Loyola College M.Sc. Mathematics Nov 2006 Topology Question Paper PDF Download

November 15, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. DEGREE EXAMINATION – MATHEMATICS

AA 23

THIRD SEMESTER – NOV 2006

MT 3803 – TOPOLOGY

(Also equivalent to MT 3800)

Date & Time : 25-10-2006/9.00-12.00 Dept. No. Max. : 100 Marks

Answer all the questions.

01.(a)(i) Let X be a metric space with metric d. Show that d₁. defined by

d₁(x,y) =

is also a metric on X.

(OR)

(ii) Let X and Y be metric spaces and f be a mapping of X into Y.

Show that f ^–¹(G) is open in X whenever G is open in Y.

(b)(i) Let X be a metric space. Prove that any arbitrary union of open sets in X is
open and any finite intersection of open sets in X is open.

(ii) Give an example to show that any arbitrary intersection of open sets in X
need not be open.

(iii) In any metric space X, prove that each closed sphere is a closed set.(6+4+5)

(OR)

(iv) If a convergent sequence in a metric space has infinitely many distinct
points, prove that its limit is a limit point of the set of points of the
sequence.

(v) State and prove Cantor’s Intersection Theorem.

(vi) If {A_n} is a sequence of nowhere dense sets in a complete metric space X,
show that there exists a point in X which is not in any of the A_n’s. (4+6+5)

02.(a) (i) Prove that every separable metric space is second countable.

(OR)

(ii) Let X be a non–empty set, and let there be give a “closure” operation
which assigns to each subset A of X a subset of X in such a manner
that (1) = , (2) A Í , (3) , and (4) =.

If a “closed” set A is defined to be one for which A = , show that the
class of all complements of such sets is a topology on X whole closure
operation is precisely that initially given.

(i) Show that any closed subspace of a compact space is compact.

(ii) Give an example to show that a proper subspace of a compact space need
not be closed.

(iii) Prove that any continuous image of a compact space is compact. (5+4+6)

(OR)

(iv) Let C(X đ) be the set of all bounded continuous real functions defined
on a topological space X. Show that (1) C (X đ) is a real Banach space
with respect to pointwise addition and multiplication and the norm
defined by = sup; (2) If multiplication is defined pointwise
C(X, R) is a commutative real algebra with identity in which
£ and = 1.

03.(a) (i) State and prove Tychonoff’s Theorem.

(OR)

(ii) Show that a metric space is compact Û it is complete and totally
bounded.

(b) (i) Prove that in a sequentially compact space, every open cover has a
Lesbesgue number.

(ii) Show that every sequentially compact metric space is totally bounded.(9+6)

(OR)

(iii) State and prove Ascoli’s Theorem.

04.(a)(i) Show that every subspace of Hausdorff is also a Hausdorff.

(OR)

(ii) Prove that every compact Haurdolff space is normal.

(b)(i) Let X be a T₁ – space.

Show that X is a normal Û each neighbourhood of a closed set F contains
the closure of some neighbourhood of F.

(ii) State and prove Uryjohn’s Lemma. (6+9)

(OR)

(iii) If X is a second countable normal space, show that there exists a
homeomorphism f of X onto a subspace of R^¥_.

05.(a)(i) Prove that any continuous image of a connected space is connected.

(OR)

(ii) Show that the components of a totally disconnected space are its points.

(b)(i) Let X be a topological space and A be a connected subspace of X. If B is a
subspace of X such that A Í B Í , show that B is connected.

(ii) If X is an arbitrary topological space, then prove the following:

(1) each point in X is contained in exactly one component of X;

each connected subspace of X is contained in a component of X;
a connected subspace of X which is both open and closed is a component of X. (6+9)

(OR)

(iii) State and prove the Weierstrass Approximation Theorem.

Go To Main page

Loyola College M.Sc. Mathematics Nov 2006 Ordinary Differential Equations Question Paper PDF Download

November 15, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. DEGREE EXAMINATION – MATHEMATICS

AA 20

FIRST SEMESTER – NOV 2006

MT 1806 – ORDINARY DIFFERENTIAL EQUATIONS

Date & Time : 31-10-2006/1.00-4.00 Dept. No. Max. : 100 Marks

ANSWER ALL QUESTIONS

(a) If the Wronskian of 2 functions x₁(t) and x₂(t) on I is non-zero for at

least one point of the interval I, show that x₁(t) and x₂(t) are linearly

independent on I.

Consider the Differential Equation x” + λ² x = 0, prove that

A cos λx + B sin λx is also a solution of the Differential equation.

(5 Marks)

(b) State and prove the method of variation of parameters.

By the method of variation of parameters solve x”’ − x’ = t. (15 Marks)

(a) Obtain the indicial form of the equation

2x² (d²y/dx²) + (dy/dx) + y = 0

Obtain the indicial form of the Bessel’s differential equation. (5 Marks)

(b) Solve the differential equation using Frobenius Method ,

x² (d²y/dx²)+ x q(x) (dy/dx) + r(x) y = 0 and discuss about their

solutions when it’s roots differ by an integer .

Solve the Legendre’s equation,

(1 – x²) (d²y/dx²)– 2x (dy/dx) + L(L+1)y = 0. (15 Marks)

III. (a) Prove that ∫⁺¹_-1 P_n(x) dx = 2 if n = 0 and

∫⁺¹_-1 P_n(x) dx = 0 if n ≥ 1

Show that Hypergeometric function does not change if the parameter α and

β are interchanged, keeping γ fixed. (5 Marks)

(b) Obtain Rodrigue’s Formula and hence find P₀(x), P₁(x), P₂(x) & P₃(x).

Show that P_n(x) = ₂F₁[-n, n+1; 1; (1-x)/2] (15 Marks)

IV.(a) Considering an Initial Value Problem x’ = -x, x(0) = 1, t ≥ 0, find x_n(t).

Find the eigen value and eigen function of x” + λ x = 0, 0 < t ≤  (5 Marks)

(b) State and prove Picard’s Boundary Value Problem.

State Green’s Function. Show that x(t) is a solution of L(x) + f(t) = 0 if and

only if x(t) = ∫^b_a G(t,s) f(s) ds. (15 Marks)

V.(a) Discuss the fundamental Theorem on the stability of the equilibrium of

the system x’ = f(t, x).

Obtain the condition for the null solution of the system x’ = A(t) x is

asymptotically stable. (5 Marks)

(b) Study the stability of a linear system by Lyapunov’s direct method.

Study the stability of a non-linear system by Lyapunov’s direct method.

(15 Marks)

Go To Main Page

Loyola College M.Sc. Mathematics Nov 2006 Mathematical Methods In Biology Question Paper PDF Download

November 15, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – MATHEMATICS

AA 27

THIRD SEMESTER – NOV 2006

MT 3875 – MATHEMATICAL METHODS IN BIOLOGY

Date & Time : 06-11-2006/9.00-12.00 Dept. No. Max. : 100 Marks

I a) Draw the state diagram for M = { (q_0,q_1,q_2,q₃), {0,1}, δ,q₀,{q₀} }

q₀

q₁

q₂

q₃

q₀,q₁

q₃

_{_}

q₃

q_0, q₂

_{_}

q₃

(or)

b) Why do we need to install a program from web ? (5)

c) How do you generate Data base? Explain with an example .

