Geometry Mathematics 2 Shaalaa.com Model Set 5 2019-2020 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

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

Choose the correct alternative answer for the following question.

1 + tan² \[\theta\]  = ?

cot²θ 

cosec²θ 

sec²θ    

tan²θ

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

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)

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°

Prove the following.

tan⁴θ + tan²θ = sec⁴θ - sec²θ

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

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 )

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

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.

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

1. arc RS ≅ arc QS ≅ arc QR
2. m(arc QRS) = 240°.
   

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

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.

Show that the points A(1, 2), B(1, 6), C(1 + 2`sqrt3`, 4) are vertices of an equilateral triangle.

In the given figure, if A(P-ABC) = 154 cm²  radius of the circle is 14 cm, find

(1) `∠APC` 

(2) l ( arc ABC) .

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

Walls of two buildings on either side of a street are parallel 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.

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

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.

Prove the following trigonometric identities.

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

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

The areas of two similar triangles are 121 cm² and 64 cm² respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other.

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

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.

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.  

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?