V55/V62/T63/T14012/T07012/T04012/EE/20150812
2015
Marks-80
Basic Mathematics
Instructions
Time: 3 Hrs
1. All questions are compulsory.
2. “Long Answer type Question (LAQ)” is a supply type
question of 15 marks which required a typical answer of about
60-80 lines in bout 32-40 minutes.
3. “Sort Answer type Question (SAQ)” is a supply type question
of 5 marks which required a typical answer of about 15-20 lines
in bout 08-10 minutes.
4. Figures to the right indicate marks allotted to the questions.
5. Assume suitable data if necessary
6. Use a nonprogrammable type of scientific calculator is
allowed
Marks
SECTION-A
Q.1 a) Resolve into partial fraction
10
(
)(
)(
b)Solve the following equation for for x :
(
−
+
)
5
) = 5
OR
Q.1 a)
Resolve into partial fraction:
b) Prove that
=
{1 -
}
10
(
)
5
Q.2 a)
,
(i)
10
√
)
(ii)(
/
5
−
b) If A=
and B=
,Verify that
(AB)'=B'A'
OR
Q.2 a) The following equations are obtained in electrical experiments .Find
5
by Crammer's Rule .
4
-3
=2,
9
-4
=3
( .
b)
√
=0
5
5
Q.3 .Resolve into partial fraction
Show that
+9
) to 4 decimal places.
c) Find the value of A=
Q.4
-4
(
√
)
=
5
5
SECTION-B
Q.5 a)
=
b)Prove that :
c)
=
5
and A is not in the first quadrant ,find
√
+
= sin A+cos A
5
and 0 < < , find the value of
5
OR
Q.5 a) Find x if,
b) If tan x =
c)
5
=
and tan y =
( +
show that x+y =
∏
radians
) .cos( + B) - cos( + A ).sin( + B) =
5
5
sin(A-B)
Q.6 a) Show that the points (1,1) (- 2, -11) ( 0 ,-3) are collinear .
5
b) Find the equation of circle which passes through the origin
and points (2,0 ) and (0,4)
5
c) Show that the points (5,4) (2,3) ( 1, 0) (4,1)are the vertices
of rhombus.
5
OR
Q.6 a) If A ,B ,C are points(-1,5 ) (3,1) (5,7) and D ,E,F are mid
points of BC CA AND AB respectively .Prove that the area of
∆ ABC= 4 × Area of ∆ DEF.
5
b) Find the equation of straight line passing through the points
(5,4) and (3,-2) .Also find the slope of the line.
5
c) Find the equation of straight line passing through the points
(4,5) and perpendicular to the line 3x+5y-20=0
5
Q.7 Calculate the distance of the point (-2,3) from the straight line
5x-3y+7=0
Q.8
+
−
−
+
=
+
5
5