11.

Find the value of the limit $\underset{\mathrm{x}\to 0}{\lim }\frac{\sqrt{1 - \cos \left(\mathrm{x}\right)}}{\mathrm{x}}$

• 0

• 1

• $\sqrt{2}$

• does not exist

If one AM 'A' and two GM p and q are inserted between two given numbers, then. find the value of $\frac{{\mathrm{p}}^2}{\mathrm{q}} + \frac{{\mathrm{q}}^2}{\mathrm{p}}$.

• A

• 2A

• 3A

• 4A

If the roots of the equation x² + ax + b = 0 are c and d, then one of the roots of the equation x² + (2c + a)x + c² + ac + b = 0

• c

• d - c

• 2d

• 2c

The sum of the coefficients of (6a - 5b)ⁿ, where n is a positive integer, is

• 1

• - 1

• 2ⁿ

• 2^{n - 1}

Find the value of (7.995)^1/3 correct to four decimal places.

• 1.9995

• 1.9996

• 1.9990

• 1.9991

The values of constants a and b so that

$\underset{\mathrm{x}\to \infty }{\lim }\left(\frac{{\mathrm{x}}^2 + 1}{\mathrm{x} + 1} - \mathrm{ax} - \mathrm{b}\right) = 0$ are

• a = 0, b = 0

• a = 1, b = - 1

• a = - 1, b = 1

• a = 2, b = - 1

A line making angles 45° and 60° with the positive directions of the axes of x and y makes with the positive direction of z-axis, an angle of

• 60°

• 120°

• 60° or 120°

• None of these

If I = $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, J = $\left[\begin{array}{cc}0& 1\\ - 1& 0\end{array}\right]$ and $\mathrm{B} = \left[\begin{array}{cc}\cos \left(\mathrm{\theta }\right)& \sin \left(\mathrm{\theta }\right)\\ - \sin \left(\mathrm{\theta }\right)& \cos \left(\mathrm{\theta }\right)\end{array}\right]$, then B is equal to

• $\mathrm{I} \cos \left(\mathrm{\theta }\right) + \mathrm{Jsin}\left(\mathrm{\theta }\right)$

• $\mathrm{I} \sin \left(\mathrm{\theta }\right) + \mathrm{Jcos}\left(\mathrm{\theta }\right)$

• $\mathrm{I} \cos \left(\mathrm{\theta }\right) - \mathrm{Jsin}\left(\mathrm{\theta }\right)$

• $- \mathrm{I} \cos \left(\mathrm{\theta }\right) + \mathrm{Jsin}\left(\mathrm{\theta }\right)$

If the axes are shifted to the point (1, - 2) without solution, then the equation 2x² + y² - 4x + 4y = 0 becomes

• 2X² + 3Y² = 6

• 2X² + Y²

• X² + 2Y²

• None of the above

In a group ( G, *), then equation x * a = b has a

• unique solution b * a^-1

• unique solution a^-1 * b

• unique solution a^-1 * b^-1

• many solutions