If $\frac{1}{4}, a, b, \frac{1}{19}$ form a $H.P.$,then the values of $a$ and $b$ are respectively:

An automobile driver travels from a plane to a hill station $120 \ km$ distant at an average speed of $30 \ km/hr$. He then makes the return trip at an average speed of $25 \ km/hr$. He covers another $120 \ km$ distance on the plane at an average speed of $50 \ km/hr$. His average speed over the entire distance of $360 \ km$ will be:

If the $7^{th}$ term of a harmonic progression is $8$ and the $8^{th}$ term is $7$,then its $15^{th}$ term is

An aeroplane flies around a square,the sides of which measure $100$ miles each. The aeroplane covers the first side at a speed of $100 \text{ mph}$,the second side at $200 \text{ mph}$,the third side at $300 \text{ mph}$,and the fourth side at $400 \text{ mph}$. The average speed of the aeroplane around the square is ....... $\text{mph}$.

If the roots of the equation $k x^3 - 18 x^2 - 36 x + 8 = 0$ are in harmonic progression,then $k =$

If the roots of the equation $x^3 - ax^2 + bx - c = 0$ are in harmonic progression $(HP)$,then the harmonic mean of the roots is