(or)

d) Comment on ‘ Internet is a powerful tool for bio informatics ’. (15)

II a) Expand HTTP and explain Motif.

(or)

b) Define Edit graph and explain it for ANN and CAN. (5)

c) Write notes on recurrence relation and about the correctness

of general relation

(or)

d) Briefly describe on dynamic programming. (15)

III a) Explain briefly on calculations of edit distance using tabulation method .

(or)

b) Construct a deterministic finite automata accepting words over {0,1}

ending with ‘111’. (5)

c) When both i and j are strictly positive, prove that

D(i,j) = min [D(i-1,j)+1, D(i,j-1)+1, D(i-1,j-1)+t(i,j)]

(or)

d). What skills does a bioinformatician should have ? (15)

IV What do you mean by sequence alignment data ?

(or)

Define Global alignment problem . (5)

c) Describe the salient features of Human Genome project.

(or)

d) Bio informatics is just a collection of Building Data bases- Explain. (15)

V a) What type of questions does the bio informatics to be answered in the field of

biomaths ?

(or)

b) Define string alignment with an example. (5)

c) What does informatics mean to biologists ?

(or)

d) Explain about the sequence matching of aniridia a human gene and

eyeless a fruit fly gene.

(15)

Go To Main Page

Loyola College M.Sc. Mathematics Nov 2006 Real Analysis Question Paper PDF Download

November 15, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. DEGREE EXAMINATION – MATHEMATICS

AA 19

FIRST SEMESTER – NOV 2006

MT 1805 – REAL ANALYSIS

Date & Time : 28-10-2006/1.00-4.00 Dept. No. Max. : 100 Marks

a)(1) When does the Riemann-Stieltjes integral reduce to Riemann integral. Explain with usual notations.

(2) If a < s < b, f ÎÂ (a) on [a,b] and a (x) = I (x – s), the unit step function, then prove that = f (s). (5)

b)(1) Let f be a bounded function on [a,b] having finitely many points of discontinuity on [a,b]. Let a be continuous at every point at which f is discontinuous. Prove that f ÎÂ(a). (8)

(2) Suppose f is strictly increasing continuous function that maps an interval [A.B] onto [a,b]. Suppose a is monotonically increasing on [a,b] and f ÎÂ (a) on [a,b]. Define b and g on [A,B] by b (y) = a (f (y)), g (y) = f (f (y)). Then prove that g ÎÂ (b) and . (7)

(3) Let a be monotonically increasing function on [a,b] and let a¢ Î R on [a,b]. If f is a bounded real function on [a,b] then prove that f ÎÂ (a) on [a,b] Û f a¢ ÎÂ (a) on [a,b].(8)

(4) Let f ÎÂ (a) on [a,b]. For a £ x £ b, define F(x) = , then prove that F is continuous on [a,b]. Also, if f is continuous at some x_o Î (a,b) then prove that F is differentiable at x_oand F¢ ( x_o ) = f (x_o). (7)

a) Let : [a,b] ® R ^m and let x Î (a,b). If the derivatives of exist at x then prove that it is unique.

(2) Suppose that maps a convex open set E Í Rⁿ into R^m, is differentiable on E and there exists a constant M such that M, ” x Î E, then prove that

ú (b) – (a)ú £ M ú b – aú , ” a, b Î E. (5)

b) (1) Suppose E is an open set in R ⁿ; maps R into R ^m; is differentiable at x_o Î E, maps an open set containing (E) into R ^k and is differentiable at f (x_o). Then the mapping of E into R ^k, defined by is differentiable at x_o and . (8)

(2) Suppose maps an open set EÍ Â ⁿ into Â ^m. Let be differentiable at x Î E, then prove that the partial derivatives (D_jf _i) (x) exist and , 1£ j £ m, where {e ₁, e_2,e_3,…, e _n} and {u ₁, u _2,u _3,…, u _m} are standard bases of R ⁿ and R ^m. (7)

(3) If X is a complete metric space and if f is a contraction of X into X, then prove that there exists one and only one x ÎX such that f (x) = x. (15)

III. a) (1) Prove: where {f _n} converges uniformly to a function f on E and x is a limit point of a metric space E.

(2) Suppose that {f _n} is a sequence of functions defined on E and suppose that ½f _n(x)½£ M _n, x ÎE, n = 1,2,… Then prove that converges uniformly on E if converges. (5)

b) (1) Suppose that K is a compact set and

* {f _n} is a sequence of continuous functions on K

** {f _n} converges point wise to a continuous function f on K

*** f _n(x) ³ f _n+1(x), ” n ÎK, n= 1,2,… then prove that f _n ® f uniformly on K. (7)

(2) State and prove Cauchy criterion for uniform convergence of complex functions defined on some set E. (8)

(3) State and prove Stone-Weierstrass theorem. (15)

IV a) (1)Show that converges if and only if n >0.

(2) Prove that G = . (5)

b)(1) Derive the relation between Beta and Gamma functions. (7)

(2) State and prove Stirling’s formula. (8)

3) If f is a positive function on (0,¥) such that f (x+1) = x f (x); f (1) =1 and log f is convex then prove that f (x) = G (x). (8)

(4) If x >0 and y >0 then (7)

a) (1)If f (x) has m continuous derivatives and no point occurs in the sequence x ₀, x ₁, ..,x _n more than (m+1) times then prove that there exists exactly one polynomial P_n (x) of degree £ n which agrees with f (x) at x ₀, x ₁, …, x _n.

2) Show that the error estimation for sine or cosine function f in linear interpolation is given by the formula ½f(x)-P(x)½£ . (5)

b)(1) Let x₀, x₁, …, x_n be n+1 distinct points in the domain of a function f and let P be the interpolation polynomial of degree £ n, that agrees with f at these points. Choose a point x in the domain of f and let [a,b] be any closed interval containing the points x ₀, x ₁, …, x _n and x. If f has a derivative of order n+1 in the interval [a,b], then prove that there is at least one point c in the open interval (a,b) such that where A (x) = (x – x₀) (x – x₁)…(x – x _n). (7)

(2) Let P _n+1 (x)= x ⁿ⁺¹ +Q(x) where Q is a polynomial of degree £ n and let maximum of ½P _n+1 (x)½, -1 £ x £ 1. Then prove that we get the inequality . Moreover , prove that if and only if , where T _n+1 is the Chebyshev polynomial of degree n+1. (8)

3) Let f be a continuous function on [a,b] and assume that T is a polynomial of degree £ n that best approximates f on [a,b] relative to the maximum norm. Let R(x) = f (x) –T(x) denote the error in the approximation and let D = . Then prove that

(i) If D= 0 the function R is identically zero on [a,b].

(ii) If D >0, the function R has at least (n+1) changes of sign on [a,b]. (15).

Go To Main Page

Loyola College M.Sc. Mathematics Nov 2006 Fluid Dynamics Question Paper PDF Download

November 15, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. DEGREE EXAMINATION – MATHEMATICS

AA 29

THIRD SEMESTER – NOV 2006

MT 3953 – FLUID DYNAMICS

Date & Time : 01-11-2006/9.00-12.00 Dept. No. Max. : 100 Marks

Answer ALL Questions.

