$6 \Omega$ and $12 \Omega$ resistors are connected in parallel. This combination is connected in series with a $10 \text{ V}$ battery and a $6 \Omega$ resistor. What is the potential difference between the terminals of the $12 \Omega$ resistor (in $\text{ V}$)?

$A$ uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. $A$ horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face,at a height $\frac{3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to tilt about the edge is (Assume that the cube does not slide):

The approximate value of $(1.0002)^{3000}$ is

Match the organism with its use in biotechnology.

$(a)$ Bacillus thuringiensis	$(i)$ Cloning vector
$(b)$ Thermus aquaticus	$(ii)$ Construction of first $rDNA$ molecule
$(c)$ Agrobacterium tumefaciens	$(iii)$ $DNA$ polymerase
$(d)$ Salmonella typhimurium	$(iv)$ Cry proteins

Select the correct option from the following:

Three samples of the same gas $A, B$ and $C$ $(\gamma = 3/2)$ initially have equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$,isobaric for $B$ and isothermal for $C$. If the final pressures are equal for all three samples,the ratio of their initial pressures is:

Which of the following is not an insectivorous plant?