If A is a square matrix that IAI = 2, than for any positive integer n, |Aⁿ| = _______

(a)

0

(b)

2n

(c)

2ⁿ

(d)

n²

If \(\rho\) (A) = r then which of the following is correct?

(a)

all the minors of order n which do not vanish

(b)

'A' has at least one minor of order r which does not vanish and all higher order minors vanish

(c)

'A' has at least one (r + 1) order minor which vanish

(d)

all (r + 1) and higher order minors should not vanish

If z = \(\frac { 1 }{ 1-cos\theta -isin\theta } \), the Re(z) = ___________

(a)

0

(b)

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

(c)

cot\(\frac { \theta }{ 2 } \)

(d)

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

Let a > 0, b > 0, c >0. Theh n both the root of the equation ax²+bx+c = 0 are _________

(a)

real and negative

(b)

real and positive

(c)

rational numbers

(d)

none

Equation of tangent at (-4, -4) on x² = -4y is _____________

(a)

2x - y + 4 = 0

(b)

2x + y - 4 = 0

(c)

2x - y - 12 = 0

(d)

2x + y + 4 = 0

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

The point on the curve y = x² is the tangent parallel to X-axis is __________

(a)

(1, 1)

(b)

(2, 2)

(c)

(4, 4)

(d)

(0, 0)

If y = sin x and x changes from \(\frac{\pi}{2}\) to ㅠ the approximate change in y is ..............

(a)

0

(b)

1

(c)

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

(d)

\(\frac{22}{14}\)

The solution of \(\frac{dy}{dx}+y\) cot x = sin 2x is ___________

(a)

y sin x = \(\frac{2}{3}\)sin³x+c

(b)

y sec x = \(\frac{x^2}{2}+c\)

(c)

y sin x = c+x

(d)

2y sin x = sin x - \(\frac{sin\ 3x}{3}+c\)

If \(f(x)={ Cx }^{ 2 }={ cx }^{ 2 },0 is the p.d.f, of x then c is _____________

(a)

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

(b)

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

(c)

\(\frac { 8 }{ 3 } \)

(d)

\(\frac { 3 }{ 8 } \)