I a) (i) Derive the equation of continuity in the form

[OR]

(ii)State and prove Euler’s equation of motion. (8)

b) (i) The velocity of an incompressible fluid is given by .

Prove that the liquid motion possible and that the velocity potential is .

Also find the stream lines.

[OR]

(ii)State and prove Holemn Hortz vorticity theorem (17)

II a) (i)Show that the two dimensional flow described by the equation

is irrotational. Find the stream lines and equaipotentials.

[OR]

(ii)State and prove Milne Thomson circle theorem. (8)

b) (i) In a two dimensional fluid motion the stream lines are

given by .Then show that where A and B are constants. Also find the velocity.

[OR]

(ii) State and prove Blasius theorem. (17)

P.T.O.

III a)(i)Write a note on Joukowskis transformation.

[OR]

(ii) State and prove Kutta and Joukowskis theorem. (8)

b)(i) Discuss the geometrical construction of an aerofoil.

[OR]

(ii) Discuss the liquid motion past a sphere. (17)

IV a) (i) Find the exact solution of a liquid past a pipe of elliptical cross section.

[OR]

(ii) Discuss the flow between two parallel plates. (8)

b) (i) Prove that .

[OR} (ii) Derive the Navier-Stokes equation of motion for viscous fluid. (17)

Go To Main Page

Loyola College M.Sc. Mathematics Nov 2006 Linear Algebra Question Paper PDF Download

November 15, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. DEGREE EXAMINATION – MATHEMATICS

AA 18

FIRST SEMESTER – NOV 2006

MT 1804 – LINEAR ALGEBRA

Date & Time : 26-10-2006/1.00-4.00 Dept. No. Max. : 100 Marks

Answer ALL Questions.

I ) a) Let T be a linear operator on an n-dimensional vector space V. Then prove that the characteristic and the minimal polynomials for T have the same roots, except for multiplicities.

[OR]

Let W be an invariant subspace for T. Then prove that the characteristic polynomial for the restriction operator divides the characteristic polynomial for T. Also prove that the minimal polynomial for divides the minimal polynomial for T. (5)

b) State and prove Cayley-Hamilton theorem.

[OR]

Let V be a finite-dimensional vector space V over F and let T be a linear transform on V. Then prove that T is diagonalizable if and only if the minimal polynomial for T has the form where are distinct elements of F. (15)

II )a) Let V be a finite-dimensional vector space. Let be the subspaces of V and let . Then prove the following are equivalent.

i) are independent.
ii) For each we have = {0}.

[OR]

Let be a non-zero vector in V and let be the T-annihilator of .Then prove that

i) If the degree ofis k, then the vectors form a basis for.
ii) If U is the linear operator on induced by T, then the minimal polynomial for U is. (5)

b) State and prove the primary decomposition theorem.

[OR]

Let T be a linear operator on a finite-dimensional vector space V over F. If T is diagonalizable and if are the distinct characteristic values of T, then prove that there exist linear operators on V such that

(i) T;

(ii) I=;

(iii);

(iv)

(v) the range of is the characteristic space for T associated with

Conversely, if there exist k distinct scalars and k non-zero linear operators which satisfy conditions (i),(ii) and (iii), then show that T is diagonalizable, are the distinct characteristic values of T, and conditions (iv) and (v) are satisfied . (15)

III a) Write a note on the Jordon form.

[OR]

Let T be a linear operator on which is represented in the standard basis by the matrix. Find the minimal polynomial for T. (5)

b) State and prove cyclic decomposition theorem.

[OR]

State and prove generalized Cayley-Hamilton theorem. (15)

IV a) Prove that a form f is Hermitian if and only if the corresponding linear operator T is self adjoint.

[OR]

If , then prove that . (5)

b) i) State and prove Principal Axis Theorem.
ii) Let V be a complex vector space and f a form on V such that fis real for every .Then prove that f is Hermitian. (9+6)

[OR]

Let T be a diagonalizable normal operator with spectrum S on a finite-dimensional inner product space V .Suppose f is a function whose domain contains S. Then prove that f(T) is a diagonalizable normal operator with spectrum f(S) .If U is a unitary map of V onto V’ and T’=UTU, prove that S is the spectrum of T’ and f(T)= Uf(T)U . (15)

V a) Find all bilinear forms of F over F.

[OR]

Let f be a non-degenerate bilinear form on a finite-dimensional vector space V.

Then prove that the set of all linear operators on V which preserve f is a group under the operation of composition. (5)

Let V be a finite-dimensional vector space V over a field of characteristic zero, and let f be a symmetric bilinear form on V. Then prove that there is an ordered basis for V in which f is represented by a diagonal matrix.

[OR]

Let V be an n-dimensional vector space over a sub field of the complex numbers, and let f be a skew-symmetric bilinear form on V. Then prove that the rank r of f is even, and if r = 2k, then there is an ordered basis for V in which the matrix of f is the direct sum of the (n-r) x (n-r) zero matrix and k copies of the 2×2 matrix

. (15)

Go To Main Page

Loyola College M.Sc. Mathematics Nov 2006 Differential Geometry Question Paper PDF Download

November 15, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – MATHEMATICS

AA 21

FIRST SEMESTER – NOV 2006

MT 1807 – DIFFERENTIAL GEOMETRY

Date & Time : 02-11-2006/1.00-4.00 Dept. No. Max. : 100 Marks

Answer ALL the questions

I a) Obtain the equation of tangent at any point on the circular helix.

(or)

b) Show that the necessary and sufficient condition for a curve to be a plane curve

is = 0. [5]

c) Derive the equation of the osculating plane at a point on the curve of intersection of

two surfacesin terms of the parameter u. [15]

(or)

d) Derive the Serret-Frenet formulae and deduce them in terms of Darboux vector.

II a) Define involute and find the curvature of it.

(or)

b) Prove that a curve is of constant slope if and only if the ratio of curvature to torsion

is constant . [5]

c) State and prove the fundamental theorem for space curve. [15]

(or)

d) Find the intrinsic equations of the curve given by

III a) What is metric? Prove that the first fundamental form is invariant under the

transformation of parameters.

(or)

b) Derive the condition for a proper transformation from regular point. [5]

c) Show that a necessary and sufficient condition for a surface to be developable is

that the Gaussian curvature is zero. [15]

(or)

d) Define envelope and developable surface. Derive rectifying developable associated

with a space curve.

IV a) State and prove Meusnier Theorem.

