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?

Chapter: [3] Circle

Choose the correct alternative answer for the following question.

(B) angle of depression.

(C) 0

(D) 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 .............. .

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 is 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: [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 radius 15 cm subtends an angle of 60^{°} with the centre 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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