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1 Polymers

Nylon-66 is a

1) Natural polymer
2) Condensation polymer
3) Addition polymer
4) Substitution polymer

Option 1

Option 2 Solution:

SOLUTION

Nylon 6,6 or polyamide is a substance obtained from the repeated condensation reaction of Hexamythyline di amine and adipic acid which when undergoes polymerisation gives rives polyamide and water molecules

Nylon 6,6 is a condensation product of adipic acid and hexamethylenediamine

Nylon 6 is a condensation product of only one monomer caprolactum.

Nylon 6,6 is stronger and more resistant to heat as compared to Nylon 6.
Nylon 6,6 is used for making carpets, tyre ropes etc. due to its strength and toughness.
Nylon 6 on the other hand is used for making clothes, nets, threads etc.

Option 3

Option 4

2 Probability

A bag contains 17 tickets numbered 1 to 17. A tickets is drawn and replaced, then one more ticket is drawn and replaced. Probability that first drawn number is even and second is odd, is

1) $$\frac { 81 }{ 289 } $$
2) $$\frac { 72 }{ 289 } $$
3) $$\frac { 64 }{ 289 } $$
4) None of these

Option 1

Option 2 Solution:

Solution

Let $$A$$ be the event that first drawn number is even

and $$B$$ be event that the second number drawn number is odd.

Total number of even number $$\displaystyle \left[ \frac { 17 }{ 2 } \right] =8$$

$$\displaystyle \Rightarrow P\left( A \right) =\frac { 8 }{ 17 } $$ and $$\displaystyle P\left( B \right) =\frac { 9 }{ 17 } \Rightarrow P\left( A\cap B \right) =\frac { 72 }{ 289 } $$

Option 3

Option 4

3 Limits Continuity and Differentiability

For the function which of the following is incorrect?

1) Continuous at x=1
2) Continuous at x=3
3) Derivable at x =1
4) Derivable at x =3

Option 1

Option 2

Option 3

Option 4 Solution:

SOLUTION

4 S � Block Elements

For which of the following crystalline substances does the solubility in water increase upto 32^? and then decrease rapidly?

1) CaCl₂.2H₂O
2) Na₂SO₄.10H₂O
3) FeSO₄.7H₂O
4) Alums

Option 1

Option 2 Solution:

Solution

For sodium sulphate decahydrate $$\displaystyle \displaystyle\:Na_{2}SO_{4}.10H_{2}O $$, also known as Glauber's salt, the solubility in water increase upto $$32^0$$C and then decrease rapidly. As thereafter H-bond breaks so solubility decreases rapidly for $$\displaystyle\:Na_{2}SO_{4}.10H_{2}O$$.

Option 3

Option 4

5 Differentiation

If f(x) = then the derivative of f(x) on the interval [0, 7] is

1) 1
2) -1
3) 0
4) Does not exist

Option 1

Option 2

Option 3

Option 4 Solution:

SOLUTION

f( x) = |x- 5|

6 Surface Chemistry

Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25^oC. For this purpose the correct statement is:

1) The adsorption requires activation at 25^oC
2) The adsorption is accompanied by a decrease in enthalpy
3) The adsorption increases with increase of temperature
4) The adsorption is irreversible

Option 1 Solution:

Solution

Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25 degree Centigrade.

For this purpose the correct statement is The adsorption requires activation at 25 degree centigrade.

Option 2

Option 3

Option 4

7 Capacitance

The charge on the capacitor of capacitance C shown in the figure below will be

Option 1

Option 2

Option 3 Solution:

SOLUTION

Option 4

8 Probability

For a biased die the probabilities for different faces to turn up are given below: The die is tossed and you are told that either face 1 or 2 has turned up. Then the probability that it is face 1 is .....

Face	1	2	3	4	5	6
Probability	0.1	0.32	0.21	0.15	0.05	0.17.

1) $$\displaystyle \frac{5}{42}$$
2) $$\displaystyle \frac{16}{21}$$
3) $$\displaystyle \frac{5}{21}$$
4) $$\displaystyle \frac{16}{42}$$

Option 1

Option 2

Option 3 Solution:

Solution

Let $$A$$ be the event that face 1 turns up
$$ B$$ be the event that face 2 turns up.
Then $$\displaystyle P\left ( A \right )= 0.10$$ and $$\displaystyle P\left ( B \right )= 0.32,$$
Since A, B are mutually exclusive, we have
$$\displaystyle P\left ( A\cup B \right )= P\left ( A \right )+P\left ( B \right )= 0.10+0.32= 0.42.$$
We are to find $$\displaystyle P\left ( A|A\cup B \right )$$
But $$\displaystyle P\left ( A|A\cup B \right )= \frac{P\left [ A\cap \left ( A\cup B \right ) \right ]}{P\left ( A\cup B \right )}$$

$$= \dfrac{P\left ( A \right )}{P\left ( A\cup B \right )}$$

Hence $$\displaystyle P\left ( A|A\cup B \right )= \frac{0.10}{0.42}= \frac{5}{21}$$

Option 4

9 Solutions

33.6 L of water vapour at STP are condensed to liquid state. The volume occupied by it is approximately:

1) 1 mL
2) 18 mL
3) 27 mL
4) 127 mL

Option 1

Option 2

Option 3 Solution:

Solution

At 1 STP, 1 mole of a gas is equal to 22.4 L.
Hence, 33.6 L of water vapour corresponds to33.6 / 22.4 ?=1.5 moles.
The molar mass of water is 18 g/mol.
The mass of water is 1.5mol × 18 g/mol = 27g.
The density of water is 1 g/mL.
The volume of water vapour =27g / 1g/mL?=27mL

Option 4

10 Rotational Motion

The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is 'I'. It is rotating with angular velocity $$'\omega'$$. Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis then loss in kinetic energy is

1) $$\frac{I \omega^2}{2}$$
2) $$\frac{I \omega^2}{4}$$
3) $$\frac{I \omega^2}{6}$$
4) $$\frac{I \omega^2}{8}$$

Option 1

Option 2 Solution:

Solution:

$$\frac{I \omega^2}{4}$$

Option 3

Option 4

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