The solution of (x² - ay)dx = (ax - y²)dy is ___________

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 __________

If x = r cos θ, y = r sin, then \(\frac { \partial r }{ \partial x } \) = ....................

Equation of the normal to the curve y = 2x²+3 sin x at x = 0 is __________

If a = 3 + i and z = 2 - 3i, then the points on the Argand diagram representing az, 3az and - az are ___________

If \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } \times \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right) +\overset { \rightarrow }{ c } \times \left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \), then __________

Equation of tangent at (-4, -4) on x² = -4y is _____________

If x is real and \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then ________

If A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) is ________