English Medium इयत्ता ९ - CBSE Question Bank Solutions for Mathematics

If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.

If `a = (3 + sqrt(5))/2`, then find the value of `a^2 + 1/a^2`.

If `x = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))` and `y = (sqrt(3) - sqrt(2))/(sqrt(3) + sqrt(2))`, then find the value of x² + y².

Simplify:

`(256)^(-(4^((-3)/2))`

Find the value of `4/((216)^(-2/3)) + 1/((256)^(- 3/4)) + 2/((243)^(- 1/5))`

If x + 2a is a factor of x⁵ – 4a²x³ + 2x + 2a + 3, find a.

Factorise:

2x³ – 3x² – 17x + 30

Factorise:

x³ – 6x² + 11x – 6

Factorise:

x³ + x² – 4x – 4

Factorise:

3x³ – x² – 3x + 1

The equation 2x + 5y = 7 has a unique solution, if x, y are ______.

Any point on the x-axis is of the form ______.

The point of the form (a, a) always lies ______.

Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is the value of y when x = 5?

In the following figure, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that ∆ABC ≅ ∆DEF.

ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, AB = AC and DB = DC. Show that AD is the perpendicular bisector of BC.

ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC. Prove that AE = BD.

Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.

In a right triangle, prove that the line-segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse.

Two lines l and m intersect at the point O and P is a point on a line n passing through the point O such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m.