In the following reactions, $\mathbf{P},\mathbf{Q},\mathbf{R}$, and $\mathbf{S}$ are the major products.




The correct statement(s) about $\mathbf{P},\mathbf{Q},\mathbf{R}$, and $\mathbf{S}$ is(are)

Match each of the compounds is Column I with its characteristic reaction(s) is Column II.

Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.
Question :
Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is

Copper is purified by electrolytic refining of blister copper. The correct statement(s) about this process is (are)

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Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator automobiles.
A solution \(M\) is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixtrue is \(0.9\)
Given Freezing point depression constant of water \(\left(k^{\text {water }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\)
Freezing point depression constant of ethanol \(\left(k_f^{\text {ethanol }}\right)=2.0 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of water \(\left(k_b^{\text {water }}\right)=0.52 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Boiling point elevation constant of ethanol \(\left(k_b^{\text {ethanol }}\right)=1.2 \mathrm{Kkg} \mathrm{mol}^{-1}\)
Standard freezing point of water \(=273 \mathrm{~K}\)
Standard freezing point of ethanol \(=155.7 \mathrm{~K}\)
Standard boiling point of water \(=373 \mathrm{~K}\)
Standard boiling point of ethanol \(=351.5 \mathrm{~K}\)
Vapour pressure of pure water \(=328 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Vapour pressure of pure ethanol \(=40 \mathrm{~mm}\) of \(\mathrm{Hg}\)
Molecular weight of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\)
Molecular weight of ethanol \(=46 \mathrm{~g} \mathrm{~mol}^{-1}\)
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.

Question:
Water is added to the solution \(M\) such that the mole fraction of water in the solution becomes \(0.9\) The boiling point of this solutions is

Paragraph: When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex \(\mathrm{P}\) is formed. In a strong acidic medium, the equilibrium shifts completely towards \(\mathrm{P}\). Addition of zinc chloride to \(\mathrm{P}\) in a slightly acidic medium results in a sparingly soluble complex Q.
Question: The number of moles of potassium iodide required to produce two moles of \(\mathbf{P}\) is

The smallest ketone and its next homologoue are reacted with \(\mathrm{NH}_2 \mathrm{OH}\) to form oxime

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A circle \(C\) of radius 1 is inscribed in an equilateral \(\triangle P Q R\). The points of contact of \(C\) with the sides \(P Q, Q R, R P\) are \(D, E, F\) respectively. The line \(P Q\) is given by the equation
\(\sqrt{3} x+y-6=0\) and the point \(D\) is \(\left(\frac{3 \sqrt{3}}{2}, \frac{3}{2}\right)\). Further, it is given that the origin and the centre of \(C\) are on the same side of the line \(P Q\).Question:
Points \(E\) and \(F\) are given by

A ball is thrown from the location \(\left(x_0, y_0\right)=(0,0)\) of a horizontal playground with an initial speed \(v_0\) at an angle \(\theta_0\) from the \(+x\)-direction. The ball is to be hit by a stone, which is thrown at the same time from the location \(\left(x_1, y_1\right)=(L, 0)\). The stone is thrown at an angle \(\left(180-\theta_1\right)\) from the \(+x\)-direction with a suitable initial speed. For a fixed \(v_0\), when \(\left(\theta_0, \theta_1\right)=\left(45^{\circ}, 45^{\circ}\right)\), the stone hits the ball after time \(T_1\), and when \(\left(\theta_0, \theta_1\right)=\left(60^{\circ}, 30^{\circ}\right)\), it hits the ball after time \(T_2\). In such a case, \(\left(T_1 / T_2\right)^2\) is _______ .

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A box \(B_{1}\) contains \(1\) white ball, \(3\) red balls and \(2\) black balls. Another box \(B_{2}\) contains \(2\) white balls, \(3\) red balls and \(4\) black balls. A third box \(B_{3}\) contains \(3\) white balls, \(4\) red balls and \(5\) black balls.


Question:

If \(2\) balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these \(2\) balls are drawn from box \(B_{2}\) is

Consider a triangle $\mathrm{\Delta }$ whose two sides lie on the $x$-axis and the line $x+y+1=0$. If the orthocenter of $\mathrm{\Delta }$ is $(1,1)$, then the equation of the circle passing through the vertices of the triangle $\mathrm{\Delta }$ is

A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature $\mathrm{T}$ . Assuming the gases are ideal, the correct statement(s) is (are)

A conducting loop in the shape of right angled isosceles triangle of height 10 cm is kept such that the ${90}^o$ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at constant rate of $10A{s}^{-1}.$ Which of the following statement(s) is (are) true?