# Rajasthan Board Secondary Examination 2014 Mathematics Paper

**Rajasthan Board Secondary Examination, 2014**

**Mathematics**

**PART – A**

- Number
__3/365__is a terminating decimal or a non-terminating repeating decimal ? Write it in decimal form.

- Write the solution of the pair of linear equations 3x + 4y = 0 and 2x – y = 0.

- Write the next two terms of P. 4, 1, – 2, – 5, …… .

- Write the distance of the point ( 3, – 2 ) from y-axis.

- 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.

- 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.
- Construct a tangent to any point on the circle of radius 3
- Write the area of a sector of a circle with radius r and angle with degree measure θ.
- Find the area of a circle whose circumference is 44
- 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** - 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.
- If sin θ = 1/2 , then find the value of (1 – 2 sin
^{2}θ)/ sin θ . - Find the value of cos
^{2}12° + cos^{2}78°. - Show that tan 36° tan 17° tan 54° tan 73° = 1.
- 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** - Find the H.C.F. and L.C.M. of the numbers 180, 72 and 252.
- If the sum of zeroes of the quadratic polynomial kx
^{2}+ 5x + 3k is equal to their product, find the value of k. - If the sum of the first 12 terms of an A.P. is 468 and its common difference is 6, find the 10th term.
- Prove that √(1 + cos A/1 – cos A) = cosec A + cot A.
- 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.
- In the figure, a quadrilateral PQRS is drawn to circumscribe a circle. Prove that PQ + RS = PS + QR.
- 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.
- 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.