SEE EXAMINATION MODEL QUESTIONS 2076
(2020)
Sub:
Optional Mathematics
Candidates
are required to answer in their own words as for as practicable. Credit shall
be given to originality in expression, creativity and neatness in hand, not to
rote learning.
Time: 3:00hrs
FM: 100,
PM: 40
Attempt all the questions
Group A 10×1=10
1. a. What does n represent
in the formula r=(b/a)1/n+1,where the symbols have their usual
meanings?
b. State the remainder theorem of polynomial.
2. a. Write the
symbolic notation of left hand limit.
b. Find the determinant of 
3. a. If the
intersection plane is parallel to the base of cone, what conic does it form?
b. What is the formula of angle between the lines represented
byax2 +2hxy + by2 =0?
4. a. Express sin2A in
terms of tanA.
b. What acute value of 
satisfies the trigonometric equation tan
= 0?
satisfies the trigonometric equation tan = 0?
5. a. Define the scalar
product between 
and
having same initial
point.
and having same initial
point.
b. If the radius of the adjoining inversion circle is P cm
then find OP×OP’.
Group: ‘B’ 13×2 =26
6. a. If f(x+2) = 2x +3 then find f -1(4).
b. What must be added
to x3 – 6x2 + 11x -8 to make it a polynomial having a
factor (x-3)?
c. The parabola of a quadratic equation is symmetric with Y
axis. If it passes through (0,0) and (2,4), find the equation.
7. a. If A= 
and B= 
for what value of p, AB is a singular matrix?
and B= for what value of p, AB is a singular matrix?
b. In the equation 2x+3y=12 and x+y=5, the value of D=-1 find
the value of x using Cramer’s rule.
8. a. Find the
homogeneous equation of second degree from the pair of lines
=2 and
=2
=2 and =2
b. Find the centre and radius of circle (x-2)2 +
(y-3)2 =49
9. a. Find the value
of (sin75o + sin15o) without using table or calculator.
b. Prove that: 
=cot
=cot
c. Solve for acute angle: 2 sin2
10. a. If
+ + 
=0,
= 6,
=10 and 
=14. Find the angle
between and .
+ + =0,= 6,=10 and =14. Find the angle
between and .
b. The position vectors of the point A and B are (8 
+
) and (3 +
) respectively. Find the position vectors of the point C,
which divides AB in the ration of 2:3 respectively.
+ ) and (3 +) respectively. Find the position vectors of the point C,
which divides AB in the ration of 2:3 respectively.
c. In a continuous data, the value of the first quartile is
two times of the value of quartile deviation. Find the coefficient of quartile
deviation.
Group ‘C’ 11×4=44
11. Two functions are f (x) =
+ 
and fog (x) = 
If (gof)-1 (x) is an identity
function, find the value of x.
+ and fog (x) = If (gof)-1 (x) is an identity
function, find the value of x.
12. The sum of three
numbers in an AP is 21. If the second number is reduced by 1 and the third term
is increased by 1, we obtain the GP. Find the numbers.
13. Identify whether the function h(x) = 
has continuity or
discontinuity at x=2.5.
has continuity or
discontinuity at x=2.5.
14. Solve by the
matrix method 
=
.
=.
15. P(3,6), Q (10,7)
and R (7,3) are the points at the circumference of a circle. If 
PRQ = 90o then find the equation of circle and the
equation of radius (RC).
PRQ = 90o then find the equation of circle and the
equation of radius (RC).
16. Prove that:
Cos3α+Cos3(120+α)+Cos3(240+α)
17. If A+B+C = 
then prove that:
then prove that:
Cos A+ Cos B +CosC= 4 Cos 
-1
-1
18. The height of a
tower is half the height of the flagstaff at its top. The angle of elevation of
the top of the tower as seen for any point on the ground is 30o.
Find the angle of elevation of the top of the flagstaff from the same point.
19. Find the 2×2 transformation matrix which transforms a square ABCD with
vertices A(2,3), B(4,3), C(4,5) and D(2,5) into a square A’B’C’D’ with vertices
A’(3,2), B’(3,4), C’(5,4) and D’(5,2).
20. Find the mean
deviation from median of the data given below:
|
Class interval
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
|
Frequency
|
5
|
8
|
15
|
16
|
6
|
21. Calculate the
standard deviation from the data.
|
x
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
|
f
|
5
|
4
|
4
|
6
|
1
|
Group D 4×5=20
22. Find the minimum
value of Z= 2x-3y under the following constraints.
.
23. Find the equation
of the straight lines passing through the point (4,5) and making an angle of 45o
with the line 2x-y+7=0.
24. Prove by vector
method that, the diagonals of rhombus intersect to each other at right angle.
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