1. **Problem (01a):** Suman took a loan of 60000 at an 18% annual simple interest rate to be paid in 3 years. (i) Find the interest for 1 year. **Step 1:** Simple interest for 1 year is calculated as $I = P \times R \times T$, where $T$ is in years. Here, $P = 60000$, $R = 18\% = 0.18$, $T=1$ year. $$I = 60000 \times 0.18 \times 1 = 10800$$ (ii) Find total amount to be paid at end of 3 years. **Step 2:** Total simple interest for 3 years is: $$I_{total} = 60000 \times 0.18 \times 3 = 32400$$ **Step 3:** Total amount = Principal + Interest: $$A = 60000 + 32400 = 92400$$ (iii) Find monthly instalments if paid equally including interest. **Step 4:** Number of months = $3 \times 12 = 36$ **Step 5:** Monthly instalment = Total amount / Number of months $$\text{Monthly instalment} = \frac{92400}{36} = 2566.67$$ 2. **Problem (01b):** 12 men complete work in 10 days. 2 days after starting, 4 men leave. Find how many more days needed. **Step 1:** Total work = $12 \times 10 = 120$ man-days. **Step 2:** Work done in first 2 days by 12 men: $$12 \times 2 = 24$$ man-days. **Step 3:** Remaining work: $$120 - 24 = 96$$ man-days. **Step 4:** Remaining men = 12 - 4 = 8 men. **Step 5:** Days needed to complete remaining work: $$\text{Days} = \frac{\text{Remaining work}}{\text{Remaining men}} = \frac{96}{8} = 12$$ days. 3. **Problem (02a)(i):** Evaluate $y$ at $x=1$ for $y = 2x^2 - 3$. Substitute $x=1$, $$y = 2(1)^2 - 3 = 2 - 3 = -1$$ 4. **Problem (02b)(i):** Find minimum value of $y = 2x^2 -3$. **Step 1:** The quadratic opens upwards (coefficient of $x^2$ is positive), so minimum at vertex. **Step 2:** Vertex $x = -\frac{b}{2a} = -\frac{0}{2 \times 2} = 0$. **Step 3:** Minimum value: $$y_{min} = 2(0)^2 - 3 = -3$$ 5. **Problem (02b)(iii):** Find roots of equation $2x^2 - 3 = 0$. **Step 1:** Solve for $x$: $$2x^2 = 3$$ $$x^2 = \frac{3}{2}$$ **Step 2:** Roots: $$x = \pm \sqrt{\frac{3}{2}} = \pm \frac{\sqrt{6}}{2}$$ **Answers:** (i) Interest for 1 year = 10800 (ii) Total amount = 92400 (iii) Monthly instalment = 2566.67 (iv) Additional days needed = 12 (v) $y$ at $x=1$ is $-1$ (vi) Minimum value = $-3$ (vii) Roots are $x = \pm \frac{\sqrt{6}}{2}$