August
2015
V62/T63/T07032/T04032/EE/20150819
APPLIED MATHEMATICS-2
Instructions
Marks-80
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)Evaluate:-
∫
B)Evaluate:-
∫
10
dx
.
5
dx
OR
Q.1 A) Evaluate:-
B)Evaluate:
∫
∫
√
√
√
10
dx
dx
5
Q.2 A)Solve the differential equation:
2
+ =y
10
B)Find the order and degree of differential equation :
5
=
.
OR
Q.2 A) Find the C.G. of an area enclosed by the parabola y=x2-2x and
the x-axis.
10
5
B)Calculate the area enclosed by curve y2=8x and the line x=2
Q.3 Evaluate:-
5
+ 4 + 25
Q.4 Solve: x. dy - y.dx=0.
5
SECTION-B
Q.5 A)
2
10
The acceleration of a particle is given by
=3t -6t+8.
Find the distance covered in 2 second given that v=0,s=0 at t=0
B) Solve using Jacobi's method; 2x+y+z=4, x+2y+z=-4 and x+y+2z=4.
5
(three iteration only)
OR
Q.5 A) Using Newton's Raphson method evaluate, upto three
iteration only.
√10
B) A body is released from a height of 490m.Find the time taken by
the body to reach the ground(g=9.8 m/sec2).
Q.6 A)In 200 sets of tosses of 5 fair coins, In how many ways you can
expect:
i) at least two heads
ii) at most two heads.
B) A coin is tossed 5 times. What is the probability of getting
exactly 3 heads?
10
05
10
5
OR
Q.6 A) In a certain examination 500 students appeared.Mean score is 68
with S.D 8. Find the number of students scoring.
1)less than 50
2)more than 60
10
(Given that area between z=0 to z=2.25 is 0.4878 and area between
z=0 to z=1 is 0.3413)
B) From a class of 12 students,5 are boys and rest are girls.Find the
probability a student selected is a girl.
5
Q.7 A particle moves with acceleration (3-t) m/s2 with initial velocity
2m/sec.Find the velocity of particle at the end of 5 sec.
5
Q.8 Using Poissondistribution, Find the probability that the king of
diamond will be drawn from a pack of well shuffled card at least
one in 156 consecutive trial.(Given e3= 20)
5