If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle of $45^{\circ}$ at the major segment of the circle,then the value of $m$ is:

The inverse of the proposition $(p \wedge \sim q) \Rightarrow r$ is

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_1$ and $k_2,$ respectively. If the maximum velocities during oscillations are equal,the ratio of amplitudes of $A$ and $B$ is

The slope of the tangent to the curve $x=t^{2}+3t-8, y=2t^{2}-2t-5$ at the point $(2,-1)$ is

An ideal gas expands isothermally from volume $V_1$ to volume $V_2$. It is then compressed to the original volume $V_1$ adiabatically. If $p_1$ and $p_2$ represent the initial pressure and final pressure respectively,and $W$ represents the net work done by the gas during the entire process,then:

The temperature of a body on the Kelvin scale is found to be $x \ K$. When it is measured by a Fahrenheit thermometer,it is found to be $x \ ^\circ F$. The value of $x$ is: