If the slope of one of the lines given by $ax^2+2hxy+by^2=0$ is two times the other,then:

Two similar plano-convex lenses are combined together in three different ways as shown in the figure. The ratio of the focal lengths in the three cases will be

An object with a mass $10 \ kg$ moves at a constant velocity of $10 \ m/s$. $A$ constant force then acts for $4 \ s$ on the object and gives it a speed of $2 \ m/s$ in the opposite direction. The impulse acting on the object is ........ $N \cdot s$.

The potential energy of a body of mass $m$ is given by $U = ax + by$,where $x$ and $y$ are the position coordinates of the particle. The acceleration of the particle is

What is $Z$ in the following reaction sequence?
$C_6H_5NH_2$ $\xrightarrow[(i) NaNO_2 + HCl / 273 \ K]{(ii) H_3PO_2 + H_2O}$ $\xrightarrow[(iii) CO, HCl, \text{anhydrous } AlCl_3/CuCl]{} Z$

In a playground,there is a merry-go-round of mass $120 \ kg$ and radius $4 \ m$. The radius of gyration is $3 \ m$. $A$ child of mass $30 \ kg$ runs at a speed of $5 \ m/s$ tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglecting friction,find the angular velocity of the merry-go-round and child in $rad/s$.