11.

The equation y² + 4x + 4y + k = 0 represents a parabola whose latusrectum is

• 1

• 2

• 3

• 4

If the circles x² + y² + 2x + 2ky + 6 = 0 and x² + y² + 2ky + k = 0 intersect orthogonally, then k is equal to

• $2 \mathrm{or} - \frac{3}{2}$

• $- 2 \mathrm{or} - \frac{3}{2}$

• $2 \mathrm{or} \frac{3}{2}$

• $- 2 \mathrm{or} \frac{3}{2}$

If four distinct points (2k, 3k), (2, 0), (0, 3), (0, 0) lie on a circle, then

• k < 0

• 0 < k < 1

• k = 1

• k > 1

The line joinining $\mathrm{A}\left(\mathrm{bcos}\left(\mathrm{\alpha }\right), \mathrm{bsin}\left(\mathrm{\alpha }\right)\right)$ and $\mathrm{B}\left(\mathrm{acos}\left(\mathrm{\beta }\right), \mathrm{asin}\left(\mathrm{\beta }\right)\right)$, where a $\ne$ b, is produced to the point M(x, y) so that AM : MB = b : a. Then, $\mathrm{xcos}\left(\frac{\mathrm{\alpha } + \mathrm{\beta }}{2}\right) + \mathrm{ysin}\left(\frac{\mathrm{\alpha } + \mathrm{\beta }}{2}\right)$ is equal to

• 0

• 1

• - 1

• a² + b²

Let the foci of the ellipse $\frac{{\mathrm{x}}^2}{9} + {\mathrm{y}}^2 = 1$ subtend a right angle at a point P. Then, the locus of P is

• x² + y² = 1

• x² + y² = 2

• x² + y² = 4

• x² + y² = 8

Number of solutions of the equation tan(x) + sec(x) = 2cos(x), x $\in$ [0, $\mathrm{\pi }$] is

• 0

• 1

• 2

• 3

The maximum value of $\left|\mathrm{z}\right|$, when the complex number z satisfies the condition $\left|\mathrm{z} + \frac{2}{\mathrm{z}}\right|$ = 2 is

• $\sqrt{3}$

• $\sqrt{3} + \sqrt{2}$

• $\sqrt{3} + 1$

• $\sqrt{3} - 1$

If ${\left(\frac{3}{2} + \mathrm{i}\frac{\sqrt{3}}{2}\right)}^{50} = 3^{25}\left(\mathrm{x} +\hspace{0.17em}\mathrm{iy}\right)$, where x and y are real, then the ordered pair (x, y) is

• $\left(- 3, 0\right)$

• $\left(0, 3\right)$

• $\left(0, - 3\right)$

• $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$

If $\frac{\mathrm{z} - 1}{\mathrm{z} + 1}$ is pure imaginary, then

• $\left|\mathrm{z}\right| = \frac{1}{2}$

• $\left|\mathrm{z}\right| = 1$

• $\left|\mathrm{z}\right| = 2$

• $\left|\mathrm{z}\right| = 3$

There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then, the number of students failing in all the three subjects

• is 12

• is 4

• is 2

• cannot be determined from the given information