August
V55/V62/T63/T14022/T07022/T04022//EE/20150813
2015
Applied Mathematics - 1
Instructions
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
Marks80
Time:
3 Hrs
Marks
SECTION-A
Q.1
If f ( ) = Log , g (x) = x2, show that f [g (2)] = 3f (2).
15
OR
Q.1
Q.2
Evaluation
If
10 − 2 − 5 + 1
15
→
= k, show that
=-
15
.
OR
Q.2
a) Differentiate
√
With respect to x.
05
b) If y = 2. e-3x + 3.e 2x, show that d2y/dx2+dy/dx-6y=0
05
c) Differentiate the following w. r. to x :
05
i) (3x2 + 2)5
ii) sin (3x +5)
iii) e3x -7
Q.3
Q.4
Evaluate
05
→
Differentiate (Log x) sin x With respect to x.
05
SECTION-B
Q.5
a) Find the equation of a tangent to the curve y= x2-2x-3, where it cuts
the X-axis
b) Find the equation of the tangent to the ellipse 2x2+3y2=5, which is
perpendicular to the line 3x+2y+7=0.
10
05
OR
Q.5
.Fine the median of the following distribution
Marks
obtained
Number of
students
Q.6
010
5
10
10-20
20-30
30-40
40-50
8
27
14
6
b) Find the mode from the following data.
05
a) Express in the form a+ ib,
10
+
b) The crushing strength of 45 cement concrete blocks are recorded as :
05
Q.6
a) The age distribution of 25 students is given below.
10
Calculate the standard deviation.
Age in years
10
12
14
16
18
20
Number of
students
2
3
5
6
7
2
b) Find cube roots of unity and show that one root is square of the other.
05
1-cos∝ + i sin∝
Q.7
Calculate the mean of the following distribution :
xi
fi
Q.8
10
7
20
9
30
12
40
10
Simplify the following by using Demoiver’s theorem.
( Cos2 + i Sin2 ) 3/2 ( Cos - i Sin)3
***BEST OF LUCK***
05
50
8
05