The number of moles of NH₃, that must be added to 2L of 0.80 M AgNO₃ in order to reduce the concentration of Ag⁺ ions to 5.0 $$\times$$ 10^$$-$$8 M (K_formation for [Ag(NH₃)₂]⁺ = 1.0 $$\times$$ 10⁸) is ____________. (Nearest integer)

[Assume no volume change on adding NH₃]

When 10 mL of an aqueous solution of KMnO₄ was titrated in acidic medium, equal volume of 0.1 M of an aqueous solution of ferrous sulphate was required for complete discharge of colour. The strength of KMnO₄ in grams per litre is __________ $$\times$$ 10^$$-$$2. (Nearest integer)

[Atomic mass of K = 39, Mn = 55, O = 16]

Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is :

If $${({\sin ^{ - 1}}x)^2} - {({\cos ^{ - 1}}x)^2} = a$$; 0 < x < 1, a $$\ne$$ 0, then the value of 2x² $$-$$ 1 is :