Let R denote the set of all real numbers and RT denote the set of all positive real numbers. For the subsets A and B of R define f : A $\to$ B by f(x) = x² for x $\in$ A. Observe the two lists given below

A	f is one-one and onto, 1. A = R, B = R If	1	A = R+, B = R
B	f is one-one but not onto, If	2	A = B = R
C	f is onto but not one-one, if	3	A = R, B = R+
D	f is neither one-one nor onto If	4	A = B + R+

An urn A contains 3 white and 5 black balls. Another um B contains 6 white and 8 black balls. A ball is picked from A at random andthen transferred to B. Then, a ball is picked at random from B. The probability that it is a white ball is

• $\frac{14}{40}$

• $\frac{15}{40}$

• $\frac{16}{40}$

• $\frac{17}{40}$

If a straight line L is perpendicular to the line 4x- 2y = 1 and forms a triangle of area 4 sq unit with the coordinate axes, then the equation of the line L is

• 2x + 4y + 7 = 0

• 2x - 4y + 8 = 0

• 2x + 4y + 8 = 0

• 4x - 2y - 8 = 0

$\mathrm{The} \mathrm{image} \mathrm{of} \mathrm{the} \mathrm{point} \left(4, - 13\right) \mathrm{with} \mathrm{respect} \mathrm{to} \mathrm{the} \mathrm{line} 5\mathrm{x} + \mathrm{y} + 6 = 0 \mathrm{is}$

• (- 1, - 14)

• (3, 4)

• (1, 2)

• (- 4, 13)

The image of the line x + y - 2 = 0 in the y-axis is

• x - y + 2 = 0

• y - x + 2 = 0

• x + y + 2 = 0

• x + y - 2 = 0

A straight line which makes equal intercepts on positive X and Y axes and which is at a distance 1 unit from the origin intersects the straight line $\mathrm{y} = 2\mathrm{x} + 3 + \sqrt{2} \mathrm{at} \left({\mathrm{x}}_0, {\mathrm{y}}_0\right). \mathrm{Then} 2{\mathrm{x}}_0 + {\mathrm{y}}_0 = ?$

• $3 + \sqrt{2}$

• $\sqrt{2} - 1$

• 1

• 0

The distance between the two lines represented by 8x² - 24xy + 18y² - 6x + 9y - 5 = 0 is

• 0

• $\frac{3}{4\sqrt{13}}$

• $\frac{6}{\sqrt{13}}$

• $\frac{7}{2\sqrt{13}}$

A pair of perpendicular lines passes through the origin and also through the points of intersection of the curve x² + y² = 4 with x + y = a, where a > 0. Then a is equal to

• 2

• 3

• 4

• 5

If 3x² - 11xy + 10y² - 7x + 13y + k = 0 denotes a pair of straight lines, then the point of intersection of the lines is

• (1, 3)

• (3, 1)

• (- 3, 1)

• (1, - 3)

$$\begin{gathered} \mathrm{The} \mathrm{equation} \mathrm{of} \mathrm{the} \mathrm{radical} \mathrm{axis} \mathrm{of} \mathrm{the} \mathrm{pair} \mathrm{of} \mathrm{circles} \\ 7{\mathrm{x}}^2 + 7{\mathrm{y}}^2 - 7\mathrm{x} + 14\mathrm{y} + 18 = 0 \mathrm{and} 4{\mathrm{x}}^2 + 4{\mathrm{y}}^2 - 7\mathrm{x} + 8\mathrm{y} + 20 = 0 \mathrm{is} \end{gathered}$$

• x - 2y - 5 = 0

• 2x - y + 5 = 0

• 21x - 68 = 0

• 23x - 68 = 0