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JEE Mains | PYQ

The solubility of \( \mathrm{AgCl} \) will be maximum in which of the following?

Given below are two statements one is labeled as Assertion A and the other is labeled as Reason R:
Assertion A: The amphoteric nature of water is explained by using Lewis acid/base concept.
Reason R: Water acts as an acid with \( \text{\(NH_3\)} \) and as a base with \( \text{\(H_2S\)} \).
In the light of the above statements choose the correct answer from the options given below:

\( 20 \,\mathrm{mL} \) of \( 0.1 \,\mathrm{M} \; \mathrm{NH_4OH} \) is mixed with \( 40 \,\mathrm{mL} \) of \( 0.05 \,\mathrm{M} \; \mathrm{HCl} \). The pH of the mixture is nearest to :
(Given : \( K_b(\mathrm{NH_4OH}) = 1 \times 10^{-5} \), \( \log 2 = 0.30 \), \( \log 3 = 0.48 \), \( \log 5 = 0.69 \), \( \log 7 = 0.84 \), \( \log 11 = 1.04 \))

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Phenolphthalein is a pH dependent indicator, remains colourless in acidic solution and gives pink colour in basic medium.
Reason R: Phenolphthalein is a weak acid. It doesn't dissociate in basic medium.
In the light of the above statements, choose the most appropriate answer from the options given below

At \( 310 \, \text{K} \), the solubility of \( \mathrm{CaF_2} \) in water is \( 2.34 \times 10^{-3} \, \text{g}/100 \, \text{mL} \). The solubility product of \( \mathrm{CaF_2} \) is _____ \( \times 10^{-8} \, (\text{mol}/\text{L})^3 \). (Give molar mass : \( \mathrm{CaF_2} = 78 \, \text{g mol}^{-1} \) )

The plot of pH-metric titration of weak base \( \mathrm{NH_4OH} \) vs strong acid \( \mathrm{HCl} \) looks like:

pH value of \( 0.001 \, \mathrm{M} \) NaOH solution is ______.

If the solubility product of \( \mathrm{PbS} \) is \( 8 \times 10^{-28} \), then the solubility of \( \mathrm{PbS} \) in pure water at \( 298 \, \text{K} \) is \( x \times 10^{-16} \; \text{mol L}^{-1} \). The value of \( x \) is __________. (Nearest Integer)
[Given: \( \sqrt{2} = 1.41 \)]

\( 50 \, \text{mL} \) of \( 0.1 \, \text{M} \, \mathrm{CH_3COOH} \) is being titrated against \( 0.1 \, \text{M} \, \mathrm{NaOH} \). When \( 25 \, \text{mL} \) of \( \mathrm{NaOH} \) has been added, the pH of the solution will be ____________ \( \times 10^{-2} \). (Nearest integer)
(Given: \( pK_a(\mathrm{CH_3COOH}) = 4.76 \) )
\( \log 2 = 0.30 \)
\( \log 3 = 0.48 \)
\( \log 5 = 0.69 \)
\( \log 7 = 0.84 \)
\( \log 11 = 1.04 \)