If $(1+2x+3x^2)^{10} = a_0+a_1x+a_2x^2+\ldots+a_{20}x^{20}$,then $\frac{a_2}{a_1}$ is equal to

Which of the following is a fossil plant?

Two fair dice are rolled. The probability of the sum of digits on their faces being greater than or equal to $10$ is

The sensitivity of a galvanometer that measures current is decreased by $\frac{1}{40}$ times by using a shunt resistance of $10 \Omega$. Then,the value of the resistance of the galvanometer is (in $Omega$)

If $\left|\begin{array}{ccc}\cos (A+B) & -\sin (A+B) & \cos 2 B \\ \sin A & \cos A & \sin B \\ -\cos A & \sin A & \cos B\end{array}\right|=0$,then $B$ is equal to

The plates of a parallel plate capacitor are charged up to $100\;V$. $A$ $2\;mm$ thick plate is inserted between the plates. Then,to maintain the same potential difference,the distance between the plates is increased by $1.6\;mm$. The dielectric constant of the plate is: