Solve the linear inequation, write down the solution set and represent it on the real number line :

5(2 - 4x) > 18 - 16x > 22 - 20x, x ∈ R

If a polynomial x³ + 2x² – ax + b leaves a remainder -6 when divided by x + 1 and the same polynomial has x - 2 as a factor, then find the values of a and b.

In the given figure (not drawn to scale), BC is parallel to EF, CD is parallel to FG, AE : EB = 2 : 3, ∠BAD = 70°, ∠ACB = 105°, ∠ADC = 40° and AC is bisector of ∠BAD.

(a) Prove Δ AEF ~ Δ AGF

(b) Find :

(i) AG : AD

(ii) area of Δ ACB: area Δ ACD

(iii) area of quadrilateral ABCD: area of Δ ACB.

In the given figure, angle ABC = 70° and angle ACB = 50°. Given, O is the centre of the circle and PT is the tangent to the circle. Then calculate the following angles

(a) ∠CBT

(b) ∠BAT

(c) ∠PBT

(d) ∠APT