Geometry Set A 2015-2016 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Geometry [Set A]
Date & Time: 10th March 2016, 11:00 am
Duration: 2h

 1 | Solve any five sub-questions
 1.1

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

Concept: Similar Triangles
Chapter: [0.01] Similarity
 1.2

In the following figure, in ΔABC, ∠B = 90°, ∠C = 60°, ∠A = 30°, AC = 18 cm. Find BC. Concept: 30 - 60 - 90 and 45 - 45 - 90 Theorem
Chapter: [0.02] Pythagoras Theorem
 1.3

In the following figure, m(arc PMQ) = 130o, find ∠PQS. Concept: Angle Subtended by the Arc to the Point on the Circle
Chapter: [0.03] Circle
 1.4

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

Concept: Trigonometric Ratios of Complementary Angles
Chapter: [0.06] Trigonometry
 1.5

Find the slope of the line with inclination 30° .

Concept: Slope of a Line
Chapter: [0.04] Co-ordinate Geometry
 1.6

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

Concept: Euler's Formula
Chapter: [0.07] Mensuration
 2 | Solve any four sub-questions:
 2.1

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR. Concept: Similarity of Triangles
Chapter: [0.01] Similarity
 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. Concept: Tangent - Secant Theorem
Chapter: [0.03] Circle
 2.3

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

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

Concept: Angles in Standard Position
Chapter: [0.06] Trigonometry
 2.5

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

Concept: Areas of Sector and Segment of a Circle
Chapter: [0.07] Mensuration
 2.6

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

Concept: Surface Area of a Combination of Solids
Chapter: [0.07] Mensuration
 3 | Solve any three sub-questions:
 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.

Concept: Appolonius Theorem
Chapter: [0.01] Similarity
 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 Concept: Angle Subtended by the Arc to the Point on the Circle
Chapter: [0.03] Circle
 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.

Concept: Construction of Tangent Without Using Centre
Chapter: [0.05] Geometric Constructions
 3.4

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

Concept: Trigonometric Identities
Chapter: [0.06] Trigonometry
 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.

Concept: General Equation of a Line
Chapter: [0.04] Co-ordinate Geometry
 4 | Solve any two sub-questions:
 4.1

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

Concept: Number of Tangents from a Point on a Circle
Chapter: [0.03] Circle [0.03] Circle
 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)

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

Concept: General Equation of a Line
Chapter: [0.04] Co-ordinate Geometry
 5 | Solve any two sub-questions:
 5.1

In the following figure, AE = EF = AF = BE = CF = a, AT ⊥ BC. Show that AB = AC =  sqrt3xxa Concept: Similarity in Right Angled Triangles
Chapter: [0.02] Pythagoras Theorem
 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.

Concept: Division of a Line Segment
Chapter: [0.04] Co-ordinate Geometry [0.05] Geometric Constructions
 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?

Concept: Surface Area of a Combination of Solids
Chapter: [0.07] Mensuration

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