# Rajasthan Board Secondary Examination 2011 – Maths Paper II

## Rajasthan Board Secondary Examination 2011 – Maths Paper II

1. (i)The area of a parallelogram and a triangle are equal and their base is common. If altitude of parallelogram is 6 cm, then altitude of triangle will be
(A)12 cm               (B) 6 cm
(C) 4 cm                 (D) 3 cm.                                                                        ½

(ii)In figure, 0 is the centre of the circle and L POR = 140″. then the value of L PQR will be                                                                              ½ (A)40°                                                               (B)100°
(C)110°                                                            (D)220°.

(iii)Diameter of a semicircle is 16 cm. Its area will be                           ½
(A)8 π sq.cm                                                 (B)16 π sq.cm
(C) 32 π sq.cm.                                            (D)64 π sq.cm.

(iv)If cos Θ = √3/2 , then the value of Θ will be                                             ½
(A)90°                                                              (B)60°
(C)45°                                                              (D)30°

2. Find the ratio of the lengths a side and a diagonal of a square.           ½

3. Write the relation between angles in the same segment of a circle.½

4. Circumference of a circle is 220 metres. Find its radius. (π=22/7)    ½

5. If cot Θ = 1/ √3 , then find the value of sin Θ.

6. Write the simplified form of cot Θ/ √(1+cot² Θ)

7. Find the value of 2 sin 45°. cos 45°.

8. Write the locus of a point equidistant from two intersecting straight lines.                                                                                                              1

9. Find the length of a chord which is a t a distance 5 cm from the centre of circle of radius 13 cm.                                                                        1

10. In figure. PQ is diameter of the circle and L SPQ = 40°. Then find the value of L PRS.                                                                                                      1 11. Find the opposite angles of a cyclic quadrilateral, if one of them is 2/3 of the other.                                                                                                           1

12. If the distance between two points ( x , 3 ) and ( 5, 7 ) is √17, then find the value of x.                                                                                             1

13. Prove that sin 65°+ cos 25°= 2 sin 65°.

14. Prove that 4 cot²45° – sec²45°+ sin²30° = 1/4

15. In figure, AD is the right bisector of side BC, then prove that L ABP = L ACP.                                                                                                          2 16. Prove that the quadrilateral formed by joining the mid-points of the adjacent sides of a quadrilateral is a parallelogram.                            2

17. Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of L BAC.                                                            2

18. With the help of the measurements of the table given below, prepare a rough diagram of the field and calculate the area.                    2

 Meter 32 towards E UP to D80 50 40 54 towards C   26 towards B From A towards north

19. A sector is cut from a circle of radius 10.5 cm such that angle of the sector is 45°. Find the length of the arc and area of the sector.   2

20. The length, breadth and height of a cuboid are 9 cm, 6 cm and 4 cm respectively. It is melted to form a new cube. Find the total surface area of the new cube.                                                                                 2

21. Find in what ratio the line x + y = 4 divides the line segment joining the points ( – 1, 1 ) and ( 5 , 7 )                                                                  2

22. Prove that sin Θ/(1+cos Θ) + (1+cos Θ)/sinΘ = 2 cosec Θ.             2

23. In figure, a toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the base of the conical portion is 6 cm and its height is 4 cm. Find the surface area of the toy.               3 24. A person from a point on the level ground observes, the angle of elevation of the top of a tower a s 30°. He walks 50 metres towards the foot of the tower along level ground and finds the angle  of elevation of the top of tower a s 45°. Show that the height of tower is 25 ( √3 + 1 ) metres.                                                                                                       3

25. In figure, PAB is a secant of a circle intersecting the circle a t A and B. PT is a tangent at point T. Prove that PA . PB = PT².                                 3 OR

In figure,. a circle touches the side B C of triangle ABC at P and touches AB and AC produced at Q and R respectively. Prove that
AQ =1/2( perimeter of Δ ABC). 26. Construct a triangle ABC, in which side BC = 5.4 cm, L B = 60″ and L C = 75″. Draw incircle of the constructed triangle and also write the steps of construction.                                                                              3

OR

Construct a triangle PQR in which side QR = 4.2 cm, L P = 55″ and L Q = 65″. Draw its circumcircle and also write the steps of construction. 3