$A$ straight conductor of length $4 ~m$ moves at a speed of $10 ~m/s$. When the conductor makes an angle of $30^{\circ}$ with the direction of the magnetic field of induction $0.1 ~Wb/m^2$,the induced emf is: (in $~V$)

$A$ husband and wife have normal vision,but the fathers of both of them were colour blind. What is the probability of their first daughter being colour blind (in $\%$)?

In an acute angled triangle,$\cot B \cot C + \cot A \cot C + \cot A \cot B$ is equal to

$A$ meter bridge is set up as shown,to determine an unknown resistance '$X$' using a standard $10 \, \Omega$ resistor. The galvanometer shows a null point when the tapping-key is at the $52 \, cm$ mark. The end corrections are $1 \, cm$ and $2 \, cm$ respectively for the ends $A$ and $B$. The determined value of '$X$' is $.......... \Omega$.

The relaxation time in conductors

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 $rad/s$.