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JEE Advanced 2008Paper 1
Exam
JEE Advanced
Year
2008
Paper
Paper 1
Subject
Mathematics
Chapter
Probability

JEE Advanced 2008 · Paper 1 · Mathematics · Probability

Consider the system of equations where a, b, c, d ∈\ 0,1\ Statement...

Consider the system of equations where a,b,c,d∈{0,1}\quad a, b, c, d \in\{0,1\} Statement 1 The probability that the system of equations has a unique solution, is 3/83 / 8. Statement 2 The probability that the system of equations has a solution, is 1 .Consider the system of equations where a, b, c, d ∈\ 0,1\ Statement 1 The probability that the system of equations hasConsider the system of equations where a, b, c, d ∈\ 0,1\ Statement 1 The probability that the system of equations has

Options

  1. AStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  2. BStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  3. CStatement 1 is true, Statement 2 is false.
  4. DStatement 1 is false, Statement 2 is true

Correct answer

B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

Step-by-step solution

The number of all possible deteminants of the form Consider the system of equations where a, b, c, d ∈\ 0,1\ Statement 1 The probability that the system of equations has
Out of which only 10 determinants given byConsider the system of equations where a, b, c, d ∈\ 0,1\ Statement 1 The probability that the system of equations has
vanish and remaining six determinants have non-zero values. Hence, the required probability =616=38=\frac{6}{16}=\frac{3}{8} ⇒\Rightarrow Statement 1 is correct. Statement 2 is also correct as the homogeneous equations have always a solution and Statement 2 is not a correct explanation of Statement 1.
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