Geometry Mathematics 2 Shaalaa.com Model Set 3 2019-2020 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

 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. 

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?

One 

Two 

Three 

Four 

Choose the correct alternative answer for the following question.

angle of elevation.

angle of depression.

0

straight angle.

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 .............. .

2

1

one and only one

0

Determine whether the following point is collinear.
A(–1, –1), B(0, 1), C(1, 3)

Prove the following.

secθ (1 – sinθ) (secθ + tanθ) = 1

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.

Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm.

In the given figure, a toy made from a hemisphere, a cylinder and a cone are shown. Find the total area of the toy.

In ∆MNP, NQ is a bisector of ∠N. If MN = 5, PN = 7 MQ = 2.5 then find QP. 

Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.

∆ABC ~ ∆LMN. In ∆ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ∆ABC and ∆LMN such that `"BC"/"MN" = 5/4`.

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.

In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF

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

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. 

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 )

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.

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.

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.

A chord PQ of a circle with a radius of cm subtends an angle of 60^° with the center of the circle. Find the area of the minor as well as the major segment. ( \[\pi\] = 3.14,  \[\sqrt{3}\] = 1.73)

In the given figure, A is the center of the circle. ∠ABC = 45^° and AC = 7√2 cm. Find the area of segment BXC.

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.