SSC (Marathi Semi-English) १० वीं कक्षा - Maharashtra State Board Important Questions for Geometry Mathematics 2

Prove that:

sec²θ + cosec²θ = sec²θ x cosec²θ

From the top of a lighthouse, an observer looks at a ship and finds the angle of depression to be 60° . If the height of the lighthouse is 90 meters, then find how far is that ship from the lighthouse? (√3 = 1.73)

If the angle θ = –45° , find the value of tan θ.

Prove that: If the angles of a triangle are 45° – 45° – 90°^, then each of the perpendicular sides is \[\frac{1}{\sqrt{2}}\]times the hypotenuse.”

Eliminate θ, if
x = 3 cosec θ + 4 cot θ
y = 4 cosec θ – 3 cot θ

Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`

Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:

sin θ × cosec θ = ______

The volume of a cube is 1000 cm³. Find the side of a cube.

A test tube has diameter 20 mm and height is 15 cm. The lower portion is a hemisphere. Find the capacity of the test tube. (π = 3.14)

Find the circumferences of a circle whose radius is 7 cm.

A toy is a combination of a cylinder, hemisphere and a cone, each with radius 10 cm as shown in the figure. Height of the conical part is 10 cm and total height is 60 cm. Find the total surface area of the toy.
(π=3.14, √2=1.41)

Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.

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

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.

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

(1) `∠APC` 

(2) l ( arc ABC) .

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

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?