DU SOL Question Paper 2018 BA (Hons.) Mathematical Awareness

This question paper contains 8 printed pages]

471

B.A. (H)/Concurrent Course G

Paper Code : A-531

MATHEMATICAL AWAREN ESS

(lnterdisciplinary)

^, Time .. 2 Hours Maxirnun iVlarks : 50
I

l

(lvrire ),otrr Rolt ,\o. on the top immedratell' on receipt of thts tlttestion paper.)

Note :- The maximum marks printed on the'question paper are

applicable for the candidates registered with the School

of Open Learning for the B.A'(Hons.). These marks will.

however, be scaled down proportionately in respect of

the students of regular colleges, at the time of posting

of awards for compilation of result.

Attempt All the questions as Per

directed questionwise.
P.T.O.

2
471

UNIT-I

L Do any two parts :

\u) (i) Who are the two mathematicians
with whom

Ramanujan collaborated in Cambridges
?

(i i) Give the result about perfect number
that was

established by Euclid.

(iiil State Newton's .lnverse Squa.re
Law..

(iv) In which year did Riemann presented
his

doctoral thesis and what was
the title of the

thesis ?
an

(6) (, What was fhe name given to the
geometry created

by Euctid ?

(ii) What distinction was Ramanujan
awarded on

graduating flom school ?

411
(

the
of Ramanujan ? Name
liii) What is the full name

Ramanujan was suftering
disease lronr which

about Noether ?
(tv) What did WeYl write

are True ,r False'
State rvhether the
following statements
(c)

answer :
lf false, then give the correct

of Riemann deal with
the
(r) The doctoral thesis

Number theory'

the field
contribution was in
(ii ) Emmy Noether's main

of graPh theory'

number carlnot
(t,t) Euclid proved that the fifth Fermat

be factorized'

(iv) Ramanujan was
born on Christmas DaY

in 1887.
P.T,O.

n
471

UNIT-2

Do any three parts :

\a) (t) State the prime Number Theorem
as conjectured

by Legendre.

(ii) If

a = b(mod m)

then

d : U(mod m).

Using this show that

22' : l(mod 3).
JAJ

(b) (/) ..,,." 6237 as
writ" ^, a continued fraction.
2520

(ii) The st{rdent welfare committee
has 2 faculty,
2 administration members and 5
students on it.

In how many ways can a sub_committee
of
I faculty, I administrative member and
2 students

be formed ?

471

(iii) What is a RSA System ? 2+2+l

(.) Briefly explain the following :

(i) Algebraic numbers

(i0 Transcendental numbers

(ilt) Mersenne numbers

(lv) Fractions

(v) Irrational numbers. J

@ (0 Why was Fermat's lasl theorem also called an

impossible theorem ?

(ii) Find the integer x such that (16)":xmodl7.

(iii) State the Euclidean Algorithm. Using the above

Algorithm, find greatest common divisor of

6237 and2520. l+l+3

P.T.O.

(6) 471

UNIT-3

3. Do any three Parts :

\a) Draw the graphs of the following functions and indicate

where the function is increasing or decreasing :

(t F(x) = lx + ll

1ii) nr'l: .f J .

Also, find their domain and range. 6

(b) Briefly explain any four of the following : 6

(l) Mobius StriP

(ti) Klein Bottle

(tti) Basic Tillings

(,v) Fire Altars

(v) Platonic solids.

(c) (D Verify Euler's formula for the five regular

polyhedral.

471

is formed' What
(il) Explain how the snow flake curve

perimeter ? 3+3
can be said about its area and

Give the set of symmetrics of
(,) an equilateral
\d)

triangle.

problem'
(r,) Briefly explain Konigsberg bridge

arrangements
\ilt) Find the number of different 8-letter

that can be made from letters of
the word

occur together'
DAUGHTER so that all vowals

UNIT4

Do anY tYvo Parrs I

5 and 12
(a) The AM and GM of two numbers are
1

mean of two numbers' 4'5
resPectivelY' Find Harmonic

(b) A die is loaded so that :

1

P(r) : P(2): P(3)
:
4

P(4) : P(5) : P(6) : n
1

P.T.O.

(8) 471

E: {1,2},F: {2,3}.

Show that E and F are independent but not mutually

exclusive. 4.5

(c) Use graphical method to solve the following Lp

problem ' 4.5

Min. Z: 2x * 5Y

Subject to

x+3y221

4x+y>24

x+y>9

x,!)0'

471 1,000