Geometry March 2015 Board Paper with Solution.

1. Solve any five of the sub – questions: [5]

(i) In the following figure set AB ⊥ seg BC, seg DC ⊥ seg BC. If AB = 2 and DC = 3, find A(∆ ABC) ÷ A(∆ DCB). [Solution Video]

(iii) In the following figure, in ∆ ABC, BC = 1, AC = 2, ∠B = 900. Find the value of sin θ.

(vi) If two circles with radii 5 cm and 3 cm respectively touch internally, find the distance between their centres. [Solution Video]

2. Solve any four sub - questions: [8]

(i) If sin θ = 5/13, where θ is an acute angle, find the value of cos θ. [Solution Video]

(iii) Find the slope of the line passing through the points C (3 , 5) and D ( - 2, - 3 ) [Solution Video]

(iv) Find the area of the sector whose arc length and radius are 10 cm and 5 cm respectively.

(v) In the following figure, in ∆ PQR, seg RS is the bisector of ∠ PQR, PA = 6, SQ = 8, PR = 15. Find QR.

(vi) In the following figure, if m(arc DXE) = 1000 and m(arc AYC) = 400, find ∠ DBE.

3. Solve any three sub - questions: [9]

(i) In the following figure, Q is the centre of a circle and PM, PN are tangent segments to the circle. If ∠ MPN = 400, find ∠ MQN.

(ii) Draw the tangents to the circle from the point L with radius 2.8 cm. Point ‘L’ is at a distance 7 cm from the centre ‘M’.

(iii) The ratio of the areas of two triangles with the common base is 6:5. Height of the larger triangle is 9cm, then find the corresponding height of the smaller triangle.

(iv) Two buildings are in front of each other on either side of a road of width 10 metres. From the top of the first building which is 30 metres high, the angle of elevation to the top of the second is 450. What is the height of the second building?

(v) Find the volume and surface are of a sphere of radius 4.2 cm. (π = 22/7)

4. Solve any two sub – questions: [8]

(i) Prove that ‘the opposite angles of a cyclic quadrilateral are supplementary”.

(ii) Prove that sin6θ + cos6θ = 1 – 3sin2θ .cos2θ.

(iii) A test tube has diameter 20 mm and height is 15 cm. The lower portion is a hemisphere. Find the capacity of the test tube. (π = 3.14)

5. Solve any two sub – questions: [10]

(i) Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

(ii) Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2 , 6) and B(3, -4) in the ratio 2 : 3. [Solution]

(iii) ∆ RST ∼ ∆ UAY. In ∆ RST, RS = 6 cm, ∠ S = 500, ST = 7.5 cm. The corresponding sides of ∆ RST and ∆ UAY are in the ratio 5 : 4. Construct ∆ UAY.