(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

If x = `sqrt3 - sqrt2`, find the value of:

(i) `x + 1/x`

(ii) `x^2 + 1/x^2`

(iii) `x^3 + 1/x^3`

(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`

Show that Negative of an irrational number is irrational.

Draw a line segment of length `sqrt5` cm.

Draw a line segment of length `sqrt3` cm.

Draw a line segment of length `sqrt8` cm.

Show that:

`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`

Show that: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`

Show that: `x^2 + 1/x^2 = 34,` if x = 3 + `2sqrt2`

Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`

Using the following figure, show that BD = `sqrtx`.

If 3( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log x, find x.

If x = (100)^a , y = (10000)^b and z = (10)^c , find log`(10sqrty)/( x^2z^3)` in terms of a, b and c.

Given 3log x + `1/2`log y = 2, express y in term of x.

Given 2 log₁₀ x + 1 = log₁₀ 250, find :
(i) x
(ii) log₁₀ 2x

If log 2 = 0.3010 and log 3 = 0.4771 ;  find the value of : log 12

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 2.25

If log 2 = 0.3010 and log 3 = 0.4771 ; find the value of : log 1.2

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 15

If log (a + b) = log a + log b, find a in terms of b.

If log₁₀ 8 = 0.90; find the value of : log 0.125