Duration: 2h

Four alternative answers for the following question is given. Choose the correct alternative.

Two circles intersect each other such that each circle passes through the centre of the other. If the distance between their centres is 12, what is the radius of each circle ?

Chapter: [3] Circle

If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false?

\[\frac{EF}{PR} = \frac{DF}{PQ}\]

\[\frac{DE}{PQ} = \frac{EF}{RP}\]

\[\frac{DE}{QR} = \frac{DF}{PQ}\]

\[\frac{EF}{RP} = \frac{DE}{QR}\]

Chapter: [1] Similarity

If a, b, c are sides of a triangle and a^{2 }+ b^{2 }= c^{2}, name the type of triangle.

Obtuse angled triangle

Acute angled triangle

Right angled triangle

Equilateral triangle

Chapter: [2] Pythagoras Theorem

Select the correct alternative for the following question.

The number of tangents that can be drawn to a circle at a point on the circle is ............... .

Chapter: [5] Geometric Constructions

Find the ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8).

Chapter: [4] Co-ordinate Geometry

Prove that:

\[\cos^2 \theta\left( 1 + \tan^2 \theta \right) = 1\]

Chapter: [6] Trigonometry

Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.

Chapter: [7] Mensuration

Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).

Chapter: [4] Co-ordinate Geometry

In the given figure, chord MN and chord RS intersect at point D.

(1) If RD = 15, DS = 4,

MD = 8 find DN

(2) If RS = 18, MD = 9,

DN = 8 find DS

Chapter: [3] Circle

In the given figure, if AB || CD || FE then Find *x *and AE.

Chapter: [1] Similarity

If tanθ = 2, find the values of other trigonometric ratios.

Chapter: [6] Trigonometry

Observe the measures of pots In the given figure. How many jugs of water can the cylindrical pot hold?

Chapter: [7] Mensuration

Determine whether the point is collinear.

A(1, –3), B(2, –5), C(–4, 7)

Chapter: [4] Co-ordinate Geometry

If \[\sec\theta = \frac{13}{12}\], find the values of other trigonometric ratios.

Chapter: [6] Trigonometry

In the given figure, altitudes YZ and XT of ∆WXY intersect at P. Prove that,

(1) ▢WZPT is cyclic.

(2) Points X, Z, T, Y are concyclic.

Chapter: [3] Circle

Prove the following.

\[\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac{1}{\sin\theta - \tan\theta}\]

Chapter: [6] Trigonometry

Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from the centre. Construct tangents to the circle from point Q.

Chapter: [5] Geometric Constructions

For finding AB and BC with the help of information given in the figure, complete following activity.

AB = BC ..........

\[\therefore \angle BAC = \]

\[ \therefore AB = BC =\] \[\times AC\]

\[ =\] \[\times \sqrt{8}\]

\[ =\] \[\times 2\sqrt{2}\]

=

Chapter: [2] Pythagoras Theorem

Line *l *touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following.

(1) What is *d*(O, P) = ? Why ?

(2) If *d*(O, Q) = 8 cm, where does the point Q lie ?

(3) If d(OQ) = 15 cm, How many locations of point Q are line on line l? At what distance will each of them be from point P?

Chapter: [3] Circle

In the given fig, bisectors of ∠B and ∠C of ∆ABC intersect each other in point X. Line AX intersects side BC in point Y. AB = 5, AC = 4, BC = 6 then find \[\frac{AX}{XY}\]

Chapter: [1] Similarity

Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.

Chapter: [5] Geometric Constructions

If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.

Chapter: [4] Co-ordinate Geometry

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =22/7]

Chapter: [7] Mensuration

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre

Chapter: [3] Circle

In ∆ABC, B – D – C and BD = 7, BC = 20 then Find following ratios.

(1) \[\frac{A\left( ∆ ABD \right)}{A\left( ∆ ADC \right)}\]

(2) \[\frac{A\left( ∆ ABD \right)}{A\left( ∆ ABC \right)}\]

(3) \[\frac{A\left( ∆ ADC \right)}{A\left( ∆ ABC \right)}\]

Chapter: [1] Similarity

In the given fig, XY || seg AC. If 2AX = 3BX and XY = 9. Complete the activity to Find the value of AC.

Chapter: [1] Similarity

In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS^{2 }+ TQ^{2 }= TP^{2 }+ TR^{2 }(As shown in the figure, draw seg AB || side SR and A-T-B)

Chapter: [2] Pythagoras Theorem

In the given figure, A is the centre of the circle. \[\angle\]ABC = 45^{° }and AC = 7 \[\sqrt{2}\]cm. Find the area of segment BXC.

Chapter: [7] Mensuration

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## Maharashtra State Board previous year question papers 10th Geometry with solutions 2019 - 2020

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