Live practice

For triangle PQR with P(2,1), Q(−2,3), and R(4,5), find the median through R.

Expand (1+\(\frac{x}{2}\)−\(\frac{2}{x}\))^4 fully, for x≠0.

Complete every requested part of exercise 5.1, question 19: 3 (1 – x) < 2 (x + 4)

Complete every requested part of exercise 3.2, question 12: If none of the angles x, y and (x + y) is a multiple of π, then cot x cot y – 1 cot ( x + y) = cot y + cot x Since, none of the x, y and (x + y) is multiple of π, we find that sin x sin y and sin (x + y) are non-zero. Now, cos ( x + y ) cos x cos y – sin x sin y cot ( x + y) = = sin ( x + y ) sin x cos y + cos x sin y Dividing numerator and denominator by sin x sin y, we have cot x cot y – 1 cot (x + y) = cot y + cot x cot x cot y + 1

On \(\mathbb Z\), let \(aRb\) when \(a-b\) is an integer. Find domain and range.

Why does benzene undergo electrophilic substitution reactions easily and nucleophilic substitutions with difficulty?

Describe how to separate two compounds that have different solubilities in the same solvent.

Balance the following equations in basic medium by ion-electron method and oxidation number methods and identify

A sample of pure PCl 5 was introduced into an evacuated vessel at 473 K. After equilibrium was attained, concentration of PCl 5 was found to be 0.5 × 10–1 mol L–1. If value of Kc is 8.3 × 10–3, what are the concentrations of PCl3 and Cl2 at equilibrium? PCl5 (g) PCl3 (g) + Cl2(g)

For 2A(g)+B(g)→2D(g), ΔU°=−10.5 kJ and ΔS°=−44.1 J K⁻¹ at 298 K. Calculate