Maharashtra State Board course SSC (Marathi Semi-English) 10th
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Geometry 2013-2014 SSC (Marathi Semi-English) 10th Question Paper Solution

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Geometry
Marks: 40Academic Year: 2013-2014
Date: October 2013

All questions are compulsory. 


[5]1
[1]1.i

In the given, seg BE ⊥ seg AB and seg BA ⊥ seg AD.

if BE = 6 and AD = 9 find `(A(Δ ABE))/(A(Δ BAD))`.

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

If two circles having centers P and Q and radii 3 cm and 5 cm. touch each other externally, find the distance PQ.  

Concept: Heights and Distances
Chapter: [6] Trigonometry
[1]1.iii

The terminal is in II (second ) quadrant. what is the possible measure of an angle?

Concept: Angles in Standard Position
Chapter: [6] Trigonometry
[1]1.iv

Find the slope of a line having inclination 60°.

Concept: Slope of a Line
Chapter: [4] Co-ordinate Geometry
[1]1.v

Find the area of a sector of a circle having radius 6 cm and length of the arc 15 cm. 

Concept: Areas of Sector and Segment of a Circle
Chapter: [7] Mensuration
[1]1.vi

Sides of the triangle are 7 cm, 24 cm, and 25 cm. Determine whether the triangle is a right-angled triangle or not. 

Concept: Converse of Pythagoras Theorem
Chapter: [2] Pythagoras Theorem
[8]2 | Solve any four sub questions :
[2]2.i

In the figure, ray YM is the bisector of ∠XYZ, where seg XY ≅ seg YZ, find the relation between XM and MZ. 

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

As shown in the figure. two concentric circles are given and line AB is the tangent to the smaller circle at T. Shown that T is the midpoint of Seg AB 

Concept: Co-ordinates of the Midpoint of a Segment
Chapter: [4] Co-ordinate Geometry
[2]2.iii

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

Concept: Slope of a Line
Chapter: [4] Co-ordinate Geometry
[2]2.iv

If tan θ = 2, where θ is an acute angle, find the value of cos θ. 

Concept: Trigonometric Identities
Chapter: [6] Trigonometry
[2]2.v

Draw the tangent at any point M on the circle with centre O and radius 2.9 cm. 

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

If (4,-3) is a point on line 5x +8y = c, find the value of c.

Concept: General Equation of a Line
Chapter: [4] Co-ordinate Geometry
[9]3 | Solve any three sub-questions:
[3]3.i

In ΔPQR, seg PM is the median. If PM = 9, PQ2 + PR2 = 290, Find QR. 

Concept: Apollonius Theorem
Chapter: [2] Pythagoras Theorem
[3]3.ii

In the figure, two chords AB and CD of the same circle are parallel to each other. P is the centre of the circle. show that ∠CPA = ∠DPB.

Concept: Inscribed Angle
Chapter: [3] Circle
[3]3.iii

Draw the circumcircle of Δ PMT in which PM = 5.4, P = 60°, M = 70°.

Concept: Problems Based on Areas and Perimeter Or Circumference of Circle, Sector and Segment of a Circle
Chapter: [7] Mensuration
[3]3.iv

Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A. 

Concept: Trigonometric Identities
Chapter: [6] Trigonometry
[3]3.v

Find the equation of a lined passage through (3,6) and making intercepts equal magnitude but opposite in sign-on both the axes. 

Concept: Intercepted Arc
Chapter: [3] Circle
[8]4 | Solve any two of the following sub-questions:
[4]4.i

Prove that the lengths of two tangent segments drawn to the circle from an external point are equal. 

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

A tree is broken by the wind. The top struck the ground at an angle of 30° and at a distance 30 m from the root. Find the whole height of the tree. (`sqrt(3)`=1.73)

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

The dimensions of a metallic cuboid are 44 cm × 42 cm × 21 cm. it is molten and recast into a sphere. Find the surface area of the sphere.

Concept: Introduction of Surface Areas and Volumes
Chapter: [7] Mensuration
[10]5 | Solve any two sub-questions:
[5]5.i

If the angles of a triangle are 30°, 60°, and 90°, then shown that the side opposite to 30° is half of the hypotenuse, and the side opposite to 60° is `sqrt(3)/2` times of the hypotenuse.

Concept: Pythagoras Theorem
Chapter: [2] Pythagoras Theorem
[5]5.ii

Δ AMT ∼ ΔAHE. In  Δ AMT, MA = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(MA)/(HA) = 7/5`. construct  Δ AHE. 

Concept: Division of a Line Segment
Chapter: [5] Geometric Constructions
[5]5.iii

Water flows at the rate of 10 meters per minute through a cylindrical pipe having its diameter 20 mm. how much time will it take to fill a conical vessel of diameter 40 cm and depth 24 cm? 

Concept: Heights and Distances
Chapter: [6] Trigonometry

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