If A is a 3 \(\times\) 3 non-singular matrix such that AA^T = A^TA and B = A^-1A^T, then BB^T = 

(a)

A

(b)

B

(c)

I₃

(d)

B^T

If A, B and C are invertible matrices of some order, then which one of the following is not true?

(a)

adj A = |A|A^-1

(b)

adj(AB) = (adj A)(adj B)

(c)

det A^-1 = (det A)^-1

(d)

(ABC)^-1 = C^-1B^-1A^-1

If A = \(\left[ \begin{matrix} \frac { 3 }{ 5 } & \frac { 4 }{ 5 } \\ x & \frac { 3 }{ 5 } \end{matrix} \right] \) and A^T = A⁻¹, then the value of x is

(a)

\(\frac { -4 }{ 5 } \)

(b)

\(\frac { -3 }{ 5 } \)

(c)

\(\frac { 3 }{ 5 } \)

(d)

\(\frac { 4 }{ 5 } \)

If A = \(\left[ \begin{matrix} 2 & 3 \\ 5 & -2 \end{matrix} \right] \) be such that λA⁻¹ = A, then λ is

(a)

17

(b)

14

(c)

19

(d)

21

The area of the triangle formed by the complex numbers z, iz and z+iz in the Argand’s diagram is

(a)

\(\cfrac { 1 }{ 2 } \left| z \right| ^{ 2 }\)

(b)

|z|²

(c)

\(\cfrac { 3 }{ 2 } \left| z \right| ^{ 2 }\)

(d)

2|z|²

If z is a non zero complex number, such that 2iz² = \(\bar { z } \) then |z| is

(a)

\(\cfrac { 1 }{ 2 } \)

(b)

1

(c)

2

(d)

3

If |z₁| = 1, |z₂| = 2, |z₃| = 3 and |9z₁z₂ + 4z₁z₃ + z₂z₃| = 12, then the value of |z₁+z₂+z₃| is 

(a)

1

(b)

2

(c)

3

(d)

4

The principal argument of \(\cfrac { 3 }{ -1+i } \) is

(a)

\(\cfrac { -5\pi }{ 6 } \)

(b)

\(\cfrac { -2\pi }{ 3 } \)

(c)

\(\cfrac { -3\pi }{ 4 } \)

(d)

\(\cfrac { -\pi }{ 2 } \)

If the coordinates at one end of a diameter of the circle x² + y² − 8x − 4y + c = 0 are (11, 2), the coordinates of the other end are

(a)

(-5, 2)

(b)

(-3, 2)

(c)

(5, -2)

(d)

(-2, 5)

The area of the parallelogram having diagonals \(\overset { \rightarrow }{ a } =3\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +\overset { \wedge }{ 4k } \) is ____________

(a)

4

(b)

2\(\sqrt { 3 } \)

(c)

4\(\sqrt { 3 } \)

(d)

5\(\sqrt { 3 } \)