Question 1: Palette 1/15

JEE Advanced 2024 MCQ

In a metal deficient oxide sample, $\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4$ ( $\mathbf{M}$ and $\mathbf{Y}$ are metals), $\mathbf{M}$ is present in both +2 and +3 oxidation states and $\mathbf{Y}$ is in +3 oxidation state. If the fraction of $\mathbf{M}^{2+}$ ions present in $\mathbf{M}$ is $\frac{1}{3}$, the value of $\mathbf{X}$ is _______ .

A

0.25

B

0.33

C

0.67

D

0.75

Question 2: Palette 2/15

JEE Advanced 2023 MSQ

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 $\mathrm{L}_y$, and simple cubic unit cell of edge length $\mathrm{L}_z$, respectively.

If $\mathrm{r}_{\mathrm{z}}=\frac{\sqrt{3}}{2} r_{\mathrm{y}} ; \mathrm{r}_{\mathrm{y}}=\frac{8}{\sqrt{3}} \mathrm{r}_{\mathrm{x}} ; M_{\mathrm{z}}=\frac{3}{2} M_{\mathrm{y}}$ and $M_{\mathrm{z}}=3 M_{\mathrm{x}}$, 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.
$\mathrm{r}_{\mathrm{x}}, \mathrm{r}_{\mathrm{y}}$, and $\mathrm{r}_{\mathrm{z}}$ are atomic radii of metals $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$, 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 $y$

Question 3: Palette 3/15

JEE Advanced 2022 MCQ

Atom $\mathrm{X}$ occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to

A

25

B

35

C

55

D

75

Question 4: Palette 4/15

JEE Advanced 2021 MCQ

For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction = ${{packing\,efficiency} \over {100}}$)

A

0.74

B

0.63

C

0.52

D

0.48

Question 5: Palette 5/15

JEE Advanced 2020 MSQ

The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

A

The empirical formula of the compound is MX.

B

The cation M and anion X have different coordination geometries.

C

The ratio of M$-$X bond length of the cubic unit cell edge length is 0.866.

D

The ratio of the ionic radii of cation M to anion X is 0.414.

Question 6: Palette 6/15

JEE Advanced 2016 MSQ

The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is (are) :

A

The number of the nearest neighbours of an atom present in the topmost layer is 12

B

The efficiency of an atom packing is 74%

C

The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively

D

The unit cell edge length is $2 \sqrt 2$ times the radius of the atom

Question 7: Palette 7/15

JEE Advanced 2015 MCQ

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are

A

1/2, 1/8

B

1, 1/4

C

1/2, 1/2

D

1/4, 1/8

Question 8: Palette 8/15

JEE Advanced 2013 MCQ

The arrangement of X^$-$ ions around A⁺ ion in solid AX is given in the figure (not drawn to scale). If the radius of X^$-$ is 250 pm, the radius of A⁺ is

A

104 pm

B

125 pm

C

183 pm

D

57 pm

Question 9: Palette 9/15

JEE Advanced 2012 MCQ

A compound M_pX_q has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical formula of the compound is

A

MX

B

MX₂

C

M₂X

D

M₅X₁₄

Question 10: Palette 10/15

JEE Advanced 2010 MCQ

The packing efficiency of the twodimensional square unit cell shown below is

A

$39.27 \%$

B

$68.02 \%$

C

$74.05 \%$

D

$78.54 \%$

Question 11: Palette 11/15

JEE Advanced 2009 MSQ

The correct statement(s) regarding defects in solids is (are)

A

Frenkel defect is usually favoured by a very small difference in the sizes of cation and anion.

B

Frenkel defect is a dislocation defect.

C

Trapping of an electron in the lattice leads to the formation of F-centre.

D

Schottky defects have no effect on the physical properties of solids.

Question 12: Palette 12/15

JEE Advanced 2008 MCQ

The number of atoms in this HCP unit cell is :

A

4

B

6

C

12

D

17

Question 13: Palette 13/15

JEE Advanced 2008 MCQ

The volume of this HCP unit cell is :

A

$24\sqrt 2 \,{r^3}$

B

$16\sqrt 2 \,{r^3}$

C

$12\sqrt 2 \,{r^3}$

D

${{64} \over {3\sqrt 3 }}\,{r^3}$

Question 14: Palette 14/15

JEE Advanced 2008 MCQ

The empty space in this HCP unit cell is :

A

74%

B

47.6%

C

32%

D

26%

Question 15: Palette 15/15

JEE Advanced 2007 MCQ

Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $\times$ 4 matrix given in the ORS.

	Column I		Column II
(A)	Simple cubic and face-centred cubic	(P)	have these cell parameters $a=b=c$ and $\alpha=\beta=\gamma$
(B)	cubic and rhombohedral	(Q)	are two crystal systems
(C)	cubic and tetragonal	(R)	have only two crystallographic of 90$^\circ$
(D)	hexagonal and monoclinic	(S)	belong to same crystal system

A

$\mathrm{A-(s);B-(q);C-(q);(d)-(q,r)}$

B

$\mathrm{A-(p,s);B-(p);C-(q);(d)-(r)}$

C

$\mathrm{A-(p,s);B-(p,q);C-(q);(d)-(q,r)}$

D

$\mathrm{A-(s);B-(q);C-(q);(d)-(q)}$