Match the following
List -I
(Products)
List -II
(Reactants-Reaction)
A) Methane (1) Sabatier - Senderens reaction of propylene
B) Ethane (2) Wurtz reaction of methyl iodide
C) Propane (3) Decarboxylation of sodium acetate
D) Butane (4) Sodium butanoate by Kolbes electrolysis
(5) Sodium propanoate by Kolbes electrolysis
The correct match is :

A-2 B-3 C-1 D-5

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A-4 B-2 C-1 D-5

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A-3 B-2 C-1 D-5

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

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Solution

The correct option is C A-3 B-2 C-1 D-5
Wurtz reaction: $R X + 2 N a + X R \to R - R + 2 N a X$
Sabatier senderens reaction: $C_{n} H_{2 n} + H_{2} \to C_{n} H_{2 n + 2} + h e a t$
Kolbe's electrolysis: $2 R C O O K + 2 H_{2} O \to R - R + 2 C O_{2} + 2 K O H + H_{2}$
In decarboxylatioin of sodium acetate $R - H$ form as a product, In all other reaction $R - R$ forms as a product.
In Sodium propanoate by Kolbes electrolysis reaction occur at anode:
$2 C_{2} H_{5} C O O^{∙} \to 2 C_{2} H_{5}^{∙} + 2 C O_{2}$
$2 C_{2} H_{5}^{∙} \to C_{4} H_{10}$

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(a) Methane into chloroform,
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(c) Methyl iodide into ethane,
(d) Aluminium carbide into methane.

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$⎡ ⎢ ⎣ \begin{matrix} a 1 & b 1 & c 1 a 2 & b 2 & c 2 a 3 & b 3 & c 3 \end{matrix} ⎤ ⎥ ⎦$ then $∣ ∣ ∣ \begin{matrix} B 2 & C 2 B 3 & C 3 \end{matrix} ∣ ∣ ∣ =$

Q. If each pair of equations

a_{1} x^{2} + b_{1} x + c_{1} = 0, a_{2} x^{2} + b_{2} x + c_{2} = 0

and

a_{3} x^{2} + b_{3} x + c_{3} = 0

has a common root, then show that
(i)

\frac{c_{1} a_{2} + c_{2} a_{1}}{c_{1} a_{2} - c_{2} a_{1}} + \frac{a_{1} a_{2} b_{3}}{a_{3} (a_{1} b_{2} - a_{2} b_{1})} = 0

(ii)

{(\frac{a_{1} b_{2} - a_{2} b_{1}}{a_{1} c_{2} - a_{2} c_{1}})}^{2} = \frac{a_{1} a_{2} c_{3}}{c_{1} c_{2} a_{3}}

Condition satisfied by the pair of equation $2 x + 3 y = - 5$ and $4 x + 6 y - 10 = 0$ is

Q. Let

a_{1}, b_{1}, c_{1}

be natural numbers. We define

a_{2} = g c d (b_{1}, c_{1}), b_{2} = g c d (c_{1}, a_{1}), c_{2} = g c d (a_{1}, b_{1}),

and

a_{3} = l c m (b_{2}, c_{2}), b_{3} = l c m (c_{2}, a_{2}), c_{3} = l c m (a_{2}, b_{2}) .

Show that

g c d (b_{3}, c_{3}) = a_{2}

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List -I (Products)	List -II (Reactants-Reaction)
A) Methane	(1) Sabatier - Senderens reaction of propylene
B) Ethane	(2) Wurtz reaction of methyl iodide
C) Propane	(3) Decarboxylation of sodium acetate
D) Butane	(4) Sodium butanoate by Kolbes electrolysis