(B) $B_{y}=2 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^{7}}{3} z\right)\right] \mathrm{Wb} \mathrm{m}^{-2}$.
(C) The wave is polarized in the $x y$-plane with polarization
angle $30^{\circ}$ with respect to the $x$-axis.
(D) The refractive index of the medium is 2 . |
phy | JEE Adv 2023 Paper 2 | 5 | 27 | Integer | A string of length $1 \mathrm{~m}$ and mass $2 \times 10^{-5} \mathrm{~kg}$ is under tension $T$. When the string vibrates, two successive harmonics are found to occur at frequencies $750 \mathrm{~Hz}$ and $1000 \mathrm{~Hz}$. What is the value of tension $T$ in Newton? |
phy | JEE Adv 2023 Paper 2 | 16 | 29 | Integer | In a radioactive decay process, the activity is defined as $A=-\frac{d N}{d t}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources, $S_{1}$ and $S_{2}$ have same activity at time $t=0$. At a later time, the activities of $S_{1}$ and $S_{2}$ are $A_{1}$ and $A_{2}$, respectively. When $S_{1}$ and $S_{2}$ have just completed their $3^{\text {rd }}$ and $7^{\text {th }}$ half-lives, respectively, what is the ratio $A_{1} / A_{2}$? |
chem | JEE Adv 2023 Paper 2 | A | 36 | MCQ | Consider the following statements related to colloids.
(I) Lyophobic colloids are not formed by simple mixing of dispersed phase and dispersion medium.
(II) For emulsions, both the dispersed phase and the dispersion medium are liquid.
(III) Micelles are produced by dissolving a surfactant in any solvent at any temperature.
(IV) Tyndall effect can be observed from a colloidal solution with dispersed phase having the same refractive index as that of the dispersion medium.
The option with the correct set of statements is
(A) (I) and (II)
(B) (II) and (III)
(C) (III) and (IV)
(D) (II) and (IV) |
chem | JEE Adv 2023 Paper 2 | CD | 39 | MCQ(multiple) | The complex(es), which can exhibit the type of isomerism shown by [ $\left.\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Br}_{2}\right]$, is(are) [en $=\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}$ ]
(A) $\left[\operatorname{Pt}(\mathrm{en})(\mathrm{SCN})_{2}\right]$
(B) $\left[\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]$
(C) $\left[\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{4}\right]$
(D) $\left[\mathrm{Cr}(\mathrm{en})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)\left(\mathrm{SO}_{4}\right)\right]^{+}$ |
chem | JEE Adv 2023 Paper 2 | ABD | 40 | MCQ(multiple) | Atoms of metals $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$ form face-centred cubic (fcc) unit cell of edge length $\mathrm{L}_{\mathrm{x}}$, body-centred cubic (bcc) unit cell of edge length $\mathrm{L}_{\mathrm{y}}$, and simple cubic unit cell of edge length $\mathrm{L}_{\mathrm{z}}$, respectively.
If $\mathrm{r}_{\mathrm{z}}=\frac{\sqrt{3}}{2} \mathrm{r}_{\mathrm{y}} ; \mathrm{r}_{\mathrm{y}}=\frac{8}{\sqrt{3}} \mathrm{r}_{\mathrm{x}} ; \mathrm{M}_{\mathrm{z}}=\frac{3}{2} \mathrm{M}_{\mathrm{y}}$ and $\mathrm{M}_{\mathrm{Z}}=3 \mathrm{M}_{\mathrm{x}}$, then the correct statement(s) is(are)
[Given: $M_{x}, M_{y}$, and $M_{z}$ are molar masses of metals $x, y$, and $z$, respectively.
$r_{x}, r_{y}$, and $r_{z}$ are atomic radii of metals $x, y$, and $z$, respectively.]
(A) Packing efficiency of unit cell of $x>$ Packing efficiency of unit cell of $y>$ Packing efficiency of unit cell of $z$
(B) $\mathrm{L}_{\mathrm{y}}>\mathrm{L}_{\mathrm{z}}$
(C) $\mathrm{L}_{\mathrm{x}}>\mathrm{L}_{\mathrm{y}}$
(D) Density of $x>$ Density of $y$ |
chem | JEE Adv 2023 Paper 2 | 18 | 42 | Integer | $\quad \mathrm{H}_{2} \mathrm{~S}$ (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this reaction, the number of moles of water produced is $\mathbf{x}$, and the number of moles of electrons involved is $\mathbf{y}$. The value of $(\mathbf{x}+\mathbf{y})$ is |
chem | JEE Adv 2023 Paper 2 | 5 | 43 | Integer | Among $\left[\mathrm{I}_{3}\right]^{+},\left[\mathrm{SiO}_{4}\right]^{4-}, \mathrm{SO}_{2} \mathrm{Cl}_{2}, \mathrm{XeF}_{2}, \mathrm{SF}_{4}, \mathrm{ClF}_{3}, \mathrm{Ni}(\mathrm{CO})_{4}, \mathrm{XeO}_{2} \mathrm{~F}_{2},\left[\mathrm{PtCl}_{4}\right]^{2-}, \mathrm{XeF}_{4}$, and $\mathrm{SOCl}_{2}$, what is the total number of species having $s p^{3}$ hybridised central atom? |
chem | JEE Adv 2023 Paper 2 | 6 | 44 | Integer | Consider the following molecules: $\mathrm{Br}_{3} \mathrm{O}_{8}, \mathrm{~F}_{2} \mathrm{O}, \mathrm{H}_{2} \mathrm{~S}_{4} \mathrm{O}_{6}, \mathrm{H}_{2} \mathrm{~S}_{5} \mathrm{O}_{6}$, and $\mathrm{C}_{3} \mathrm{O}_{2}$.
