# Rajasthan Board Secondary Examination 2010 – Maths Paper II

##### Rajasthan Board Secondary Examination 2010 – Maths Paper II

1. (i)In a parallelogram ABCD, ∠A = 7 0°, then the value of∠B is
(A) 20°                              (B) 70°
(C) 110°                           (D) 90°.                                                          ½

(ii)If the distance between points ( x, 3 ) and ( 5, 7 ) is 5, then the value of x is
(A) 2                                 (B) 4
(C) 0                                 (D) 3                                                                ½

(iii) sin Θ cosec Θ + cos Θ sec Θ is equal to
(A) 2                                 (B) 1
(C) 0                                 (D) -1                                                                   ½

(iv)In figure, if the diameter EC is parallel to AD and ∠ABC = 50°, then the Value of ∠CAD is (A) 50°                          (B) 40°
(C) 130°                       (D) 25°.                                                                      ½

2. In figure, ABCD and AEFG are two parallelograms. If ∠C = 60°, write the value of ∠GFE.                                                                            ½ 3. Write the name of that are of the circle which subtends a right angle on the remaining part of the circle.                                             ½

4. The opposite Vertices of a square are ( — 5, — 4 ) and ( 3, 2 ). Write the length of its diagonal.                                                                                 ½

5. Write the Value of : sin4Θ—cos4Θ / sin²Θ—cos²Θ.                        ½

6.Diameter of a semicircle is 8 cm. Find its area.                                 ½

7. Write the length of arc which subtends an angle of 180° at the centre of circle of radius r.                                                                            ½

8. Write the name of the triangle, in which the orthocentre, the incentre and the circumcentre are the same.                                1

9. Write the name of area enclosed by any two radii and are determined by the end points of the radii.                                    1

10. In an equilateral triangle ABC, AD is perpendicular to BC, then find AB² : AD² .

11. Find the Value of 3sin 60° — 4 sin³ 60°.                           1

12. If sum of the squares of the sides of a rhombus is 64 sq.cm, then find the sum of squares of its diagonals.                                1 1

3. In figure, if ∠ ADC = 80°, then write the value of ∠ CBE.            1 14. In figure, O is the centre of the circle and O C is the bisector of ∠ ACB. If AC = 4 cm, then find BC.                                 1 15. Two circles of radii 5 cm intersect each other at A and B . If the common chord AB = 6 cm, then find the distance between their centres.                                                2

16. The sum of length, breadth and height of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the total surface area of the cuboid.                                                     2

17.  From the table given below, prepare a rough diagram of the field book and calculate the area.                 2

 Metre 75 towards E Upto D 150 125 100 50 towards C 25 towards B From A towards north

18. In a triangle ABC , AD is the bisector of ∠ A . D E and D F are perpendiculars on AB and AC respectively. Prove that DE = DF.   2

19. In figure, PQRS is a rectangle. The side PQ = 10 cm and QR = 7 cm. As shown in figure circles of same radius are drawn at each vertex of the rectangle. Find the area of shaded portion.                                         2

20. If sec θ + tan θ = p, then prove that p²-1/p²+1= sin θ.                           2

21. If the point P ( – 1, 2 ) divides the line segment joining A ( 2, 5 ) and B internally in ratio 3 : 4, find the coordinates of B.                          2

22. If θ = 30°, then find

(3 cot ( 90 ̊ – θ ) – tan³ θ) / (1 – 3 cot² ( 90 ̊ – θ ))

23. If h, c and v are the height, the area of the curved surface and the volume of a cone respectively, then prove that

3 πvh³ – c 2 h² + 9v²= 0.                                                                                        3

24. The angle of elevation of top of a pillar from a point on the ground is 15°. On walking 100 metre towards the pillar, the angle of elevation becomes 30°. Find the height of the pillar.                       3

25. In figure, PA and PB are tangents to a circle. If M is a point on the circle, then prove that PL + LM = PN + NM.                                     3 OR

If PQ and PR are two equal chords of a circle, prove that the tangent
at P is parallel to the chord QR.                                                                         3

26. Construct a triangle ABC, in which BC = 5·8 cm, ∠ A = 65° and altitude AD = 3·1 cm.                                                                                       3

OR

Construct a triangle ABC, when BC = 4·8 cm, ∠ A = 70° and the median from A is 3·2 cm.                                                                              3