If A^TA⁻¹ is symmetric, then A² =

(a)

A^-1

(b)

(A^T)²

(c)

A^T

(d)

(A^-1)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

The product of all four values of \(\left( cos\cfrac { \pi }{ 3 } +isin\cfrac { \pi }{ 3 } \right) ^{ \frac { 3 }{ 4 } }\) is

(a)

-2

(b)

-1

(c)

1

(d)

2

If x³+12x²+10ax+1999 definitely has a positive zero, if and only if

(a)

a ≥ 0

(b)

a > 0

(c)

a < 0

(d)

a ≤ 0

If \(x = \frac{1}{5}\), the value of cos (cos^-1x+2sin^-1x) is

(a)

\(-\sqrt { \frac { 24 }{ 25 } } \)

(b)

\(\sqrt { \frac { 24 }{ 25 } } \)

(c)

\(\frac{1}{5}\)

(d)

\(-\frac{1}{5}\)

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

(a)

1

(b)

3

(c)

\( \sqrt {10}\)

(d)

\( \sqrt {11}\)

If \([\vec{a}, \vec{b}, \vec{c}]=1\), then the value of \(\frac{\vec{a} \cdot(\vec{b} \times \vec{c})}{(\vec{c} \times \vec{a}) \cdot \vec{b}}+\frac{\vec{b} \cdot(\vec{c} \times \vec{a})}{(\vec{a} \times \vec{b}) \cdot \vec{c}}+\frac{\vec{c} \cdot(\vec{a} \times \vec{b})}{(\vec{c} \times \vec{b}) \cdot \vec{a}}\) is

(a)

1

(b)

-1

(c)

2

(d)

3

The position of a particle moving along a horizontal line of any time t is given by s(t) = 3t² -2t- 8. The time at which the particle is at rest is

(a)

t = 0

(b)

\(\\ \\ \\ t=\cfrac { 1 }{ 3 } \)

(c)

t =1

(d)

t = 3

Linear approximation for g(x) = cos x at \(x=\frac{\pi}{2}\) is

(a)

\(x+\frac{\pi}{2}\)

(b)

\(-x +\frac{\pi}{2}\)

(c)

\(x - \frac{\pi}{2}\)

(d)

\(-x - \frac{\pi}{2}\)

Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus. Then E(X) and E(Y) respectively are

(a)

50,40

(b)

40,50

(c)

40.75,40

(d)

41,41