If P = $$\left[ {\matrix{ {{{\sqrt 3 } \over 2}} & {{1 \over 2}} \cr { - {1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right],A = \left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\,\,\,$$

Q = PAP^T, then P^T Q²⁰¹⁵ P is :

If the equations x² + bx−1 = 0 and x² + x + b = 0 have a common root different from −1, then $$\left| b \right|$$ is equal to :

The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there $$2\sqrt 2 $$ units in the south-westwardsdirection. Then its new position in the Argand plane is at the point represented by :

For x $$ \in $$ R, x $$ \ne $$ 0, Let f₀(x) = $${1 \over {1 - x}}$$ and
f_n+1 (x) = f₀(f_n(x)), n = 0, 1, 2, . . . .

Then the value of f₁₀₀(3) + f₁$$\left( {{2 \over 3}} \right)$$ + f₂$$\left( {{3 \over 2}} \right)$$ is equal to :