Download Mathematics-II - st Martin`s Engineering college

St.MARTIN'S ENGINEERING COLLEGE
DHULAPALLY, SECUNDERABAD-14
DEPARTMENT OF SCIENCE & HUMANITIES
1ST YEAR B.TECH(A.Y: 2016-2017)
I MID TERM EXAMINATION
Common to All Branches: MECH, CIVIL (Non-Circuit Branches)
SUBJECT : MATHEMATICS-II
CODE
: MA102BS
S No
QUESTION
Blooms
Course
taxonomy Outcomes
level
UNIT - I
Part - A (Short Answer Questions)
1 Find the Laplace transform of
2
3
4
Find the Laplace Transforms of t 3e 3t
Find Laplace transform of
Find the Laplace transform of 1  te
6
7
8
5
Understand
Apply
2
2
Apply
5
APPLY
Find
5

t 2
Remember
Find the inverse transform of
knowledge
Find
State Convolution theorem
 2s  4s  5 
L1 

s3


Find
5
5
Remember
knowledge
6
Understand
3
Remember
knowledge
3
3
2
9


0
10
11
te3t sin t dt
Find L(5sint+2sin3t)
12
13
14
15
Find L(sin2tcos3t)
Find L(u(t-a))
Find Laplace transform of 3cos4(t-2)u(t-2)
Find L(sin(at+b))
Apply
Remember
Remember
knowledge
4
6
6
6
Part - B (Long Answer Questions)
1
Find the Laplace transform of g(t), where g(t)
  2 
2
cos  t  3  , if t  3

= 

0,
if t  2
3

Find
i)
2
Remember
5
L e3t sin 2 t
ii) e3t  2cos5t  3sin 5t 
knowledge
5
Find
3
5
Understand
Find
4
5
Understand
Find
Apply
s3


Find L1  2

 s  10 s  29 
6
Remember
2
Using Laplace Transform Solve
that y 
7
d y
dy
 2  3 y  sin t , given
2
dt
dt
dy
 0 when t=0
dt
Understand


s2
Use convolution theorem to evaluate L1  2
2
2
2 
 ( s  a )( s  b ) 
8
9
knowledge


1
Find L1  2 2
2 
 s (s  a ) 
Solve
Apply
using Laplace Transformation
given that y  0  1and y1  0  1
10
Part - C (Theory Questions)
Apply
1
2
3
4
Define Laplace transform
State first shifting theorem of Laplace Transform
State first shifting theorem of inverse Laplace Transform
Define change of scale property
5
Define heavisides unit step function
6
7
Apply
skill
knowledge
skill
5
5
5
2
skill
7
Define Dirac delta function
Apply
7
State laplace transform for periodic function
Apply
7
Apply
7
Apply
7
Apply
7
Remember
6
Remember
6
Remember
6
Understand
6
Remember
6
Remember
6
Remember
6
Remember
6
Remember
Remember
Remember
6
6
6
Remember
6
8
Define inverse laplace transform
9
state second shifting theorem of laplace transform
10
Define convolution
UNIT-II
Part - A (Short Answer Questions)
1
2
Solve
1
Show that    
2

3
13 3 
e
 x2

dx 
2
0

2
4
7
2
Evaluate  sin  cos  d
5
0
  m, n     m  1, n     m, n  1
5
Prove that
6
show that gamma 1=1
Evaluate
7
.Evaluate
8
Show that
9
10
11
12
Prove that B(m,n)=B(n,m)
Show that Gamma 1=1
Prove that
13
Show that
14
Express
15
Evaluate
dx=2B(8,6)
Remember
4
interms of Beta function
Apply
4
Understand
6
Remember
1
Remember
4
Part - B (Long Answer Questions)
 /2
1
Provethat  (m, n)  2  sin 2 m1  cos 2 n1  d
0
Show that
2
1
x m1  x n 1
0
1  x 
  m, n   
m n
dx
Prove that
  m, n  
3
 m .  n 
 m  n
where m  0, n  0
1
4
0

1
0

( n) =  log 1
prove that
n
x m  log x  dx 
5
Apply
x
n 1
4
dx, n  0
Remember
 1 n !
n 1
 m  1
4
n
Apply
4
.If n is a positive integer,prove that
6
Remember
6
Remember
6
Remember
6
Provethat

1
0
7
x
m
 1 n !
 log x  dx 
n 1
 m  1
n
n
Evaluate
8
Express the integral
in terms of gamma function
9
Prove that
.
Apply
6
where p>0, q>0
10
Understand
6
Define beta function
Apply
1
2 Define gamma function
Apply
1
Part – C (Theory Questions)
1
3
Write the relation between beta and gamma function
Apply
1
4
Apply beta function in trigonometric form
Apply
1
5
Evaluate the value of B(1,2)+B(2,1)
Apply
1
6
Write the value of B(3,5)
Write the value of gamma of
Apply
1
7
Apply
1
Write the value of gamma of (n+1)
8
Apply
1
7
9
Write the value of
Apply
10
Write the value of
Apply
7
UNIT-III
Part - A (Short Answer Questions)
. Evaluate  a1cos  r dr d
0 0
1
1
z x z
2
Evaluate
1 0 x z  x  y  z dx dy dz
Remember
6
Understand
6
Remember
6
Remember
6
Remember
6
Remember
6
Remember
6
Remember
6
Understand
10
Evaluate
3
Evaluate
4
Evaluate
5
Evalate
6
Part – B (Long Answer Questions)
Evaluate
  y dx dy
where R is the region bounded by the Parabolas
R
y 2  4 x and x 2  4 y
1
Evaluate
2
3
Evaluate
4
evaluate
5
evaluate
Remember
Understand
6
6
Part – C (Problem Solving and Critical Thinking)
1 Define double integral
2
Apply
8
Apply
8
Apply
8
Evaluate
Evaluate
3
PREPARED BY:
1)G.CHANDRA MOHAN
2)K.VARALAXMI
3)K.SHIVAKUMARI