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

Evaluate:

`(27/8)^(2/3) - (1/4)^-2 + 5^0`

Simplify the following and express with positive index :
`(3^-4/2^-8)^(1/4)`

Simplify the following and express with positive index :
`([27^-3]/[9^-3])^(1/5)`

Simplify the following and express with positive index :
`(32)^(-2/5) ÷ (125)^(-2/3)`

Simplify the following and express with positive index:

`[ 1 - { 1 - ( 1 - n )^-1}^-1]^-1`

If 2160 = 2^a. 3^b. 5^c, find a, b and c. Hence calculate the value of 3^a  x 2^-b x 5^-c.

If 1960 = 2^a. 5^b. 7^c, calculate the value of 2^-a. 7^b. 5^-c.

Simplify :
`[ 8^3a xx 2^5 xx 2^(2a) ]/[ 4 xx 2^(11a) xx 2^(-2a) ]`

Simplify:

`[ 3 xx 27^( n + 1 ) + 9 xx 3^(3n - 1 )]/[ 8 xx 3^(3n) - 5 xx 27^n ]`

Show that :
`( a^m/a^-n)^( m - n ) xx (a^n/a^-l)^( n - l) xx (a^l/a^-m)^( l - m ) = 1`

Simplify:

`( 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 )`

Simplify:

`( 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 )`

If a = x^{m + n}. y^l ; b = x^n + l. y^m and c = x^{l + m}. yⁿ,

Prove that : a^{m - n}. b^n - l. c^{l - m} = 1

From the following figure, prove that: AB > CD.

In a triangle PQR; QR = PR and ∠P = 36^o. Which is the largest side of the triangle?

If two sides of a triangle are 8 cm and 13 cm, then the length of the third side is between a cm and b cm. Find the values of a and b such that a is less than b.

In the following figure, write BC, AC, and CD in ascending order of their lengths.

Arrange the sides of ∆BOC in descending order of their lengths. BO and CO are bisectors of angles ABC and ACB respectively.

D is a point in side BC of triangle ABC. If AD > AC, show that AB > AC.

In the following figure, ∠BAC = 60^o and ∠ABC = 65^o.

Prove that:
(i) CF > AF
(ii) DC > DF