Date: March 2020

Duration: 2h

Some question and their alternative answer are given. Select the correct alternative.

Find perimeter of a square if its diagonal is \[10\sqrt{2}\]

10 cm

\[40\sqrt{2}\]cm

20 cm

40 cm

Chapter: [2] Pythagoras Theorem

Choose the correct alternative answer for the following question.

1 + tan^{2} \[\theta\] = ?

cot^{2}θ

cosec^{2}θ

sec^{2}θ

tan^{2}θ

Chapter: [6] Trigonometry

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

Chords AB and CD of a circle intersect inside the circle at point E. If AE = 5.6, EB = 10, CE = 8, find ED.

7

8

11.2

9

Chapter: [3] Circle

Fill in the blank using correct alternative.

Out of the following, point ........ lies to the right of the origin on X– axis.

(–2,0)

(0,2)

(2,3)

(2,0)

Chapter: [4] Co-ordinate Geometry

Some question and their alternative answer are given. Select the correct alternative.

In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.

30°

60°

90°

45°

Chapter: [2] Pythagoras Theorem

Prove the following.

tan^{4}θ + tan^{2}θ = sec^{4}θ - sec^{2}θ

Chapter: [6] Trigonometry

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its curved surface area

Chapter: [7] Mensuration

The radius of a circle is 10 cm. The measure of an arc of the circle is 54^{°}. Find the area of the sector associated with the arc. (\[\pi\]= 3.14 )

Chapter: [7] Mensuration

In ∆ABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C to side AB

Chapter: [2] Pythagoras Theorem

In the given figure, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.

(1) ∠ AOB (2)∠ ACB

(3) arc AB (4) arc ACB.

Chapter: [3] Circle

In the given figure, ∆QRS is an equilateral triangle. Prove that,

(1) arc RS ≅ arc QS ≅ arc QR

(2) m(arc QRS) = 240°.

Chapter: [3] Circle

Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.

Chapter: [5] Geometric Constructions

Construct ∆PYQ such that, PY = 6.3 cm, YQ = 7.2 cm, PQ = 5.8 cm. If \[\frac{YZ}{YQ} = \frac{6}{5},\] then construct ∆XYZ similar to ∆PYQ.

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

Show that the points A(1, 2), B(1, 6), \[C\left( 1 + 2\sqrt{3}, 4 \right)\] are vertices of an equilateral triangle.

Chapter: [4] Co-ordinate Geometry

Two buildings are in front of each other on a road of width 15 meters. From the top of the first building, having a height of 12 meter, the angle of elevation of the top of the second building is 30°.What is the height of the second building?

Chapter: [6] Trigonometry

In the given figure, if A(P-ABC) = 154 cm^{2 }radius of the circle is 14 cm, find

(1) `∠APC`

(2) l ( arc ABC) .

Chapter: [7] Mensuration [7] Mensuration

In adjoining figure, seg PS ⊥ seg RQ seg QT ⊥ seg PR. If RQ = 6, PS = 6 and PR = 12, then Find QT.

Chapter: [1] Similarity

Walls of two buildings on either side of a street are parellel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street , its top touches the window of the other building at a height 4.2 m. Find the width of the street.

Chapter: [2] Pythagoras Theorem

** **In trapezium PQRS, side PQ || side SR, AR = 5AP, AS = 5AQ then prove that, SR = 5PQ

Chapter: [1] Similarity

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.

Chapter: [5] Geometric Constructions

Prove the following trigonometric identities.

`1/(sec A + tan A) - 1/cos A = 1/cos A - 1/(sec A - tan A)`

Chapter: [6] Trigonometry

In the given figure, BC is a tangent to the circle with centre O. OE bisects AP. Prove that ΔAEO~Δ ABC.

Chapter: [3] Circle

The areas of two similar triangles are 121 cm^{2} and 64 cm^{2} respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other.

Chapter: [1] Similarity

In the given figure, OQ : PQ = 3.4 and perimeter of Δ POQ = 60 cm. Determine PQ, QR and OP.

Chapter: [3] Circle

Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

Chapter: [4] Co-ordinate Geometry

In the given figure,

\[\square\] PQRS is a rectangle. If PQ = 14 cm, QR = 21 cm, find the areas of the parts x, y, and z.

Chapter: [7] Mensuration [7] Mensuration

Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm, 90 cm, and 30 cm respectively. How many balls were melted to make the tube?

Chapter: [7] Mensuration

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