SEE Booster Examination
Optional Mathematics
2078(2022)
Time: 3:00 hrs. Full Marks:100
Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.
Attempt ALL the questions
Group 'A' [10 × 1=10]
1. a) What is the y- intercept of = sin X.
b) Define Sequence with an example.
2. a) Write the set of numbers which is continuous in number line?
b) Find determinant of |-5|
3. a) If a plane intersects a cone parallel to its generator, write the Name of section so formed?
b) Prove that the straight line having equation px+qy+r=0 and qx-py+s=0 are perpendicular to each other.
4. a) Express cos , find the value of cos θ.
b) Express 2sin A.cos B in sum and difference form?
5. a) Writhe the formula for finding the angle between two vectors?
b) In an inversion transformation if P' is image of P and r is radius of inversion circle with Centre O, write the relation of OP. OP' and r.
Group 'B' [13×2=26]
6. a) If f(x) =3x+2 and g(x)=2x-1, find the function gof(x).
b) The arithmetic mean of m and 8 is 5, find the value of m.
c) If find Q(x) by using synthetic division method.
7. a) If the matrices and are inverse to each other, find the value of .
b) If D = 7, Dx = 14 and Dy = 21. Find the value of x and y by using Cramer's rule.
8. a) If the lines and are parallel to each other, prove that .
b) Find the separate equation of: ab(x2-y2)+(a2-b2)xy=0
9. a) If cos A = , find the value of cos3A.
b) Prove that: =tan55°
c) Solve: = 0 (0° £ q £ 90°)
10. a) If A (3, 5), B (5, -1) and C (2, 4) are the vertices of ΔABC and G is the centroid of ΔABC. Find the position vector of G.
b) In the given pentagon ABCDE, prove that:
.
c) In a continuous series 35 and 75 find the quartile deviation and its coefficient.
Group 'C' [11×4=44]
11. Solve: x3 = 0
12.Optimize P = 5x + 4y under the given conditions: x – 2y ≤ 1, x + y ≤ 4, x≥ 0 and y≥ 0.
13. For a real valued function
a) Find the values of and
b) Is this function continuous at x = 3.
14. Solve by matrix method: 3x+5y=11 and 2x-3y=1
15. If the straight lines represented by are perpendicular to each other, then find the value of Also find the equation of straight lines represented by
16. Prove that:
17. If A+B+C= , prove that:
18. The angles of elevation of the top of a tower observed from 49m and 64m from the foot of the tower are found to be complementary. Find the height of the tower.
19. If the matrix transforms a unit square to the parallelogram , find the values of m, n, p and q.
20. Find the mean deviation from median of the given data.
|
Class |
0-10 |
10-20 |
20-30 |
30-40 |
40-50 |
|
Frequency |
2 |
3 |
6 |
5 |
4 |
21. Find mean and standard deviation from the given data
|
Class |
0-4 |
4-8 |
8-12 |
12-16 |
16-20 |
|
Frequency |
10 |
9 |
12 |
11 |
8 |
Group 'D' [4×5=20]
|
A |
|
B |
|
Y |
|
X |
|
|
23. In the given figure the circle A with the center X passes through center Y of the circle B. If the equation of circle B is and the coordinate of X are (-4, 5), then find the equation of circle A.
24. Prove that the diagonals of a parallelogram bisect each other.
25. The vertices of LOVE are L (2, 2), O (6, 2), V (7, 4) and E (3, 4). Find the coordinates of the vertices of the image of LOVE under the rotation of positive about origin followed by enlargement E[(0, 0), 3]. Represent the object and images on the same graph paper.
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