Correct Answer: A. 2

Explanation

\(Variance (\sigma^{2}) = \frac{\sum (x - \mu)^2}{n}\)

The mean \((\mu)\) of the data = \(\frac{11 + 12 + 13 + 14 + 15}{5} = \frac{65}{5} = 13\)

\(\sigma^{2} = \frac{10}{5} = 2\)

Correct Answer: B. EDVAC

Correct Answer: A. 10

Explanation

\((x + \frac{2}{x^2})^5\)

n = 5, r = 4, p = x and q = \(\frac{2}{x^2}\)

5C\(_4\)x\(^4\) (\(\frac{2}{x^2}\))1 = 5C\(_4\) \(\frac{2x^4}{x^2}\)

5C\(_4\) 2x\(^2\) = \(\frac{5!}{[5-4]!4!}\) * 2x\(^2\)

\(\frac{5*4!}{4!} * 2x^2\) = 5 * 2x\(^2\) = 10x\(^2\)

The coefficient is 10.

Correct Answer: D. 1 and 4

Explanation

\(s = ut + \frac{at^{2}}{2}\)

This movement is against gravity, so it is negative.

\(s = ut - \frac{gt^{2}}{2}\)

\(s = 20m, u = 25ms^{-1}\)

\(20 = 25t - \frac{10t^{2}}{2} \implies 20 = 25t - 5t^{2}\)

\(5t^{2} - 25t + 20 = 0 \)

\(5t^{2} - 5t - 20t + 20 = 0 \implies 5t(t - 1) - 20(t - 1) = 0\)

\(5t - 20 = \text{0 or t - 1 = 0}\)

\(t = \text{1 or 4}\)

Correct Answer: C. sums up a play

Correct Answer: D. hygrometer

Correct Answer: C. NaOH + HCL → NaCL + H\(_2\)O

Explanation

The enthalpy change of neutralisation involving weak acids are smaller in magnitude compared to that between strong acids and strong bases. This is because weak acids/bases are partially dissociated, which means not all hydrogen ions are free to react with hydroxide ions.

For strong acids and bases, the enthalpy of neutralisation values are always closely similar with the values -57 and -58 KJ/mol. We know that strong acids completely ionize in water. In case of weak acids, only partial dissociation of its ions occurs.

Correct Answer: D. alluvial deposits

Explanation

(ii) (a) < RTS = 65° - 34° (exterior angles of triangle PST)

= 31°

(ii) (b) < SRP = 65° (angles in alternate segment are equal)

\(\therefore < SRP = 180° - 65° = 115°\).

(b) <XYZ = 180 - 52 = 128° (angles on a straight line)

If < XYZ = 128°

then < XZY = 128° + 20° = 148°

< XZV = 180° - 148° = 32°

< YVZ = < VYZ = 52° (Isoceles triangle)

< WYZ = 52° - 32° = 20°

Correct Answer: D) differ only by a proton

Explanation

The question is asking which of the given options best describes the relationship between an acid and its conjugate base. The correct answer is Option D: an acid and its conjugate base differ only by a proton. This means that an acid can lose its proton to become its conjugate base, and its conjugate base can gain a proton to become the original acid.

It is important to note that the other options are not correct. Option A is incorrect because an acid and its conjugate base can have the same charge, depending on the specific acid and base involved. Option B is incorrect because a hydroxide ion (OH-) is not involved in the relationship between an acid and its conjugate base. Option C is incorrect because an electron is not involved in the transfer of a proton between an acid and its conjugate base.

Understanding the relationship between acids and bases is important in Chemistry, as it is the basis for the concept of pH and acid-base reactions. For more information, please see the recommended textbooks.