If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I₂ - A = 

(a)

A^-1

(b)

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

(c)

3A^-1

(d)

2A^-1

If z is a non zero complex number, such that 2iz² = \(\bar { z } \) then |z| is

(a)

\(\cfrac { 1 }{ 2 } \)

(b)

1

(c)

2

(d)

3

The polynomial x³ - kx² + 9x has three real zeros if and only if, k satisfies

(a)

|k| ≤ 6

(b)

k = 0

(c)

|k| > 6

(d)

|k| ≥ 6

If \((2+\sqrt{3})^{x^{2}-2 x+1}+(2-\sqrt{3})^{x^{2}-2 x-1}=\frac{2}{2-\sqrt{3}}\) then x = _________

(a)

0, 2

(b)

0, 1

(c)

0, 3

(d)

0, √3

\(\sin ^{-1}\left(\tan \frac{\pi}{4}\right)-\sin ^{-1}\left(\sqrt{\frac{3}{x}}\right)=\frac{\pi}{6}\). Then x is a root of the equation

(a)

x²−x−6 = 0

(b)

x²−x−12 = 0

(c)

x²+x−12 = 0

(d)

x²+x−6 = 0

The domain of cos^-1(x² - 4) is______

(a)

[3, 5]

(b)

[-1, 1]

(c)

\(\left[ -\sqrt { 5 } ,-\sqrt { 3 } \right] \cup \left[ \sqrt { 3 } ,\sqrt { 5 } \right] \)

(d)

[0, 1]

If \(\vec { a } .\vec { b } =\vec { b } .\vec { c } =\vec { c } .\vec { a } =0\) , then the value of \([\vec { a } ,\vec { b } ,\vec { c } ]\) is

(a)

\(\left| \vec { a } \right| \left| \vec { b } \right| \left| \vec { c } \right| \)

(b)

\(\frac{1}{3}\)\(\left| \vec { a } \right| \left| \vec { b } \right| \left| \vec { c } \right| \)

(c)

1

(d)

-1

The point on the curve 6y = x³ + 2 at which y-coordinate changes 8 times as fast as x-coordinate is 

(a)

(4, 11)

(b)

(4, -11)

(c)

(-4, 11)

(d)

(-4,-11)

The value of \(\int _{ 0 }^{ 1 }{ x{ (1-x) }^{ 99 }dx } \) is

(a)

\(\frac{1}{11000}\)

(b)

\(\frac{1}{10100}\)

(c)

\(\frac{1}{10010}\)

(d)

\(\frac{1}{10001}\)

If the solution of the differential equation \(\frac{d y}{d x}=\frac{a x+3}{2 y+f}\)represents a circle, then the value of a is

(a)

2

(b)

-2

(c)

1

(d)

-1