(or)

b) Prove that the necessary and sufficient condition that the lines of curvature may be

parametric curve is that [5]

c) Prove that on the general surface, a necessary and sufficient condition that the curve

be a geodesic is for all values of the parameter . [15]

(or)

d) Find the principal curvature and principal direction at any point on a surface

V a) Derive Weingarten equation. [5]

(or)

b) Prove that in a region R of a surface of a constant positive Gaussian curvature

without umbilics, the principal curvature takes the extreme values at the boundaries.

c) Derive Gauss equation. [15]

(or)

d) State the fundamental theorem of Surface Theory and illustrate with an example

Go To Main Page

Loyola College M.Sc. Mathematics Nov 2006 Analytic Number Theory Question Paper PDF Download

November 15, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – MATHEMATICS

AA 25

THIRD SEMESTER – NOV 2006

MT 3805 – ANALYTIC NUMBER THEORY

Date & Time : 30-10-2006/9.00-12.00 Dept. No. Max. : 100 Marks

Answer ALL questions.

a) i) Define Mobius function and Euler function
ii) Prove that for n≥1. (2+3)

iii) Prove that log n = and. (5)

b) i) Prove that the set of all arithmetical functions f with f(1)≠0 forms an abelian group

with respect to Dirichlet product , the identity element being the function I.

ii) Let f be multiplicative. Then prove that f is completely multiplicative if and only if

f for all n1.

iii) If f is multiplicative then prove that. (10+5)

a) i) State and prove Euler’s summation formula.

ii) Prove that where C is Euler’s constant. (5)
b) i) State and prove weak and strong versions of Dirichlet asymptotic formulae for

the partial sums of the divisor function d(n).

ii) ) State and prove Asymptotic formulae for the partial sums of divisor functions

and (15)

III. a) i) An integer n>0 is divisible by 9 if and only if the sum of its digits in its decimal

expansion is divisible by 9. Prove this using congruences.

ii) If acand if d= (m,c), then prove that a≡b. (5)
b) i) State and prove Lagrange’s theorem.
ii) For any prime p prove that all the coefficients of the polynomial

f(x)=(x-1)(x-2)(x-3)…………(x-p+1)-x+1 are divisible by p. (10+5)

iii) If (a,m)=1, prove that the solution of the linear congruence ax≡b (mod m) is

is given by x≡ba (mod m).

iv) State and prove Chinese remainder theorem. (6+9)

a) i) Let p be an odd prime. Then for all n prove that.

ii) Prove that Legendre’s symbol () is a completely multiplicative

function of n. (5)

b) i) For every odd prime p, Prove that and

ii) State and prove Gauss’ Lemma. (7+8)

iii) State and prove Quadratic reciprocity law. Use it to determine those odd

primes p for which 3 is a quadratic residue and those for which it is a

nonresidue (15)

a) i) Evaluate where P is an odd positive integer.

ii) Determine whether 888 is a quadratic residue or nonresidue of the prime 1999.
b) i) Prove that for <1 ,,where p(0)=1 and

p(n) is the partition function.

ii) State and prove Euler’s pentagonal-number theorem. (15)

Go To Main Page

Loyola College M.Sc. Computer Science Nov 2006 Visual Basic-Oracle Programming Question Paper PDF Download

November 14, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

AK 14

FIRST SEMESTER – NOV 2006

CS 1808 – VISUAL BASIC – ORACLE PROGRAMMING

Date & Time : 02-11-2006/1.00-4.00 Dept. No. Max. : 100 Marks

PART-A

Answer all Questions 10 x 2 = 20

What is a Variable?
What is a Control Array?
List out any four chart types.
What is flex grid?
How to register an Activex control?
List out MAPI message control methods
What is a table?
Write any two date functions in SQL?
Write about on..Delete..Cascade?

List out Data report components.

PART-B

Answer all Questions 5 x 8 = 40

(a) Explain data types and their ranges in VB. (or)

(b) Write a short note on Tool bar and Status bar

(a) Write a program using VB to demonstrate

chart and grid controls (or)

(b) Explain about Timer and Shape Control

(a) How to write a program using VB to create

Tree view and List view control (or)

(b) What is DHTML? Discuss the advantages of

DHTML over HTML

(a) Explain Oracle Internal Data types (or)

(b) Explain different types of joins in SQL

(a) Write about trigger. (or)

(b) Generate a report for student mark sheet processing.

PART-C

Answer any Two Questions 2 x 20 = 40

a) Explain the various control structures in VB with examples
b) Explain different types of arrays in VB with suitable examples.

a) Explain about Activex controls and Activex documents
b) Explain different methods of Common dialogs in VB.

Write a short note on
1. Constraints Sequences c. Views d. Function

Go To Main page

Loyola College M.Sc. Computer Science Nov 2006 Microprocessor & Micro Controller Question Paper PDF Download

November 14, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

AK 17

THIRD SEMESTER – NOV 2006

CS 3875 – MICROPROCESSOR AND MICRO CONTROLLER

Date & Time : 06-11-2006/9.00-12.00 Dept. No. Max. : 100 Marks

PART A

Answer ALL the Questions 2 X 10 = 20

List the features of 8086 Processor?
what is the purpose of segment register?
What is the use of zero flag?
When halt state will be enable?
What is base address?
Define batch processing?
What is the use of I/O ?
What is double Buffer?
Define Operation Command Word?
What are the advantages of Micro Controller?

PART B

Answer All the Questions 8 X 5 = 40

a) Explain 8086 pin configuration with diagram.

Explain multi queuing processor function?

a) Explain internal operation of computers ?

Explain the concept of direct and indirect addressing mode.

a) Explain the concept of Multi Processing.

Explain shortest job First scheduling process.

a) Explain the advantages Interrupt routine.

b) Write the features of Minimum mode system

a) Discuss the 8051 data transfer instruction.

b) Write about Execution of 8051 Interrupt.

PART C

Answer Any Two Questions 2 X 20 = 40

Explain 8086 bus Architecture with diagram?
Discuss various microprocessor programming Instruction formats.
Explain the operation of DMA and its pros and Cons with diagram.

Go To Main page

Loyola College M.Sc. Computer Science Nov 2006 Computers In Chemistry Question Paper PDF Download

November 14, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – CHEMISTRY

AK 19

THIRD SEMESTER – NOV 2006

CS 3902 – COMPUTERS IN CHEMISTRY

Date & Time : 03-11-2006/9.00-12.00 Dept. No. Max. : 100 Marks

PART-A

ANSWER ALL. 10X2=20

1.What is identifier?

2.Differentiate between if and else if statement.

3.What is reserved words?

4.What is the purpose of math.h?

5.Write the syntax of for loop.

6.Write the Heats of reactions using kirchoff’s equations.

7.What is Beer-lambert’s law?

8.What is the purpose to use union?

9.What are the two woodward-hoffmann rules?

10.Define structure?

PART-B

ANSWER ALL. 5X8=40

11.a)Brief about contents of c program?

(or)

b)Differentiate between while and do…while control statements.

a) Explain.
i) structure and union with example.

ii)differentiate structure and union.

(or)

b)Write the C program to find the Gibbs free energy.

a)Write a C program to determine the constants a,b,d and Axial Ratio.a’:b’:c’ for crystals?

(or)

b)Write a program in C to determine the roots of a quadratic equation?

a) Write a C program to determination of electronegativity of an atom from bond energy data using Pauling’s Relation?

(or)

b)Explain and write a C program to calculation of wavelength maximum for conjugated dienes and enones.

a)Write a C program to interconvert units of molecular weight of a macromolecular?

(or)

b)Explain Glucose and Titrimetric methods and write corresponding C program?

