If the line 3x - 2y + 6 = 0 meets X-axis and Y-axis, respectively at A and B, then the equation of the circle with radius AB and centre at A is

• x² + y² + 4x + 9 = 0

• x² + y² + 4x - 9 = 0

• x² + y² + 4x + 4 = 0

• x² + y² + 4x - 4 = 0

A line l meets the circle x² + y² = 61 in A, B and P(- 5, 6) is such that PA = PB = 10. Then,the equation of l is

• 5x + 6y + 11 = 0

• 5x - 6y - 11 = 0

• 5x - 6y + 11 = 0

• 5x - 6y + 11 = 0

If (1, a), (b, 2) are conjugate points with respect to the circle x² + y² = 25, then 4a + 2b is equal to

• 25

• 50

• 100

• 150

The eccentricity of the conic 36x² + 144y² - 36x - 96y -119 = 0 is

• $\frac{\sqrt{3}}{2}$

• $\frac{1}{2}$

• $\frac{\sqrt{3}}{4}$

• $\frac{1}{\sqrt{3}}$

The polar equation $\cos \left(\mathrm{\theta }\right) + 7\sin \left(\mathrm{\theta }\right) = \frac{1}{\mathrm{r}}$ represents a

• circle

• parabola

• straight line

• hyperbola

The centre of the circle ${\mathrm{r}}^2 - 4\mathrm{r}\left(\cos \left(\mathrm{\theta }\right) + \sin \left(\mathrm{\theta }\right)\right) - 4 = 0$ in cartesian coordinates is

• (1, 1)

• (- 1, - 1)

• (2, 2)

• (- 2, - 2)

The radius of the circle r = $\sqrt{3}\sin \left(\mathrm{\theta }\right) + \cos \left(\mathrm{\theta }\right)$ is

• 1

• 2

• 3

• 4

The value of $\underset{\mathrm{n}\to \infty }{\lim }\frac{1}{{\mathrm{n}}^3}\sum _{\mathrm{k}=1}^{\mathrm{n}}\left({\mathrm{k}}^2\mathrm{x}\right)$ is

• x

• $\frac{\mathrm{x}}{2}$

• $\frac{\mathrm{x}}{3}$

• $\frac{\mathrm{x}}{4}$

If f(x) = $$\begin{gathered} \left\{\left[\mathrm{x}\right], \mathrm{if} - 3 < \mathrm{x} \le - 1 \\ \left|\mathrm{x}\right|, \mathrm{if} - 1 < \mathrm{x} <\hspace{0.17em}1 \\ \left|\left[\mathrm{x}\right]\right|, \mathrm{if} 1 \le \mathrm{x} < 3\right\} \end{gathered}$$ then the set $\left(\mathrm{x} : \mathrm{f}\left(\mathrm{x}\right) \ge 0\right)$ is equal to

• (- 1, 3)

• [- 1, 3)

• (- 1, 3]

• [- 1, 3)

50.

If f: $\mathrm{R} \to \mathrm{R}$ is an even function having derivatives of all orders, then an odd function among the following is

• f''

• f'''

• f' + f''

• f'' + f'''