If z₁ , z₂ are complex numbers such that
Re(z₁) = |z₁ – 1|, Re(z₂) = |z₂ – 1| , and
arg(z₁ - z₂) = $${\pi \over 6}$$, then Im(z₁ + z₂ ) is equal to :

The probability that a randomly chosen 5-digit number is made from exactly two digits is :

If the value of the integral
$$\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$$

is $${k \over 6}$$, then k is equal to :

If $$\int {{{\sin }^{ - 1}}\left( {\sqrt {{x \over {1 + x}}} } \right)} dx$$ = A(x)$${\tan ^{ - 1}}\left( {\sqrt x } \right)$$ + B(x) + C,
where C is a constant of integration, then the ordered pair (A(x), B(x)) can be :