$A$ lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I$. If the central region of the lens with diameter $\frac{d}{2}$ is covered by black paper,what will be the new focal length and intensity of the image?

Which pigment is present in all algae?

The tyre of a bicycle has a volume of $2 \times 10^{-3} ~m^3$. Initially,the tube is filled to $75 \%$ of its volume with air at an atmospheric pressure of $10^5 ~Nm^{-2}$. When a rider is on the bicycle,the area of contact of the tyre with the road is $24 \times 10^{-4} ~m^2$. The mass of the rider with the bicycle is $120 ~kg$. If a pump delivers a volume of $500 ~cm^3$ of air in each stroke,then the number of strokes required to inflate the tyre is $\left(g=10 ~ms^{-2}\right)$.

If the angle between the circles $x^2+y^2-2x-4y+c=0$ and $x^2+y^2-4x-2y+4=0$ is $60^{\circ}$,then $c$ is equal to

Which of the following processes can be used to obtain heavy water $(D_2O)$?

The new crop $Triticale$ was developed by intergeneric hybridization between which of the following?