# JEE Main

Explore popular questions from Solutions for JEE Main. This collection covers Solutions previous year JEE Main questions hand picked by experienced teachers.

## Mathematics

Solutions

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Q 1. If {tex} P _ { A } ^ { 0 } {/tex} is the vapour pressure of a pure liquid {tex} A {/tex} and the mole fraction of {tex} A {/tex} in the mixture of two liquids {tex} A {/tex} and {tex} B {/tex} is {tex} x , {/tex} the partial vapour pressure of {tex} A {/tex} is

A

{tex} ( 1 - x ) P _ { A } ^ { 0 } {/tex}

{tex} x P _ { A } ^ { 0 } {/tex}

C

{tex} \frac { x } { ( 1 - x ) } P _ { A } ^ { 0 } {/tex}

D

{tex} \frac { ( 1 - x ) } { x } P _ { A } ^ { 0 } {/tex}

##### Explanation

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Q 2. In a mixture of {tex} A {/tex} and {tex} B {/tex} if the mole fraction of the component {tex} A {/tex} in vapour phase is {tex} x _ { 1 } {/tex} and mole fraction of component {tex} A {/tex} in liquid mixture {tex} x _ { 2 } \left( P _ { A } ^ { 0 } = \text { vapour pressure of pure } A ; P _ { B } ^ { 0 } = \text { vapour pressure of pure } B \right) , {/tex} then total vapour pressure of the liquid mixture is

{tex} \frac { P _ { A } ^ { 0 } x _ { 2 } } { x _ { 1 } } {/tex}

B

{tex} \frac { P _ { A } ^ { 0 } x _ { 1 } } { x _ { 2 } } {/tex}

C

{tex} \frac { P _ { B } ^ { 0 } x _ { 1 } } { x _ { 2 } } {/tex}

D

{tex} \frac { P _ { B } ^ { 0 } x _ { 2 } } { x _ { 1 } } {/tex}

##### Explanation

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Q 3. At {tex} 40 ^ { \circ } \mathrm { C } , {/tex} the vapour pressure in torr of methanol and ethanol solution is {tex} P = 119 x + 135 , {/tex} where {tex} x {/tex} is the mol. fraction of methanol. Hence

A

vapour pressure of pure methanol is 119 torr.

vapour pressure of pure ethanol is 135 torr.

C

vapour pressure of equimolar mixture of each is 127mm

D

mixture is completely immiscible.

##### Explanation

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Q 4. A solution that obeys Raoult's law is

A

non-ideal solution

B

colloid

ideal

D

saturated

##### Explanation

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Q 5. In a mixture {tex} A {/tex} and {tex} B {/tex} components show negative deviation as

A

{tex} \Delta V _ { \operatorname { mix } } = + \mathrm { ve } {/tex}

{tex} \Delta H _ { \operatorname { mix } } = - \mathrm { ve } {/tex}

C

{tex} A - B {/tex} interaction is weaker than {tex} A - A {/tex} and {tex} B - B {/tex} interaction.

D

None of the above.

##### Explanation

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Q 6. {tex} 100\mathrm { mL } {/tex} of liquid {tex} A {/tex} was mixed with {tex} 25\mathrm { mL } {/tex} of liquid {tex} B {/tex} to give a non-ideal solution of {tex} A - B {/tex} mixture. The volume of this mixture would be

A

{tex} 75\mathrm { mL } {/tex}

Either less or more than {tex} 125\mathrm { mL } {/tex}

C

Close to {tex}125 \mathrm { mL } {/tex} but not exceeding {tex}125 \mathrm { mL } {/tex} .

D

Just more than {tex} 75 \mathrm { mL } {/tex}

##### Explanation

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Q 7. Which of the following liquid pairs shows a positive deviation from Raoult's law?

A

Water-nitric acid

Benzene-methanol

C

Water-hydrochloric acid

D

Acetone-chloroform

##### Explanation

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Q 8. Liquids {tex} A {/tex} and {tex} B {/tex} form an ideal solution.

The enthalpy of mixing is zero.

B

The entropy of mixing is zero.

C

The free energy of mixing is zero.

D

The free energy as well as the entropy of mixing are each zero.

##### Explanation

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Q 9. Which of the following solution in {tex}(\mathrm { { H } _ { 2 } { O }} ) {/tex} has the highest boiling point elevation?

