If $\left|\frac{\mathrm{z} - 25}{\mathrm{z} - 1}\right| = 5$,  find the value of $\left|\mathrm{z}\right|$

• 3

• 4

• 5

• 6

Argument of the complex number $\left(\frac{- 1 - 3\mathrm{i}}{2 +\hspace{0.17em}\mathrm{i}}\right)$ is

• 45°

• 135°

• 225°

• 240°

The shortest distance between the straight lines through the points A₁ = (6, 2, 2) and A₂ = (- 4, 0, - 1) in the directions of (1, - 2, 2) and (3, - 2, - 2) is

• 6

• 8

• 12

• 9

The centre and radius of the sphere x² + y² + z² + 3x - 4z + 1 = 0 are

• $\left(- \frac{3}{2}, 0, - 2\right); \frac{\sqrt{21}}{2}$

• $\left(\frac{3}{2}, 0, 2\right); \sqrt{21}$

• $\left(- \frac{3}{2}, 0, 2\right); \frac{\sqrt{21}}{2}$

• $\left(- \frac{3}{2}, 0, 2\right); \frac{21}{2}$

Let A and B are two fixed points in a plane, then locus of another point Con the same plane such that CA + CB = constant, (> AB) is

• circle

• ellipse

• parabola

• hyperbola

The directrix of the parabola y² + 4x + 3 = 0 is

• $\mathrm{x} - \frac{4}{3} = 0$

• $\mathrm{x} + \frac{1}{4} = 0$

• $\mathrm{x} - \frac{3}{4} = 0$

• $\mathrm{x} - \frac{1}{4} = 0$

If g(x) is a polynomial satisfying g(x) g(y) = g(x) + g(y) + g(xy) - 2 for all real x and y and g(2) = 5, then $\underset{\mathrm{x}\to 3}{\lim }$ g(x) is

• 9

• 10

• 25

• 20

The length of the parabola y² = 12x cut off by the latusrectum is

• $6\left[\sqrt{2} + \log \left(1 + \sqrt{2}\right)\right]$

• $3\left[\sqrt{2} + \log \left(1 + \sqrt{2}\right)\right]$

• $6\left[\sqrt{2} - \log \left(1 + \sqrt{2}\right)\right]$

• $3\left[\sqrt{2} - \log \left(1 + \sqrt{2}\right)\right]$

9.

Area enclosed by the curve $\mathrm{\pi }\left[4{\left(\mathrm{x} - \sqrt{2}\right)}^2 + {\mathrm{y}}^2\right] = 8$ is

• $\mathrm{\pi }$ sq unit

• 2 sq unit

• 3$\mathrm{\pi }$ sq unit

• 4 sq unit

Let p, q, r and s be statements and suppose that $\mathrm{p} \to \mathrm{q} \to \mathrm{r} \to \mathrm{p}$. If $~ \mathrm{s} \to \mathrm{r}$, then

• $\mathrm{s} \to ~ \mathrm{q}$

• $~ \mathrm{q} \to \mathrm{s}$

• $~ \mathrm{s} \to ~ \mathrm{q}$

• $\mathrm{q} \to ~ \mathrm{s}$