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Question Paper Solutions - Geometry 2015 - 2016-S.S.C-10th Maharashtra State Board (MSBSHSE)


Marks: 40
[5]1 | Solve any five sub-questions
[1]1.1

ΔDEF ~ ΔMNK. If DE = 5, MN = 6, then find the value of A(ΔDEF)/A(ΔMNK)

Chapter: [1] Similarity
Concept: Similar Triangles
[1]1.2

In the following figure, in ΔABC, ∠B = 90°, ∠C = 60°, ∠A = 30°, AC = 18 cm. Find BC.

Chapter: [1] Similarity
Concept: 30 - 60 - 90 and 45 - 45 - 90 Theorem
[1]1.3

In the following figure, m(arc PMQ) = 130o, find ∠PQS.

Chapter: [2] Circle
Concept: Angle Subtended by the Arc to the Point on the Circle
[1]1.4

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

Chapter: [5] Trigonometry
Concept: Trigonometric Ratios of Complementary Angles
[1]1.5

Find the slope of the line with inclination 30° .

Chapter: [2.07] Co-ordinate Geometry
Concept: Slope of a Line
[1]1.6

Using Euler’s formula, find V if E = 30, F = 12.

Chapter: [6] Mensuration
Concept: Euler's Formula
[8]2 | Solve any four sub-questions:
[2]2.1

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR.

Chapter: [3.01] Triangles
Concept: Similarity of Triangles
[2]2.2

In the following figure, a tangent segment PA touching a circle in A and a secant PBC is shown. If AP = 15, BP = 10, find BC.

Chapter: [2] Circle
Concept: Tangent - Secant Theorem
[2]2.3

Draw an equilateral ΔABC with side 6.2 cm and construct its circumcircle

Chapter: [4] Geometric Constructions
Concept: Construction of Triangle If the Base, Angle Opposite to It and Either Median Altitude is Given
[2]2.4

For the angle in standard position if the initial arm rotates 25° in anticlockwise direction, then state the quadrant in which terminal arm lies (Draw the figure and write the answer).

Chapter: [5] Trigonometry
Concept: Angles in Standard Position
[2]2.5

Find the area of sector whose arc length and radius are 10 cm and 5 cm respectively

Chapter: [3.04] Circles
Concept: Areas of Sector and Segment of a Circle
[2]2.6

Find the surface area of a sphere of radius 4.2 cm. (π=22/7)

Chapter: [7.02] Surface Areas and Volumes
Concept: Surface Area of a Combination of Solids
[9]3 | Solve any three sub-questions:
[3]3.1

Adjacent sides of a parallelogram are 11 cm and 17 cm. If the length of one of its diagonal is 26 cm, find the length of the other.

Chapter: [1] Similarity
Concept: Appolonius Theorem
[3]3.2

In the following figure, secants containing chords RS and PQ of a circle intersects each other in point A in the exterior of a circle if m(arc PCR) = 26°, m(arc QDS) = 48°, then find:
(i) m∠PQR
(ii) m∠SPQ
(iii) m∠RAQ

Chapter: [2] Circle
Concept: Angle Subtended by the Arc to the Point on the Circle
[3]3.3

Draw a circle of radius 3.5 cm. Take any point K on it. Draw a tangent to the circle at K without using centre of the circle.

Chapter: [4] Geometric Constructions
Concept: Construction of Tangent Without Using Centre
[3]3.4
 

If `sec alpha=2/sqrt3`  , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.

 
Chapter: [5] Trigonometry
Concept: Trigonometric Identities
[3]3.5

Write the equation of the line passing through the pair of points (2, 3) and (4, 7) in the form of y = mx + c.

Chapter: [3] Co-ordinate Geometry
Concept: General Equation of a Line
[8]4 | Solve any two sub-questions:
[4]4.1

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

Chapter: [2] Circle
Concept: Number of Tangents from a Point on a Circle
[4]4.2

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)`

Chapter: [4.03] Heights and Distances
Concept: Heights and Distances
[4]4.3

A (5, 4), B (-3, -2) and C (1, -8) are the vertices of a triangle ABC. Find the equations of the median AD and line parallel to AC passing through the point B.

Chapter: [3] Co-ordinate Geometry
Concept: General Equation of a Line
[10]5 | Solve any two sub-questions:
[5]5.1

In the following figure, AE = EF = AF = BE = CF = a, AT ⊥ BC. Show that AB = AC =  `sqrt3xxa`

Chapter: [1] Similarity
Concept: Similarity in Right Angled Triangles
[5]5.2

ΔSHR ~ ΔSVU. In ΔSHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and `(SH)/(SV)=3/5`. Construct ΔSVU.

Chapter: [4] Geometric Constructions
Concept: Division of a Line Segment
[5]5.3

Water flows at the rate of 15 m per minute through a cylindrical pipe, having the diameter 20 mm. How much time will it take to fill a conical vessel of base diameter 40 cm and depth 45 cm?

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

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