# Geometry Set B 2014-2015 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Geometry [Set B]
Marks: 40 Academic Year: 2014-2015
Date: March 2015
Duration: 2h

[5] 1 | Solve any five sub-questions :
[1] 1.1

In the following figure seg AB ⊥ seg BC, seg DC ⊥ seg BC. If AB = 2 and DC = 3, find (A(triangleABC))/(A(triangleDCB))

Concept: Properties of Ratios of Areas of Two Triangles
Chapter: [0.01] Similarity
[1] 1.2

Find the slope and y-intercept of the line y = -2x + 3.

Concept: Intercepts Made by a Line
Chapter: [0.04] Co-ordinate Geometry
[1] 1.3

In the following figure, in ΔABC, BC = 1, AC = 2, ∠B = 90°. Find the value of sin θ.

Concept: Heights and Distances
Chapter: [0.06] Trigonometry
[1] 1.4

Find the diagonal of a square whose side is 10 cm.

Concept: Circumference of a Circle
Chapter: [0.07] Mensuration [0.07] Mensuration
[1] 1.5

The volume of a cube is 1000 cm3. Find the side of a cube.

Concept: Surface Area of a Combination of Solids
Chapter: [0.07] Mensuration
[1] 1.6

If two circles with radii 5 cm and 3 cm respectively touch internally, find the distance between their centres.

Concept: Touching Circles
Chapter: [0.03] Circle
[8] 2 | Solve any four sub-questions :
[2] 2.1

If sin θ =3/5, where θ is an acute angle, find the value of cos θ.

Concept: Trigonometric Ratios of Complementary Angles
Chapter: [0.06] Trigonometry
[2] 2.2

Draw ∠ABC of measure 105° and bisect it.

Concept: Basic Geometric Constructions
Chapter: [0.05] Geometric Constructions
[2] 2.3

Find the slope of the line passing through the points A(-2, 1) and B(0, 3).

Concept: Slope of a Line
Chapter: [0.04] Co-ordinate Geometry
[2] 2.4

Find the area of the sector whose arc length and radius are 8 cm and 3 cm respectively.

Concept: Areas of Sector and Segment of a Circle
Chapter: [0.07] Mensuration
[2] 2.5

In the following figure, in Δ PQR, seg RS is the bisector of ∠PRQ.

PS = 3, SQ = 9, PR = 18. Find QR.

Concept: Similarity of Triangles
Chapter: [0.01] Similarity
[2] 2.6

In the following figure, if m(are DXE) = 90° and m(are AYC) = 30°. Find ∠DBE.

Concept: Areas of Sector and Segment of a Circle
Chapter: [0.07] Mensuration
[9] 3 | Solve any three sub-questions :
[3] 3.1

In the following figure, Q is the centre of a circle and PM, PN are tangent segments to the circle. If ∠MPN = 50°, find ∠MQN.

Concept: Number of Tangents from a Point on a Circle
Chapter: [0.03] Circle [0.03] Circle
[3] 3.2

Draw the tangents to the circle from the point L with radius 2.7 cm. Point ‘L’ is at a distance 6.9 cm from the centre ‘M’.

Concept: Construction of Tangents to a Circle
Chapter: [0.05] Geometric Constructions
[3] 3.3

The ratio of the areas of two triangles with the common base is 14 : 9. Height of the larger triangle is 7 cm, then find the corresponding height of the smaller triangle.

Concept: Properties of Ratios of Areas of Two Triangles
Chapter: [0.01] Similarity
[3] 3.4

Two building 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 40 metres high, the angle of elevation to the top of the second is 45°. What is the height of the second building?

Concept: Heights and Distances
Chapter: [0.06] Trigonometry
[3] 3.5

Find the volume and surface area of a sphere of radius 2.1 cm.

(pi=22/7)

Concept: Surface Area of a Combination of Solids
Chapter: [0.07] Mensuration
[8] 4
[4] 4.1

Prove that ‘the opposite angles of a cyclic quadrilateral are supplementary’.

Chapter: [0.03] Circle
[4] 4.2

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

Concept: Trigonometric Identities
Chapter: [0.06] Trigonometry
[4] 4.3

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)

Concept: Surface Area of a Combination of Solids
Chapter: [0.07] Mensuration
[10] 5 | Solve any two sub-questions :
[5] 5.1

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

Concept: Similarity of Triangles
Chapter: [0.01] Similarity
[5] 5.2

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.

Concept: Division of a Line Segment
Chapter: [0.04] Co-ordinate Geometry [0.05] Geometric Constructions
[5] 5.3

ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.

Concept: Division of a Line Segment
Chapter: [0.04] Co-ordinate Geometry [0.05] Geometric Constructions

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