11.

If A and B are two events, then $\mathrm{P}\left(\overline{\mathrm{A}} \cap \mathrm{B}\right)$ is equal to

• $\mathrm{P}\left(\overline{\mathrm{A}}\right)\mathrm{P}\left(\overline{\mathrm{B}}\right)$

• 1 - P(A) - P(B)

• $\mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right) - \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$

• $\mathrm{P}\left(\mathrm{B}\right) - \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$

If m = ${}^{\mathrm{n}}\mathrm{C}_2$, then ${}^{\mathrm{m}}\mathrm{C}_2$ is equal to

• $\mathrm{n} + {}^1\mathrm{C}_4$

• $3 \times {}^{\mathrm{n}}\mathrm{C}_4$

• $3 \times {}^{\mathrm{n} + 1}\mathrm{C}_4$

• None of these

The control structure of IF-THEN is a

• multiple selection

• double selection

• single selection

• None of these

If b + c = 3a, then the value of $\cot \left(\frac{\mathrm{B}}{2}\right)\cot \left(\frac{\mathrm{C}}{2}\right)$ is

• $\sqrt{2}$

• $\sqrt{3}$

• 2

• 1

The centre of the circle which circumscribes the square formed by x² - 8x + 12 = 0 and y² - 14y + 45 = 0 is

• (4, 5)

• (3, 4)

• (9, 5)

• (4, 7)

The value of $\tan \left(57°\right) - \tan \left(12°\right) - \tan \left(57°\right)\tan \left(12°\right)$ is

• $\tan \left(69°\right)$

• $\tan \left(45°\right)$

• 0

• None of these

If a and b are two vectors of magnitude 2 inclined at an angle 60°, then the angle between a and a + b is

• 30°

• 60°

• 45°

• None of these

The value of 2, 6, 10 ... (4n - 6)(4n - 2) is equal to

• C(2n, n)

• (n + 1)(n + 2)(n + 3) ... (2n)

• n! P (2n, n)

• None of above

Two dice are thrown simultaneously. The probability of getting a pair of ACE is

• 1/36

• 1/3

• 1/6

• None of these

If e₁ and e₂ are the eccentricities of the hyperbolas $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2} - \frac{{\mathrm{y}}^2}{{\mathrm{b}}^2} = 1 \mathrm{and} \frac{{\displaystyle {\mathrm{x}}^2}}{{\displaystyle {\mathrm{a}}^2}} - \frac{{\displaystyle {\mathrm{y}}^2}}{{\displaystyle {\mathrm{b}}^2}} = - 1$, then the value of $\frac{1}{{{\mathrm{e}}_1}^2} + \frac{1}{{{\mathrm{e}}_2}^2}$ is

• 3

• 2

• 1

• $\frac{1}{2}$