The potential difference V_AB = V_B - V_A = 15 V - 5 V = 10 V.

Work done W = Q(V_B - V_A) = 2 C * (15 V - 5 V) = 20 J.

If the electric potential is constant, the electric field in that region is zero, as E = -dV/dx.

The potential gradient is given as 0.6 V/m, which is the calibration value for the potentiometer.

The balancing length is calculated as L = V / (potential gradient) = 2V / 4 V/m = 0.5 m.

If the enthalpy of a system increases, the process is considered endothermic.

An increase in enthalpy indicates that the system is gaining heat.

A negative enthalpy change indicates that the reaction releases heat, making it exothermic.

An increase in entropy indicates that the process is spontaneous, as per the second law of thermodynamics.

If entropy increases, ΔG decreases, making the reaction more favorable.

To solve for x, subtract 3 from both sides to get 2x = 8, then divide by 2 to find x = 4.

Rearranging the equation into slope-intercept form (y = mx + b) gives y = -2/3x + 4, where the slope (m) is -2/3.

Rearranging the equation to y = -2/3x + 2 shows that the slope is -2/3.

Adding 3 to both sides gives 2x = 10, and dividing by 2 gives x = 5.

Substituting x = 1 gives 2(1)^2 + 3(1) + k = 0 => 2 + 3 + k = 0 => k = -5.

Using Vieta's formulas, k = 2*1*(-2) = -4.

Using Vieta's formulas, r1 + r2 = -b/a = -3/2.

Substituting x = 0 into the equation 2(0) + 3y = 6 gives 3y = 6, thus y = 2.

To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, leading to y = 2.

To find the y-intercept, set x = 0. The equation becomes -4y + 12 = 0, leading to y = 3.

Rearranging to y = 4x - 8 shows that the y-intercept is -8.

'm' represents the slope of the line in the slope-intercept form of a linear equation.

To find the x-intercept, set y = 0. The equation becomes 0 = -1/2x + 3, leading to x = 6.

Substituting x = 4 into the equation gives y = -1/2(4) + 3 = -2 + 3 = 1.

To find the x-intercept, set y = 0: 0 = -2x + 5, which gives x = 2.5.

'm' in the equation of a line represents the slope, which indicates the steepness and direction of the line.

In the equation y^2 = 4px, p = 3, hence the value of 'p' is 3.

Rewriting the equation in standard form gives (x^2/16) + (y^2/9) = 1, so semi-major axis a = 4 and semi-minor axis b = 3.

The product of the roots is given by c/a. Here, c = 6 and a = 1, so αβ = 6.

The discriminant must be negative for no real roots: 5^2 - 4*1*k < 0, which simplifies to 25 - 4k < 0, or k > 25.