Rising Nepal Secondary Boarding School

RISING NEPAL SECONDARY BOARDING SCHOOL

Class:- 10 FINAL EXAMINATION 2077 F.M:100

Time:- 3hrs. Sub:- Opt. Math P.M:32

Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

All the questions are compulsory.

Group ‘A’ [5x(1+1)=10]

1. a. Write the definition of composite function.

b. If 25, m, 35 are in arithmetic sequence, find the value of m.

2. a. Under what condition, the function f(x) will be continuous at the point x= a? Write in symbol.

b. If A= and B= , prove that AB is a null matrix.

3. a. Find the slope of a line y= 3x+7.

b. Write the condition of generating an ellipse, by the intersection of a cone and a plane surface.

4. a. If sinA= , find the value of sin2A.

b. sin, find the acute value of

5. a. If

b. Reflect point (2, 3) in the line x= 0.

Group ‘B’ [3x(2+2+2)+2x(2+2)=26)

6. a. If f(x)= 4x+k and f^-1(11)=2, find the value of k.

b. The polynomial f(x)= x³-(p-2)x² – px+28 leaves a remainder 10 when divided by (x+3), find the value of p.

c. If (p+10) is the GM of (p+2) and 9(p+2), find the value of p.

7. a. If A= , show that the 9 times inverse of A is A itself.

b. Given that A= , find the value of a, if A^T is singular.

8. a. Find the value of k, if the acute angle between the lines 2x-y= -6 and 3x+ky= -4 is 45⁰.

b. Find the angle between the lines represented by the equation x²-2xy cosec+y²= 0.

9. a. Prove that:

b. If sin= , show that sin3.

c. Solve: (0⁰: sin²

10. a. Vectors (5) and () are perpendicular to each other when and are unit vectors, find the angle between and

b. In , D and E divide AB and AC in the ratio AD:DB=AE:EC= 1:2. Prove that:

c. The sum of the squares of 7 terms is 9163. If their standard deviation is , find the co-efficient of standard deviation.

Group ‘C’ [11x4= 44]

11. Find the roots of : (x-1)(2x²+15x+15)-21= 0.

12. Solve graphically: x²-2x-8=0

13. Test the continuity of the function f(x)=2x²-3x+10 at the point x= 1 by calculating left hand limit and right hand limit.

14. Solve by Cramer’s rule: 5x+3y= 9, 4y+7x= 13

15. If the pair of lines represented by the equation (a+2)x²+8xy+(1-4a)y²= 0 are perpendicular to each other, find the equations of the line.

16. If A+B+C= , prove that

17. Solve (0⁰);

18. A man of height 1.6m stands at a distance of 4.68m from a lamp post. If it is observed that his shadow is 2.88 m long, find the height of the lamp post.

19. Reflect the with vertices M(1, 1), N(4, 1) and O(4, 5) on the line y= 1 and then the image so obtained is reflected by line x= 2. Find the coordinates of the images in both cases and draw on the graph paper.

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

Class Interval	0-10	10-20	20-30	30-40	40-50
Frequency	5	8	15	16	6

21. Find the standard deviation:

Marks Obt.	5-15	15-25	25-35	35-45	45-55
No. of sts.	7	3	6	4	5

Group ‘D’ [4x5= 20]

22. Maximize the objective function P= 8x-y+20 under the following constraints: 2x+y

23. Find the equation of a circle whose centre is (4, 5) and passes through the centre of the circle x²+y²+4x+6y-12=0.

24. Diagonals of parallelogram bisect each other. Prove by the vector method.

25. A(1, 2), B(-4, 3) and C(3, 5) are the vertices of ABC, find the coordinates of the image if under the translation T= followed by the enlargement with the centre at (3, -1) and scale factor 2. Draw and its image on graph.

The End