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Question Paper - Geometry 2015 - 2016-S.S.C-Board Exam Maharashtra State Board (MSBSHSE)

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SubjectGeometry
Year2015 - 2016 (March)


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

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

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Q: 1.2[1]

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

   

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Q: 1.3[1]

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

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Q: 1.4[1]

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

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Q: 1.5[1]

Find the slope of the line with inclination 30° .

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Q: 1.6[1]

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

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Q: 2 | Solve any four sub-questions:[8]
Q: 2.1[2]

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

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Q: 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.

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Q: 2.3[2]

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

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Q: 2.4[2]

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).

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Q: 2.5[2]

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

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Q: 2.6[2]

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

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Q: 3 | Solve any three sub-questions:[9]
Q: 3.1[3]

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.

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Q: 3.2[3]

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

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Q: 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.

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Q: 3.4[3]
 

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

 
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Q: 3.5[3]

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

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Q: 4 | Solve any two sub-questions:[8]
Q: 4.1[4]

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

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Q: 4.2[4]

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.  3=1.73

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Q: 4.3[4]

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

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Q: 5 | Solve any two sub-questions:[10]
Q: 5.1[5]

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

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Q: 5.2[5]

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

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Q: 5.3[5]

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?

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