English Medium Class 9 - CBSE Question Bank Solutions

If the volume of a cuboid is 3x² − 27, then its possible dimensions are

75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to

(x − y) (x + y) (x² + y²) (x⁴ + y⁴) is equal to ______.

If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]

If  \[x^4 + \frac{1}{x^4} = 194,\] then \[x^3 + \frac{1}{x^3} =\]

If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] = 

If  \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]

If a² + b² + c² − ab − bc − ca =0, then

If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]

If a^1/3 + b^1/3 + c^1/3 = 0, then

If a + b + c = 9 and ab + bc + ca =23, then a³ + b³ + c³ − 3abc =

\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]

The product (a + b) (a − b) (a² − ab + b²) (a² + ab + b²) is equal to

The product (x²−1) (x⁴ + x² + 1) is equal to

If \[\frac{a}{b} + \frac{b}{a} = 1\] then a³ + b³ =

If 49a² − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is 

Simplify :  \[\frac{1 . 2 \times 1 . 2 \times 1 . 2 - 0 . 2 \times 0 . 2 \times 0 . 2}{1 . 2 \times 1 . 2 + 1 . 2 \times 0 . 2 + 0 . 2 \times 0 . 2}\]

27x³ − y³ − z³ − 9xyz

Multiply: x² + y² + z² − xy + xz + yz by x + y − z

Multiply: x² + 4y² + z³ + 2xy + xz − 2yz   by x − 2y − z