If A = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 5 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 1 & 4 \\ 2 & 0 \end{matrix} \right] \) then |adj (AB)| = 

(a)

-40

(b)

-80

(c)

-60

(d)

-20

If z is a complex number such that \(z \in \mathbb{C} \backslash \mathbb{R}\) and \(z+\frac { 1 }{ z } \epsilon R\), then |z| is

(a)

0

(b)

1

(c)

2

(d)

3

\(\tan ^{-1}\left(\frac{1}{4}\right)+\tan ^{-1}\left(\frac{2}{9}\right)\) is equal to

(a)

\(\frac { 1 }{ 2 } \ { cos }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

(b)

\(\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

(c)

\(\frac { 1 }{ 2 } {tan }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

(d)

\({ tan}^{ -1 }\left( \frac { 1}{ 2 } \right) \)

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

(a)

3

(b)

-1

(c)

1

(d)

9

If \(\vec { a } ,\vec { b } ,\vec { c } \) are three non-coplanar vectors such that \(\vec { a } \times (\vec { b } \times \vec { c } )=\frac { \vec { b } +\vec { c } }{ \sqrt { 2 } } \), then the angle between \(\vec { a } \ and \ \vec { b } \) is

(a)

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

(b)

\(\frac { 3\pi }{ 4 } \)

(c)

\(\frac { \pi }{ 4 } \)

(d)

\( { \pi }\)

The function sin⁴ x + cos⁴ x is increasing in the interval

(a)

\(\left[ \frac { 5\pi }{ 8 } ,\frac { 3\pi }{ 4 } \right] \)

(b)

\(\left[ \frac { \pi }{ 2 } ,\frac { 5\pi }{ 8 } \right] \)

(c)

\(\left[ \frac { \pi }{ 4 } ,\frac { \pi }{ 2 } \right] \)

(d)

\(\left[ 0,\frac { \pi }{ 4 } \right] \)

If the rate of increase of s = x³-5x²+ 5x + 8 is twice the rate of increase of x, then one value of x is __________

(a)

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

(b)

\(\frac{10}{3}\)

(c)

\(\frac{3}{10}\)

(d)

\(\frac{1}{3}\)

\(\int _{ 0 }^{ 2a }{ f(x) } dx=2\int _{ 0 }^{ 2a }{ f(x) } dx\) if _________

(a)

f(2a -x) = f(x)

(b)

f(a -x) = f(x)

(c)

f(x) = - f(-x)

(d)

f(-x) = f(x)

Using y = vx, the differential equation \(\frac { dy }{ dx } =\frac { y }{ x+\sqrt { xy } } \) is reduced to ________.

(a)

x(1+\(\sqrt{v}\))dv = v\(\sqrt{v}\)dx

(b)

x(1-\(\sqrt{v}\))dv = v\(\sqrt{v}\)dx

(c)

x(1+\(\sqrt{v}\))dv = -v\(\sqrt{v}\)dx

(d)

v(1+\(\sqrt{v}\))dx - v\(\sqrt{v}\)dv = 0

'+' is not a binary operation on ___________

(a)

~

(b)

z

(c)

c

(d)

Q- {0}