The length of the tangent drawn to the circle $x^2+y^2-2x+4y-11=0$ from the point $(1,3)$ is:

If $A$ and $B$ are any two events,then $P(A \cup B) = $

For the reaction $A + 2B \rightleftharpoons 2C + D$,the initial concentration of $A$ is $a$ and the initial concentration of $B$ is $1.5$ times that of $A$. If the concentrations of $A$ and $D$ are equal at equilibrium,what will be the concentration of $B$ at equilibrium?

Two identical photo-cathodes receive light of frequencies $f_1$ and $f_2$. If the velocities of the photoelectrons (of mass $m$) coming out are respectively $v_1$ and $v_2$,then:

Which of the following statements is incorrect for alkali metals?

Which microorganism is used for the commercial production of citric acid?