If * is defined by a * b = a² + b² + ab + 1, then (2 * 3) * 2 is _____________

(a)

20

(b)

40

(c)

400

(d)

445

The identity element of \(\left\{ \left( \begin{matrix} x & x \\ x & x \end{matrix} \right) \right\} \) |x \(\in \) R, x ≠ 0} under matrix multiplication is __________

(a)

\(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \)

(b)

\(\left( \begin{matrix} \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \\ \frac { 1 }{ 4x } & \frac { 1 }{ 4x } \end{matrix} \right) \)

(c)

\(\left( \begin{matrix} \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \\ \frac { 1 }{ 2 } & \frac { 1 }{ 2 } \end{matrix} \right) \)

(d)

\(\left( \begin{matrix} \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \\ \frac { 1 }{ 2x } & \frac { 1 }{ 2x } \end{matrix} \right) \)

The identity element in the group {R - {1},x} where a * b = a + b - ab is __________

(a)

0

(b)

1

(c)

\(\frac { 1 }{ a-1 } \)

(d)

\(\frac { a }{ a-1 } \)

A binary operation * is defined on the set of positive rational numbers Q⁺ by a*b = \(\frac { ab }{ 4 } \). Then 3 * \(\left( \frac { 1 }{ 5 } *\frac { 1 }{ 2 } \right) \) is _____________

(a)

\(\frac { 3 }{ 160 } \)

(b)

\(\frac { 5 }{ 160 } \)

(c)

\(\frac { 3 }{ 10 } \)

(d)

\(\frac { 3 }{ 40 } \)

'-' is a binary operation on ___________

(a)

~

(b)

Q-{0}

(c)

R-{0}

(d)

Z