If the three points (3q, 0), (0, 3p) and (1, 1) are collinear, then which one is true?

• $\frac{1}{\mathrm{p}} +\hspace{0.17em}\frac{1}{\mathrm{q}} = 1$

• $\frac{1}{\mathrm{p}} +\hspace{0.17em}\frac{1}{\mathrm{q}} = 2$

• $\frac{1}{\mathrm{p}} +\hspace{0.17em}\frac{1}{\mathrm{q}} = 3$

• $\frac{1}{\mathrm{p}} +\hspace{0.17em}\frac{3}{\mathrm{q}} = 1$

The equation $\mathrm{y} = \pm \sqrt{3}\mathrm{x}$, y = 1 are the sides

• an equilateral triangle

• a right angled triangle

• a isosceles triangle

• an obtuse angled triangle

The equations of the lines through (1, 1) and making angles of 45° with the line x + y = 0 are

• x - 1 = 0, x - y = 0

• x - y = 0, y - 1 = 0

• x + y - 2 = 0, y - 1 = 0

• x - 1 = 0, y - 1 = 0

44.

The value of $\frac{\sin \left(55°\right) - \cos \left(55°\right)}{\sin \left(10°\right)}$ is

• $\frac{1}{\sqrt{2}}$

• 2

• 1

• $\sqrt{2}$

Let R be the set of real numbers and the mapping f : R $\to$ R and g : R $\to$ R be defined by f(x) = 5 - x² and g(x) =3$\text{λ}$ - 4, then the value of (fog) (- 1) is

• - 44

• - 54

• - 32

• - 64

A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5, 6} are two sets, and function f : Aa B is defined by f(x) = x + 2 $\forall$ x $\in$ A, then the function!

• bijective

• onto

• one-one

• many-one

If the matrices A = $\left[\begin{array}{ccc}2& 1& 3\\ 4& 1& 0\end{array}\right]$ and $\mathrm{B} = \left[\begin{array}{cc}1& - 1\\ 0& 2\\ 5& 0\end{array}\right]$, then AB will be

• $\left[\begin{array}{cc}17& 0\\ 4& - 2\end{array}\right]$

• $\left[\begin{array}{cc}4& 0\\ 0& 4\end{array}\right]$

• $\left[\begin{array}{cc}17& 4\\ 0& - 2\end{array}\right]$

• $\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$

w is an imaginary cube root of unity and

$\left|\begin{array}{ccc}\mathrm{x} +\hspace{0.17em}{\mathrm{w}}^2& \mathrm{w}& 1\\ \mathrm{w}& {\mathrm{w}}^2& 1 +\hspace{0.17em}\mathrm{x}\\ 1& \mathrm{x} + \mathrm{w}& {\mathrm{w}}^2\end{array}\right|$ = 0, then one of the value of x is

• 1

• 0

• - 1

• 2

If A = $\left[\begin{array}{cc}1& 2\\ - 4& - 1\end{array}\right]$, then A^{- 1} is

• $\frac{1}{7}\left[\begin{array}{cc}- 1& - 2\\ 4& 1\end{array}\right]$

• $\frac{1}{7}\left[\begin{array}{cc}1& 2\\ - 4& - 1\end{array}\right]$

• $\frac{1}{7}\left[\begin{array}{cc}- 1& - 2\\ 4& - 1\end{array}\right]$

• does not exist

For what values of x, the function f(x) = x⁴ - 4x³ + 4x² + 40 is monotonic decreasing ?

• 0 < x < 1

• 1 < x < 2

• 2 < x < 3

• 4 < x < 5