Live practice

In a geometric progression the fourth term equals the square of the second term, and the first term is −3. Find the seventh term.

Determine r in each equation: (i) {}^5P_r=2\,{}^6P_{r-1}(ii) {}^5P_r={}^6P_{r-1}.

Complete every requested part of exercise 5.1, question 18: 5x – 3 > 3x – 5 x (5 x – 2) (7 x – 3)

Given x−iy=(a−ib)/(c−id), prove that x²+y²=(a²+b²)/(c²+d²).

Complete every requested part of exercise 3.2, question 11: tan ( x – y) = 1 + tan x tan y If we replace y by – y in Identity 10, we get tan (x – y) = tan [x + (– y)] tan x + tan (− y ) tan x − tan y = = 1 − tan x tan ( − y ) 1+ tan x tan y

If \(A=\{x,y,z\}\), \(B=\{1,2\}\), how many relations are possible from \(A\) to \(B\)?

Arrange benzene, n-hexane and ethyne in decreasing order of acidic behaviour. Also give reason for this behaviour.

State the principles of crystallisation, distillation and chromatography, giving one example of each.

Balance the four stated redox equations by the ion-electron method in the specified acidic or basic medium.

Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as: CH3COOH (l) + C2H5OH (l) CH3COOC2H5 (l) + H2O (l) (i) Give the concentration ratio (reaction quotient), Qc, for this reaction (note: water is not in excess and is not a solvent in this reaction) (ii) At 293 K, if one starts with 1.00 mol of acetic acid and 0.18 mol of ethanol, there is 0.171 mol of ethyl acetate in the final equilibrium mixture. Determine the equilibrium constant. (iii) Starting with 0.5 mol of ethanol and 1.0 mol of acetic acid and maintaining it at 293 K, 0.214 mol of ethyl acetate is found after sometime. Has equilibrium been reached?