If A = \(\left[ \begin{matrix} 1 & \tan { \frac { \theta }{ 2 } } \\ -\tan { \frac { \theta }{ 2 } } & 1 \end{matrix} \right] \) and AB = I₂, then B = 

(a)

\(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) A\)

(b)

\(\left( \cos ^{ 2 }{ \frac { \theta }{ 2 } } \right) { A }^{ T }\)

(c)

\(\left( \cos ^{ 2 }{ \theta } \right) I\)

(d)

(Sin²\(\frac { \theta }{ 2 } \))A

If \(\rho\) (A) = r then which of the following is correct?

(a)

all the minors of order n which do not vanish

(b)

'A' has at least one minor of order r which does not vanish and all higher order minors vanish

(c)

'A' has at least one (r + 1) order minor which vanish

(d)

all (r + 1) and higher order minors should not vanish

In the system of liner equations with 3 unknowns If \(\rho\) (A) = \(\rho\) ([A|B]) =1, the system has ________

(a)

unique solution

(b)

inconsistent

(c)

consistent with 2 parameter -family of solution

(d)

consistent with one parameter family of solution.

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 = a + ib lies in quadrant then \(\frac { \bar { z } }{ z } \) also lies in the III quadrant if _________

(a)

a > b > 0

(b)

a < b < 0

(c)

b < a < 0

(d)

b > a > 0

If ax² + bx + c = 0, a, b, c \(\in\) R has no real zeros, and if a + b + c < 0, then __________

(a)

c>0

(b)

c<0

(c)

c=0

(d)

c≥0

The value of \({ cos }^{ -1 }\left( \cos\cfrac { 5\pi }{ 3 } \right) +sin^{ -1 }\left( \sin\cfrac{5\pi }{ 3 } \right) \) is ______________ 

(a)

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

(b)

\(\cfrac { 5\pi }{ 3 } \)

(c)

\(\cfrac { 10\pi }{ 3 } \)

(d)

0

The pricipal value of \({ sin }^{ -1 }\left( \frac { -1 }{ 2 } \right) \) is _________

(a)

\(\frac { \pi }{ 6 } \)

(b)

\(\frac { -\pi }{ 6 } \)

(c)

\(\frac { \pi }{ 3 } \)

(d)

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

Angle between y² = x and x² = y at the origin is

(a)

\({ tan }^{ -1 }\cfrac { 3 }{ 4 } \)

(b)

\({ tan }^{ -1 }\left( \cfrac { 4 }{ 3 } \right) \)

(c)

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

(d)

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

Consider a game where the player tosses a six-sided fair die. If the face that comes up is 6, the player wins Rs. 36, otherwise he loses Rs. k², where k is the face that comes up k = {1, 2, 3, 4, 5}.
The expected amount to win at this game in Rs. is

(a)

\(\cfrac { 19 }{ 6 } \)

(b)

\(-\cfrac { 19 }{ 6 } \)

(c)

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

(d)

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