If $2x + 3y + 12 = 0$ and $x - y + 4\lambda = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $\lambda$ is equal to

Let $l_1$ and $l_2$ be two lines intersecting at $P$. If $A_1, B_1, C_1$ are points on $l_1$,and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and if none of these coincides with $P$,then the number of triangles formed by these eight points is:

$A$ particle moves with simple harmonic motion in a straight line. In the first $\tau \, s$,after starting from rest,it travels a distance $a$,and in the next $\tau \, s$,it travels $2a$ in the same direction. Then:

Which one of the following does not involve coagulation?

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P, Q,$ and $R$ having emf's $E, E,$ and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is:

The upper half of an inclined plane with an angle of inclination $\phi$ is smooth, while the lower half is rough. $A$ body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is