Chemistry: The Solid State

Q. Teacher explained the stoichiometric defects in a class room. 

 a) Explain with the help of diagrams the important differences in Schottky and Frenkel defects.

 b) What are the consequences?

Q.  a) Write an equation for the calculation of density of a crystal from its structure?

b) Calculate the density of PbS crystal (fcc)  if the edge length of its unit cell is 500pm. (NA = 6.022 x 1023, atomic mass of Pb = 207.2, S = 32) 

Q.  Defects are found even in crystals prepared very carefully.
     a) Which stoichiometric defect causes decrease in density of the solid?
     b) Frenkel defect is not found in NaCl. Why?
     c) KCl crystal is colourless.But on heating it in an atmosphere of potassium vapour, it becomes
 violet in colour.Account for this.

Q.  In magnesium crystal, the layers of atoms are being stacked in a pattern AB AB AB …… type of arrangement.
    a) Name the close packed structure.
    b) Calculate the number of tetrahedral and octahedral voids, if the Mg crystal contains ‘n’ atoms.


 Q. a) Schottky and Frenkel defects are two stoichiometric defects shown by crystals.
      i) Classify the crystals into those showing Schottky defects and Frenkel defects: NaCl, AgCl,CsCl,CdCl2
      ii) Name a crystal showing both Schottky defect and Frenkel defect.
      b) Schematic alignment of magnetic moments of ferromagnetic, antiferromagnetic and ferrimagnetic substances are given below. Identify each of them

 

Mathematics: Matrices

Q. If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

Q. If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Mathematics: Inverse Trigonometric Functions

Q. Find the principal value of cosec−¹ (2)

Q. Find the principal value of tan-¹ (- √3 )

Q. Find the principal value of tan−¹ (−1)

Mathematics: Relations and Functions

Q. Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive.

Q. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.

Q. Check whether the relation R in R defined as R = {(a, b): a ≤ b³} is reflexive, symmetric or transitive.

Q. Show that the relation R in the set A of points in a plane given by R = {(P, Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all point related to a point P ≠ (0, 0) is the circle passing through P with origin as centre.

Q. Given an example of a relation. Which is

• Symmetric but neither reflexive nor transitive.
• Transitive but neither reflexive nor symmetric.
• Reflexive and symmetric but not transitive.
• Reflexive and transitive but not symmetric.
• Symmetric and transitive but not reflexive.

Q. Show that the relation R in the set A of points in a plane given by R = {(P, Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all point related to a point P ≠ (0, 0) is the circle passing through P with origin as centre.

Q. Show that the relation R defined in the set A of all triangles as R = {(T1, T2): T1 is similar to T2}, is equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, 10. Which triangles among T1, T2 and T3 are related?

Q. Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?

Q. Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2): L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

Q. Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Q. Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation.