The major product in the following reaction is:

Force acting on a particle moving in a straight line varies with the velocity of the particle as $F = \frac{K}{v}$. Here $K$ is a constant. The work done by this force in time $t$ is

If $x$ is real,then the minimum value of $y = \frac{x^2-x+1}{x^2+x+1}$ is

Two bodies of masses $0.1 \,kg$ and $0.4 \,kg$ move towards each other with the velocities $1 \,m/s$ and $0.1 \,m/s$ respectively. After collision,they stick together. In $10 \,s$,the combined mass travels .......... $m$.

If the angular velocity of a disc depends on the angle rotated $\theta$ as $\omega = \theta^2 + 2\theta$,then its angular acceleration $\alpha$ at $\theta = 1 \ rad$ is ......... $rad/sec^2$.

The transformed equation of $x^2+6xy+8y^2=10$ when the axes are rotated through an angle $\frac{\pi}{4}$ is: