If \(\rho\) (A) = \(\rho\) ([A/B]) = number of unknowns, then the system is _________--

(a)

consistent and has infinitely many solutions

(b)

consistent

(c)

inconsistent

(d)

consistent and has unique solution

If z = \(\frac { 1 }{ (2+3i)^{ 2 } } \) then |z| = ____________

(a)

\(\frac { 1 }{ 13 } \)

(b)

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

(c)

\(\frac { 1 }{ 12 } \)

(d)

none of these

The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has ____________

(a)

no solution

(b)

one solution

(c)

two solution

(d)

more than one solution

\({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 11 } \right) \) = ____________

(a)

0

(b)

\(\frac { 1 }{ 2 } \)

(c)

-1

(d)

none

The eccentricity of the ellipse 9x²+ 5y² - 30y = 0 is __________

(a)

\(\frac13\)

(b)

\(\frac23\)

(c)

\(\frac34\)

(d)

none of these

If \(\overset { \rightarrow }{ a } \), \(\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \) are any three vectors, then \(\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) \) if and only if __________

(a)

\(\overset { \rightarrow }{ b } \), \(\overset { \rightarrow }{ c } \) are collinear

(b)

\(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ c } \) are collinear

(c)

\(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) are collinear

(d)

none

In LMV theorem, we have f'(x₁) = \(\frac { f(b)-f(a) }{ b-a } \) then a < x₁ _________

(a)

<b

(b)

≤b

(c)

=b

(d)

≠b

If u = log (x³ + y³ + z³ - 3xyz) then \(\frac { { \partial }u }{ \partial { x } } +\frac { { \partial }u }{ { \partial y } }+ \frac { { \partial }u }{ \partial z } \) = _____________

(a)

\(\frac { 3 }{ x+y+z } \)

(b)

x+y+z

(c)

\(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)

(d)

\(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)

The transformation y = vx reduces \(\\ \\ \\ \frac { dy }{ dx } =\frac { x+y }{ 3x } \) __________ 

(a)

\(\frac { 3av }{ 4v+1 } =\frac { dx }{ x } \)

(b)

\(\frac { 3dv }{ v+1 } =\frac { dx }{ x } \)

(c)

\(2x\frac { dv }{ dx } =v\)

(d)

\(\frac { 3dv }{ 1-2v } ==\frac { dx }{ x } \)

If a random variable X has the p.d.f.\(f(x)=\frac { k }{ { x }^{ 2 }+1 }\) ,0 then k is _____________

(a)

\(\pi \)

(b)

\(\frac { 1 }{ \pi } \)

(c)

1

(d)

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