PART-C

ANSWER ANY TWO QUESTIONS. 2X20=40

Explain the control structures with examples.
Describes the application of rotation and partition and write the corresponding C program?
a) Explain and write a c program to huckel molecular orbital calculations of delocalisation

energy of butadiene using group theory?

b)Write a c program for find de-brogly wavelength?

Go To Main page

Loyola College M.Sc. Computer Science Nov 2006 Computer Peripheral & Interfacing Question Paper PDF Download

November 14, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

AK 20

THIRD SEMESTER – NOV 2006

CS 3903 – COMPUTER PERIPHERAL AND INTERFACING

Date & Time : 03-11-2006/9.00-12.00 Dept. No. Max. : 100 Marks

PART A (10 x 2 = 20 marks)

Answer all questions. All questions carry equal marks.

What is a LCD display?

Define serial interface?

Define Error control and retry logic?

What are the functions of compact disc read/write drive?

Define memory access time?

What are the types of network?

What are the bus standards used?

Write notes on I/O bus?

What are the nature of faults?

What are the faults that occur in a hardware unit?

PART B (5 x 8 = 40 marks)

Answer all questions. All questions carry equal marks.

(a).Explain the various input devices?

(b).Explain the different categories of printers?

(a).Briefly explain about magnetic storage techniques?

(b).Briefly explain about floppy disk controller?

(a).Explain device controller functions?

(b).Explain ROM BIOS?

(a). Explain communication interface?

(b).What are the various topologies used in networks?

(a).What are the steps involved in fault rectification?

(b).Explain about the hardware diagnostic tools?

PART C (2 x 20 = 40 marks)

Answer any two questions. All questions carry equal marks.

(a).Explain interface standards for peripheral devices?

(b).Explain hard disk controller and interface standard?

(a). Explain IBM PC hardware and motherboard components?

(b).Explain briefly about plug and play systems?

(a). Briefly explain about power on self test?

(b). Explain the network architecture of OSI reference model?

Go To Main page

Loyola College M.Sc. Computer Science Nov 2006 Computer Network Question Paper PDF Download

November 14, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

AK 15

THIRD SEMESTER – NOV 2006

CS 3808 – COMPUTER NETWORKS

Date & Time : 25-10-2006/9.00-12.00 Dept. No. Max. : 100 Marks

Part – A
Answer all the questions:	(10 x 2 = 20)

What is meant by X.25?
Differentiate between copper wire and fiber optics.
Define Parity bit.
What are collision free protocols?
Differentiate between broadcast and multicast routing.
What is the work of foreign agent in mobile host routing.
Define cryptography.
List the design issues of presentation layer.
What is meant by three-way handshake?
Define File management.

Part – B
Answer all the questions:	(5 x 8 = 40)

a) Explain the following with suitable diagrams:

ATM virtual circuits.
Broadcast links.

(Or)

b) Discuss any two types of Guided media with suitable diagrams.

a) Explain the different types of framing with examples.

(Or)

b) Explain Ethernet with suitable examples.

a) Explain Bluetooth protocol stack with a neat diagram.

(Or)

b) Explain Internetworking with suitable diagrams.

a) Explain Window management in TCP with suitable diagrams.

(Or)

b) Explain substitution ciphers and transposition ciphers with examples.

a) Explain Frequency dependent coding.

(Or)

b) Explain File servers with suitable examples.

Part – C
Answer any two:	(2 x 20 = 40)

a) Explain OSI Reference model with a neat diagram.

b) Differentiate between circuit and packet switching.

a) Explain link state routing with suitable example.

b) Explain Congestion control in Data gram subnets.

Explain Connection establishment and connection release in transport layer.

Go To Main page

Loyola College M.Sc. Computer Science Nov 2006 Asp.Net Question Paper PDF Download

November 14, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 M.Sc. DEGREE EXAMINATION – COMPUTER SCIENCE

AK 16

THIRD SEMESTER – NOV 2006

CS 3809 – ASP .NET

Date & Time : 27-10-2006/9.00-12.00 Dept. No. Max. : 100 Marks

PART A

Answer all Questions 10 * 2 = 20

Mention the distinct advantage of Unsigned Integers.
“C# will become the programmers’ choice in .NET”- Comment.
“Inline Code and Inline Expression can not be used independently” – Defend or Oppose the statement with justifications.
“The availability of HTML Controls in ASP.NET is not appreciated” – Give your comment.
Provide a short description about ADO.NET.
Write the various types of commands in used in ADO.NET.
What is called as Data Caching?
Define the term Session Management.
What is the predominant distinction between HTML and XML?
What is XPath in XML?

PART B

Answer all Questions 5 *8 = 40

11 (a) Brief the Characteristics of C#.

(OR)

(b) What is a Conditional Statement? What role does it play in programming? Explain the various conditional statements in C#.

12 (a) Explain in detail about the Server-side Controls in ASP.NET.

(OR)

(b) What is the role played by Validation Controls in ASP.NET. Demonstrate their usage along with their important properties.

13 (a) Explain the Connected Architecture of ADO.NET.

(OR)

Explain the Design Goals and Key Components of ADO.NET.

14 (a) Discuss Web User Controls in ASP.NET.

(OR)

Explain the working of Datagrids with ADO.NET in ASP.NET

15 (a) Explain in short about the merits of XML

(OR)

Explain deployment of Dataset in XML

PART C

Answer any two Questions 2 * 20 = 40

(a). What is called as Entry-Controlled and Exit-Controlled loops? Explain the various looping statements in C#.

(b) Explain the Predefined Data types in C#.

(a). Distinguish Connected ADO.NET and Disconnected ADO.NET Architecture with suitable diagram.

(b) Explain the major Page Events with their properties.

(a) Discuss the various concepts that govern XML.

(b) Can we use XML for DOM? Explain.

Go To Main page

Loyola College M.Sc. Chemistry April 2006 Organics Substitution,Addition & Elimination Rxn Question Paper PDF Download

November 9, 2017 by 01 prakash

LM 29

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – CHEMISTRY

SECOND SEMESTER – APRIL 2006

CH 2808 – ORGANIC SUBSTITUTION, ADDITION & ELIMINATION RXN

Date & Time : 19-04-2006/FORENOON Dept. No. Max. : 100 Marks

Part-A

Answer ALL questions. (10 ´ 2 = 20)

Predict the product with mechanism
What is ipso attack? Give the possible mechanism for ipso attack.
What are stable, persistent and inert free radicals? Give example.
Predict the product of the reaction of dihydropyran with primary alcohols in the presence of acids with mechanism.
Predict the product.
How would you explain that trans-2-acetoxycyclohexyl brosylate with acetate in glacial acetic acid gives only trans diacetate?
Explain Grunwald-Winstein equation.
Which of the following is more nucleophilic? Why? Benzene or mesitylene; Phenoxide or p-nitrophenoxide
Explain Hofmann’s rule in elimination reactions with a suitable example.
What are ambident nucleophiles? Give an example.

