Live practice

Evaluate lim(x→π/2) tan(2x)/(x−π/2).

Determine the line through (2,3) whose x- and y-intercepts are equal.

Find the sum of n terms of the geometric progression √7, √21, 3√7, … .

Count arrangements of PERMUTATIONS that (i) begin with P and finish with S(ii) keep all vowels in one block(iii) place exactly four letters between P and S.

Complete every requested part of exercise 3.2, question 15: sin 2x = 2 sinx cos x = 2 x ≠ n π + , where n is an integer 1 + tan x 2 We have sin (x + y) = sin x cos y + cos x sin y Replacing y by x, we get sin 2x = 2 sin x cos x. 2sin x cos x Again sin 2x = cos2 x + sin 2 x 62 MATHEMATICS Dividing each term by cos2 x, we get 2tan x sin 2x = 1 +tan 2 x 2tan x π

For \(f(x)=2x-5\), find \(f(0),f(7),f(-3)\).

Arrange the following set of compounds in order of their decreasing relative + reactivity with an electrophile, E (a) Chlorobenzene, 2,4-dinitrochlorobenzene, p-nitrochlorobenzene (b) Toluene, p-H3C – C6H4 – 2, p-O2N – C6H4 – 2.

Differentiate the principles of nitrogen estimation by the Dumas and Kjeldahl methods.

Consider the elements : Cs, Ne, I and F (a) Identify the element that exhibits only negative oxidation state. (b) Identify the element that exhibits only postive oxidation state. (c) Identify the element that exhibits both positive and negative oxidation states. (d) Identify the element which exhibits neither the negative nor does the positive oxidation state.

Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium: 2BrCl (g) Br2 (g) + Cl2 (g) for which Kc= 32 at 500 K. If initially pure BrCl is present at a concentration of 3.3 × 10–3 mol L–1, what is its molar concentration in the mixture at equilibrium?