JEE Advanced 1982

Give a reason for the statement that "the

pH

of an aqueous solution of sodium acetate is more than seven".

Topic:

Equilibrium

Exam:

JEE Advanced 1982

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Question 2

sodium hydroxide is added to

20 mL

0.2 M

50 mL

0.2 M

acetic acid solution to give

70 mL

of the solution. What is the

pH

of this solution?
Calculate the additional volume of

0.2 M NaOH

required to make the

pH

of the solution 4.74.
(Ionisation constant of

CH_{3} COOH = 1.8 \times 1 0^{- 5}

Topic:

Equilibrium

Exam:

JEE Advanced 1982

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Question 3

First law of thermodynamics is not adequate in predicting the direction of a process.

Topic:

Thermodynamics and Thermochemistry

Exam:

JEE Advanced 1982

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Question 4

Hard

Without expanding a determinant at any stage, show that

∣ ∣ x^{2} + x 2 x^{2} + 3 x - 1 x^{2} + 2 x + 3 x + 1 3 x 2 x - 1 x - 2 3 x - 3 2 x - 1 ∣ ∣ = x A + B

where

A

are determinants of order 3 not involving

B

x

Topic:

Determinants

Exam:

JEE Advanced 1982

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Question 5

The system of equations

λ x + y + z = 0, - x + λ y + z = 0

will have a non-zero solution, if real values of

- x - y + λ z = 0

λ

are given by ...

Topic:

Determinants

Exam:

JEE Advanced 1982

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Question 6

Hard

Let

f

be a one-one function with domain

{x, y, z}

and range

{1, 2, 3}

. It is given that exactly one of the following statements is true and the remaining two are false

f (x) = 1, f (y) \neq = 1, f (z) \neq = 2

determine

f^{- 1} (1)

Topic:

Relations and Functions

Exam:

JEE Advanced 1982

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Question 7

A body floats in a liquid contained in a beaker. The whole system as shown in figure falls freely under gravity. The upthrust on the body is

zero
equal to the weight of liquid displaced
equal to the weight of the body in air
equal to the weight of the immersed portion of the body

Topic:

Mechanical Properties of Fluids

Exam:

JEE Advanced 1982

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Question 8

A U-tube of uniform cross-section is partially filled with a liquid I. Another liquid II which does not mix with liquid I is poured into one side. It is found that the liquid levels of the two sides of the tube on other side are the same, while the level of liquid I has risen by

2 cm

on other side. If the specific gravity of liquid I is 1.1 , the specific gravity of liquid II must be

$1.12$
$1.1$
1.05
$1.0$

Topic:

Mechanical Properties of Fluids

Exam:

JEE Advanced 1982

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Question 9

graphs for a certain amount of a perfect gas at two pressure

The volume

V

versus temperature

T

p_{1}

are as shown in figure. It follows from the graphs that

p_{2}

p_{1}

is greater than

p_{2}

Topic:

Kinetic Theory

Exam:

JEE Advanced 1982

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Question 10

Two different gases at the same temperature have equal root mean square velocities.

Topic:

Kinetic Theory

Exam:

JEE Advanced 1982

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Question 11

A solid sphere of copper of radius

R

and a hollow sphere of the same material of inner radius

r

and outer radius

R

are heated to the same temperature and allowed to cool in the same environment. Which of them starts cooling faster?

Topic:

Thermal properties of Matter

Exam:

JEE Advanced 1982

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Question 12

Two liquids

A

, the vapour pressure of a solution containing 1 mole of

B

form ideal solution. At

300 K

A

and 3 moles of

B

550 mm

Hg

. At the same temperature, if one more mole of

B

is added to this solution, the vapour pressure of the solution increases by

10 mm

Hg

. Determine the vapour pressure of

A

B

in their pure states.

Topic:

Solutions

Exam:

JEE Advanced 1982

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Question 13

Write the dimensions of the following in terms of mass, time, length and charge.
(a) Magnetic flux
(b) Rigidity modulus

Topic:

Units and Measurements

Exam:

JEE Advanced 1982

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Question 14

The mass of a hydrogen is ......

kg

Topic:

Structure of Atom

Exam:

JEE Advanced 1982

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Question 15

Isotopes of an element differ in the number of ................... in their nuclei.

Topic:

Structure of Atom

Exam:

JEE Advanced 1982

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Question 16

The outer electronic configuration of the ground state chromium atom is

3 d^{4} 4 s^{2}

Topic:

Structure of Atom

Exam:

JEE Advanced 1982

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Question 17

The energy of the electron in the second and third Bohr's orbits of the hydrogen atom is

- 5.42 \times 1 0^{- 12}

erg and

- 2.41 \times 1 0^{- 12}

erg respectively. Calculate the wavelength of the emitted light when the electron drops from the third to the second orbit.

Topic:

Structure of Atom

Exam:

JEE Advanced 1982

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Question 18

The element with the highest first ionisation potential is

boron
carbon
nitrogen
oxygen

Topic:

Classification of Elements and Periodicity in Properties

Exam:

JEE Advanced 1982

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Question 19

The energy released when an electron is added to a neutral gaseous atom is called .............

Topic:

Classification of Elements and Periodicity in Properties

Exam:

JEE Advanced 1982

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Question 20