PART B

Answer any EIGHT questions (8 ´ 5 = 40)

Give the mechanism of the following:

a) Wohl-Ziegler bromination b)Wittig rearrangement.
a) Predict the product with mechanism
b) Explain Bartons reaction.
Give the mechanism of oxymercuration reaction. Also give the evidences for the free radical mechanism for the cleavage of Hg.
Predict the product with mechanism and evidence.
Define isoinversion. Explain using a suitable example.
Using suitable resonance-stabilizing structures explain why halogens are deactivators but o, p-directors.
How would you show that the transition state in S_N2 reaction must be linear?
Threo DL pair of 3-bromo-2-butanol with HBr gave DL-2,3-dibromobutane while the erythro pair gave meso isomer. Explain.
Explain ion-pair mechaism. What are its evidences?
‘Basic hydrolysis of a-bromopropionate ion with concentrated base gives a product with inverted configuration but with dilute base, retention product is formed’. Explain.
What happens when the following are subjected to pyrolysis?
(i) 2-acetoxybutane (ii) Xanthate from isobutyl alcohol
Solvolysis in acetone-water at 85°C of syn-7-p-anisyl-anti-7-norborn-2-enyl p-nitrobenzoate was only 2.5 times faster than that of the saturated compound’.

PART C

Answer any FOUR questions (4 ´ 10 = 40)

How are the following synthesized from benezene?
a) m-nitroacetophenone b) p-chlorobenzoic acid
c)p-propylbenzen sulphonic acid d) m-bromopropylebenzene.
a) How are the following conversions effected?
b) Propose a synthesis for the following compounds using Robinson annulations.
a) Give the mechanism of free radical substitution at an aromatic substrate. Substantiate it with suitable evidences.
b) 2,3-dimethylbutane gives different ratio of products in aliphatic and aromatic solvents. Why?
a) Endo-anti-tricyclo[3.2.1.02-4]octan-8-yl-p-nitrobenzoate is solvolysed about 10¹⁴times faster than p-niotro isomer containing C=C’. Explain.
b) How would you show by reactions the mechanistic border line region between S_N1 and S_N2 reactions?
a) Solvolysis of L-threo-3-phenyl-2-butyltosylate in acetic acid gives threo product in major amount’. Explain.
b) What is ‘Product spread’ in elimination reactions? Explain with suitable examples.
a) Explain Bucherer reaction with mechanism.
b) Expalin the following:
(i) Acetolysis of both 4-methoxy-1-pentylbrosylate and 5-methoxy-2-pentylbrosylate give the same mixture of products.

Both erythro- and threo-1-acetoxy-2-deutero-1,2diphenylethane on pyrolysis give the same product.

Go To Main Page

Loyola College M.Sc. Chemistry April 2006 Organic Chemistry-II Question Paper PDF Download

November 9, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – CHEMISTRY

LM 28

SECOND SEMESTER – APRIL 2006

CH 2801 – ORGANIC CHEMISTRY – II

Date & Time : 19-04-2006/FORENOON Dept. No. Max. : 100 Marks

Part-A

Answer ALL questions. (10 ´ 2 = 20 marks)

Which of the following is a better nucleophile? Why?
a) Phenol or ethanol b) nitride or fluoride
‘Dehydrochlorination of neomenthylchloride gives two different alkenes.’ Explain
‘endo-anti-tricyclo[3.2.1.0^2-4]octan-8yl-p-nitrobenzoate is solvolysed 10¹⁴times faster than p-nitro isomer containing C=c’. Explain
Arrange the following in the decreasing order of nucleophilicity. Justify your answer. OAc^–, ClO₄^–, H₂O, p-brosyl, OH^–
Pyrolysis of iso-butylacetate gives a mixture of two alkenes in a ration 3:2. Explain with mechanism.
Give any four differences between DNA and RNA.
How are enzymes classified on the basis of their mode of action?
‘When the leaving group cannot act as a nucleophile, substitution can take place at the bridgehead’. Explain.
Write a note on NADP.
Threo DL pair of 3-bromo-2-butanol with HBr gives DL-2,3-dibromobutane while erythro isomer gives meso. Explain

Part-B

Answer any eight questions. (8 ´ 5 = 40 marks)

Solvolysis of syn-7-p-anisyl-anti-7-norborn-2-enyl-p-nitrobenzoate in acetone water is 2.5 times faster than its saturated analog. Explain.
Acetolysis of both 4-methoxy-1-pentylbrosylate and 5-methoxy-2-pentyl brosylates give the same mixture of products.
Explain the ion-pair involvement in S_N1 mechanism. What are the evidences of ion-pair mechanism?
‘2-octylbrosylate with 75% aqueous acetone gives 2-octanol with 77% inversion but with sodium azide gives 100% inversion’. Explain with mechanism.
Explain the mechanism of Steven’s rearrangement.
Explain the mechanism of Hofmann rearrangement. Is it inter or intramolecular? Explain.
Explain the primary structure of protein.
What are conjugated proteins? How does the protein structure in heamoglobin assist in oxygen transfer?
Explain normal and abnormal Claisen rearrangement with mechanism.
What are the types of RNA? How are they helpful in protein synthesis? Explain.
Explain the immobilization of enzymes.
‘2-butylacetate on pyrolysis gives a mixture containing 57% 1-butene and
43% 2-butene. Explain.

Part-C

Answer any four questions. (4 ´ 10 = 40 marks)

a) 2-bromo-2-methylbutane with EtO^– gives 70% 2-methyl-2-butene but with
Et₃C-O^– gives 12% only. Explain with mechanism.
b) Explain how free radical monobromination of 1-bromo-2-methylbutane yields a product with a high degree of retention in configuration.
a) b-(Syn-7-norbornenyl)ethylbrosylate undergoes acetolysis about 140,000 times faster than its saturated analog. Explain.
b) Explain Swain-Scott relationship with a suitable example.
a) Explain the orientation of double bond in elimination reactions with suitable examples.
b) Pyrolysis of erythro and threo isomers of 1-acetoxy-2-deutero-1, 2-diphenyl ethane gives the same alkene. Explain with mechanism.
a) What are coenzymes? Explain the various sources of coenzymes and their functions.
b) What are long and short lived free radicals? How are they prepared? How are they useful in organic synthesis?
Explain the following
a) Erythro-3-bromo-2-butanol with HBr gives meso product
b) Rate of solvoysis of Ph-CH₂-CH₂-OTs with 75% CF₃COOH is 3040 times faster than CH₃-CH₂-OTs
c) Solvolysis of exo-2-norbornyl brosylate is 350 times faster than its endoisomer
d) Pyrolysis of xanthates give COS as one of the products.
Explain the following:
a) Ambident nucleophile
b) Fischer-Indole synthesis
c) Allosteric enzymes

Go To Main Page

Loyola College M.Sc. Chemistry April 2006 Nuclear & Solid State Chemistry Question Paper PDF Download

November 9, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – CHEMISTRY

LM 43

FOURTH SEMESTER – APRIL 2006

CH 4952 – NUCLEAR AND SOLID STATE CHEMISTRY

(Also equivalent to CH 4802)

Date & Time : 22-04-2006/9.00-12.00 Dept. No. Max. : 100 Marks

Part A

Answer the following 10×2 = 20

What are unit cell parameters of (i) triclinic (ii) hexagonal?
What is ‘123’ oxide? Mention its significance.
Mention the number of space lattices and space groups in two and three dimensional lattices.
What is piezoelectric effect? Cite two examples of piezoelectric crystals.
Give two examples for organic semiconductors. Cite two advantages of them.
What is the significance of n/p ratio?
How do radio particles come out of the nucleus without spending activation energy?
What is the unique behaviour of ¹⁰B? How is this behaviour useful in nuclear reactors?
What is the mechanism of γ – emission?
Show that t_1/2= 693/λ

Part B

Answer any eight of the following: 8×5 = 40

Describe the operations that produce improper axis.
Write a note on space groups.
How is photoelectriccatalytic splitting of water carried out?
How are semiconductors used in the photovoltaic cell?
What is Kammerlingh – Onnes experiment? Write a note on Type I superconductors.
Discuss the Debye theory on the heat capacity of solids.
Explain the nature of forces in operating in the nucleii.
Describe ranges of various radio particles.
Why are the mass numbers of stable isotopes of chlorine and copper not continuous but are alternate numbers?
What is hot atom chemistry? Explain Szillard – Charmers process and its application.
What is the principle of neutron activation analysis? What are the disadvantages of this technique?
Write a note on cold fusion.

