Match List-I with List-II and choose the correct answer from the options given below.
- (a) Combination reaction: \( CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \) is a combination reaction as two reactants combine to form one product.
- (b) Decomposition reaction: \( 2H_2O \rightarrow 2H_2 + O_2 \) is a decomposition reaction, where one reactant breaks down into two products.
- (c) Displacement reaction: \( Cl_2 + 2Br^- \rightarrow 2Cl^- + Br_2 \) is a displacement reaction where one element displaces another from a compound.
- (d) Disproportionation reaction: \( 2H_2O \rightarrow 2H_2 + O_2 \) is a disproportionation reaction where the same species undergoes both oxidation and reduction.
Thus, the correct answer is 2) a-iii, b-i, c-iv, d-ii.
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 \( R_4 \)?