Let S₁, S₂ and S₃ be three sets defined as

S₁ = {z$$\in$$C : |z $$-$$ 1| $$ \le $$ $$\sqrt 2 $$}

S₂ = {z$$\in$$C : Re((1 $$-$$ i)z) $$ \ge $$ 1}

S₃ = {z$$\in$$C : Im(z) $$ \le $$ 1}

Then the set S₁ $$\cap$$ S₂ $$\cap$$ S₃ :

The number of solutions of the equation

$${\sin ^{ - 1}}\left[ {{x^2} + {1 \over 3}} \right] + {\cos ^{ - 1}}\left[ {{x^2} - {2 \over 3}} \right] = {x^2}$$, for x$$\in$$[$$-$$1, 1], and [x] denotes the greatest integer less than or equal to x, is :

If the curve y = y(x) is the solution of the differential equation

$$2({x^2} + {x^{5/4}})dy - y(x + {x^{1/4}})dx = {2x^{9/4}}dx$$, x > 0 which

passes through the point $$\left( {1,1 - {4 \over 3}{{\log }_e}2} \right)$$, then the value of y(16) is equal to :

Let O be the origin. Let $$\overrightarrow {OP} = x\widehat i + y\widehat j - \widehat k$$ and $$\overrightarrow {OQ} = - \widehat i + 2\widehat j + 3x\widehat k$$, x, y$$\in$$R, x > 0, be such that $$\left| {\overrightarrow {PQ} } \right| = \sqrt {20} $$ and the vector $$\overrightarrow {OP} $$ is perpendicular $$\overrightarrow {OQ} $$. If $$\overrightarrow {OR} $$ = $$3\widehat i + z\widehat j - 7\widehat k$$, z$$\in$$R, is coplanar with $$\overrightarrow {OP} $$ and $$\overrightarrow {OQ} $$, then the value of x² + y² + z² is equal to :