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Important Questions on Structure of Atom

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

The number of natural numbers less than

7000

which can be formed by using the digits

0, 1, 3, 7, 9

(repetition of digits allowed) is equal to:

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

Suppose that

20

pillars of the same height have been erected along the boundary of circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is:

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

The value of

\sum_{r = 1}^{10} r \cdot \frac{{}^{n}C_{r}}{{}^{n}C_{r - 1}}

is equal to

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

Consider a class of

5

girls and

7

boys. The number of different teams consisting of

2

girls and

3

boys that can be formed from this class, if there are two specific boys

A

and

B,

who refuse to be the members of the same team, is:

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

{\sum_{i = 1}^{20} (\frac{^{20} C_{i - 1}}{^{20} C_{i} +^{20} C_{i - 1}})}^{3} = \frac{k}{21},

then

k

equals

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

A committee of

11

member is to be formed from

8

males and

5

females. If

m

is the number of ways the committee is formed with at least

6

males and

n

is the number of ways the committee is formed with at least

3

females, then

EASY

Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

The Number of ways of choosing

10

objects out of

31

objects of which

10

are identical and the remaining

21

are distinct, is:

HARD

Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

Let $f (x)$ be a polynomial of degree four and having its extreme values at $x = 1$ and $x = 2$ . If $\lim_{x \to 0} [1 + \frac{f (x)}{x^{2}}] = 3$ , then $f (2)$ is equal to

EASY

Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

There are

m

men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by

84

, then the value of

m

is :

HARD

Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

If in a regular polygon the number of diagonals is

54

, then the number of sides of this polygon is:

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

Let

f (x) = \begin{array}{l} x^{2} - 1, 0 < x < 2 \\ 2 x + 3, 2 \leq x < 3 \end{array}

, find the quadratic equation whose roots are

\lim_{x \to 2^{-}} f (x)

and

\lim_{x \to 2^{+}} f (x)

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

The value of

\underset{y \to 0}{l i m} \frac{\sqrt{1 + \sqrt{1 + y^{4}}} - \sqrt{2}}{y^{4}}

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

A particle moving with a velocity

10^{6}

m / s

will have de Broglie wavelength nearly [Given,

m = 6 .62 \times 10^{- 27} kg, h = 6 .62 \times 10^{- 34} Js]

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Chemistry>Physical Chemistry>Structure of Atom>Towards Quantum Mechanical Model of the Atom

Dual behavior of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material. If the velocity of the electron in this microscope is