August
2015
T05/T24/TES12/TML012/EE/20150812
APPLIED MATHEMATICS-1
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)Find sum and product of roots of x2+px+k=0.
B)Find the value of
i] ‫׀‬9-‫ ׀‬-‫׀‬7-‫׀‬
10
ii] ‫׀‬13‫ ׀‬+‫׀‬25-‫׀‬
5
OR
Q.1 A) Simplify:-i)
ii)
√
3
2√ +√
B)Find the antilog of
10
−√ −√
−√
i] 3.1596
ii]0.7689
Q.2 A)Show that : cos(A+B).cos (A-B)= cos2A-sin2B.
B)What is de-moivre's theorem?
5
10
5
OR
Q.2 A) In a triangle ABC show that:
( − )
+( + )
10
=a
2
B) Find the modulus and argument of 2+2√3i.
5
Q.3 Find the sum of the Arithmetic progressions of -3,3,9,15……..to
20 terms.
5
Q.4 Find the area of triangle whose c=4,b=6 and angle A=600.
5
SECTION-B
Q.5 A)Draw the graph of y=2sinx and write down the period and
amplitude of that function.
10
B)Find the slope of the line passing through (3,0),(8,0).
5
OR
Q.5 A)Find the equation of a line
i) with slope 2 and passing through (5,7).
10
ii) with slope 5 and y-intercept 3.
B) Find the equation of the circle with the following points as the
ends of a diameter (2,3),(5,-1).
Q.6 A) Find two unit vectors perpendicular to both the vectors i+j-k and 3i+j-
5
10
2k.
B)Two fair dice are rolled.Find the probability that the score is 8.
5
OR
10
Q.6 A) Find the mean and standard deviation of the following data.
Class-interval
Frequency
5-15
8
15-25
10
25-35
15
35-45
20
45-55
12
55-65
5
B)Find the 1's compliment: i) 0101 ii)1111
5
Q.7 Find the centres and the radius of the circles x2+y2-4x-5=0.
5
Q.8 Show that the points A(-1,1,-2), B(1,2,3), C(5,4,13) are collinear.
5