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.

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.

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.

Using Vieta's formulas, p = -(2 + 3) = -5.

For equal roots, the discriminant must be zero. Thus, (-5)^2 - 4*1*k = 0 => 25 - 4k = 0 => k = 25/4 = 6.25.

The equilibrium constant for the reverse reaction is the reciprocal of the forward reaction, so Kc' = 1/Kc = 0.1.

A Kc value greater than 1 indicates that the products are favored at equilibrium.

A Kc value less than 1 indicates that at equilibrium, the concentration of reactants is greater than that of products, thus reactants are favored.

The term is given by C(n, 3) * a^2 * x^3. Setting C(n, 3) * a^2 = 15 gives n = 6.

The equation y = k/x represents a family of hyperbolas.

a_n = a + (n-1)d = 5 + (15-1) * 3 = 5 + 42 = 47.

Concave lenses always produce virtual and erect images regardless of the object distance.

The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 10 cm = 20 cm.

The radius of curvature (R) is twice the focal length (f). Therefore, R = 2f = 2 * 20 cm = 40 cm.

A negative focal length indicates that the lens is a concave lens.

Power (P) = 1/f (in meters). Here, f = 0.2 m, so P = 1/0.2 = +5 D.

Power (P) is given by P = 1/f (in meters). Thus, P = 1/0.25 m = +4 D.

Power is inversely proportional to focal length. If f is doubled, P = 1/f will halve.

Range = Maximum - Minimum = 14 - 3 = 11

According to Le Chatelier's principle, increasing the temperature of an exothermic reaction shifts the equilibrium position to the left, favoring the reactants.

The time period T is inversely proportional to the frequency f. If the frequency is doubled, the time period halves.

Period T = 1/f, if frequency is halved, period doubles.

Wavelength is inversely proportional to frequency; if frequency is doubled, wavelength is halved.

Wavelength is inversely proportional to frequency; if frequency is doubled, wavelength halves.

According to the wave equation v = fλ, if frequency (f) is doubled and speed (v) remains constant, the wavelength (λ) must halve.

The speed of a wave is given by the product of its frequency and wavelength (v = fλ). If the frequency is doubled, the wavelength must be halved to keep the speed constant.