The function f(x) = sin(x) + cos(x) will be

• an even function

• an odd function

• a constant function

• None of these

The solution of the equation ${\log }_7\left({\log }_5\left(\sqrt{{\mathrm{x}}^2 + 5 + \mathrm{x}}\right)\right) = 0$ is

• x = - 2

• x = 2

• x = 4

• x = 5

A balloon is coming down at the rate of4 m/min and its angle of elevation is 45° from a point on the ground which has been reduced to 30°, after 10 min. Balloonwill be on the ground at a distance ofhow many metres from the observer ?

• $20\sqrt{3} \mathrm{m}$

• $20\left(3 + \sqrt{3}\right) \mathrm{m}$

• $10\left(3 + \sqrt{3}\right) \mathrm{m}$

• None of these

If the equations 2x - y + 2z = 2, x - 2y + z = - 4 and x + y + $\mathrm{\lambda }$z = 4 have no solution, then the value of $\mathrm{\lambda }$ will be

• 1

• 2

• 3

• - 4

$\mathrm{If} \mathrm{A} = \left[\begin{array}{cc}\mathrm{\alpha }& 0\\ 1& 1\end{array}\right], \mathrm{B} = \left[\begin{array}{cc}1& 0\\ 5& 1\end{array}\right]$, then the value of $\mathrm{\alpha }$, if A² = B, will be

• 4

• 3

• 5

• None of these

If $\sin \left({\sin }^{-1}\left(\frac{1}{5}\right) + {\cos }^{-1}\left(\mathrm{x}\right)\right) = 1$, then x is

• $\frac{1}{5}$

• $\frac{2}{5}$

• $\frac{3}{5}$

• $\frac{\mathrm{\pi }}{2}$

The value of $\tan \left[{\cos }^{-1}\left(\frac{4}{5}\right) + {\tan }^{-1}\left(\frac{2}{3}\right)\right]$ will be

• $\frac{6}{11}$

• $\frac{6}{17}$

• $\frac{11}{6}$

• $\frac{17}{6}$

28.

If y = ${\tan }^{-1}\left(\sqrt{\frac{1 - \cos \left(\mathrm{x}\right)}{1 + \cos \left(\mathrm{x}\right)}}\right)$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ will be

• $\sin \left(\mathrm{x}\right)\cos \left(\mathrm{x}\right)$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{1}{2}$

• $\frac{1}{1 + {\cos }^2\left(\mathrm{x}\right)}$

The value of $\underset{\mathrm{x}\to 1}{\lim }\left(1 - \mathrm{x}\right) . \tan \left(\frac{\mathrm{\pi x}}{2}\right)$ will be

• $\frac{\mathrm{\pi }}{2}$

• $\frac{2}{\mathrm{\pi }}$

• $2\mathrm{\pi }$

• $\mathrm{\pi }$

Let f(x) = $$\begin{gathered} \left\{\frac{{\mathrm{x}}^2 - 4\mathrm{x} + 3}{{\mathrm{x}}^2 + 2\mathrm{x} - 3}, \mathrm{x} \ne 1 \\ \mathrm{k} , \mathrm{x} = 1\right\} \end{gathered}$$ If f(x) is continuous at x = 1, then the value of k will be

• 1

• $\frac{1}{2}$

• - 1

• $- \frac{1}{2}$