Count the number of atoms existing in their zero oxidation state in each molecule. What is their sum? |
chem | JEE Adv 2023 Paper 2 | 682 | 46 | Integer | $50 \mathrm{~mL}$ of 0.2 molal urea solution (density $=1.012 \mathrm{~g} \mathrm{~mL}^{-1}$ at $300 \mathrm{~K}$ ) is mixed with $250 \mathrm{~mL}$ of a solution containing $0.06 \mathrm{~g}$ of urea. Both the solutions were prepared in the same solvent. What is the osmotic pressure (in Torr) of the resulting solution at $300 \mathrm{~K}$?
[Use: Molar mass of urea $=60 \mathrm{~g} \mathrm{~mol}^{-1}$; gas constant, $\mathrm{R}=62$ L Torr K${ }^{-1} \mathrm{~mol}^{-1}$;
Assume, $\Delta_{\text {mix }} \mathrm{H}=0, \Delta_{\text {mix }} \mathrm{V}=0$ ] |
chem | JEE Adv 2023 Paper 2 | 9 | 50 | Numeric | A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of $\mathrm{Sn} / \mathrm{HCl}$ gives a major product, which on treatment with an excess of $\mathrm{NaNO}_{2} / \mathrm{HCl}$ at $0{ }^{\circ} \mathrm{C}$ provides $\mathbf{P}$ as the product. $\mathbf{P}$, upon treatment with excess of $\mathrm{H}_{2} \mathrm{O}$ at room temperature, gives the product $\mathbf{Q}$. Bromination of $\mathbf{Q}$ in aqueous medium furnishes the product $\mathbf{R}$. The compound $\mathbf{P}$ upon treatment with an excess of phenol under basic conditions gives the product $\mathbf{S}$.
The molar mass difference between compounds $\mathbf{Q}$ and $\mathbf{R}$ is $474 \mathrm{~g} \mathrm{~mol}^{-1}$ and between compounds $\mathbf{P}$ and $\mathbf{S}$ is $172.5 \mathrm{~g} \mathrm{~mol}^{-1}$. What is the number of heteroatoms present in one molecule of $\mathbf{R}$?
[Use: Molar mass (in g mol${ }^{-1}$ ): $\mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{Br}=80, \mathrm{Cl}=35.5$
Atoms other than $\mathrm{C}$ and $\mathrm{H}$ are considered as heteroatoms] |
chem | JEE Adv 2023 Paper 2 | 51 | 51 | Numeric | A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of $\mathrm{Sn} / \mathrm{HCl}$ gives a major product, which on treatment with an excess of $\mathrm{NaNO}_{2} / \mathrm{HCl}$ at $0{ }^{\circ} \mathrm{C}$ provides $\mathbf{P}$ as the product. $\mathbf{P}$, upon treatment with excess of $\mathrm{H}_{2} \mathrm{O}$ at room temperature, gives the product $\mathbf{Q}$. Bromination of $\mathbf{Q}$ in aqueous medium furnishes the product $\mathbf{R}$. The compound $\mathbf{P}$ upon treatment with an excess of phenol under basic conditions gives the product $\mathbf{S}$.
The molar mass difference between compounds $\mathbf{Q}$ and $\mathbf{R}$ is $474 \mathrm{~g} \mathrm{~mol}^{-1}$ and between compounds $\mathbf{P}$ and $\mathbf{S}$ is $172.5 \mathrm{~g} \mathrm{~mol}^{-1}$. What is the total number of carbon atoms and heteroatoms present in one molecule of $\mathbf{S}$?
[Use: Molar mass (in $\mathrm{g} \mathrm{mol}^{-1}$ ): $\mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{Br}=80, \mathrm{Cl}=35.5$
Atoms other than $\mathrm{C}$ and $\mathrm{H}$ are considered as heteroatoms] |