Geometry Mathematics 2 Model set 2 by shaalaa.com 2024-2025 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Find the value of sin 0° + cos 0° + tan 0° + sec 0°.

2

1

3

0

If x = `θ/360` × 2πr then what is x in the formula?

Length of the arc of measure θ

Area of sector of measure θ

Area of the segment of measure θ

The circumference of the circle

In the adjoining figure, a tangent is drawn to a circle of radius 4 cm and centre C, at the point S. Find the length of the tangent ST, if CT = 10 cm.

`sqrt(21)` cm

`3sqrt(21)` cm

`2sqrt(21)` cm

`4sqrt(21)` cm

Find the length of ST, if ΔPQR ∼ ΔPST.

7.2 cm

7 cm

8 cm

9 cm

Two opposite angles of a parallelogram are (2x + 60)° and (4x)°. Find the value of x.

A line is parallel to Y-axis and is at a distance of 5 units from the Y-axis. Write the equation of that line.

Find will be the value of cos 90° + sin 90°.

In a parallelogram ABCD, ∠B = 105°. Determine the measure of ∠A and ∠D.

In the figure, PQ ⊥ BC, AD ⊥ BC. To find the ratio of A(ΔPQB) and A(ΔPBC), complete the following activity.

Given: PQ ⊥ BC, AD ⊥ BC

Now, A(ΔPQB)  = `1/2 xx square xx square`

A(ΔPBC)  = `1/2 xx square xx square`

Therefore, 

`(A(ΔPQB))/(A(ΔPBC)) = (1/2 xx square xx square)/(1/2 xx square xx square)`

= `square/square`

The radius of a metal sphere is 3 cm. The sphere is melted and made into a long wire of uniform circular cross-section, whose length is 36 cm. To calculate the radius of wire, complete the following activity.

Radius of the sphere = `square`

Length of the wire = `square`

Let the radius of the wire by r cm.

Now, Volume of the wire = Volume of the `square`

`square` = `square`

r² × `square` = `square` × `square`

r² × `square` = `square`

r = `square`

Hence, the radius of the wire is `square` cm.

From the information in the figure, complete the following activity to find the length of the hypotenuse AC.

AB = BC = `square`

∴ ∠BAC = `square`

Side opposite angle 45° = `square/square` × Hypotenuse

∴ `5sqrt(2) = 1/square` × AC

∴ AC = `5sqrt(2) xx square = square`

In the figure, ΔPQR is right angled at Q, seg QS ⊥ seg PR. Find x, y.

Draw a circle of suitable radius. Take point T on it. Draw a tangent through point T.

In a right angled triangle, right-angled at B, lengths of sides AB and AC are 5 cm and 13 cm, respectively. What will be the length of side BC?

A tangent JK is drawn to a circle with centre C such that CK = 6 cm and ∠CKJ = 60°. Find the length of the tangent JK.

If ΔABC ∼ ΔDEF, length of side AB is 9 cm and length of side DE is 12 cm, then find the ratio of their corresponding areas.

Find distance between points P(– 5, – 7) and Q(0, 3).

By distance formula,

PQ = `sqrt(square + (y_2 - y_1)^2`

= `sqrt(square + square)`

= `sqrt(square + square)`

= `sqrt(square + square)`

= `sqrt(125)`

= `5sqrt(5)`

If cot θ = `40/9`, find the values of cosec θ and sinθ,

We have, 1 + cot²θ = cosec²θ

1 + `square` = cosec²θ

1 + `square` = cosec²θ

`(square + square)/square` = cosec²θ

`square/square` = cosec²θ  ......[Taking root on the both side]

cosec θ = `41/9`

and sin θ = `1/("cosec"  θ)`

sin θ = `1/square`

∴ sin θ =  `9/41`

The value is cosec θ = `41/9`, and sin θ = `9/41`

Construct any ΔABC. Construct ΔA'BC' such that AB : A'B = 5 : 3 and ΔABC ∼ ΔA'BC'.

Draw ΔRSP ∼ ΔTQP. In ΔTQP, TP = 5 cm, ∠P = 50°, PQ = 4.5 cm and `("RS")/("TQ") = 2/3`.

In the given figure, Sand Tare points on sides PQ and PR, respectively of ΔPQR such that ST is parallel to QR and SQ = TR. Prove that ΔPQR is an isosceles triangles.

A figure is in the form of rectangle PQRS having a semi-circle on side QR as shown in the figure. Determine the area of the plot.

In the following figure, a quadrilateral LMNO circumscribes a circle with centre C. ∠O = 90°, LM = 25 cm, LO = 27 cm and MJ = 6 cm. Calculate the radius of the circle.

The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base.

Given: O is the centre of the circle, AB is a diameter, OA = AP, O – A – P, PC is a tangent through C. A tangent through point A intersects PC in E and BC in D.

To prove: ΔCED is an equilateral triangle.

A tent is a shape of a triangular 'prism' resting on a rectangular side PQ = PR, PT = 1.5 m, QR = 1.8 m, length of the tent = 3 m. Find:

1. ∠PQR
2. The volume of the tent

A pizza has 8 slices all equally spaced. Suppose pizza is a flat circle of radius 28 cm, find the area covered between 3 slices of pizza.