Optional Math 10

8 Statistics i. Quartile Deviation – 1 2 – 3 10 12
170
ii. mean Deviation

iii. Standard

Deviation

Total Questions 10 13 11 4 38

Total Marks 10 26 44 20 100

K = Knowledge, U = Understanding, A = Application, HA = Higher ability

1. a. Model Question Set for SEE Examination
b.
2. a. Group : A [10 × 1 = 10]
b. Define the term composite function.
3. a. In what condition x - 2 will be the factor of a polynomial p(x)?
Write down the condition of continuity of a function f(x).
b. Find the determinant of a matrix <CSoinsii CSoinsiiF
4. a. Find the slope of a straight line which is perpendicular to the another straight line
b. a
5. a. of slope b .
b.
Prove that the line pairs of 4x2 + 6xy – 4y2 = 0 are perpendicular to each other.
Prove that Cos2A = 1 – 2Sin2A.
Prove that Sin(A + B) + Sin(A – B) = 2sinACosB.

If a = dx1 n and b = dx2n find a.b .
y1 y2

Find the image of p(x, y) under FoG where F is rotation about +270 with centre
origin and G is refection about y = x.

3x – 2 Group : B [13 × 2 = 26]
2
6. a. If f-1(x) = , find f(x).
b.
c. Insert 3 AMs between 40 and 16.

7. a. Write down the co-ordinate of the points on a parabola of ax2 + bx + c = 0 which are

b. the intersecting point of x - axis and the parabola.
8. a.
b. If D = 13, Dofx t=he39vaarniadblDeys = 26 are the determinants of the columns of two linear
equations x and y, find the value of 'x' and 'y'.
9. a.
b. If <–3 aF is the inverse of a matrix <–7 5F , find the value of 'a' and 'b'.
c. –4 7 –4 b
10. a.
If angle between the line pairs of px2 – 7xy – 15y2 = 0 is 45°, find the value of 'p'.

Find the co-ordinate of image of a point (4, 2) under a inversion circle having center
(1, 1) and radius 20 units.

Prove that : 1 + Sini + Cosi = Cot i .
1 + sin i – Cosi 2

Prove that : 2Cos(45° + A)Sin(45° – A) = 1 – Sin2A

Solve (0 ≤ q ≤ p) : Tanq + 2Sinq = 0

If the vectors 3 i + mj and 4 i – 3j are arthogonal vectors, find the value of m.

PRIME Opt. Maths Book - X 347

b. Prove that AB2 + BC2 = AC2 by vector method in the given diagram. A

c. If third quartile of the continuous frequency distribution is 80
whose quartile deviation is 30, find the coefficient of quartile
deviation.

Group : C [11 × 4 = 44] BC
11. Solve the polynomial : 6x3 + 17x2 – 5x – 6 = 0

12. Find the number of terms of an AP whose last term is 58, sum of first four terms is 48 and
sum of last four terms is 208.
2x – 1 for x < 0
13. Determine the function f(x) = 3 for x = 0 is continuous or not.

x + 1 for x > 2

14. Solve the equations 3x 5y = 7 and 5x – 3y = 1 by matrix method.
2 –3 4

15. Find the equation of diagonal AC of a square ABCD where two of the vertices are A(3, 1)
and B(–1, 7).

16. IPAfrAboov+aetBtihs+actCo:=mCoi2pns,gepctrqoow+vaeCrtodhssaettch:2qeSis+ne2CaAo-Ss+heSocir4qne2B=wCh+oeSrtie8nq2tCh–eC=ao1ntq–gl2eSoifndAeSpinrBesSsiinoCn of it from the top
of a light house is 30°. After 10 seconds depression changes to 60°. At what time the boat
17.
18.

reached to the sea-shore?

19. Find the image of unit square by using 2 × 2 matrix of a transformation where x = 2x – y
and y = x + 3y.

20. Find mean deviation from mean and its coefficient of :

Class 0-8 8-16 16-24 24-32 32-40
f 23 5 6 4

21. Find root mean square deviation of :

Marks 10-18 20-28 30-38 40-48 50-58
f 4 7 12 10 7

Group : D [4 × 5 = 20]
22. Find the inequalities represented by the given feasible region. Also maximize the function
F = 4x + 3y.
23. Find the equation of circle having equation of two Y

diameters x + 2y = 5 and 3x – y = 1 which touches the 6
straight line of equation 3x + 4y + 4 = 0. 5 (1, 5)

24. Prove by vector method that the diagonals of a rhombus 4
(0, 3) 3
are bisected at right angle.
25. Find the co-ordinate of image of DABC having vertices 2
1 (6, 0)
A(3, 2), B(1, –2) and C(0, 3) under enlargement about X' –2 –1 O –11 2 3 4 5 6 7 X
3 –2
E1[0, 2] followed by E2 [0, 2 ]. Also find the single
Y'
transformation. Plot the object and images in graph.

348 PRIME Opt. Maths Book - X