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Geometry 2016-2017 SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] Question Paper Solution

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Geometry
Marks: 40Academic Year: 2016-2017
Date: July 2017

[5]1 | Solve any five sub-questions:
[1]1.i

In the following figure RP: PK= 3:2, then find the value of A(ΔTRP):A(ΔTPK).

Concept: Properties of Ratios of Areas of Two Triangles
Chapter: [0.01] Similarity
[1]1.ii

If two circles with radii 8 cm and 3 cm respectively touch externally, then find the distance between their centres.

Concept: Touching Circles
Chapter: [0.03] Circle
[1]1.iii

If the angle θ= –60º, find the value of cosθ.

Concept: Trigonometric Ratios of Complementary Angles
Chapter: [0.06] Trigonometry
[1]1.iv

Find the Slope of the line having inclination 45°.

Concept: Slope of a Line
Chapter: [0.04] Co-ordinate Geometry
[1]1.v

Find the side of the square whose diagonal is `16sqrt(2)` cm.

Concept: Right-angled Triangles and Pythagoras Property
Chapter: [0.02] Pythagoras Theorem
[1]1.vi

Find the volume of a cube with side 6 cm.

Concept: Volume of a Combination of Solids
Chapter: [0.07] Mensuration
[8]2 | Solve any four sub-questions:
[2]2.i

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

Concept: Similarity Triangle Theorem
Chapter: [0.01] Similarity
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[2]2.ii

The diameter of a sphere is 6 cm, Find the total surface area of the sphere. (π = 3.14)

Concept: Areas of Sector and Segment of a Circle
Chapter: [0.07] Mensuration
[2]2.iii

Draw a tangent at any point ‘M’ on the circle of radius 3.3 cm and centre ‘O’.

Concept: Converse of Tangent Theorem
Chapter: [0.03] Circle
[2]2.iv

If sinθ = `8/17`, where θ is an acute angle, find the value of cos θ by using identities.

Concept: Application of Trigonometry
Chapter: [0.06] Trigonometry
[2]2.v

Find the area of the sector of a circle of radius 8 cm and arc with length 15 cm.

Concept: Areas of Sector and Segment of a Circle
Chapter: [0.07] Mensuration
[2]2.vi

In the given figure, a tangent segment PA touching a circle in A and secant PBC are shown, If AP = 15 cm BP = 10 cm, find the length of PC.

Concept: Theorem of Angle Between Tangent and Secant
Chapter: [0.03] Circle
[9]3 | Solve any the three sub-questions:
[3]3.i

In ΔPQR, ∠P = 30°, ∠Q = 60°, ∠R = 90° and PQ = 12 cm, then find PR and QR.

Concept: Application of Trigonometry
Chapter: [0.06] Trigonometry
[3]3.ii

ABCD is a cyclic quadrilateral. M (arc ABC) = 230°. Find ∠ABC, ∠CDA, and ∠CBE.

Concept: Cyclic Quadrilateral
Chapter: [0.03] Circle
[3]3.iii

Draw the circumcircle of ΔPMT in which PM = 5.6 cm, ∠P = 60°, ∠M = 70°.

Concept: Property of an Angle Bisector of a Triangle
Chapter: [0.01] Similarity
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[3]3.iv

Prove that:

sec2θ + cosec2θ = sec2θ x cosec2θ

Concept: Trigonometric Identities
Chapter: [0.06] Trigonometry
[3]3.v

Find the equation of the line passing through the points (4,-5) and (-1,-2).

Concept: General Equation of a Line
Chapter: [0.04] Co-ordinate Geometry
[8]4 | Solve any two sub-question:
[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: [0.03] Circle [0.03] Circle
[4]4.ii

A person standing on the bank of river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. `(sqrt 3=1.73)`

Concept: Heights and Distances
Chapter: [0.06] Trigonometry
[4]4.iii

If P(-2,4), Q(4,8), R(10, 5) and S(4, 1) are the vertices of a quadrilateral, show that it is a parallelogram.

Concept: Converse: If a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic.
Chapter: [0.03] Circle
[10]5
[5]5.i

Prove that “That ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.”

Concept: Basic Geometric Constructions
Chapter: [0.05] Geometric Constructions
[5]5.ii

Draw a triangle ABC with side BC = 6cm, ∠B = 45° and ∠A = 100°, then construct a triangle PBQ whose sides are `7/4` times the corresponding sides of ΔABC.

Concept: Construction of Triangle If the Base, Angle Opposite to It and Either Median Altitude is Given
Chapter: [0.05] Geometric Constructions
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[5]5.iii

A tin maker converts a cubical metallic box into 10 cylindrical tins. The side of the cube is 50 cm and the radius of the cylinder is 7 cm. Find the height of each cylinder so made, if the wastage of 12% is incurred in the process `(pi = 22/7)`

Concept: Volume of a Combination of Solids
Chapter: [0.07] Mensuration

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Maharashtra State Board previous year question papers 10th Standard [इयत्ता १० वी] Geometry with solutions 2016 - 2017

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