Date: March 2020

Duration: 2h

In ∆ABC and ∆DEF ∠B = ∠E, ∠F = ∠C and AB = 3DE then which of the statements regarding the two triangles is true ?

The triangles are not congruent and not similar

The triangles are similar but not congruent.

The triangles are congruent and similar.

None of the statements above is true.

Chapter: [1] Similarity

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

If two circles are touching externally, how many common tangents of them can be drawn?

One

Two

Three

Four

Chapter: [3] Circle

Choose the correct alternative answer for the following question.

angle of elevation.

angle of depression.

0

straight angle.

Chapter: [6] Trigonometry

Select the correct alternative for the following question.

The maximum number of tangents that can be drawn to a circle from a point out side it is .............. .

2

1

one and only one

0

Chapter: [5] Geometric Constructions

Determine whether the following point is collinear.

A(–1, –1), B(0, 1), C(1, 3)

Chapter: [4] Co-ordinate Geometry

Prove the following.

sec*θ* (1 – sin*θ*) (sec*θ* + tan*θ*) = 1

Chapter: [6] Trigonometry

Base of a triangle is 9 and height is 5. Base of another triangle is 10 and height is 6. Find the ratio of areas of these triangles.

Chapter: [1] Similarity

Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm.

Chapter: [7] Mensuration

In the given figure, a toy made from a hemisphere, a cylinder and a cone are shown. Find the total area of the toy.

Chapter: [7] Mensuration

In ∆MNP, NQ is a bisector of ∠N. If MN = 5, PN = 7 MQ = 2.5 then Find QP.

Chapter: [1] Similarity

In ∆PQR, point S is the midpoint of side QR. If PQ = 11, PR = 17, PS =13, find QR.

Chapter: [2] Pythagoras Theorem

Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.

Chapter: [2] Pythagoras Theorem

What is the distance between two parallel tangents of a circle having radius 4.5 cm ? Justify your answer.

Chapter: [3] Circle

∆ABC ~ ∆LMN. In ∆ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ∆ABC and ∆LMN such that \[\frac{BC}{MN} = \frac{5}{4} .\]

Chapter: [5] Geometric Constructions

A boy standing at a distance of 48 meters from a building observes the top of the building and makes an angle of elevation of 30°. Find the height of the building.

Chapter: [6] Trigonometry

In the given figure, seg RS is a diameter of the circle with centre O. Point T lies in the exterior of the circle. Prove that ∠ RTS is an acute angle.

Chapter: [3] Circle

In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF

Chapter: [2] Pythagoras Theorem

In the given figure, ▢PQRS is cyclic. side PQ ≅ side RQ. ∠ PSR = 110°, Find–

(1) measure of ∠ PQR

(2) m(arc PQR)

(3) m(arc QR)

(4) measure of ∠ PRQ

Chapter: [3] Circle

Find the coordinates of the circumcentre of a triangle whose vertices are (–3,1), (0,–2) and (1,3).

Chapter: [4] Co-ordinate Geometry

In the given figure, seg PA, seg QB, seg RC and seg SD are perpendicular to line AD. AB = 60, BC = 70, CD = 80, PS = 280 then Find PQ, QR and RS.

Chapter: [1] Similarity

If 5 secθ – 12 cosecθ = 0, find the values of secθ, cosθ, and sinθ.

Chapter: [6] Trigonometry

In the given figure, seg AB is a chord of a circle with centre P. If PA = 8 cm and distance of chord AB from the centre P is 4 cm, find the area of the shaded portion. ( \[\pi\] = 3.14, \[\sqrt{3}\]= 1.73 )

Chapter: [7] Mensuration

Construct a triangle of sides 4 cm, 5cm and 6cm and then a triangle similar to it whose sides are `2/3` of the corresponding sides of the first triangle. Give the justification of the construction.

Chapter: [4] Co-ordinate Geometry [5] Geometric Constructions

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle

Chapter: [3] Circle

The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

Chapter: [3] Circle

A chord PQ of a circle with a radius of cm subtends an angle of 60^{°} with the center of the circle. Find the area of the minor as well as the major segment. ( \[\pi\] = 3.14, \[\sqrt{3}\] = 1.73)

Chapter: [7] Mensuration

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

Find the lengths of the medians of a triangle whose vertices are A(–1, 1), B(5, –3) and C(3, 5).

Chapter: [4] Co-ordinate Geometry

In the given figure 1.66, seg PQ || seg DE, A(∆PQF) = 20 units, PF = 2 DP, then Find A(◻DPQE) by completing the following activity.

Chapter: [1] Similarity

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