Symbol No .....
SRE-231
SEE (Supplementary/Upgrade) 2075 (2019)
Optional Mathematics (Optional I)
Time: 3hrs FM: 100
Answer all the questions.
Group ‘A’
[8x (2+2) = 32]
1.
a. If g(x)
= 5x - 1, then find the value of gg (1).
b. If (x
+ l) is a factor of the polynomial 3x3 - 5x2 - 10,
find the value of k.
2.
a. Find the
fifteenth term of the series 2+5+8+……
b. Write
the definition of inverse matrix. In which condition the inverse matrix cannot
be defined? Write it.
3.
a. If 
find the matrix M.
find the matrix M.
b. Write
down the formula to find the angle between the lines y = m1x + c1
and y = m2x + c2. Also write the condition of
perpendicularity of these lines.
4.
a. If a
pair of straight lines represented by the equation
9x2 – mxy +16y2 = 0 are
coincident, find the value of m.
b. The
two end points of a diameter of a circle are (1, 0) and (0, 5), then
find the equation of the circle.
5.
a. Find
the value of sin1050 without using a calculator or
table.
b. 
6.
a. Prove
that: 
b. Solve:
7.
a. 
b. In the
given figure, AD = DC and centroid of the AABC. If the position c
the points B and D are 
respectively, find the position vector of G.
respectively, find the position vector of G.
8.
a. Let R1
denotes the reflection on y-axis and R2 denotes a rotation of
+900 about the center 0(0, 0), then for any point A (3,
4), find R1 R2 (A).
b. Which
transformation does the matrix 
represent? Find it.
represent? Find it.
Group ‘B’ (17x4 = 68)
9. If f(x)=
2x + 3, g(x)= 2x – 5 and g0f(x)= g-1 (x), find the value
of x.
10. Solve:
x2 -6x2 + 11x – 6 = 0
11. If the
second term of a geometric series is 6 and fifth term is 48, then find the sum
of the first 6 terms of the series.
12. Solve the given equation graphically: x2
-x – 6 = 0
13. Solve
by matrix method: 
14. Find
the equation of a straight line passing through the point (4, -l) and
perpendicular to the line 2x - 3y=5.
15. If an
angle between the pair of lines represented by 2x2 + kxy + 3y2
=0 is 450, find the positive value of k. Also find the
separate equations of the lines.
16. In the
given figure, the circle A with centre X passes through the centre Y
of the circle B. If the equation of circle B is x2+y2-4x+6y-12=0
and the co-ordinates of X are (-4, 5), then find the equation of
the circle A.
17. Without
using the calculator or table, find the value of:
cos 1000.cos 1200.cos1400.cos
1600.
18. If P,
Q and R are the angles of a APQR, prove that: 
19. Solve: 
20. From the
roof of a building16 meter high, the angles of elevation and depression of the
top and the foot of an electric pole are observed to be 600 and 300
respectively. Find the height of the pole.
21. In Δ APQR,
A and
B are the mid-points of the sides PQ and PR respectively.
Prove by vector method that: AB II QR.
22. Points
A (2, 3), B (2, 6) and C (3, 4) are vertices of a triangle ABC.
The triangle is translated by
.Then the image is enlarged by E [(O, 0), 2].
Write the co-ordinates of the vertices of the images so formed and present AABC
and its images in the same graph paper.
.Then the image is enlarged by E [(O, 0), 2].
Write the co-ordinates of the vertices of the images so formed and present AABC
and its images in the same graph paper.
23. A line
segment AB joining the points A (4, 1) and B (7, 5) is
transformed to form the image A'B', the line segment joining point A'(-4, 1)
and B'(-7, 5). Find the 2x2 matrix that represents this
transformation.
24. Find
the mean deviation and its coefficient from median of the data given below:
10, 50, 60, 40, 30, 20
25. Calculate
the coefficient of variation from the following data:
Class interval
|
0-20
|
20-40
|
40-60
|
60-80
|
80-100
|
Frequency
|
2
|
3
|
4
|
5
|
6
|
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