AIEEE 2008 PYQ Mock Test

Shown in the figure is a meter-bridge setup with null deflection in the galvanometer. One resistor is $55\Omega$ and the balancing length from left is $20\text{cm}$. The value of the unknown resistor $R$ on the right side is:

A thin rod of length $L$ is lying along the $x$ -axis from $x=0$ to $x=L$. Its linear density $\lambda$ varies as $\lambda =k(x/L{)}^n$. Which graph best approximates the dependence of the position $x_{CM}$ of the centre of mass on $n$ ($n\ge 0$)?

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance at a column length of $18\text{cm}$ during winter. Repeating the same experiment during summer, she measures the column length to be $x\text{cm}$ for the second resonance. Then:

The dimension of magnetic field $B$ in M, L, T and C (Coulomb) is given as:

Consider a uniform square plate of side ‘$a$ ’ and mass ‘$m$ ’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is: