English Medium कक्षा ९ - CBSE Question Bank Solutions for Mathematics

Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

ABC is a triangle. Locate a point in the interior of ΔABC which is equidistant from all the vertices of ΔABC.

In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

In a huge park people are concentrated at three points (see the given figure):

A: where there are different slides and swings for children,

B: near which a man-made lake is situated,

C: which is near to a large parking and exit.

Where should an ice-cream parlour be set up so that maximum number of persons can approach it?

(Hint: The parlor should be equidistant from A, B and C)

Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

In the given figure, ∠ABC = 69°, ∠ACB = 31°, find ∠BDC.

In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.

Simplify the following

`3(a^4b^3)^10xx5(a^2b^2)^3`

Simplify the following:

`(2x^-2y^3)^3`

Simplify the following

`((4xx10^7)(6xx10^-5))/(8xx10^4)`

Simplify the following

`(4ab^2(-5ab^3))/(10a^2b^2)`

Simplify the following

`((x^2y^2)/(a^2b^3))^n`

Simplify the following

`(a^(3n-9))^6/(a^(2n-4))`

If a = 3 and b = -2, find the values of :

a^a + b^b

If a = 3 and b = -2, find the values of :

a^b + b^a

If a = 3 and b = -2, find the values of :

(a + b)^ab

Prove that:

`(x^a/x^b)^(a^2+ab+b^2)xx(x^b/x^c)^(b^2+bc+c^2)xx(x^c/x^a)^(c^2+ca+a^2)=1`

Prove that:

`(x^a/x^b)^cxx(x^b/x^c)^axx(x^c/x^a)^b=1`

Prove that:

`1/(1+x^(a-b))+1/(1+x^(b-a))=1`

Prove that:

`1/(1 + x^(b - a) + x^(c - a)) + 1/(1 + x^(a - b) + x^(c - b)) + 1/(1 + x^(b - c) + x^(a - c)) = 1`