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
(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
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
|32 towards E||UP to D80
|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
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
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