If |adj(adj A)| = |A|⁹, then the order of the square matrix A is

The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is ____________

 The value of \(\sum_{n=1}^{13}\left(i^{n}+i^{n-1}\right)\) is

According to the rational root theorem, which number is not possible rational zero of 4x⁷ + 2x⁴ - 10x³ - 5?

If sin^-1 x+sin^-1 y+sin^-1 \(z = \frac{3\pi}{2}\), the value of x²⁰¹⁷+y²⁰¹⁸+z²⁰¹⁹\(-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } } \)is

\({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 11 } \right) \) = ____________

The radius of the circle 3x² + by² + 4bx − 6by + b² = 0 is

If x + y = k is a normal to the parabola y² = 12x, then the value of k is

If \(\vec { a } \times (\vec { b } \times \vec { c } )=(\vec { a } \times \vec { b } )\times \vec { c } \) where \(\vec { a } ,\vec { b } ,\vec { c } \) are any three vectors such that \(\vec{b} \cdot \vec{c} \neq 0 \text { and } \vec{a} \cdot \vec{b} \neq 0\), then \(\vec { a } \) and \(\vec { c } \) are

If the length of the perpendicular from the origin to the plane 2x + 3y + λz =1, λ > 0 is \(\frac{1}{5}\), then the value of λ is

Prove that \(\left[ \begin{matrix} \cos { \theta } & -\sin { \theta } \\ \sin { \theta } & \cos { \theta } \end{matrix} \right] \) is orthogonal.

Find the following \(\left| \frac { 2+i }{ -1+2i } \right| \) 

Construct a cubic equation with roots 1, 2 and 3

Solve tan^-1\(\left( \frac { 1-x }{ 1+x } \right) =\frac { 1 }{ 2 } { tan }^{ -1 }\) x for x > 0

Find the general equation of the circle whose diameter is the line segment joining the points (−4, −2)and (1, 1) is x²+y²+5x+3y+6=0

Find the acute angle between the following lines
2x = 3y = −z and 6x = − y = −4z.

If A = \(\left[ \begin{matrix} 3 & 2 \\ 7 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} -1 & -3 \\ 5 & 2 \end{matrix} \right] \), verify that (AB)^-1 = B^-1A^-1

If z₁ = 3, z₂ = -7i, and z₃ = 5 + 4i, show that z₁(z₂ + z₃) = z₁ z₂ + z₁ z₃

If z = 2−2i, find the rotation of z by θ radians in the counter clockwise direction about the origin when \(\theta =\frac { \pi }{ 3 } \).

Solve the equation x⁴-9x²+20 = 0.

Solve sin^-1 x > cos^-1x

Find the centre and radius of the circle 3x² + (a + 1)y² + 6x − 9y + a + 4 = 0.

If A = \(\left[ \begin{matrix} 4 & 3 \\ 2 & 5 \end{matrix} \right] \), find x and y such that A² + xA + yI₂ = O₂. Hence, find A^-1.

Find all cube roots of \(\sqrt { 3 } +i\)

ABCD is a quadrilateral with \(\overset { \rightarrow }{ AB } =\overset { \rightarrow }{ \alpha } \) and \(\overset { \rightarrow }{ AD } =\overset { \rightarrow }{ \beta } \) and \(\overset { \rightarrow }{ AC } =2\overset { \rightarrow }{ \alpha } +3\overset { \rightarrow }{ \beta } \). If the area of the quadrilateral is λ times the area of the parallelogram with \(\overset { \rightarrow }{ AB } \) and \(\overset { \rightarrow }{ AD } \) as adjacent sides, then prove that \(\lambda =\frac { 5 }{ 2 } \)