Class 12th

36.  (A)i, ii

Disproportionation/redox reaction is a reaction in which one compound is oxidised as well as reduced at the same time.

(A) Cu⁺  ?  Cu²⁺  +  Cu 

  ( + 1)       ( + 2)        (0) 

(B) 3MnO₄^- +  4H⁺  ?  2MnO₄^- +  MnO₂ +  2H₂O 

  ( + 6)                          ( + 7)           ( + 4) 

54.  (ii) Both assertion and reason are true but reason is not the correct explanation of assertion.

Explanation: The zone refining method is very useful for producing high-purity semiconductors and other metals, such as germanium.

35. (B)+3

Out of all +3 is the most common oxidation state for all the lanthanide elements.

The given equation of curve $y^2\le 4x$ i.e,  $y^2=4x$ - (1) is a parabola and

$4x^2+4y^2\le 9\Rightarrow x^2+y^2\le \frac{9}{4}\Rightarrow x^2+y^2={\left(\frac{3}{2}\right)}^2$ - (2) is a circle

With centre (0,0)and radius 

Solving (1) and (2) for x and y,                                 

$\begin{array}{l}{x}^2+4x=\frac{9}{4}\\ =x^2+4x-\frac{9}{4}=0\\ =4x^2+16x-9=0\end{array}$

The given equation of the lines are

$\begin{array}{l}2x+y=4------(1)\\ 3x-2y=6-----(2)\\ x-3y+5=0----(3)\end{array}$

$\therefore$ Area of $?ABC=area(PCBQ)-area(?APC)-area(?AQB)$

$\begin{array}{l}={\displaystyle \underset{1}{\overset{4}{\int }}{y}_{(3)}dx-}{\displaystyle \underset{1}{\overset{2}{\int }}{y}_{(1)}dx-{\displaystyle \underset{2}{\overset{4}{\int }}{y}_{(2)}dx-}}\\ ={\displaystyle \underset{1}{\overset{4}{\int }}\frac{\left(x+5\right)}{3}dx-{\displaystyle \underset{1}{\overset{2}{\int }}\left(4-2x\right)dx-{\displaystyle \underset{2}{\overset{4}{\int }}\left(\frac{3x-6}{2}dx\right)}}}\end{array}$

$\therefore$ The point of intersection of the circle and the parabola is . $A\left(\frac{1}{2},\right)\&C\left(\frac{1}{2},-\right)$

Taking in first quadrant

Area of $(OABO)=area(OADO)+area(BADB)$

34. (B) 3d⁵

Magnetic moment of an electron/dipole moment is caused by its intrinsic properties of spin and electric charge. It depends upon the number of unpaired electrons in its valence shell. The more the number of unpaired electrons, the greater will be the value of magnetic moment.

3d⁷ =  3 unpaired electrons 

3d⁵ =  5 unpaired electrons

3d⁸ =  2 unpaired electrons 

3d² =   2 unpaired electrons 

Out of all, 3d⁵ has five unpaired electrons that is maximum and hence it has the highest magnetic moment.

52. (i) Both assertion and reason are true and reason is the correct explanation of assertion.

Explanation: Van Arkel method is generally used to obtain pure forms of Zirconium (Zr) and Titanium (Ti).

The metal iodide is heated at 1800 K and is decomposed on a tungsten filament. The pure metal is dropped on the tungsten filament. This proves that ZrI4 is volatile and decomposes at 1800 K.

The given vertices of the triangle are A(2,0),B(4,5)and C(6,3)

So, equation of line AB is $y-0=\frac{5-0}{4-2}\left(x-2\right)$

$=y=\frac{5}{2}\left(x-2\right)$

Similarly equation of BC is

$\begin{array}{l}y-5=\frac{3-5}{6-4}\left(x-4\right)\\ =y=5+\left(-x+4\right)\\ y=9-x\end{array}$

And equation of AC is $y-0=\frac{3-0}{6-2}\left(x-2\right)$

= $y=\frac{3}{4}\left(x-2\right)$

$\therefore$ Area of $?ABC$

= $area(?ABE)+area(BCDE)-area(?ACD)$

$\begin{array}{l}={\displaystyle \underset{2}{\overset{4}{\int }}{y}_{AB}dx+}{\displaystyle \underset{4}{\overset{6}{\int }}{y}_{BC}dx-{\displaystyle \underset{2}{\overset{6}{\int }}{y}_{BC}dx}}\\ ={\displaystyle \underset{2}{\overset{4}{\int }}\frac{5}{2}\left(x-2\right)dx+{\displaystyle \underset{4}{\overset{6}{\int }}\left(9-x\right)dx-{\displaystyle \underset{2}{\overset{6}{\int }}\frac{3}{4}}}}\left(x-2\right)dx\\ =\frac{5}{2}{\left[\frac{x^2}{2}-2x\right]}_2^4+{\left[9x-\frac{x^2}{2}\right]}_4^6-\frac{3}{4}{\left[\frac{x^2}{2}-2x\right]}_2^6\end{array}$

$\begin{array}{l}=\frac{5}{2}\left[\left(\frac{4^2}{2}-2.4\right)-\left(\frac{2^2}{2}-2.2\right)\right]+\left[\left(9.6-\frac{6^2}{2}\right)-\left(9.4-\frac{4^2}{2}\right)\right]-\frac{3}{4}\left[\left(\frac{6^2}{2}-2.6\right)-\left(\frac{2^2}{2}-2.2\right)\right]\\ =\frac{5}{2}\left[\left(8-8\right)-\left(2-4\right)\right]+\left[54-18-36+8\right]-\frac{3}{4}\left[18-12-2+4\right]\\ =5+8-6=7uni{t}^2\end{array}$

51.  (i) Both assertion and reason are true and reason is the correct explanation of assertion.

Explanation: In the Mond process Nickel is reacted with carbon monoxide reversibly to give Nickel carbonyl,  Ni (CO)₄. Nickel carbonyl is a volatile compound. It decomposes to nickel and carbon monoxide at 460 K.