Date & Time: 16th March 2017, 11:00 am

Duration: 2h

In the following figure, seg BE ⊥ seg AB and seg BA ⊥ seg AD. If BE = 6 and \[\text{AD} = 9 \text{ find} \frac{A\left( \Delta ABE \right)}{A\left( \Delta BAD \right)} \cdot\]

Chapter: [0.01] Similarity

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

Chapter: [0.03] Circle

Find the height of an equilateral triangle whose side is 6 units.

Chapter: [0.02] Pythagoras Theorem

If the angle θ = –45° , find the value of tan θ.

Chapter: [0.06] Trigonometry

Find the slope and *y* – intercept of the line *y* = 3*x* – 5.

Chapter: [0.04] Co-ordinate Geometry

Find the circumferences of a circle whose radius is 7 cm.

Chapter: [0.03] Circle

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR.

Chapter: [0.01] Similarity

In the given figure PA = 10, PB = 2 and PC = 5. Find PD.

Chapter: [0.03] Circle [0.03] Circle

Draw ∠ABC of measures 135^{°}and bisect it.

Chapter: [0.05] Geometric Constructions

Find the sine ratio of θ in standard position whose terminal arm passes through (3, 4)

Chapter: [0.06] Trigonometry

Find the slope of the line passing through the points G(4, 5) and H (–1, –2).

Chapter: [0.04] Co-ordinate Geometry

The dimensions of a cuboid in cm are 50 × 18 × 10. Find its volume.

Chapter: [0.07] Mensuration

Prove that: If the angles of a triangle are 45° – 45° – 90°^{,} then each of the perpendicular sides is \[\frac{1}{\sqrt{2}}\]times the hypotenuse.”

Chapter: [0.06] Trigonometry

Find the angle between two radii at the centre of the circle as shown in the figure. Lines PA and PB are tangents to the circle at other ends of the radii and ∠APR = 140°.

Chapter: [0.03] Circle [0.03] Circle

Construct tangents to the circle from the point B, having radius 3.2 cm and centre 'C'. Point B is at a distance 7.6 cm from the centre.

Chapter: [0.05] Geometric Constructions

From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60° . If the height of the lighthouse is 90 meters, then find how far is that ship from the lighthouse? (√3 = 1.73)

Chapter: [0.06] Trigonometry

The volume of a cube is 343 cm^{3}. Find its total surface area.

Chapter: [0.07] Mensuration

Prove that “The opposite angles of a cyclic quadrilateral are supplementary”.

Chapter: [0.03] Circle

Eliminate θ, if

x = 3 cosec θ + 4 cot θ

y = 4 cosec θ – 3 cot θ

Chapter: [0.06] Trigonometry

A toy is a combination of a cylinder, hemisphere and a cone, each with radius 10 cm as shown in the figure. Height of the conical part is 10 cm and total height is 60 cm. Find the total surface area of the toy.

(π=3.14, √2=1.41)

Chapter: [0.07] Mensuration

In the given figure, AD is the bisector of the exterior ∠A of ∆ABC. Seg AD intersects the side BC produced in D. Prove that :

Chapter: [0.01] Similarity

Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.

Chapter: [0.04] Co-ordinate Geometry [0.05] Geometric Constructions

A (5, 4), B (–3,–2) and C (1,–8) are the vertices of a triangle ABC. Find the equation of median AD and line parallel to AB passing through point C.

Chapter: [0.04] Co-ordinate Geometry

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