1. Problem h: Find the value of $\frac{45 \times 45 - 5 \times 5}{45 - 5}$. Given options: (i) 40, (ii) 50, (iii) 45, (iv) 5. Step 1: Calculate numerator: $45 \times 45 = 2025$, $5 \times 5 = 25$, so numerator = $2025 - 25 = 2000$. Step 2: Calculate denominator: $45 - 5 = 40$. Step 3: Divide numerator by denominator: $\frac{2000}{40} = 50$. Answer: (ii) 50. 2. Problem i: Sum of two numbers is 95, one number exceeds the other by 15. Find the numbers. Step 1: Let the numbers be $x$ and $y$ with $x > y$. Step 2: Given $x + y = 95$ and $x - y = 15$. Step 3: Add the two equations: $2x = 110 \Rightarrow x = 55$. Step 4: Substitute $x=55$ into $x + y = 95$: $55 + y = 95 \Rightarrow y = 40$. Answer: (i) 40 and 55. 3. Problem j: Adjacent sides of a rectangle are 16 m and 9 m. Find the side length of a square with the same area. Step 1: Area of rectangle = $16 \times 9 = 144$ m$^2$. Step 2: Let side of square be $s$. Then $s^2 = 144$. Step 3: Solve for $s$: $s = \sqrt{144} = 12$ m. Answer: (iv) 12 m. 4. Question 2a: Find the least number to multiply 3528 to get a perfect cube and find cube root of product. Step 1: Prime factorize 3528. $3528 = 2^3 \times 3^2 \times 7^2$. Step 2: For perfect cube, powers must be multiples of 3. Step 3: Current powers: 2 has 3 (ok), 3 has 2 (needs 1 more), 7 has 2 (needs 1 more). Step 4: Multiply by $3^1 \times 7^1 = 21$. Step 5: Product = $3528 \times 21 = 74088$. Step 6: Cube root: $\sqrt[3]{74088} = 2 \times 3^1 \times 7^1 = 42$. Answer: Multiply by 21; cube root is 42. 5. Question 2b: Boundary 2 m wide around lake 70 m by 30 m. Find boundary area. Step 1: Outer rectangle dimensions: length = $70 + 2 \times 2 = 74$ m, breadth = $30 + 2 \times 2 = 34$ m. Step 2: Area of outer rectangle = $74 \times 34 = 2516$ m$^2$. Step 3: Area of lake = $70 \times 30 = 2100$ m$^2$. Step 4: Boundary area = $2516 - 2100 = 416$ m$^2$. Answer: 416 m$^2$. 6. Question 2c(i): Percent error in weight estimation. Step 1: Estimated weight = 3.5 kg, actual weight = 4.9 kg. Step 2: Percent error = $\frac{|4.9 - 3.5|}{4.9} \times 100 = \frac{1.4}{4.9} \times 100 \approx 28.57\%$. Answer: Approximately 28.57% error. 7. Question 2c(ii): Increase 600 by 12.5%. Step 1: Increase = $600 \times \frac{12.5}{100} = 75$. Step 2: New value = $600 + 75 = 675$. Answer: 675. 8. Question 3a: Given $a + b + c = 18$ and $a^2 + b^2 + c^2 = 72$, find $ab + bc + ca$. Step 1: Use identity: $(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$. Step 2: Substitute values: $18^2 = 72 + 2(ab + bc + ca)$. Step 3: Calculate: $324 = 72 + 2(ab + bc + ca)$. Step 4: Rearrange: $2(ab + bc + ca) = 324 - 72 = 252$. Step 5: Solve: $ab + bc + ca = \frac{252}{2} = 126$. Answer: 126. 9. Question 3b: Solve for $m$: $m - \frac{m - 1}{2} = 1 - \frac{m - 2}{3}$. Step 1: Multiply both sides by 6 (LCM of 2 and 3): $6m - 3(m - 1) = 6 - 2(m - 2)$. Step 2: Expand: $6m - 3m + 3 = 6 - 2m + 4$. Step 3: Simplify: $3m + 3 = 10 - 2m$. Step 4: Add $2m$ to both sides: $3m + 2m + 3 = 10$. Step 5: $5m + 3 = 10$. Step 6: Subtract 3: $5m = 7$. Step 7: Divide: $m = \frac{7}{5} = 1.4$. Answer: $m = 1.4$. 10. Question 3c: Wire bent as square area 121 cm$^2$, find area when bent as circle. Step 1: Side of square $s = \sqrt{121} = 11$ cm. Step 2: Perimeter of square = $4 \times 11 = 44$ cm (length of wire). Step 3: Circle circumference = 44 cm. Step 4: Radius $r = \frac{44}{2\pi} = \frac{22}{\pi}$ cm. Step 5: Area of circle = $\pi r^2 = \pi \left(\frac{22}{\pi}\right)^2 = \pi \times \frac{484}{\pi^2} = \frac{484}{\pi} \approx 154.14$ cm$^2$. Answer: Approximately 154.14 cm$^2$. 11. Question 4a: Shopkeeper gives 10% off, still profits 25%. Find cost price of article marked 250. Step 1: Marked price = 250. Step 2: Selling price after 10% off = $250 \times 0.9 = 225$. Step 3: Let cost price = $C$. Step 4: Profit = 25%, so $225 = C \times 1.25$. Step 5: Solve for $C$: $C = \frac{225}{1.25} = 180$. Answer: 180. 12. Question 4b: Perimeter of rhombus with diagonals 30 cm and 16 cm. Step 1: Each side $s = \sqrt{\left(\frac{30}{2}\right)^2 + \left(\frac{16}{2}\right)^2} = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} = 17$ cm. Step 2: Perimeter = $4 \times 17 = 68$ cm. Answer: 68 cm. 13. Question 4c: Construct triangle XYZ with $YZ=7.5$ cm, $\angle Y=60^\circ$, $\angle Z=75^\circ$ and construct circumcircle. Step 1: Use given side and angles to draw triangle. Step 2: Construct perpendicular bisectors of sides to find circumcenter. Step 3: Draw circle with circumcenter as center and radius equal to distance to any vertex. Answer: Triangle XYZ constructed with circumcircle.