Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Numbers are written down on each of the cards A, B and C. One number is selec

Numbers 1,2,3, \ldots, 100 are written down on each of the cards A, B and C. One number is selected at random from each of the cards. The probability that the numbers so selected can be the measures (in cm ) of three sides of right-angled triangles no two of which are similar, is

Option: 1

\frac{4}{100^3}


Option: 2

\frac{3}{50^3}


Option: 3

\frac{3 !}{100^3}


Option: 4

None of these


Answers (1)

best_answer

\mathrm{n(S)=100 \times 100 \times 100}

We know that \mathrm{(2 n+1)^2+\left(2 n^2+2 n\right)^2=\left(2 n^2+2 n+1\right)^2 for \: all \: n \in N.}

\mathrm{\therefore for \: n=1,2,3,4,5,6} we get lengths of the three sides of a right-angled triangle whose longest side \leq 100

For example, when \text{n=1} sides are 3,4,5; when \text{n=2} sides are 5,12,13 and so on.

The number of selections of 3,4,5 from the three cards by taking one from each is 3 !.

\mathrm{\therefore \quad n(E)=6(3 !) \text {. Hence, } P(E)=\frac{6(3 !)}{100 \times 100 \times 100}=\frac{1}{100}\left(\frac{3}{50}\right)^2 \text {. }}

Posted by

Riya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question