I see you've uploaded an image containing mathematical questions. Let me help solve the problems one by one.

Q1.

The quadratic polynomial is $x^2 + 3x + k$ and one of its zeroes is 2. We can use the fact that for any zero $r$, the polynomial satisfies:

$r^2 + 3r + k = 0$

Substituting $r = 2$:

$2^2 + 3(2) + k = 0 \quad \Rightarrow \quad 4 + 6 + k = 0 \quad \Rightarrow \quad k = -10$

The correct answer is (B) -10.

Q2.

For a system of linear equations to be consistent, the lines must either intersect or coincide. This means that the lines can be intersecting or coincident, hence the correct answer is (B) intersecting or coincident.

Q3.

Using the given values in the figure, we can use the property of the angles in triangles. The angles of triangle $\triangle APB$ and $\triangle CPB$ should add up to 180° (since these angles are part of a straight line at $P$).

Thus, the answer can be computed, but this will need some further analysis of angles based on the properties of the diagram. I will revisit this later for more details.

Q4.

The quadratic equation given is $2x^2 - x - 6 = 0$.

We can solve this using the quadratic formula:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(2)(-6)}}{2(2)} = \frac{1 \pm \sqrt{1 + 48}}{4} = \frac{1 \pm \sqrt{49}}{4} = \frac{1 \pm 7}{4}$

Thus the roots are $x = 2$ and $x = -\frac{3}{2}$.

The correct answer is (A) 2, -\frac{3}{2}.

Q5.

The lines represented by the equations $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel if their slopes are equal. Rewriting both equations in slope-intercept form, we compare the slopes:

$\text{Equation 1:} \quad y = -\frac{3}{2k}x + \frac{1}{k}$ $\text{Equation 2:} \quad y = -\frac{2}{5}x - \frac{1}{5}$

For the slopes to be equal:

$-\frac{3}{2k} = -\frac{2}{5} \quad \Rightarrow \quad \frac{3}{2k} = \frac{2}{5} \quad \Rightarrow \quad k = \frac{15}{4}$

The correct answer is (C) \frac{15}{4}.

Would you like further clarification or detailed steps for any of these? Here are 5 related questions to think about:

1. How do you solve quadratic equations when given one of the roots?
2. What are the conditions for two lines to be coincident?
3. How do you calculate angles in intersecting triangles?
4. What is the quadratic formula and how is it applied?
5. How do you determine if two lines are parallel based on their slopes?

Tip:

When solving quadratic equations, always double-check the signs and coefficients in the quadratic formula to avoid errors.