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

Show that \(\left| \frac { z-3 }{ z+3 } \right| \) = 2 represent a circle.

Solve: (x-1)⁴+(x-5)⁴ = 82

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

Find the value of p so that 3x + 4y - p = 0 is a tangent to the circle x² +y² - 64 = 0.

Find the value of c if y = x + c is a tangent to the hyperbola 9x² - 16y² = 144.

Prove by vector method, that in a right angled triangle the square of the hypotenuse is equal to the sum of the square of the other two sides.

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Cartesian equation

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

Find the intervals of concavity and the point of inflection of the function f(x) = 2x² + 5x² - 4x

If w = xy + z where x = cos t; y = sin t; z = t find \(\frac{dw}{dt}\)

Find the approximate value of \(\left( \frac { 17 }{ 81 } \right) ^{ \frac { 1 }{ 4 } }\) using linear approximation.

Evaluate \(\int _{ 0 }^{ 1 }{ \sqrt { 9-4{ x }^{ 2 } } dx } \)

Find the area bounded by the parabolas \({ x }^{ 2 }=\frac { y }{ 4 } \) and x²=9y and the straight line y = 2.

Evaluate \(\int _{ -2 }^{ 3 }{ \left| 1-{ x }^{ 2 } \right| } dx\)

Find the D.E of all circles touching y-axis at the origin.

Solve : \(\frac { dy }{ dx } -\frac { y }{ x } ={ 2x }^{ 2 },x>0\)