Date: July 2017

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

Chapter: [0.01] Similarity

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

Chapter: [0.03] Circle

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

Chapter: [0.06] Trigonometry

Find the Slope of the line having inclination 45°.

Chapter: [0.04] Co-ordinate Geometry

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

Chapter: [0.02] Pythagoras Theorem

Find the volume of a cube with side 6 cm.

Chapter: [0.07] Mensuration

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

Chapter: [0.01] Similarity

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

Chapter: [0.07] Mensuration

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

Chapter: [0.03] Circle

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

Chapter: [0.06] Trigonometry

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

Chapter: [0.07] Mensuration

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.

Chapter: [0.03] Circle

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

Chapter: [0.06] Trigonometry

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

Chapter: [0.03] Circle

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

Chapter: [0.01] Similarity

Prove that:

sec^{2}θ + cosec^{2}θ = sec^{2}θ x cosec^{2}θ

Chapter: [0.06] Trigonometry

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

Chapter: [0.04] Co-ordinate Geometry

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

Chapter: [0.03] Circle [0.03] Circle

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: [0.06] Trigonometry

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.

Chapter: [0.03] Circle

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

Chapter: [0.05] Geometric Constructions

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.

Chapter: [0.05] Geometric Constructions

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)`

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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