Geometry Mathematics 2 Model set 2 by shaalaa.com 2021-2022 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

Choose the correct alternative:

Out of given triplets, which is not a Pythagoras triplet?

(5, 12, 13)

(8, 15, 17)

(7, 8, 15)

(24, 25, 7)

Choose the correct alternative:

Which theorem is used while constructing a tangent to the circle by using center of a circle?

Tangent – radius theorem

Converse of tangent – radius theorem

Pythagoras theorem

Converse of Pythagoras theorem

Choose the correct alternative answer for the following question.

The curved surface area of a cylinder is 440 cm 2 and its radius is 5 cm. Find its height.

`44/pi` cm

22 \[\pi\] CM 

 44 \[\pi\] CM 

\[\frac{22}{\pi}\] cm 

If point P(1, 1) divide segment joining point A and point B(–1, –1) in the ratio 5 : 2, then the coordinates of A are ______

(3, 3)

(6, 6)

(2, 2)

(1, 1)

From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?

Construct ∠ABC = 60° and bisect it

In fig., line BC || line DE, AB = 2, BD = 3, AC = 4 and CE = x, then find the value of x

Write the X-coordinate and Y-coordinate of point P(– 5, 4)

In fig. BP ⊥ AC, CQ ⊥ AB, A−P−C, and A−Q−B then show that ΔAPB and ΔAQC are similar.

In ΔAPB and ΔAQC

∠APB = [   ]°     ......(i)

∠AQC = [   ]°  ......(ii)

∠APB ≅ ∠AQC    .....[From (i) and (ii)]

∠PAB ≅ ∠QAC    .....[______]

ΔAPB ~ ΔAQC     .....[______]

If tan θ = `9/40`, complete the activity to find the value of sec θ.

Activity:

sec²θ = 1 + `square`     ......[Fundamental trigonometric identity]

sec²θ = 1 + `square^2`

sec²θ = 1 + `square` 

sec θ = `square` 

If a triangle having sides 50 cm, 14 cm and 48 cm, then state whether given triangle is right angled triangle or not

In figure, chords AC and DE intersect at B. If ∠ABE = 108°, m(arc AE) = 95°, find m(arc DC).

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

Find distance CD where C(– 3a, a), D(a, – 2a)

Prove that `1/("cosec"  theta - cot theta)` = cosec θ + cot θ

In ∆LMN, l = 5, m = 13, n = 12 then complete the activity to show that whether the given triangle is right angled triangle or not.
*(l, m, n are opposite sides of ∠L, ∠M, ∠N respectively)

Activity: In ∆LMN, l = 5, m = 13, n = `square`

∴ l² = `square`, m² = 169, n² = 144.

∴ l² + n² = 25 + 144 = `square`

∴ `square` + l² = m²

∴By Converse of Pythagoras theorem, ∆LMN is right angled triangle.

If tan θ = `7/24`, then to find value of cos θ complete the activity given below.

Activity:

sec²θ = 1 + `square`    ......[Fundamental tri. identity]

sec²θ = 1 + `square^2`

sec²θ = 1 + `square/576`

sec²θ = `square/576`

sec θ = `square` 

cos θ = `square`     .......`[cos theta = 1/sectheta]`

In given fig., quadrilateral PQRS, side PQ || side SR, AR = 5 AP, then prove that, SR = 5PQ

Prove that `sec"A"/(tan "A" + cot "A")` = sin A

Show that the point (0, 9) is equidistant from the points (– 4, 1) and (4, 1)

Prove the following theorem:

Tangent segments drawn from an external point to the circle are congruent.

Areas of two similar triangles are equal then prove that triangles are congruent

Given: A circle inscribed in a right angled ΔABC. If ∠ACB = 90° and the radius of the circle is r.

To prove: 2r = a + b – c

A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see the given figure).  Use [π = 22/7]

AB = 6 cm, ∠BAQ = 50°. Draw a circle passing through A and B so that AQ is the tangent to the circle

In the figure, O is the centre of the circle, and ∠AOB = 90°, ∠ABC = 30°. Then find ∠CAB.