Part C

Answer any four of the following: 4×10 = 40

Describe the one dimensional conducting in (SN)_x and partially oxidized [Pt(CN)₄]^2-.
Discuss the Fourier synthesis in obtaining electron charge density in the crystal structure analysis.
Discuss the iron – thionine and Ru³⁺– bipyridyl systems in their photovoltaic behaviors.
Discuss the use of nuclear shell model in explaining magic numbers.
How is signal size in a charged particle counter affected by applied potential?
Discuss working of a nuclear reactor.

Go To Main Page

Loyola College M.Sc. Chemistry April 2006 Nuclear & Radiochemistry Question Paper PDF Download

November 9, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – CHEMISTRY

LM 35

SECOND SEMESTER – APRIL 2006

CH 2952 – NUCLEAR AND RADIOCHEMISTRY

Date & Time : 26-04-2006/9.00-12.00 Dept. No. Max. : 100 Marks

Part A

Answer the following 10´2 = 20

What are isotones? Give an example.
What is nuclear quadrupole moment?
Mention the nuclear spin of (a) ¹²C (b) ²H .
What is internal conversion?
Give the mechanism of positron emission.
How is the odd – even rule useful in predicting stability of a nucleus?
Show that t_1/2= 693/λ
How are thermal neutrons obtained?
What is the final product obtained if 2 α and 4 β^–particles are emitted from ²³⁶U?
Explain tunneling effect.

Part B

Answer any eight of the following: 8´5 = 40

Write a note on nuclear forces.
Discuss the stability of the nucleus based on n/p ratio.
Discuss the principle of Dempster mass spectrograph.
Write a note on proportional counters.
What is double β decay?
What mass of ¹⁴C with t_1/2 = 5730y has an activity equal to one curie?
How is radius of a nucleus deduced? Calculate density of ⁸¹
What is electron capture? What are its consequences?
Why are the atomic weights of elements found in fraction?
What is the significance of interaction of radiation with water?
What is the principle of isotope dilution analysis? What are the disadvantages of this technique?
Write a note on use of radio isotopes in determination of mechanism of a reaction.

Part C

Answer any four of the following: 4´10 = 40

How is binding energy calculated theoretically using liquid drop model?
Describe the mechanism of β decay emission. Explain the forbidden and allowed transitions of β decay using Kurie plot.
Write a note on (a) Geiger Counter (b) Scintillation counter
Discuss the use of nuclear shell model in explaining magic numbers.
How is the factor binding energy per nucleon significant in deciding stability of a nucleus?
Discuss working of a nuclear reactor.

Go To Main Page

Loyola College M.Sc. Chemistry April 2006 Molecular Spectroscopy Question Paper PDF Download

November 9, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – CHEMISTRY

LM 33

SECOND SEMESTER – APRIL 2006

CH 2950 – MOLECULAR SPECTROSCOPY

(Also equivalent to CH 2802)

Date & Time : 21-04-2006/FORENOON Dept. No. Max. : 100 Marks

Part-A ANSWER ALL QUESTIONS (10 x 2 = 20)

Indicate which one will have higher λ_max value and explain

CH₂= CH₂ and CH₂= CH – CH = CH₂
C₆H₆and C₆H₅OCH₃

The ¹H NMR of C₄H₉Cl gave a single peak at 1.80 δ as a singlet. Give the structure of the compound.
Sketch the EPR spectrum of C₆H₅^•radical and explain.
Which one has a higher ν(C=O) value? Explain

O O

|| ||

CH₃ – C – CH₃ and CH₂ = CH – C – CH₃

How is the mass of metastable peak calculated in the mass spectrum? Explain with one example.
Identify the point groups for the following molecules:

(a)POCl₃ (b) SF₆ (c) Br₂ (d) Ni(CN)₄^2- (square planar)

Explain the rule of mutual exclusion with a suitable example.
Explain the spectroscopic transitions (a) fundamental (b) hot bands using proper quantum
Explain the meaning and significance of x, y, and z in the T₂ representation of the T_d point group as shown below

T_d E 8C₃ 3C₂ 6S₄ 6σ_d

T₂ 3 0 -1 -1 1 (x,y,z)

Identify the symmetry operations present in the point groups C₁, C_i, and C_s. Give one example for each.

Part-B ANSWER ANY EIGHT QUESTIONS (8 x 5 = 40)

How does the solvent polarity affect the λ_max of the compound?
How are the following differentiated by the infrared spectral studies?

aliphatic and aromatic compounds
ethanol and diethyl ether (3+2)

Write a note on Nuclear Overhauser effect.
Sketch the Mossbauer spectrum of [Fe(CN)₆]^3- and explain.
Discuss the detectors used in UV-Visible double beam spectrophotometer.
Discuss the McLafferty rearrangement in the mass spectral fragmentation pattern.
Explain the factors for the broadening of spectral lines.
How are P, Q, and R branches of absorption bands obtained in vibration-rotation spectra of molecules? In which type of molecules Q branch is not observed and why?
(a) When do we say two symmetry operations are in the same class? Explain with an example.
- The equilibrium vibration frequency of the HBr molecule is 2649.7 cm^-1 and the anharmonicity constant is 0.0171; what, at 300K, is the intensity of the ‘hot band’ (v=1 to v=2 transition) relative to that of the fundamental (v=0 to v=1)? (2+3)

A microwave spectrometer capable of operating only between 60 and 90 cm^-1 was used to observe the rotational spectra of HI. Absorptions were measured as follows:

HI (cm^-1)

64.275

77.130

89.985

Find B, I and r for each of the molecule, and determine the J values between which transitions occur for the first line listed above.

(a) Explain the following with a suitable molecule for each:

(i) Principal axis of rotation (b) Inversion Center

(b) Explain the meaning of a E_g representation in the character table. (2+2+1)

Give the reduction formula and reduce the following reducible representation.

