If A is a non-singular matrix such that A^-1 = \(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \), then (A^T)⁻¹ =

(a)

\(\left[ \begin{matrix} -5 & 3 \\ 2 & 1 \end{matrix} \right] \)

(b)

\(\left[ \begin{matrix} 5 & 3 \\ -2 & -1 \end{matrix} \right] \)

(c)

\(\left[ \begin{matrix} -1 & -3 \\ 2 & 5 \end{matrix} \right] \)

(d)

\(\left[ \begin{matrix} 5 & -2 \\ 3 & -1 \end{matrix} \right] \)

If (1+i)(1+2i)(1+3i)...(1+ni) = x + iy, then \(2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right) \) is

(a)

1

(b)

i

(c)

x²+y²

(d)

1+n²

According to the rational root theorem, which number is not possible rational zero of 4x⁷ + 2x⁴ - 10x³ - 5?

(a)

-1

(b)

\(\frac { 5 }{ 4 } \)

(c)

\(\frac { 4 }{ 5 } \)

(d)

5

If |x| \(\le\) 1, then 2 tan^-1 x-sin^-1\(\frac{2x}{1+x^2}\) is equal to

(a)

tan^-1x

(b)

sin^-1x

(c)

0

(d)

\(\pi\)

If P(x, y) be any point on 16x² + 25y² = 400 with foci F₁ (3, 0) and F₂ (-3, 0) then PF₁  + PF₂ is

(a)

8

(b)

6

(c)

10

(d)

12

If the two tangents drawn from a point P to the parabola y² = 4x are at right angles then the locus of P is

(a)

2x + 1 = 0

(b)

x = −1

(c)

2x −1 = 0

(d)

x = 1

Distance from the origin to the plane 3x − 6y + 2z + 7 = 0 is

(a)

0

(b)

1

(c)

2

(d)

3

The maximum value of the function \(x^{2} e^{-2 x}, x>0\) is

(a)

\(\frac { 1 }{ e } \)

(b)

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

(c)

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

(d)

\(\frac { 4 }{ { e }^{ 4 } } \)

If w (x, y, z) = x² (y - z) + y² (z - x) + z²(x - y), then \(\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z } \) is

(a)

xy + yz + zx

(b)

x(y + z)

(c)

y(z + x)

(d)

0

The value of \(\int _{ 0 }^{ a }{ { (\sqrt { { a }^{ 2 }-{ x }^{ 2 } } ) }^{ 3 } } dx\) is

(a)

\(\frac { { \pi a }^{3 } }{ 16 } \)

(b)

\(\frac { 3\pi { a }^{ 4 } }{ 16 } \)

(c)

\(\frac { 3\pi { a }^{2 } }{ 8} \)

(d)

\(\frac { 3\pi { a }^{ 4 } }{ 8} \)