Excess of NaOH (aq) was added to 100 mL of FeCl₃ (aq) resulting into 2.14 g of Fe(OH)₃ . The molarity of FeCl₃ (aq) is :

(Given molar mass of Fe = 56 g mol⁻¹ and molar mass of Cl = 35.5 g mol₋₁)

The number of real values of $$\lambda $$ for which the system of linear equations

2x + 4y $$-$$ $$\lambda $$z = 0

4x + $$\lambda $$y + 2z = 0

$$\lambda $$x + 2y + 2z = 0

has infinitely many solutions, is :

If (27)⁹⁹⁹ is divided by 7, then the remainder is :

Let A be any 3 $$ \times $$ 3 invertible matrix. Then which one of the following is not always true ?