A

{tex}0.2 \mathrm { m } {/tex} urea

B

{tex} 0.1\mathrm { m }\, \mathrm { K } _ { 4 } \left[ \mathrm { Fe } ( \mathrm { CN } ) _ { 6 } \right] {/tex}

{tex}0.2 \mathrm { m } \, \mathrm { K } _ { 2 } \mathrm { SO } _ { 4 } {/tex}

D

{tex}0.3 \mathrm { m }{/tex} Glucose

##### Explanation

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Q 10. When mango is placed in dilute aqueous solution of hydrochloric acid, it

shrinks

B

swells

C

brusts

D

Nothing happens

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Q 11. If {tex}32 \mathrm { g } {/tex} of an unknown molecule (assumed to be unionised in solution) dissolved in {tex}200 \mathrm { g } {/tex} of {tex} \mathrm { H } _ { 2 } \mathrm { O } {/tex} of, then elevation in boiling point is found to be {tex} 1.04 ^ { \circ } \mathrm { C } {/tex} . Find out the molar mass of the unknown molecule (given {tex} K _ { b } {/tex} {tex} \left. \text { for } \mathrm { H } _ { 2 } \mathrm { O } = 0.52 \mathrm { kg } \mathrm { mol } ^ { - 1 } \right) {/tex}

A

{tex}160 \mathrm { g } / \mathrm { mole } {/tex}

{tex}80 \mathrm { g } / \mathrm { mole } {/tex}

C

{tex} 40\mathrm { g } / \mathrm { mole } {/tex}

D

{tex}320 \mathrm { g } / \mathrm { mole } {/tex}

##### Explanation

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Q 12. Arrange the following compounds in order of decreasing the depression in freezing point of aqueous solution.
(i) Acetic acid
(ii)Trichloroacetic acid
(iii)Trifluoroacetic acid

A

{tex} { i } > { i i } > { iii } {/tex}

B

{tex}ii > iii {tex} > i {/tex}

C

{tex}iii > i > ii {/tex}

{tex} { iii } > { ii } > { i } {/tex}

##### Explanation

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Q 13. Nitrobenzene freezes at {tex} 278.98 ^ { \circ } \mathrm { C } .0 .25 {/tex} molal solution of a solute in nitrobenzene causes freezing point depression of {tex} 2 ^ { \circ } \mathrm { C } . K _ { f } {/tex} for nitrobenzene is

A

{tex}2 \mathrm { Km } ^ { - 1 } {/tex}

B

{tex}4 \mathrm { Km } ^ { - 1 } {/tex}

{tex} 8\mathrm { Km } ^ { - 1 } {/tex}

D

{tex} 12\mathrm { Km } ^ { - 1 } {/tex}

##### Explanation

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Q 14. {tex}0.15 \mathrm { g } {/tex} of a substance dissolved in {tex}15 \mathrm { g } {/tex} of a solvent is boiled at a temperature higher by {tex} 0.216 ^ { \circ } \mathrm { C } {/tex} than that of the pure solvent. Find out the molecular weight of the substance. {tex} \left( K _ { b } \text { for solvent is } 2.16 \mathrm { k } . \mathrm { kg } . \mathrm { m } ^ { - 1 } \right) . {/tex}

A

1.01

B

10.1

100

D

10

##### Explanation

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Q 15. The freezing point of equimolal aqueous solution will be highest for

A

{tex} \mathrm { C } _ { 6 } \mathrm { H } _ { 5 } \mathrm { NH } _ { 3 } \mathrm { Cl } {/tex} (aniline hydrochloride)

B

{tex} \mathrm { Ca } \left( \mathrm { NO } _ { 3 } \right) _ { 2 } {/tex}

C

{tex} \mathrm { La } \left( \mathrm { NO } _ { 3 } \right) _ { 3 } {/tex}

{tex} \mathrm { C } _ { 6 } \mathrm { H } _ { 12 } \mathrm { O } _ { 6 } {/tex} (glucose)

##### Explanation

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Q 16. When mercuric iodide is added to the aqueous solution of potassium iodide, the

freezing point is raised.

B

freezing point is lowered.

C

freezing point does not change.

D

boiling point does not change.

##### Explanation

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Q 17. Which of the following is not a colligative property?

A

Osmotic pressure

B

Elevation in B.P.

Vapour pressure

D

Depression in freezing point

##### Explanation

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Q 18. Arrange the following in order of decreasing solubility in {tex} \mathrm { H } _ { 2 } \mathrm { O } {/tex} .
Phenol (i)
Toluene (ii)
Chloroform (iii)

A

{tex} (i)>( { ii }) > (iii){/tex}

B

{tex} ( i i i ) > ( i i ) > ( i ) {/tex}

{tex}(i)>(iii)>(ii){/tex}

D

{tex} (iii)>(i)>(ii) {/tex}

##### Explanation

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Q 19. A {tex} X {/tex} molal solution of a compound in benzene has mole fraction of solute equal to {tex} 0.2 . {/tex} The value of {tex} X {/tex} is

A

14

3.2

C

1.4

D

2