Match the plant growth hormones of Column-I with suitable chemical derivatives present Column-II and choose the correct option given below:
The table below lists potential environmental conditions in future climates, related to atmospheric carbon dioxide concentrations (CO2) and mean annual temperature (MAT). The table also lists potential outcomes with respect to whether conditions will favour grasses with C3 or C4 photosynthetic pathways. Assuming no other changes in environmental conditions, match the options in the two columns.
A convex lens has power \( P \). It is cut into two halves along its principal axis. Further, one piece (out of two halves) is cut into two halves perpendicular to the principal axis as shown in the figure. Choose the incorrect option for the reported lens pieces.
The equation \[ 2 \cos^{-1} x = \sin^{-1} \left( 2 \sqrt{1 - x^2} \right) \] is valid for all values of \(x\) satisfying:
A metallic sphere of radius \( R \) carrying a charge \( q \) is kept at a certain distance from another metallic sphere of radius \( R_4 \) carrying a charge \( Q \). What is the electric flux at any point inside the metallic sphere of radius \( R \) due to the sphere of radius \( R_4 \)?