C_2h E C₂ i σ_h

8 0 6 2

C_2h E C₂ i σ_h

A_g 1 1 1 1 R_z x², y², z², xy

B_g1 -1 1 -1 R_x, R_y xz, yz

A_u 1 1 -1 -1 z

B_u 1 -1 -1 1 x, y

Part-C ANSWER ANY FOUR QUESTIONS (4 x 10 = 40)

How are the UV-Visible spectral studies useful in (a) charge-transfer transition
(b) electronic effect in the organic molecules? (5+5)
Describe the following:

Proton noise decoupled ¹³C-NMR
Spin-spin coupling in ¹H NMR (5+5)

Discuss the principle and instrumentation involved in the EPR spectroscopy. Explain the nuclear hyperfine splitting. (4+3+3)
(a) State and explain Franck-Condon Principle. How are intensity variations of electronic spectra explained by this principle?

(b) The Bond length of NO is 115.1 pm. Bond force constant is 1595 Nm^-1. Calculate (a) Zero-point energy and the energy of the fundamental vibration ν₀.
(b) Calculate the rotational constant B. (c) Calculate the wave numbers of the lines P₁, P₂, R₀ and R₁ (5+5)

(a) What are Stokes and anti-Stokes lines and Rayleigh lines? Compare their intensities in the Raman vibrational spectrum of a compound.

(b) Consider the molecules N₂, CCl₄, CH₃Cl and H₂O. Predict which of them will show (a) Pure rotational spectrum (b) infrared absorption (c) electronic transition. Give reasons for your choice. (5+5)

Find the number, symmetry species of the infrared and Raman active vibrations of CH₄, which belongs to T_d point group. State how many of them are coincident.

(You may, if you wish, use the table of f(R) given below for solving this).

Operation: E σ i C₂ C₃ C₄ C₅ C₆ S₃ S₄ S₅ S₆ S₈

f(R): 3 1 -3 -1 0 1 1.618 2 -2 -1 0.382 0 0.414

For any C_n, f(R) = 1 + 2cos(2π/n), For any S_n, f(R) = -1 + 2cos(2π/n)

T_d E 8C₃ 3C₂ 6S₄ 6σ_d

A₁ 1 1 1 1 1 x²+y²+z²

A₂ 1 1 1 -1 -1

E 2 -1 2 0 0 (2z²-x²-y², x²-y²)

T₁ 3 0 -1 1 -1 (R_x,R_y,R_z)

T₂ 3 0 -1 -1 1 (x,y,z) (xy,xz,yz)

Go To Main page

Loyola College M.Sc. Chemistry April 2006 Instrumental Methods Of Chemical Analysis Question Paper PDF Download

November 9, 2017 by 01 prakash

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – ZOOLOGY & BIOMEDICAL INSTRUMENTATION

LM 32

SECOND SEMESTER – APRIL 2006

CH 2901 – INSTRUMENTAL METHODS OF CHEMICAL ANALYSIS

Date & Time : 28-04-2006/9.00-12.00 Dept. No. Max. : 100 Marks

Part-A ANSWER ALL QUESTIONS (10 ´ 2 = 20)

Define: (i) a mole (ii) molarity
If drinking water contains 1.5 ppm of NaF, how many liters of water can be fluoridated with 454 g of NaF?
Explain hypsochromic shift with an example.
Sketch and explain the fundamental difference in instrumentation between Flame Emission and Atomic Absorption Spectrometers?
What is optical activity? Give an example.
Compare the energy of the following electromagnetic radiation

(i) Radio wave (ii) Infrared rays (iii) Visible light

Mention the nuclear spin quantum number (I) for ₆C¹², ₁H¹
Compare the absorption frequencies of C-C and C=C.
Define ‘base peak’.
What kind of electromagnetic radiation is used to study crystal structure?

Part-B ANSWER ANY FIVE QUESTIONS (5 ´ 8 = 40)

(a) State Beer-Lambert’s law and explain under what conditions it is not applicable.

(b) The molar absorptivity of a particular solute is 2.1 x 10⁴ L cm^-1mol^-1. Calculate the transmittance through a cuvette with a 5 cm light path for

a 2.0 x 10^-6 M solution.

(a) Explain the significance of λ_max and ε values in UV-Visible spectroscopy with a suitable example.

(b) Spectrophotometry is a very useful quantitative technique in the applications of biological systems. Can you substantiate this statement with two examples?

Discuss in detail the instrumentation and application of nephelometry.
Explain briefly the principle of ICP AES and its advantages over AAS methods?

1. Determine the force constant for the C-H bond, given the stretching frequency of the C-H bond as 3000cm^-1.

Calculate the pH of the following solutions.

10^-2 M Ca(OH)₂
Mixture containing 10^-2 M NH₄Cl and 10^-1 M NH₄ K_b of NH₄OH is 10^-5.

Discuss the applications of isotopic dilution analysis.
Draw the low resolution NMR spectrum of ethyl alcohol and explain.

Part-C ANSWER ANY TWO QUESTIONS (2 ´20 = 40)

(a) Define Beer-Lambert’s law explaining the terms involved and state under what conditions it is not applicable.

(b) With a schematic diagram explain the different parts and working of a Double-Beam Spectrophotometer. What are its advantages over a single-beam instrument? (10+10)

(a) Discuss the principle and working of an Atomic Absorption Spectrometer and how it can be used in the quantitative determination of lead (Pb²⁺) in blood.

(b) Give an account of how AAS can be used in studying the toxicological effects of mercury. (15+5)

(a) Describe the method of determining the pH of a solution using a potentiometer.

(b) Discuss the instrumentation of Gas Chromatography.

(a) Discuss the principle involved in NMR spectroscopy and explain its instrumentation.

(b) Distinguish the following

(i) CH₃CHCl CH₃ and CH₃– CH₂ -CH₂Cl by NMR

(ii) CH₃CH₂ CHO and CH₃-CO -CH₃ by IR

(iii) CH₃OH and CH₃CH₂ OH by mass spectrum.

Go To Main page

MT 3803 – TOPOLOGY

MT 1806 – ORDINARY DIFFERENTIAL EQUATIONS

MT 3875 – MATHEMATICAL METHODS IN BIOLOGY

MT 1805 – REAL ANALYSIS

MT 3953 – FLUID DYNAMICS

MT 1804 – LINEAR ALGEBRA

MT 1807 – DIFFERENTIAL GEOMETRY

MT 3805 – ANALYTIC NUMBER THEORY

CS 1808 – VISUAL BASIC – ORACLE PROGRAMMING

CS 3875 – MICROPROCESSOR AND MICRO CONTROLLER

CS 3902 – COMPUTERS IN CHEMISTRY

PART-A

ANSWER ALL. 5X8=40

PART-C

CS 3903 – COMPUTER PERIPHERAL AND INTERFACING

CS 3808 – COMPUTER NETWORKS

Part – A

Part – B

Part – C

CS 3809 – ASP .NET

CH 2808 – ORGANIC SUBSTITUTION, ADDITION & ELIMINATION RXN

PART B

CH 2801 – ORGANIC CHEMISTRY – II

Part-A

Part-B

Part-C

CH 4952 – NUCLEAR AND SOLID STATE CHEMISTRY

CH 2952 – NUCLEAR AND RADIOCHEMISTRY

CH 2950 – MOLECULAR SPECTROSCOPY

O O

CH 2901 – INSTRUMENTAL METHODS OF CHEMICAL ANALYSIS