If A = \(\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{matrix} \right] \), then adj(adj A) is

(a)

\(\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{matrix} \right] \)

(b)

\(\left[ \begin{matrix} 6 & -6 & 8 \\ 4 & -6 & 8 \\ 0 & -2 & 2 \end{matrix} \right] \)

(c)

\(\left[ \begin{matrix} -3 & 3 & -4 \\ -2 & 3 & -4 \\ 0 & 1 & -1 \end{matrix} \right] \)

(d)

\(\left[ \begin{matrix} 3 & -3 & 4 \\ 0 & -1 & 1 \\ 2 & -3 & 4 \end{matrix} \right] \)

If \(\omega =cis\cfrac { 2\pi }{ 3 } \), then the number of distinct roots of \(\left| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right| \)=0

(a)

1

(b)

2

(c)

3

(d)

4

The equation \(\tan ^{-1} x-\cot ^{-1} x=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)has

(a)

no solution

(b)

unique solution

(c)

two solutions

(d)

infinite number of solutions

In a \(\Delta ABC\)  if C is a right angle, then  \({ tan }^{ -1 }\left( \frac { a }{ b+c } \right) +{ tan }^{ -1 }\left( \frac { b }{ c+a } \right) =\) ________

(a)

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

(b)

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

(c)

\(\frac { 5\pi }{ 2 } \)

(d)

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

If x = r cos θ, y = r sin, then \(\frac { \partial r }{ \partial x } \) = ....................

(a)

sec θ

(b)

sin θ

(c)

cos θ

(d)

cosec θ

If is a homogeneous function of x and y of degree n, then \(x\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +y\frac { { \partial }^{ 2 }u }{ \partial x\partial y } \) = ...... \(\frac { { \partial }u }{ \partial { x } } \)

(a)

n

(b)

0

(c)

1

(d)

n - 1

The area enclosed by the curve y² = 4x, the x-axis and its latus rectum is ________ sq.units.

(a)

\(\frac23\)

(b)

\(\frac43\)

(c)

\(\frac83\)

(d)

\(\frac{16}{3}\)

P is the amount of certain substance left in after time t. If the rate of evaporation of the substance is proportional to the amount remaining, then

(a)

P = Ce^kt

(b)

P = Ce^-kt

(c)

P = Ckt

(d)

Pt = C

The solution of log \(\left( \frac { dy }{ dx } \right) \) = ax + by is______.

(a)

\(\frac { { e }^{ ax } }{ a } +\frac { { e }^{ -by } }{ b } +c=0\)

(b)

ae^ax- be^-by + c = 0

(c)

ae^x + be^y = k

(d)

be^ax + ae^-by = k

If a * b = a²b² - ab then 3 * (1 * 1)

(a)

0

(b)

1

(c)

2

(d)

4