If Δ is the value of the determinant

$\left| {\begin{array}{*{20}{c}} {{a_1}}&{{b_1}}&{{c_1}}\\ {{a_2}}&{{b_2}}&{{c_2}}\\ {{a_3}}&{{b_3}}&{{c_3}} \end{array}} \right|$

then what is the value of the following determinant?

$\left| {\begin{array}{*{20}{c}} {{pa_1}}&{{b_1}}&{{qc_1}}\\ {{pa_2}}&{{b_2}}&{{qc_2}}\\ {{pa_3}}&{{b_3}}&{{qc_3}} \end{array}} \right|$

(p ≠ 0 or 1, q ≠ 0 or 1)

If C₀, C₁, C₂, _ _ _ _ _, C_n are the coefficients in the expansion of (1 + x)ⁿ, then what is the value of C₁ + C₂ + C₃ + _ _ _ _ _ + C_n?

If a + b + c = 4 and ab + bc + ca = 0, then what is the value of the following determinant?

$\left| {\begin{array}{*{20}{c}} {{a}}&{{b}}&{{c}}\\ {{b}}&{{c}}&{{a}}\\ {{c}}&{{a}}&{{b}} \end{array}} \right|$

The number of integer values of k, for which the equation 2sinx = 2k + 1 has a solution, is