The middle term in the expansion of ${\left(\frac{\mathrm{b}\sqrt{\mathrm{a}}}{5} - \frac{5}{\mathrm{a}\sqrt{\mathrm{b}}}\right)}^{12}$ is

• ${}^{12}\mathrm{C}_6{\left(\frac{\mathrm{b}}{\mathrm{a}}\right)}^3$

• $- {}^{12}\mathrm{C}_6{\left(\frac{\mathrm{b}}{\mathrm{a}}\right)}^3$

• ${}^{12}\mathrm{C}_7{\frac{\mathrm{b}}{\mathrm{a}}}^5$

• $- {}^{12}\mathrm{C}_7\frac{{\mathrm{b}}^5}{\mathrm{a}}$

If in an AP, 3rd term is 18 and 7th term is 30, the sum of its 17 terms is

• 600

• 612

• 624

• None of these

The sum of the digitsin the unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is

• 432

• 108

• 36

• 18

The number of solutions of ${\mathrm{x}}^2 + 3\left|\mathrm{x}\right| + 2 = 0$ the equation is

• 0

• 1

• 2

• 4

In a throw of two dice, the probability of getting a sum of 7 or 11 is

• $\frac{2}{9}$

• $\frac{7}{9}$

• $\frac{5}{9}$

• None of these

The probability that at least one of the events A and B occurs is 0.7 and they occur simultaneously with probability 0.2. Then, $\mathrm{P}\left(\overline{\mathrm{A}}\right) + \mathrm{P}\left(\overline{\mathrm{B}}\right)$ is equal to

• 0.8

• 0.6

• 1.1

• 1.4

If $\sin \left(\mathrm{\theta }\right) + \csc \left(\mathrm{\theta }\right) = 2, \mathrm{then} {\sin }^2\left(\mathrm{\theta }\right) + {\csc }^2\left(\mathrm{\theta }\right)$ is equal to

• 1

• 4

• 2

• None of these

The maximum value of $5\cos \left(\mathrm{\theta }\right) + 3\cos \left(\mathrm{\theta } + \frac{\mathrm{\pi }}{3}\right) + 3$ is

• 10

• - 10

• 14

• None of these

If $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$ are the solutions of $\mathrm{atan}\left(\mathrm{\theta }\right) + \mathrm{bsec}\left(\mathrm{\theta }\right) = \mathrm{c}$, then $\tan \left(\mathrm{\alpha } + \mathrm{\beta }\right)$ is equal

• $\frac{2\mathrm{ac}}{{\mathrm{a}}^2 - {\mathrm{c}}^2}$

• $\frac{2\mathrm{ac}}{{\mathrm{c}}^2 - {\mathrm{a}}^2}$

• $\frac{2\mathrm{ac}}{{\mathrm{a}}^2 + {\mathrm{c}}^2}$

• None of these

If ${\sin }^{-1}\left(\frac{\mathrm{x}}{5}\right) + {\csc }^{-1}\left(\frac{5}{4}\right) = \frac{\mathrm{\pi }}{2}$, then x is equal to

• 4

• 5

• 1

• 3