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1. A
   A $\sqrt{\frac{M}{M + m}}$
2. B
   A $\sqrt{\frac{M}{M - m}}$
3. C
   $A\sqrt{\frac{M - m}{M}}$
4. D
   $A\sqrt{\frac{M + m}{M}}$

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1. A
   $\frac{2Q}{3\sqrt{3}\pi\varepsilon_{0}a^{2}}(\widehat{x} + \widehat{y} + \widehat{z})$
2. B
   $\frac{Q}{3\sqrt{3}\pi\varepsilon_{0}a^{2}}(\widehat{x} + \widehat{y} + \widehat{z})$
3. C
   $\frac{- 2Q}{3\sqrt{3}\pi\varepsilon_{0}a^{2}}(\widehat{x} + \widehat{y} + \widehat{z})$
4. D
   $\frac{- Q}{3\sqrt{3}\pi\varepsilon_{0}a^{2}}(\widehat{x} + \widehat{y} + \widehat{z})$

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1. A
   $\frac{4}{3}\pi a^{3}\alpha\Delta T$
2. B
   $4\pi a^{3}\alpha\Delta T$
3. C
   $3a^{3}\alpha\Delta T$
4. D
   $4a^{3}\alpha\Delta T$

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1. A
   Global warming and cancer
2. B
   Acid rain
3. C
   Corrosion of metals
4. D
   Ozone hole

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1. A
   Ionic bonding
2. B
   Hydrogen bonding
3. C
   vander Waals forces
4. D
   Covalent bonding

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1. A
   A and $C$ only
2. B
   A and B only
3. C
   B and C only
4. D
   C and D only

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1. A
   
2. B
   
3. C
   
4. D
   

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1. A
   
2. B
   
3. C
   
4. D
   

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1. A
   $Zn$
2. B
   Co
3. C
   $Fe$
4. D
   $Cu$

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1. A
   Formation of anilinium ion
2. B
   $- {NO}_{2}$ substitution always takes place at meta-position
3. C
   low temperature
4. D
   $- {NH}_{2}$ group is highly meta-directive

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1. A
   $H_{2}O_{2}$ act as oxidizing and reducing agent respectively in equations (A) and (B).
2. B
   $H_{2}O_{2}$ acts as oxidizing agent in equations $(A)$ and $(B)$.
3. C
   $H_{2}O_{2}$ acts as reducing agent in equations (A) and (B).
4. D
   $H_{2}O_{2}$ acts as reducing and oxidising agent respectively in equation (A) and (B).

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1. A
   Sphalerite
2. B
   Siderite
3. C
   Malachite
4. D
   Calamine

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1. A
   
2. B
   
3. C
   
4. D
   

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1. A
   
2. B
   
3. C
   
4. D
   

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1. A
   Potassium permanganate
2. B
   Molybdenum oxide
3. C
   Copper at high temperature and pressure
4. D
   Manganese acetate

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1. A
   $\frac{1}{n}$ with $\frac{1}{n} = 0$ to 1
2. B
   $\log\frac{1}{n}$ with $(n < 1)$
3. C
   $\log n$ with $(n > 1)$
4. D
   $n$ with ( $n,0.1$ to 0.5)

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1. A
   $Al,Cu,Mg$ and $Mn$
2. B
   $Cu,Sn$ and $Zn$
3. C
   $Cu,Zn$ and $Ni$
4. D
   $Cu,Ni$ and $Fe$

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1. A
   
2. B
   
3. C
   
4. D
   

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1. A
   
2. B
   
3. C
   
4. D
   

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1. A
   $Al < Mg < Si < S < P$
2. B
   $Al < Mg < S < Si < P$
3. C
   $Mg < Al < Si < S < P$
4. D
   $Mg < Al < Si < P < S$

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1. A
   Statement I is false but statement II is true.
2. B
   Statement I is true but Statement II is false.
3. C
   Both Statement I and Statement II are true.
4. D
   Both Statement I and Statement II are false.

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1. A
   $X = Na\left\lbrack Al(OH)_{4} \right\rbrack,Y = {CO}_{2},Z = {Al}_{2}O_{3} \cdot {XH}_{2}O$
2. B
   $X = Na\left\lbrack Al(OH)_{4} \right\rbrack,Y = {SO}_{2},Z = {Al}_{2}O_{3}$
3. C
   $X = Al(OH)_{3},Y = {SO}_{2},Z = {Al}_{2}O_{3} \cdot {XH}_{2}O$
4. D
   $X = Al(OH)_{3},Y = {CO}_{2},Z = {Al}_{2}O_{3}$

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1. A
   (A) $\rightarrow$ (iii), (B) $\rightarrow$ (iv), (C) $\rightarrow$ (i), (D) $\rightarrow$ (ii)
2. B
   (A) $\rightarrow$ (i), (B) $\rightarrow$ (ii), (C) $\rightarrow$ (iii), (D) $\rightarrow$ (iv)
3. C
   (A) $\rightarrow$ (ii), (B) $\rightarrow$ (i), (C) $\rightarrow$ (iv), (D) $\rightarrow$ (iii)
4. D
   (A) $\rightarrow$ (iv), (B) $\rightarrow$ (iii), (C) $\rightarrow$ (ii), (D) $\rightarrow$ (i)

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1. A
   $x = a$
2. B
   $x = 0$
3. C
   $x = - \frac{a}{2}$
4. D
   $x = \frac{a}{2}$

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1. A
   560
2. B
   1050
3. C
   1625
4. D
   575

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