# Rajasthan Board Secondary Examination 2014 Mathematics Paper

Rajasthan Board Secondary Examination, 2014

Mathematics

PART – A

1. Number 3/365 is a terminating decimal or a non-terminating repeating decimal ? Write it in decimal form.
1. Write the solution of the pair of linear equations 3x + 4y = 0 and 2x – y = 0.
1. Write the next two terms of P. 4, 1, – 2, – 5, …… .
1. Write the distance of the point ( 3, – 2 ) from y-axis.
1. If M ( 4, 5 ) is the mid-point of the line segment AB and co-ordinates of A are ( 3, 4 ), then find the co-ordinates of point B.
1. If tangents TA and TB from a point T to a circle with centre O are inclined to each other at an angle of 70°, then find ∠ AOB.
2. Construct a tangent to any point on the circle of radius 3
3. Write the area of a sector of a circle with radius r and angle with degree measure θ.
4. Find the area of a circle whose circumference is 44
5. If the probability of solving a problem by a student is 2/3 , then find the probability of not solving the problem by the student.

PART – B

6. A boy 2 m long casts a shadow 1 m long on the plane ground. At the same time, a tower casts a shadow 5 m long on the ground. Find the height of the tower.
7. If sin θ = 1/2 , then find the value of (1 – 2 sin2 θ)/ sin θ .
8. Find the value of cos 2 12° + cos 2 78°.
9. Show that tan 36° tan 17° tan 54° tan 73° = 1.
10. Two cubes each of volume 27 cm 3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.

PART – C

11. Find the H.C.F. and L.C.M. of the numbers 180, 72 and 252.
12. If the sum of zeroes of the quadratic polynomial   kx 2 + 5x + 3k is equal to their product, find the value of k.
13. If the sum of the first 12 terms of an A.P. is 468 and its common difference is 6, find the 10th term.
14. Prove that √(1 + cos A/1 – cos A) = cosec A + cot A.
15. From the top of a 10 m high building, the angle of elevation of a tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.
16. In the figure, a quadrilateral PQRS is drawn to circumscribe a circle. Prove that PQ + RS = PS + QR. 17. Construct a tangent to a circle of radius 3 cm from a point on the concentric circle of radius 5 cm and measure its length.
18. Find the area of the shaded region in the figure, if AB = 5 cm, AC = 12 cm and O is the centre of the circle. 