Applied mathematics-2
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Question paper 1
SECTION-A
Q1. a) Choose the correct answer.
i. If A is a non singular matrix, then A-1 is
a) |A| adj A b)
c) (adj A)T d)
Answer:
(b)
ii.
a) π b)
c)
d) 
Answer:
(c)
(iii) limx->0
a) 1 b) π
c)
d) -πAnswer:
(a)
iv. Order of differential equation (y''')2 + 2y'' + 3y = x is
a) 3 b) 4 c) 1 d) 2
Answer:
(a)
v. The differential coefficient of sinx2 w.r.t cosx2 is
a) -tan x2 b) -cot x2 c) 2x d) -2xAnswer:
(b)
b) State True or False.
vi. The differential coefficient of a constant is one.Answer:
False
(vii)
if 
is even.Answer:
False
viii. Mean Deviation =
Standard DeviationAnswer:
True
ix. Volume of a sphere of radius 'a' is
π 
Answer:
True
x. cos 2A = cos2A - sin2A
Answer:
True
c) Fill in the blanks
xi. The angles in trigonometric functions are supposed to be measured in ______.
Answer:
Degree or radian
xii. A square matrix is said to be a diagonal matrix if all its non-diagonal elements are______.
Answer:
Zero
xiii.
is equal to______.Answer:
Log(g(x)) + constant
xiv. Central value of the set of observation is called_______.
Answer:
Central Tendency
xv. The derivative of ?ex is equal to________.
Answer:
ex
SECTION-B
Q2. Attempt any six questions.
a. In a class of 30 students with roll no. 1 to 30, a student is picked up at random to answer a question. Find the probability that the roll number of selected students is either a multiple of 4 or 7.Answer:
= 4,8, 12,16,20,24, 28
& 
b. If ?y = ex+y prove that
= 
Answer:
c. Calculate by Simpson’s rule an approximate value of
by taking seven equidistant ordinates.Answer:
7 equidistant co-ordinate
Equation..
d. Find the equation of the tangent to the curve y = x2 whose slope is
. Answer:
Y =
------------- 1The slope of tangent to 1 at point (
is 
Y =
Slope =
Also
lies on curve 1
∴Requrid equation of tangent is
Y =
16y= 8x-1
8x -16y =1
e. Evaluate
.Answer:
I =
Put
Dx =
=
= 
=
= 2
= 2 tan
f. Find the area bounded by the curve y = log x between the x-axis and the ordinates x = 2 and x = 3.
Answer:
Y =logx
=
=
= log
-1g. If y = tan-1x , prove that (1 +x2) y2 + 2xy1 = 0
Answer:
Y =
=
= (1+
= -2x.
h. Solve the equations by Crammer’s rule.
Answer:
A=
= 
X =
y = 
X= -1 y = 4
i. 5x + 2y = 3
Answer:
j. 3x + 2y = 5
Answer:
k. Evaluate
Answer:
I =
Put logx = t
=
=
=
=
SECTION-C
Q3. Attempt any three questions.
i. Solve the following equations by matrix method
3x + y + 2z = 32x - 3y - z = -3
x + 2y + z = 4
Answer:
3x+ y+2z=3
2x-3y-z=-3
X+2y+z=4
Ax=B
X =
Where
A=
A =
= -3-3+14= 8 ≠ 0
(adj.A)=
= 
Ax = B
X=
X =
=
= 
X = 1 , y= -2 , x=1
ii. Find the maximum and minimum values of the function x3 - 6x2 + 9x + 15
Answer:
= 6(3) -12>0∴x=3 is Point of minima
Maximum value is
= 1-6 + 9 + 15 = 19
Min. value is =
= 27-54+27+15
= 15
iii. Find the standard deviation from the following data
Wages
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
Frequency
12
18
35
42
50
45
20
8
Answer:
Wages
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
F
12
18
35
42
50
45
20
8
N= 230
X
5
15
25
35=a
45
55
65
75
D=x-35
-30
-20
-10
0
10
20
30
40
Fd
-360
-360
-350
0
500
900
600
320
10800
7200
3500
0
5000
18000
12800
Standard deviation =
=
= 
=
= 17.25 iv. Solve the differential equation
y2(x2 - 1)
- x2 (y2 - 1) = 0Answer:
=
=
v. Integrate x2 sin2x dx
Answer:
I =
=
=
=
=
=
=
