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

Geometry [Set A]
Date: March 2015
Duration: 2h

 1 | Solve any five sub-questions :
 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
 1.2

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

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

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
 1.4

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

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

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
 1.6

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
 2 | Solve any four sub-questions :
 2.1

If sin θ =7/25, where θ is an acute angle, find the value of cos θ.

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

Draw ∠ABC of measure 120° and bisect it.

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

Find the slope of the line passing through the points M(4,0) and N(-2,-3).

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

Find the area of the sector whose arc length and radius are 14 cm and 6 cm respectively.

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

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

PS = 11, SQ = 12, PR = 22. Find QR. Concept: Similarity of Triangles
Chapter: [0.01] Similarity
 2.6

In the following figure, if m(arc DXE) = 120° and m(arc AYC) = 60°. Find ∠DBE. Concept: Areas of Sector and Segment of a Circle
Chapter: [0.07] Mensuration
 3 | Solve any three sub-questions :
 3.1

In the following figure, Q is the centre of a circle and PM, PN are tangent segments to the circle. If ∠MPN = 60°, find ∠MQN. Concept: Number of Tangents from a Point on a Circle
Chapter: [0.03] Circle [0.03] Circle
 3.2

Draw the tangents to the circle from the point L with radius 3 cm. Point ‘L’ is at a distance 8 cm from the centre ‘M’.

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

The ratio of the areas of two triangles with the common base is 4 : 3. Height of the larger triangle is 2 cm, then find the corresponding height of the smaller triangle.

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

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 20 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
 3.5

Find the volume and surface area of a sphere of radius 8.4 cm.

(pi=22/7)

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

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

Chapter: [0.03] Circle
 4.2

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

Concept: Trigonometric Identities
Chapter: [0.06] Trigonometry
 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
 5 | Solve any two sub-questions :
 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
 5.2

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
 5.3

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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