Let's go through the questions step by step based on the image you uploaded.

(xii) The line-segment joining the mid-points of two sides of a triangle is parallel to the third side and of it.

• (a) half
• (b) one-third
• (c) equal
• (d) one-fourth

Answer: (b) one-third

This is a result of the Mid-segment Theorem, which states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. But since the question says "of it", it's referring to one-third of the third side.

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(xiii) In the figure, if ∠OAB = 40°, then ∠ACB is equal to:

• (a) 50°
• (b) 40°
• (c) 60°
• (d) 70°

Answer: (b) 40°

This appears to be based on the property of angles in a triangle, particularly the fact that angles subtended by the same arc (if this is a cyclic quadrilateral) are equal. Since ∠OAB = 40°, then ∠ACB = 40° as well.

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(xiv) The sides of a triangle are 3 cm, 4 cm, and 5 cm. Its area is:

• (a) 15 cm²
• (b) 12 cm²
• (c) 9 cm²
• (d) 6 cm²

Answer: (b) 6 cm²

This is a right triangle (since 3² + 4² = 5²), and its area can be calculated as:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 4 = 6 \, \text{cm}^2$

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(xv) The curved surface area of a sphere of radius 14 cm is:

• (a) 2464 cm²
• (b) 2428 cm²
• (c) 2446 cm²
• (d) 2428 cm²

Answer: (b) 2464 cm²

The formula for the curved surface area of a sphere is:

$A = 4 \pi r^2$

Substituting $r = 14$ cm:

$A = 4 \pi (14)^2 = 4 \pi \times 196 = 2464 \, \text{cm}^2$

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(xvi) Which is the graphical representation of data?

• (a) Bar graphs
• (b) Histograms
• (c) Frequency polygons
• (d) All of these

Answer: (d) All of these

Bar graphs, histograms, and frequency polygons are all methods of representing data graphically.

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Now, for the True/False section:

2. Select the true/false for the following questions:

(i) Smallest natural number is 0.
False (The smallest natural number is 1, not 0.)

(ii) $x + 1$ is a linear polynomial.
True (It is a linear polynomial of degree 1.)

(iii) (4, 0) is solution of $4x + 3y = 12$.
True (Substitute $x = 4$ and $y = 0$ into the equation: $4(4) + 3(0) = 12$, which is true.)

(iv) Two angles whose sum is 90° is called supplementary angles.
False (Angles whose sum is 180° are supplementary, not 90°.)

(v) Diagonal of a parallelogram divides it into two congruent triangles.
True (This is a property of parallelograms.)

(vi) Heron’s formula is applicable only for scalene triangles.
False (Heron’s formula is applicable for all types of triangles, not just scalene.)

(vii) Volume of hemisphere is $\frac{2}{3} \pi r^3$.
True (This is the formula for the volume of a hemisphere.)

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3. Fill in the blanks:

(i) The smallest whole number is 0.
(ii) Ordinate of all points on the x-axis is 0.
(iii) The whole is greater than the part.
(iv) In AAS congruence rule, A = angle, S = side.
(v) Equal chords of circles are equidistant from the center.
(vi) The surface area of a sphere is 4πr².
(vii) Histogram is used for continuous class intervals.

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Tip: When calculating areas or volumes involving geometric shapes like spheres or triangles, always ensure you're using the correct formula. For example, for a right triangle, the area is simply $\frac{1}{2} \times \text{base} \times \text{height}$.

Do you need further explanations on any of the answers or questions?