If $a$ and $b$ are unit vectors, then the vector $(a+b) \times (a \times b)$ is parallel to the vector

The acute angle between the line $\vec{r}=(\hat{i}+2\hat{j}+\hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})$ and the plane $\vec{r} \cdot(2\hat{i}+\hat{j}+\hat{k})=5$ is

$A$ coil is suspended in a uniform magnetic field with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil,it starts oscillating and is very difficult to stop. However,if an aluminium plate is placed near the coil,it stops. This is due to:

$A$ smooth cylinder of mass $m$ and radius $R$ is resting on two corner edges $A$ and $B$ as shown in the figure. The relation between the normal reactions at the edges $A$ and $B$ is

The value of the integral $\int_0^4 \frac{dx}{1+x^2}$ obtained by using the Trapezoidal rule with $h=1$ is

Consider the situation shown in the figure. The wire $AB$ is sliding on the fixed rails with a constant velocity $V$. If the wire $AB$ is replaced by a semicircular wire of the same end-to-end distance,the magnitude of the induced current will: