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:

$A$ pressure $P-$ absolute temperature $T$ diagram was obtained when a given mass of gas was heated. During the heating process from state $1$ to state $2$,the volume:

In the figure shown, if the internal resistance of the battery is $1\, \Omega$, the reading of the ammeter will be ............... $A$.

$A$ particle executes simple harmonic oscillation with an amplitude $a$. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

$A$ ray of light of intensity $I$ is incident on a parallel glass slab at point $A$ as shown in the diagram. It undergoes partial reflection and refraction. At each reflection, $25\%$ of incident energy is reflected. The rays $AB$ and $A'B'$ undergo interference. The ratio of $I_{max}$ and $I_{min}$ is (in $: 1$)

If ${}^n P_r = 30240$ and ${}^n C_r = 252$,then the ordered pair $(n, r)$ is equal to