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Question Paper Solutions - Geometry 2014 - 2015-S.S.C-10th Maharashtra State Board (MSBSHSE)


Marks: 40
[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))`

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

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

Chapter: [3] Co-ordinate Geometry
Concept: Intercepts Made by a Line
[1]1.3

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

Chapter: [4.03] Heights and Distances
Concept: Heights and Distances
[1]1.4

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

Chapter: [6] Mensuration
Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle
[1]1.5

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

Chapter: [7.02] Surface Areas and Volumes
Concept: Surface Area of a Combination of Solids
[1]1.6

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

Chapter: [2] Circle
Concept: Touching Circles
[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.

Chapter: [5] Trigonometry
Concept: Trigonometric Ratios of Complementary Angles
[2]2.2

Draw ∠ABC of measure 105° and bisect it.

Chapter: [4] Geometric Constructions
Concept: Basic Geometric Constructions
[2]2.3

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

Chapter: [2.07] Co-ordinate Geometry
Concept: Slope of a Line
[2]2.4

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

Chapter: [3.04] Circles
Concept: Areas of Sector and Segment of a Circle
[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.

Chapter: [3.01] Triangles
Concept: Similarity of Triangles
[2]2.6

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

Chapter: [3.04] Circles
Concept: Areas of Sector and Segment of a Circle
[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.

Chapter: [2] Circle
Concept: Number of Tangents from a Point on a 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’.

Chapter: [3.03] Constructions
Concept: Construction of Tangents to a Circle
[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.

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

Chapter: [4.03] Heights and Distances
Concept: Heights and Distances
[3]3.5

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

`(pi=22/7)`

 

Chapter: [7.02] Surface Areas and Volumes
Concept: Surface Area of a Combination of Solids
[8]4
[4]4.1

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

Chapter: [2] Circle
Concept: Cyclic Quadrilateral
[4]4.2

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

Chapter: [5] Trigonometry
Concept: Trigonometric Identities
[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)

Chapter: [7.02] Surface Areas and Volumes
Concept: Surface Area of a Combination of Solids
[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.

Chapter: [3.01] Triangles
Concept: Similarity of Triangles
[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.

Chapter: [4] Geometric Constructions
Concept: Division of a Line Segment
[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.

Chapter: [4] Geometric Constructions
Concept: Division of a Line Segment

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