When $CO_2$ concentration in blood increases,breathing becomes

The vector $c \cdot (b+c) \times (a+b+c)$ is equal to

$A$ centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers $140^{\circ}F$. What is the fall in temperature as registered by the Centigrade thermometer in $^{\circ}C$?

Both the blocks shown in the figure have mass $m$ and are moving with constant velocity in the directions shown. They are in a resistive medium which exerts an equal constant force $F$ on both blocks in the direction opposite to their velocity. The tension in the string connecting them is (Neglect friction):

$A$ hollow pipe of length $0.8 \ m$ is closed at one end. At its open end,a $0.5 \ m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \ N$ and the speed of sound is $320 \ ms^{-1}$,the mass of the string is: (in $g$)

In a $\triangle ABC$,$\cos \left(\frac{B+2C+3A}{2}\right) + \cos \left(\frac{A-B}{2}\right)$ is equal to