If A^TA⁻¹ is symmetric, then A² =

(a)

A^-1

(b)

(A^T)²

(c)

A^T

(d)

(A^-1)²

Every homogeneous system ______

(a)

Is always consistent

(b)

Has only trivial solution

(c)

Has infinitely many solution

(d)

Need not be consistent

If A is a non-singular matrix then IA^-1| = ______

(a)

\(\left| \frac { 1 }{ { A }^{ 2 } } \right| \)

(b)

\(\frac { 1 }{ |A^{ 2 }| } \)

(c)

\(\left| \frac { 1 }{ A } \right| \)

(d)

\(\frac { 1 }{ |A| } \)

If x + iy = \(\frac { 3+5i }{ 7-6i } \), they y = ___________

(a)

\(\frac { 9 }{ 85 } \)

(b)

-\(\frac { 9 }{ 85 } \)

(c)

\(\frac { 53 }{ 85 } \)

(d)

none of these

If x + y = 8, then the maximum value of xy is _________

(a)

8

(b)

16

(c)

20

(d)

24

If u = y sin x then \(\frac { { \partial }^{ 2 }u }{ \partial x\partial y } \) = ..........

(a)

cos x

(b)

cos y

(c)

sin x

(d)

0

\(\int _{ -\frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ \frac { sinx }{ 2+cosx } dx= } \) __________

(a)

0

(b)

2

(c)

log 2

(d)

log 4

The differential equation corresponding to xy = c² where c is an arbitrary constant is ________.

(a)

xy"+ x = 0

(b)

y" = 0

(c)

xy'+ y = 0

(d)

xy"-x = 0

If \(f(x)=\frac { 1 }{ 2 } \) ,\(E\left( { x }^{ 2 } \right) =\frac { 1 }{ 4 } \) then var(x) is _____________

(a)

0

(b)

\(\frac { 1 }{ 4 } \)

(c)

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

(d)

1

In (S, *), is defined by x * y = x where x, y \(\in \) S, then

(a)

associative

(b)

Commutative

(c)

associative and commutative

(d)

neither associative nor commutative