SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

Find the total surface area of frustum, if its radii are 15 cm and 7 cm. Also, the slant height of the frustum is 14 cm.

Radii of the frustum = `square` cm and `square` cm

Slant height of the frustum = `square` cm

Total surface area = `π[(r_1^2 + r_2^2 + (r_1 + r_2)l]`

= `22/7 [square + square + (square + square) square]`

= `22/7 (square)`

= `square` cm²

Hence, the total surface area of the frustum is `square`.

Find the value of y, if the points A(3, 4), B(6, y) and C(7, 8) are collinear.

If radius of the base of cone is 7 cm and height is 24 cm, then find its slant height.

If `sec alpha=2/sqrt3`  , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.

Prove that sin⁶θ + cos⁶θ = 1 – 3 sin²θ. cos²θ.

Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.

Prove that:

sec²θ + cosec²θ = sec²θ x cosec²θ

Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.

if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`

Show that `sqrt((1+cosA)/(1-cosA)) = cosec A + cot A`

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

Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.

Given below is the triangle and length of line segments. Identify in the given figure, ray PM is the bisector of ∠QPR.

Given below is the triangle and length of line segments. Identify in the given figure, ray PM is the bisector of ∠QPR.

Given below is the triangle and length of line segments. Identify in the given figure, ray PM is the bisector of ∠QPR.

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

Measures of some angles in the figure are given. Prove that `"AP"/"PB" = "AQ"/"QC"`.

Find QP using given information in the figure.