The probability of finding a green signal on a busy crossing X is 30 % . What is the probability of finding a green signal on X on two consecutive days out of three?

Let A be the event of finding a green signal on a busy crossing X The probability of finding a green signal on a busy crossing X is 30 % . P A = 30 100 = 3 10 The probability of not finding a green signal on a busy crossing X is P A ¯ = 1 - 3 10 = 7 10 . The probability of finding a green signal on X on two consecutive days out of three = P A P A P A ¯ + P A ¯ P A P A = 3 10 × 3 10 × 7 10 + 7 10 × 3 10 × 3 10 = 63 500 .

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Important Questions on Nuclei

HARD

Physics>Modern Physics>Nuclei>Nuclear Energy

Explain the principle and working of a nuclear reactor with the help of a labelled diagram.

EASY

Physics>Modern Physics>Nuclei>Nuclear Energy

The principal value of

\tan^{- 1} (\tan \frac{3 π}{5})

MEDIUM

Physics>Modern Physics>Nuclei>Nuclear Energy

2 M e V

neutron is emitted in a fission reactor. If it looses half of its kinetic energy in each collision with a moderator atom, how many collisions must it undergo to achieve thermal energy of

0.039 e V

EASY

Physics>Modern Physics>Nuclei>Nuclear Energy

The ratio of mass densities of nuclei of

^{40} C a

and

^{16} O

is close to:

MEDIUM

Physics>Modern Physics>Nuclei>Nuclear Energy

A die marked

1, 2, 3

in red

4, 5, 6

in green tossed. Let

A

be the event "number is even" and

B

be the event "number is marked red". Find whether the events

A

and

B

are independent or not.

MEDIUM

Physics>Modern Physics>Nuclei>Nuclear Energy

α = {c o s}^{- 1} (\frac{3}{5})

β = {t a n}^{- 1} (\frac{1}{3})

, where

0 < α, β < \frac{π}{2},

then

α - β

is equal to

EASY

Physics>Modern Physics>Nuclei>Nuclear Energy

\sin^{- 1} x = y

, then

MEDIUM

Physics>Modern Physics>Nuclei>Nuclear Energy

A problem in mathematics is given to three students

A, B, C

and their respective probability of solving the problem is

\frac{1}{2}, \frac{1}{3}

and

\frac{1}{4}

, the probability that the problem will be solved is

EASY

Physics>Modern Physics>Nuclei>Nuclear Energy

The probability of finding a green signal on a busy crossing

X

30 %

. What is the probability of finding a green signal on

X

on two consecutive days out of three?

HARD

Physics>Modern Physics>Nuclei>Nuclear Energy

α = 3 \sin^{- 1} (\frac{6}{11}) & β = 3 \cos^{- 1} (\frac{4}{9}),

where the inverse trigonometric functions take only the principal values, then the correct options(s) is(are)

MEDIUM

Physics>Modern Physics>Nuclei>Nuclear Energy

Four persons can hit a target correctly with probabilities

\frac{1}{2}, \frac{1}{3}, \frac{1}{4}

and

\frac{1}{8}

respectively. If all hit at the target independently, then the probability that the target would be hit, is

EASY

Physics>Modern Physics>Nuclei>Nuclear Energy

Iodoform test is not given by

HARD

Physics>Modern Physics>Nuclei>Nuclear Energy

Match the Column I with Column II and choose the correct option from the codes given below.

Column I (Distinguish)	Column II (By reagent)
A. Methanol and diethyl ether	1. Lucas reagent
B. Methanol and ethanol	2. Sodium metal
C. Phenol and cyclohexanol	3. Iodoform test
D. n-propyl alcohol and tert-butyl alcohol	4. Ferric chloride

HARD

Physics>Modern Physics>Nuclei>Nuclear Energy

Which of the following alcohols reacts most readily with Lucas reagent ?

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Physics>Modern Physics>Nuclei>Nuclear Energy

How does Lucas reagent help in the distinction of primary, secondary and tertiary alcohols? Discuss the reactions involved.

HARD

Physics>Modern Physics>Nuclei>Nuclear Energy

How will you distinguish between the following pair by suitable chemical tests? butan- $1$ -ol and butan- $2$ -ol.

EASY

Physics>Modern Physics>Nuclei>Nuclear Energy

Which reacts rapidly with Lucas reagent?

MEDIUM

Physics>Modern Physics>Nuclei>Nuclear Energy

An unknown alcohol is treated with the "Lucas reagent" to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism?

MEDIUM

Physics>Modern Physics>Nuclei>Nuclear Energy

Which of the following reacts fastest with a mixture of anhydrous

Z n {Cl}_{2}

and concentrated

HCl

HARD

Physics>Modern Physics>Nuclei>Nuclear Energy

Give structures of the products you would expect when the following alcohol reacts with (a)

H C l - Z n C l_{2}

(b)

H B r

and (c)

S O C l_{2}

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Important Questions on Nuclei

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