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

Factorise the following by taking out the common factors:
p(p² + q² - r²) + q(r² - q² -p²) - r(p² + q² - r²)

Factorise:

`y^2 + (1)/(4y^2) + 1 - 6y - (3)/y`

Factorise:

`4"a"^2 + (1)/(4"a"^2) - 2 - 6"a" + (3)/(2"a")`

Factorise:
x⁴ + y⁴ - 6x²y²

Factorise:
4x⁴ + 25y⁴ + 19x²y²

Factorise:

`"p"^2 + (1)/"p"^2 - 3`

Factorise:
5x² - y² - 4xy + 3x - 3y

Solve the following simultaneous equations by the substitution method:
2x + y = 8
3y = 3 + 4x

Solve the following simultaneous equations by the substitution method:
x + 3y= 5
7x - 8y = 6

Solve the following simultaneous equations by the substitution method:
5x + 4y - 23 = 0
x + 9 = 6y

Solve the following simultaneous equations by the substitution method:
2x + 3y = 31
5x - 4 = 3y

Solve the following simultaneous equations by the substitution method:
7x - 3y = 31
9x - 5y = 41

Solve the following simultaneous equations by the substitution method:
13 + 2y = 9x
3y = 7x

Solve the following simultaneous equations by the substitution method:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5

Solve the following simultaneous equations by the substitution method:
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8

Solve the following simultaneous equations by the substitution method:
3 - (x + 5) = y + 2
2(x + y) = 10 + 2y

Solve the following simultaneous equations by the substitution method:
7(y + 3) - 2(x + 2) = 14
4(y - 2) + 3(x - 3) = 2

Solve the following pairs of equations:

`(6)/(x + y) = (7)/(x - y) + 3`

`(1)/(2(x + y)) = (1)/(3( x - y)`
Where x + y ≠ 0 and x - y ≠ 0

Solve the following equations graphically :
x + 3y = 8
3x = 2 + 2y

Solve the following equations graphically :
2x + 4y = 7
3x + 8y = 10