If the equation cos⁴ $$\theta $$ + sin⁴ $$\theta $$ + $$\lambda $$ = 0 has real solutions for $$\theta $$, then $$\lambda $$ lies in the interval :

If the sum of first 11 terms of an A.P.,
a₁, a₂, a₃, .... is 0 (a $$ \ne $$ 0), then the sum of the A.P.,
a₁ , a₃ , a₅ ,....., a₂₃ is ka₁ , where k is equal to :

The imaginary part of
$${\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1 \over 2}}}$$ can be :

Let f(x) be a quadratic polynomial such that
f(–1) + f(2) = 0. If one of the roots of f(x) = 0
is 3, then its other root lies in :