JEE Advanced 2014 · Paper 2 · Mathematics Q56

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MathematicsSingle correct+3 / -1Question 56 of 60

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Paragraph For Questions 55 and 56

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3, 4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let $x_i$ be the number on the card drawn from the $i^{th}$ box, $i=1,2,3$ .

The probability that $x_1$ , $x_2$ , $x_3$ are in an arithmetic progression, is

\dfrac9{105}

\dfrac{10}{105}

\dfrac{11}{105}

\dfrac7{105}

Answer and worked solution

Official answer: C

Condition. $x_1+x_3=2x_2$ : $x_1$ and $x_3$ have the same parity and their mean lies in 1-5.

$x_1=1$ : $x_3\in\{1,3,5,7\}$ (means 1, 2, 3, 4): 4.
$x_1=2$ : $x_3\in\{2,4,6\}$ (means 2, 3, 4): 3.
$x_1=3$ : $x_3\in\{1,3,5,7\}$ (means 2, 3, 4, 5): 4.

Probability. $\dfrac{11}{105}$ .

(C)

Topics:Classical probability Arithmetic progression

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JEE Advanced 2014 · Paper 2, Mathematics question 56