SEE Opt. Math Set IV

Prepared By Keshav Saud RE – 231 Prepared By Keshav Saud RE – 231

SEE Practice Model Set I 2078 (2021) (b) What is the inversion point of a point P(x, y) with respect to the
circle with the centre at origin O (0, 0) and radius ‘r’?

Optional I (Mathematics) Group ‘B’ [3 × (2 + 2 + 2) + 2 × (2 + 2) = 26]
Max. Marks – 100
Time - 3 hours 6. (a) Find the remainder and quotient of the polynomial x3 – 5x2 + 2x
(b) – 5 when divided by (x – 3) by using synthetic division.
Candidates are required to answer in their own words as far as practicable. (c) Show that (3x + 2) is a factor of the polynomial 6x3 + 13x2 – 4.
The figures in the margin represent the full marks.
Attempt all the questions. 7. (a) What is the vertex and equation of line of symmetry of the

(b) parabola having equation y = – x2 + 6x – 5? Calculate it.
8. (a)
x 1  2 –1 
(b) If A =   and B =   are inverse to each other, find
 5 2   –5 x 
Group ‘A’ [5 × (1 + 1) = 10] 9. (a)

1. (a) Which type of function is shown (b) the value of x.
by the given graph? (c)
10. (a) In the equations, 2x + 3y = 12 and x + y = 5, find the value of x
(b) What is the geometric mean using the Cramer’s rule if the value of D = –1.
between p and q? Write it. If the straight lines 2x + 3y + 6 = 0 and ax – 5y + 20 = 0 are

perpendicular to each other, find the value of a.

2. (a) If matrix A = a b , what is the value of | A |? Find the angle between the pair of lines represented by the
c d equation x2 – 2xycot – y2 = 0.

(b) Under what condition, the limit of a function (x) is continuous 1 + secA
Express tanA in the terms of sub - multiple angle of

at x = a? cotangent angle.
sin(80 + A) – sin(80 – A)
3. (a) What is the angle between two straight lines whose equations are
Prove that: cos(80 + A) + cos(80 – A) = tanA.
y = m1x + c1 and y = m2x + c2? Write it.
(b) If the intersection of the plane is parallel to the base of cone, Solve for x: (3sinx – 4) (2sinx + 3 ) = 0 [0  x  360]

which conic section does it form? If x and y are two vectors such that |x | = 6, |y | = 4 andx .y

4. (a) What is the value of cos2 in terms of sin? Write it.

(b) For 2sin, what is the least positive angle of ? Find it. = 12 2 , then find the angle between x andy .

5. (a) What is the scalar product of two vectors a and b if the angle

between them is ?

Prepared By Keshav Saud RE – 231 Prepared By Keshav Saud RE – 231

(b) In the given figure, ABC is a triangle in which of the top of the first electric pole is found to be 60. Find the

angle of elevation of the top of the second electric pole from the
D is the mid - point of AB and BC = 2 DE .
Prove that E is the mid – point of AC. foot of the first electric pole.
(c) In a grouped data, quartile deviation is 10 and coefficient of
19. Find the 2 × 2 matrix which transformed the unit square
1
quartile deviation is 2 , then find the value of first quartile. 0 1 1 0 0 3 4 1
matrix  into a parallelogram .
0 0 1 1 0 1 3 2

20. Find the mean deviation from median of the following data:

Wages in Rs. 0-4 4-8 8-12 12-16 16-20 20-24

Group ‘C’ [11 × 4 = 44] No. of people 7 7 10 15 7 6

21. Calculate the standard deviation and coefficient of variation from

x–2 the data given below:
11. If g(x) = 3 and h(x) = 3x + 2, show that gh(x) is an identity
Expenditure in Rs. 0 - 10 10- 20 20- 30 30- 40 40- 50
function.
12. There are 6 arithmetic means between m and n. If the value of No. of workers 5 8 15 16 6

second mean and fifth mean are 11 and 23 respectively, then Group ‘D’ [4 × 5 = 20]
estimate the value of m and n.
13. Solve the following system of linear equations by using the 22. Write one importance of linear programming in daily life.
Calculate the maximum and minimum value of the objective
2x y function F = 3x + 5y – 2 subject to x – y  2, x + y  4, x  0 and
inverse matrix method: 3 + y = 16 and x + 4 =14. y  0.
14. If : R  R denoted by (x) = x + 5, then show that the function
(x) is continuous at x = 1. 23. The circular ring A with centre P passes through the centre Q of
15. What is the single equation of straight lines which passes through the circular ring B. If the equation of circular ring B represents
the point (1, 1) and parallel to the pair of lines represented by the as x2 + y2 – 4x + 6y – 12 = 0 and the co – ordinates of centre P of
equation x2 – y2 = 0? Find it. the circular ring A is (–4, 5), then find the equation represented
16. Find the value of cosec290 – 3 sec250 . by the circular ring A. Also, calculate the distance between their
17. If A, B and C are the vertices of ABC, then prove the following centres.
relation: 2 – sin2A – sin2B – sin2C = – 2cosA. cosB. cosC.
18. There are two electric poles of height 90m and 30m respectively. 24. Prove by vector method that the diagonals of rectangle are equal.
From the foot of the second electric pole, the angle of elevation

Prepared By Keshav Saud RE – 231 Prepared By Keshav Saud RE – 231

25. The vertices of a quadrilateral ABCD are A (1, 1), B (2, 3),
C (4, 2) and D (3, –2). First rotate this quadrilateral about origin
in anticlockwise direction through 180 and then reflect the
images of quadrilateral ABCD so formed by the reflection about
the line y = – x. Then, find the final images of quadrilateral
ABCD by drawing all the figures in the same graph paper. Also,
state the name of transformation which denotes the combined
transformation of above two transformations.

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