The shortest distance between the curves $ y^2 = 8x $ and $ x^2 + y^2 + 12y + 35 = 0 $ is:
Let the distance between two parallel lines be 5 units and a point \( P \) lies between the lines at a unit distance from one of them. An equilateral triangle \( POR \) is formed such that \( Q \) lies on one of the parallel lines, while \( R \) lies on the other. Then \( (QR)^2 \) is equal to _______.
If the four distinct points $ (4, 6) $, $ (-1, 5) $, $ (0, 0) $ and $ (k, 3k) $ lie on a circle of radius $ r $, then $ 10k + r^2 $ is equal to
The steam volatile compounds among the following are:Choose the correct answer from the options given below:
Given below are two statements: Statement (I): The first ionization energy of Pb is greater than that of Sn. Statement (II): The first ionization energy of Ge is greater than that of Si. In light of the above statements, choose the correct answer from the options given below:
The product (A) formed in the following reaction sequence is:
Given below are two statements:Statement (I): The first ionization energy of Pb is greater than that of Sn.Statement (II): The first ionization energy of Ge is greater than that of Si.In light of the above statements, choose the correct answer from the options given below:
$\mathrm{KMnO}_{4}$ acts as an oxidising agent in acidic medium. ' X ' is the difference between the oxidation states of Mn in reactant and product. ' Y ' is the number of ' d ' electrons present in the brown red precipitate formed at the end of the acetate ion test with neutral ferric chloride. The value of $\mathrm{X}+\mathrm{Y}$ is _______ .
In Carius method for estimation of halogens, 180 mg of an organic compound produced 143.5 mg of AgCl. The percentage composition of chlorine in the compound is ___________%. [Given: Molar mass in g mol\(^{-1}\) of Ag = 108, Cl = 35.5]