SSC (Marathi Semi-English) 10thMaharashtra State Board
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Geometry Shaalaa.com Model Set 2 2019-2020 SSC (Marathi Semi-English) 10th Question Paper Solution

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Geometry [Shaalaa.com Model Set 2]
Marks: 40Date: 2019-2020 March
Duration: 2h

[8]1
[4]1.A | MCQs
[1]1.A.i

Four alternative answers for the following question is given. Choose the correct alternative.
Two circles intersect each other such that each circle passes through the centre of the other. If the distance between their centres is 12, what is the radius of each circle ?

(A) 6 cm (B) 12 cm (C) 24 cm (D) can’t say
Concept: Touching Circles
Chapter: [3] Circle
[1]1.A.ii

 If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false? 

\[\frac{EF}{PR} = \frac{DF}{PQ}\] 

\[\frac{DE}{PQ} = \frac{EF}{RP}\] 

\[\frac{DE}{QR} = \frac{DF}{PQ}\] 

\[\frac{EF}{RP} = \frac{DE}{QR}\]

Concept: Similarity of Triangles
Chapter: [1] Similarity
[1]1.A.iii

If a, b, c are sides of a triangle and a+ b= c2, name the type of triangle.

Obtuse angled triangle

Acute angled triangle 

Right angled triangle 

Equilateral triangle

Concept: Apollonius Theorem
Chapter: [2] Pythagoras Theorem
[1]1.A.iv

Select the correct alternative for the following question.

The number of tangents that can be drawn to a circle at a point on the circle is ............... .

(A) 3 (B) 2 (C) 1 (D) 0
Concept: Construction of Tangent to the Circle from the Point on the Circle
Chapter: [5] Geometric Constructions
[4]1.B
[1]1.B.i

Find the ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8).

Concept: Division of a Line Segment
Chapter: [4] Co-ordinate Geometry
[1]1.B.ii

Prove that:

\[\cos^2 \theta\left( 1 + \tan^2 \theta \right) = 1\]

Concept: Application of Trigonometry
Chapter: [6] Trigonometry
[1]1.B.iii

Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.

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

Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).

Concept: Co-ordinates of the Midpoint of a Segment
Chapter: [4] Co-ordinate Geometry
[12]2
[4]2.A | Solve any 2 of the following
[2]2.A.i

In the given figure, chord MN and chord RS intersect at point D.
(1) If RD = 15, DS = 4,
MD = 8 find DN
(2) If RS = 18, MD = 9,
DN = 8 find DS

Concept: Theorem of External Division of Chords
Chapter: [3] Circle
[2]2.A.ii

In the given figure, if AB || CD || FE then Find and AE.  

Concept: Property of an Angle Bisector of a Triangle
Chapter: [1] Similarity
[2]2.A.iii

If tanθ = 2, find the values of other trigonometric ratios.

 
Concept: Trigonometric Ratios of Complementary Angles
Chapter: [6] Trigonometry
[8]2.B | Solve any 4 of the following
[2]2.B.i

Observe the measures of pots In the given figure. How many jugs of water can the cylindrical pot hold?

Concept: Surface Area of a Combination of Solids
Chapter: [7] Mensuration
[2]2.B.ii

Determine whether the point is collinear.
A(1, –3), B(2, –5), C(–4, 7)

Concept: Distance Formula
Chapter: [4] Co-ordinate Geometry
[2]2.B.iii

If \[\sec\theta = \frac{13}{12}\], find the values of other trigonometric ratios.

Concept: Trigonometric Ratios of Complementary Angles
Chapter: [6] Trigonometry
[2]2.B.iv

In the given figure, altitudes YZ and XT of ∆WXY intersect at P. Prove that,
(1) ▢WZPT is cyclic.
(2) Points X, Z, T, Y are concyclic.

Concept: Angle Subtended by the Arc to the Centre
Chapter: [3] Circle
[2]2.B.v

Prove the following.
\[\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac{1}{\sin\theta - \tan\theta}\]

Concept: Application of Trigonometry
Chapter: [6] Trigonometry
[9]3
[3]3.A | Solve any 1 of the following
[3]3.A.i

Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from the centre. Construct tangents to the circle from point Q.

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

For finding AB and BC with the help of information given in the figure, complete following activity.

AB = BC ..........

\[\therefore \angle BAC = \]

\[ \therefore AB = BC =\] \[\times AC\]

\[ =\] \[\times \sqrt{8}\]

\[ =\] \[\times 2\sqrt{2}\]

 =

Concept: Pythagoras Theorem
Chapter: [2] Pythagoras Theorem
[6]3.B | Solve any 2 of the following
[3]3.B.i

Line touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following.
(1) What is d(O, P) = ? Why ?
(2) If d(O, Q) = 8 cm, where does the point Q lie ?
(3) If d(OQ) = 15 cm, How many locations of point Q are line on line l? At what distance will each of them be from point P?

Concept: Touching Circles
Chapter: [3] Circle
[3]3.B.ii

In the given fig, bisectors of ∠B and ∠C of ∆ABC intersect each other in point X. Line AX intersects side BC in point Y. AB = 5, AC = 4, BC = 6 then find \[\frac{AX}{XY}\] 

Concept: Property of an Angle Bisector of a Triangle
Chapter: [1] Similarity
[3]3.B.iii

Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.

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

If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.

Concept: Division of a Line Segment
Chapter: [4] Co-ordinate Geometry
[8]4 | Solve any 2 of the following
[4]4.A

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =22/7]

Concept: Surface Area of a Combination of Solids
Chapter: [7] Mensuration
[4]4.B

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre

Concept: Number of Tangents from a Point on a Circle
Chapter: [3] Circle
[4]4.C

In ∆ABC, B – D – C and BD = 7, BC = 20 then Find following ratios. 

(1) \[\frac{A\left( ∆ ABD \right)}{A\left( ∆ ADC \right)}\]  

(2) \[\frac{A\left( ∆ ABD \right)}{A\left( ∆ ABC \right)}\] 

(3) \[\frac{A\left( ∆ ADC \right)}{A\left( ∆ ABC \right)}\] 

 

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

In the given fig, XY || seg AC. If 2AX = 3BX and XY = 9. Complete the activity to Find the value of AC.  

Concept: Property of three parallel lines and their transversals
Chapter: [1] Similarity
[3]5 | Solve any 1 of the following
[3]5.A

In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS+ TQ= TP+ TR(As shown in the figure, draw seg AB || side SR and A-T-B)

Concept: Pythagoras Theorem
Chapter: [2] Pythagoras Theorem
[3]5.B

In the given figure, A is the centre of the circle. \[\angle\]ABC = 45° and AC = 7 \[\sqrt{2}\]cm. Find the area of segment BXC.

 

 
 
Concept: Areas of Sector and Segment of a Circle
Chapter: [7] Mensuration

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