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

Solve the following pairs of linear (simultaneous) equation using method of elimination by substitution:
`x/6 + y/15 = 4`

`x/3 - y/12 = 4 3/4` 

Evaluate : 
`3^3 xx ( 243 )^(-2/3) xx 9^(-1/3)`

Evaluate:

`5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)`

Evaluate:

`( 27/125 )^(2/3) xx ( 9/25 )^(-3/2)`

Evaluate:

`7^0 xx (25)^(-3/2) - 5^(-3)`

Evaluate: 
`(16/81 )^(-3/4) xx (49/9)^(3/2) ÷ (343/216)^(2/3)`

Simplify :
`( 8x^3 ÷ 125y^3 )^(2/3)`

Simplify :
`( a + b )^(-1) . ( a^(-1) + b^(-1) )`

Simplify:

`[ 5^( n + 3 ) - 6 xx 5^( n + 1 )]/[ 9 xx 5^n - 5^n xx 2^2 ]`

Simplify :
`( 3x^2 )^(-3) xx ( x^9 )^(2/3)`

Evaluate :
`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`

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 ]`