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# Question Paper Solutions for Geometry Balbharati Model Question Paper Set 1 2018-2019 SSC (Marathi Semi-English) 10th

Geometry
Balbharati Model Question Paper Set 1
2018-2019 March
Marks: 40

[8]1
[4]1.A
[1]1.A.1

Ponit M is the mid point of seg AB and AB = 14 then AM = ?

Chapter: [5] Geometric Constructions
Concept: Basic Geometric Constructions
[1]1.A.2

Observe the adjoining figure and write down one pair of interior angles.

Chapter: [5] Geometric Constructions
Concept: Basic Geometric Constructions
[1]1.A.3

If Δ ABC ∼ Δ XYZ then complete the following brackets.
(AB)/(XY) =  /(YZ) = (AC)/

Chapter: [5] Geometric Constructions
Concept: Basic Geometric Constructions
[1]1.A.4

Draw ∠ ARP= 115° and bisect it.

Chapter: [5] Geometric Constructions
Concept: Basic Geometric Constructions
[1]1.A.5

From the figure find the value of sinθ.

Chapter: [5] Geometric Constructions
Concept: Basic Geometric Constructions
[1]1.A.6

Write down the equation of X- axis.

Chapter: [5] Geometric Constructions
Concept: Basic Geometric Constructions
[4]1.B | Solve any two of the following
[2]1.B.1

Radius of a sphere is 14 cm. Find the surface area of the sphere.

Chapter: [7] Mensuration
Concept: Introduction of Surface Areas and Volumes
[2]1.B.2

P is the centre of the circle and its radius is
10 cm. Distance of a chord AB from the centre is 6 cm. Find the length of chord AB.

Chapter: [3] Circle
Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius
[2]1.B.3

LMNP is a parallelogram. From the information given in the figure fill in the following boxes.
MN = cm
PN = cm
∠ M =
∠ N =

Chapter: [4] Co-ordinate Geometry
Concept: Centroid Formula
[8]2
[4]2.A | Select the correct alternative answer and write it.
[1]2.A.1

Select the correct alternative answer and write it.

The ratio of corresponding sides of similar triangles is 5 : 7, then what is
the ratio of their areas ?

(A)25 : 49 (B) 49 : 25 (C) 5 : 7 (D) 7 : 5

Chapter: [1] Similarity
Concept: Similar Triangles
[1]2.A.2

Select the correct alternative answer and write it.

What is the total surface area of a solid hemisphere whose radius is r ?
(A) 4pr (B) pr2  (C) 2pr (D) 3pr2

Chapter: [7] Mensuration
Concept: Surface Area of a Combination of Solids
[1]2.A.3

Find the length of the hypotenuse in a right angled triangle where the sum
of the squares of the sides making right angle is 169.
(A)15 (B) 13 (C) 5 (D) 12

Chapter: [2] Pythagoras Theorem
Concept: Similarity in Right Angled Triangles
[1]2.A.4

How many common tangents can be drawn to two circles, touching each
other externally?

One

Two

Three

Four

Chapter: [3] Circle
Concept: Tangent to a Circle
[4]2.B | Solve any two of the following.
[2]2.B.1

In the given figure, CB ⊥ AB, DA ⊥ AB.
if BC = 4, AD = 8 then (A(Δ ABC))/(A(Δ ADB)) find.

Chapter: [1] Similarity
Concept: Similar Triangles
[2]2.B.2

Find the length of the hypotenuse of a square whose side is 16 cm.

Chapter: [4] Co-ordinate Geometry
Concept: Section Formula
[2]2.B.3

Radius of a sector of a circle is 21 cm. If length of arc of that sector is
55 cm, find the area of the sector.

Chapter: [3] Circle
Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers
[8]3
[4]3.A | Carry out any two of the following activities.
[2]3.A.1

In the figure m(arc LN) = 110o,
m(arc PQ) = 50o then complete the following activity to find ∠ LMN.
∠ LMN = 12 [m(arc LN) - ]
∴ ∠ LMN = 12 [ - 50o]
∴ ∠ LMN = 12 ×
∴ ∠ LMN =

Chapter: [3] Circle
Concept: Cyclic Properties
[2]3.A.2

Complete the following activity to draw a tangent to a circle at a point on
the circle.
Draw a circle of radius 2.2 cm with O as centre.

↓
Take any point P on the circle and draw ray OP.

↓
Draw a perpendicular line to the ray at point P.

↓
Name the perpendilcular line as l

l is the tangent at point P.

Chapter: [5] Geometric Constructions
Concept: Construction of Tangents to a Circle
[2]3.A.3

A tank of cylindrical shape has radius 2.8 m and its height 3.5 m. Complete
the activity to find how many litres of water the tank will contain.
Capacity of water tank = Volume of cylindrical tank

= pire^2h
= 227 × 2.8 × 2.8 ×
= m3
= × 1000 litre
= litre
Chapter: [7] Mensuration
Concept: Introduction of Surface Areas and Volumes
[4]3.B
[2]3.B.1 | Solve any two of the following:

In Δ DEF, line PQ || side EF, If DP = 2.4,
PE = 7.2, PQ = 1 then find QF.

Chapter: [4] Co-ordinate Geometry
Concept: General Equation of a Line
[2]3.B.2

In the figure Q is the contact point. If
PQ = 12, PR = 8, then PS = ?

Chapter: [3] Circle
Concept: Cyclic Properties
[2]3.B.3

If secθ = 25/7  then find tanθ.

Chapter: [6] Trigonometry
Concept: Trigonometric Identities
[9]4 | Solve any three of the following
[3]4.A

Prove that, in a right angled triangle, the square of the hypotenuse is
equal to the sum of the squares of remaining two sides.

Chapter: [2] Pythagoras Theorem
Concept: Similarity in Right Angled Triangles
[3]4.B

Show that A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are the vertices of a
rhombus ABCD.

Chapter: [4] Co-ordinate Geometry
Concept: Concepts of Coordinate Geometry
[3]4.C

A storm broke a tree and the tree top rested on ground 20 m away from the
base of the tree, making an angle of 60o with the ground. Find the height
of the tree.

Chapter: [6] Trigonometry
Concept: Heights and Distances
[3]4.D

Draw a circle with centre P and radius 2.1 cm. Take point Q at a distance
5.2 cm from the centre. Draw tangents to the circle from point Q. Measure
and write the length of a tangent segment.

Chapter: [5] Geometric Constructions
Concept: Construction of Tangents to a Circle
[4]5 | Solve any one of the following.
[4]5.A

AB and AC are the two chords of a circle whose radius is r. If p and q are
the distance of chord AB and CD, from the centre respectively and if
AB = 2AC then proove that 4q2 = p2 + 3r2.

Chapter: [4] Co-ordinate Geometry
Concept: Distance Formula
[4]5.B

Δ SHR ∼ Δ SVU. In Δ SHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and
SHSV = 53 then draw Δ SVU.

Chapter: [5] Geometric Constructions
Concept: Division of a Line Segment
[3]6 | Solve any one of the following.
[3]6.A

Radius of circular base of an ear of corn is 6.6 cm and its length is
11.2 cm. If on an average 1 sqcm area contains 2 corn kernels, find the
total number of kernels on a corn.

Chapter: [3] Circle
Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius
[3]6.B

In Δ ABC and Δ PQR,
∠ ABC ≅ ∠ PQR, seg BD and
seg QS are angle bisector.
If  (l(AD))/(l(PS)) = (l(DC))/(l(SR))
Prove that : Δ ABC ∼ Δ PQR

Chapter: [1] Similarity
Concept: Property of an Angle Bisector of a Triangle

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