Question

Match the following and choose the correct option.

r reduction

• A. a → (i), b → (ii), c → (iii), d → (iv)
• B. a → (iv), b → (iii), c → (ii), d → (i)
• C. a → (iii), b → (ii), c → (iv), d → (i)
• D. a → (i), b → (ii), c → (iv), d → (iii)

Hint:

In organic chemistry, each reagent has specific applications, such as Tollen's reagent for aldehyde detection and Fehling solution for reducing sugars.

Answer 1

The Correct Option is C

Concept: The electric field is the negative gradient of the potential: \(\vec{E} = -\nabla V\). Therefore, the potential difference can be found by integrating the field: \(V = -\int \vec{E} \cdot d\vec{r}\). Step 1: Integrate to find the potential function \(V(x,y)\). \[ dV = -E_x dx - E_y dy = -(10x)dx - (5y)dy \] \[ V(x,y) = \int -10x dx - \int 5y dy \] \[ V(x,y) = -5x^2 - \frac{5}{2}y^2 + C \]
Step 2: Determine constant C. We are given \(V(10, 20) = 500\). \[ 500 = -5(10)^2 - \frac{5}{2}(20)^2 + C \] \[ 500 = -500 - \frac{5}{2}(400) + C \] \[ 500 = -500 - 1000 + C \] \[ 500 = -1500 + C \implies C = 2000 \]
Step 3: Calculate potential at origin. At \((0,0)\): \[ V(0,0) = -5(0) - \frac{5}{2}(0) + C = 2000\,\text{V} \] \[ \boxed{V_{\text{origin}} = 2000\ \text{volt}} \]