Q1. Define Total differential and write the rules for Absolute change, Relative Change and
Percentage change.
[2]
Q2. If
x
f
and
y
f
f x y x find y
( , ) (2 ) ,
( 5 )
[2]
Q3. Write two real life applications of Integration in the field of Engineering. [2]
Q4.
Solve
x
x
x
1 2 1
lim
0
[2]
Q5. Find the volume of the solid generated by revolving
6
2
y x
between x=1 and
x= 4 about the x-axis.
[2]
PART – 2 (20 Marks)
INSTRUCTIONS: SHORT ANSWER
Q6. Draw the circuit diagram for two resistors
R1 and R2
connected in Parallel. Consider
values for resistors
R1 12K ,and R2 18K
and change in resistors
150 , 255 . dR1 and dR2
Find the percentage change in total resistance R.
[4]
Q7.
Solve
log (6 7)
log (7 8)
9
6
lim
x
x
x
[4]
Q8.
Find the arc length of the curve
2
3
y 1 6x
from
x 2
to
x 3.
[4]
Q9.
Evaluate the integral
dx
x x x
x x
3 6 9
6 8
2
2
by using the Partial Fraction.
[4]
Q10. Explain the steps for evaluating the double integral and triple integral? Give an
example for each one.
[4]
Page 4 of 4
PART – 3 (20 Marks)
INSTRUCTIONS: ANSWER SHOULD NOT BE MORE THAN 2 PAGES
Q11.
Evaluate the integral
dx
x x x
x x x
4 4
3 4 7 5
3 2
3 2
by using the Partial Fraction.
[5]
Q12. Find the areas of the regions enclosed by the two curves
2 5
2
x y and
x 45. [5]
Q13. Evaluate the Integral
e x dx x
cos(2 )
3
using Integration by Parts. [5]
Q14. (a) Find
y
z
if
3 2
yz sin(2z) zx y
, defines z as a function of two independent
variables x and y and the partial derivative exists.
(b) If
z
f
and
x
f
f x y z e find x y z
( , , ) ,
cos3 sin 2
2
.
Sample Solution
