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JEE Main/Advance

IMPORTANT

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Let $p, q$ be chosen one by one from the set $\{1, \sqrt{2}, \sqrt{3}, 2, e, π\}$ with replacement. Now a circle is drawn taking $(p, q)$ as its centre. Then the probability that at the most two rational points exist on the circle is (rational points are those points whose both the coordinates are rational)

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Important Questions on Probability I

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 39

Three integers are chosen at random from the set of first

20

natural numbers. The chance that their product is a multiple of

3

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 40

5

different balls are placed in

5

different boxes randomly. Find the probability that exactly two boxes remain empty. Given each box can hold any number of balls.

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 41

There are

10

Prizes, five

A' s,

three

B' s,

and two

C' s,

placed in identical sealed envelopes for the top

10

Contestants in a mathematics contest. The prizes are awarded by allowing winner to select an envelope at random from those remaining. When the

8^{t h}

Contestant goes to select the prize, the probability that the remaining three prizes are one

A,

one

B

and one

C

is,

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 42

A car is parked among

N

car standing in a row, but not at either end. On his return, the owner finds that exactly

r

of the

N

places are still occupied. The probability that the places neighbouring his car are empty is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 43

Let

A

be a set containing

n

elements. A subset

P

of the set

A

is chosen at random. The set

A

is reconstructed by replacing the elements of

P,

and another subset

Q

A

is chosen at random. The probability that

P \cap Q

contains exactly

m (m < n)

elements is

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 44

Consider

f (x) = x^{3} + a x^{2} + b x + c

. Parameters

a, b, c

are chosen respectively by throwing a die three times, then the probability that

f (x)

is an increasing function is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 45

a

and

b

are chosen randomly from the set consisting of numbers

1, 2, 3, 4, 5 and 6

with replacement. Then the probability that

\lim_{x \to 0} {[\frac{(a^{x} + b^{x})}{2}]}^{\frac{2}{x}} = 6

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 9 - Probability I>Exercises>Q 46

Mr.

A

lives at origin on the Cartesian place and has his office at

(4, 5)

. His friend lives at

(2, 3)

on the same plane. Mr.

A

can go to his office travelling one block at a time either in the

+ y

+ x

direction. If all possible paths are equally likely then the probability that Mr.

A

passed his friend house is (shortest path for any event must be considered)

Let p, q be chosen one by one from the set 1,2,3,2,e,π with replacement. Now a circle is drawn taking p,q as its centre. Then the probability that at the most two rational points exist on the circle is (rational points are those points whose both the coordinates are rational)

Important Questions on Probability I

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