Verify that (A^-1)^T = (A^T)^-1 for A =\(\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right] \).

Find the locus of z if |3z - 5| = 3 |z + 1| where z = x + iy.

Solve: (x-1)⁴+(x-5)⁴ = 82

Evaluate \(cos\left[ { cos }^{ -1 }\left( \frac { -\sqrt { 3 } }{ 2 } +\frac { \pi }{ 6 } \right) \right] \)

For the hyperbola 3x² - 6y² = -18, find the length of transverse and conjugate axes and eccentricity.

If \(\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } =0\) then show that \(\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } =\overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } =\overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \)

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lies in the plane containing \(\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \)

Find the equation of normal to the curve y⁴=ax²at(a,a)

Find the intervals of monotonicities of the function f(x) = sin x, xદ[0, 2π]

Evaluate : \(\underset { \left( x,y \right) \rightarrow \left( 2,0 \right) }{ lim } \frac { \sqrt { 2x-y-2 } }{ 2x-y-4 } \)

Evaluate \(\int _{ 0 }^{ \pi }{ \sqrt { 1+4{ sin }^{ 2 }\frac { x }{ 2 } -4sin\frac { x }{ 2 } dx } } \) 

Form the D.E to y²=a(b-x)(b+x) by eliminating a and b as its parameters.