Find the vertical asymptote(s) of \(f\left( x \right) = \dfrac{1}{{{x^2} + 4x + 3}}\).

Solve \( 3x^2 – 10x + 4 \lt 2x^2 – 5x – 2 \).

Find  \(a\) and \(b\),  if \(\dfrac{{\sin 2\theta + \sin \theta }}{{1 + \cos 2\theta + \cos \theta }} = a\tan \left( {b\theta } \right)\).

A particle  \(P\)   moves in a straight line with a velocity function of  \(s\left( t \right) = {t^3} – 6{t^2} + 1\) metres,  where  \(t \ge 0\),  \(t\)   in seconds.    Find the total distance travelled in the time from  \(t = 1\)  and  \(t = 6\).

The mass of radioactive \(t \) hours after establishment is \({R_t} = 200 \times {1.4^{ – t}}\) grams. Find the time for the mass to reach 150 grams. Answer correct to the nearest minute.

Simplify \(\dfrac{{n! + \left( {n – 1} \right)!}}{{\left( {n – 1} \right)!}}\).

Find the coefficient of \({x^{9}}\) in the expansion of \({\left( {{x^2} + \frac{2}{x}} \right)^{15}}\).

Find the Cartesian equation of \( \displaystyle x = t+1, y = t + \frac{1}{t} \).

Factorise \( f(x) = x^4 – 2x^2 – 16x – 15 \) over real number field.

State the domain and range of \( y = \cos^{-1} (x+2) – \displaystyle \frac{\pi}{2} \).