2018-2019 March

The co-ordinates of point A and B are 4 and -8 respectively. Find d(A, B).

Concept: Concepts of Coordinate Geometry

In the adjoining figure line RP ||line MS , line DK is a transversal . If ∠DHP = 85° find ∠RHG and ∠HGS.

Concept: General Equation of a Line

∠ACD is an exterior angle of Δ ABC. If ∠B = 40o, ∠A = 70o find ∠ACD.

Concept: Trigonometric Ratios of Complementary Angles

Digonals of parallelogram WXYZ intersect at point O. If OY =5, find WY.

Concept: Pythagoras Theorem

In which qudrant does point A(-3, 2) lie?

On which axis does point B(12, 0) lie?

Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers

Find the curved surface area of a sphere of radius 1cm. (π = 3.14)

Concept: Surface Area of a Combination of Solids

Simplify : 2 sin30 + 3 tan45.

Concept: Trigonometric Identities

In the adjoining figure, point O is the centre of the cirlcle, seg OM ⊥ chord AB. If OM = 8cm, AB = 12 cm, then find OB.

Concept: Angle Subtended by the Arc to the Point on the Circle

In ΔPQR, PQ = 10 cm, QR = 12cm, PR = 8 cm, find the biggest and the smallest angle of the triangle.

Concept: Similarity of Triangles

How many common tangents can be drawn to two circles which touch each other internally?

(A) One (B) Two (C) Three (D) Four

Concept: Touching Circles

Distance of point (-3, 4) from the origin is .....

(A) 7 (B) 1 (C) 5 (D) 4

Concept: Distance Formula

Measure of an arc of a sector of a circle is 900 and its radius is 7cm. Find the perimeter of the sector.

(A) 44 cm (B) 25 cm (C) 36 cm (D) 56 cm

Concept: Length of an Arc

ΔABC ∼ ΔDEF and A(ΔABC) : A Δ(DEF) = 1 : 2 If AB = 4 find DE.

Concept: Similarity of Triangles

In the adjoing figure, m(arc NS) = 1250 m(arc EF) = 37o, find ∠NMS.

Concept: Cyclic Properties

Find th co-ordinates of the midpoint of the line segment joining P(0, 6) and Q(12, 20).

Concept: Co-ordinates of the Midpoint of a Segment

With the help of the information given in the figure, fill in the boxes to find AB and BC .

AB = BC (Given)

∴∠ BAC = ∠ BCA =

∴ AB = BC = × AC

= × `sqrt8`

= × `2sqrt2`

= 2

Concept: Similar Triangles

In the adjoining figure chord EF || chord GH.

Prove that chord EG ≅ chord FH.

Fill in the boxes and write the complete proof.

Concept: Inscribed Angle Theorem

Side of square ABCD is 7 cm. With D as the centre and DA as radius, arc AXC is drawn.Find the area of the shaded region with the help of the following flow chart .

Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius

In ΔMNP, ∠MNP = 90˚,

seg NQ ⊥ seg MP, MQ = 9,

QP = 4, find NQ.

Concept: Pythagoras Theorem

Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.

Concept: Trigonometric Identities

Radii of the top and the base of a frustum of a cone are 5 cm and 2 cm respectively. Its height is 9 cm. Find its volume. (π = 3.14)

Concept: Heights and Distances

Prove that :

“If a line parallel to a side of a triangle intersects the remaining sides in two distince points, then the line divides the sides in the same proportion.”

Concept: General Equation of a Line

Draw a circle with centre O and radius 3.5 cm. Take point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.

Concept: Construction of Tangent to the Circle from the Point on the Circle

Line PQ is parallel to line RS where points P,Q,R and S have

co-ordinates (2, 4), (3, 6), (3, 1) and (5, k) respectively. Find value of k.

Concept: General Equation of a Line

From the top of a light house, an abserver looking at a boat makes an angle of depression of 600. If the height of the lighthouse is 90 m then find how far is the boat from the lighthouse. (3 = 1.73)

Concept: Property of an Angle Bisector of a Triangle

Two circles intersect each other at points P and Q. Secants drawn through P and Q intersect the circles at points A,B and D,C. Prove that : ∠ADC + ∠BCD = 180°

Concept: Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers

ΔXYZ ∼ ΔPYR; In ΔXYZ, ∠Y = 60o, XY = 4.5 cm, YZ = 5.1 cm and XYPY =` 4/7` Construct ΔXYZ and ΔPYR.

Concept: Concepts of Coordinate Geometry

O is any point in the interior of ΔABC. Bisectors of ∠AOB, ∠BOC and ∠AOC intersect side AB, side BC, side AC in

F, D and E respectively.

Prove that

BF × AE × CD = AF × CE × BD

Concept: Similarity Triangle Theorem

There is a hemispherical bowl. A cone is to be made such that, if it is filled with water twice and the water is poured in the bowl, it will be filled just completely. State how will you decide the radius and perpendicular height of the cone.

Concept: Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius

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## Maharashtra State Board previous year question papers 10th Geometry with solutions 2018 - 2019

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