Basic Mathematics
Previous year question paper with solutions for Basic Mathematics May-2017
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Question paper 1
SECTION-A
1. (a) Find square root of .
Answer:
= a+ ib
Squaring on fothsides ;
=
Since =
= 7
.
Also
(b) Prove that
Answer:
(b)
Ans .
L.H.S.
=
=
...
=
=
=
= -81
= R.H.S.
2. (a) Find the equation of circle passing through the points
Answer:
(a) at the q of the circle be
And
And
Put in
(b) Find equation of circle having end points of diameter As(2,5) and (3,9).
Answer:
Ans .thererd .q.will be
3, (a) Show that points (0,-1),(-2,3),(6,7) and (8,3) are the vertices of a rectangle.
Answer:
Ans,
=
= = =
= = =
= = = 10
=- = 1 = 10
= = =
(b) Find equations of sides of triangle containing sides with vertices (4,-2),(-2,4) and (5,5) Also Find area of triangle.
Answer:
Ans ,
.
.
4. (a) Form an equation whose roots are squares of the reciprocal of the roots of the equation
Answer:
Ans. Let the roots of the given
.
The roots of the read.eqn.
Are .
:
;
Now,put,in (2);
.
8. (a) A pur of dles in thrown twlce . Find the probability of ncoring n total of 7
(i) once.
(ii) at least once.
(iii) at most once.
Answer:
Ans ..
.
To get score 7(E)
.
(i)
(ii)
(iii)
(b) Find Initial solution of following problem by NWCM and LCEM:
A
B
C
D
E
SUPPLY
X
55
30
40
50
50
40
Y
35
30
100
45
60
20
Z
45
60
95
35
30
40
Demand
25
10
20
30
15
Answer:
SECTION-C
(9) (a) Define symmetric and skew-symmetric matrices.
Answer:
. Symmetric Matruics :
Skew – sym :
.
(b) Find a point on the line joining (0,4) and (2,0) that divides the line in 2 :3.
Answer:
( 0,4) ( 2,o)
(c) Find the probability that a leap year selected at random has 53 Sunday.
Answer:
A leap yeas has 52 weabs and 2 days other . possibilities of remaining 2 day
are : (Sum , Mon ) , ( Mon, Tue) , ( Tue ,Wed) ,(Wed,Th),(Th,fri) , (Fri, Sat), (Sat, Sun).
∴favourable cases= Sun , Mon&(Sat , Sun )
(d) What is Unbalancesd Assignment Problom ?
Answer:
Unbalanced Assignment problom : If number of jobs is not equal to the number of operators than The assignment problom is known as UNBALANCED Assignment problom . In other words , in a pay off . assignmentproblom if no of roves no of columns; than it is unbalanced problom.
(e) Express in the form of.
Answer: