Which of the following amine do not respond to Hinsberg test?

Mercury is not considered as transition metal however it has tendency to react with chlorine to form chlorides \(X\) and \(Y\).
\(X\) reacts with \(K I\) to give red ppt while \(Y\) doesn't react. On the contrary, \(Y\) reacts with \(NH _4 OH\) to give a black ppt. Predict the formula of \(X\) and \(Y\) :

Decreasing order of freezing point of 0.1 M aqueous solution of following will be :
(A) \(\text{K}_4\text{[Fe(CN)}_6\text{]}\)
(B) \(\text{K}_2\text{SO}_4\)
(C) \(\text{NH}_2\text{CONH}_2\)
(D) \(\text{AlCl}_3\)
(E) \(\text{HCl}\)
Choose the correct answer from the options given below :

The molality of a solution prepared by dissolving \(4 . 0 ~ g ~ N a O H\) in \(1 0 0 0 ~ m L\) distilled water is _________ (Assume that the density of water is \(1 g mL ^{-1}\) )

In the metallurgy of Al , purified \(Al _2 O _3\) is mixed with \(Na _3 AlF _6\) or \(CaF _2\). The role of \(Na _3 AlF _6\) or \(CaF _2\) is to:

A compound is formed by 2 elements P and Q. Atoms of element Q (as anions) makes ccp and those of P (as cations) fill all tetrahedral voids and also occupy half of the octahedral voids. What is the correct formula of this compound?

When a nucleotide from DNA containing adenine is hydrolyzed, the products obtained are

Match List I with List II

List-l	List-II
A. \(K _2 SO _4( aq )\) with \(60 \%\) dissociation	I. \(i = 3 . 7\)
B. \(K _3\left[ Fe ( CN )_6\right]( aq )\) with \(90 \%\) dissociation	II. \(i=1.8\)
C. \(AlCl _3( aq )\) with \(80 \%\) dissociation	III. \(i=2.2\)
D. \(K _2 HgI _4( aq )\) with \(40 \%\) dissociation	IV. \(i=3.4\)

Choose the correct answer from the options given below :

A relation \(f: N \rightarrow N\) be defined by \(f(x)=x^2, x \in N\) (Set of Natural numbers), Then \(f(x)\) is

A problem in Mathematics is given to two students \(X\) and \(Y\) whose chances of solving it are \(\frac{1}{3}\) and \(\frac{1}{4}\) respectively. The probability that only \(X\) solves the problem, is:

Read the passage carefully and answer the Questions
Molar conductivity \(\left(\Lambda_m\right)\) of a solution at a given concentration (c) is the conductance of volume, V of solution, containing one mole of electrolyte kept between the two electrodes with area of cross-section A and at a distance of unit length. It increases with the decrease in concentration and when the concentration approaches zero, the molar conductivity is called limiting molar
conductivity \(\left(\Lambda_m^0\right)\). For a strong electrolyte, \(\Lambda_m\) increases linearly with dilution and is given by \(\Lambda_m=\Lambda_m^0-A c^{1 / 2}\). The value of the constant A for a given solvent depends on the type of electrolyte along with temperature. According to Kohlrausch law, the value of \(\Lambda_m^0\) for an electrolyte is \(\Lambda_m^0=\nu_{+} \lambda_{+}^0+\nu_{-} \lambda_{-}^0\), where \(\nu_{+}\)and \(\nu_{-}\) are the number of cations and anions, respectively, per molecule of the electrolyte and \(\lambda_{+}^0\) and \(\lambda_{-}^0\) are limiting molar conductivities of cation and anion, respectively. Kohlrausch law finds many applications, like determining the solubility of a sparingly soluble salt, determining the degree of dissociation \(\left(\Lambda_m / \Lambda_m^0\right)\), and the dissociation constant of a weak electrolyte.
The plot between \(\Lambda_m\) and \(c^{1 / 2}\) is a straight line with

There are two thin parallel charged sheets having surface charge density \( \sigma \) placed at a small distance apart. Which of the following statements are correct?
(A) If both the sheets are positively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(B) If both the sheets are negatively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(C) If the left sheet is positively charged and the right sheet is negatively charged the field between them is \( \sigma/\epsilon_0 \)
(D) If the right sheet is positively charged and the left sheet is negatively charged then the field between them is \( \sigma/\epsilon_0 \)
Choose the correct answer from the options given below:

The relation \(R\) on the set \(N \times N\) defined by \((a, b) R(c, d) \Longleftrightarrow a+d=b+c\), \(\forall(a, b),(c, d) \in N \times N\), where N is the set of natural numbers, is: