JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q87

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MathematicsSingle correct+4 / -1Question 87 of 90

If two different numbers are taken from the set {0, 1, 2, 3, ......, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :

\dfrac{12}{55}

\dfrac{14}{45}

\dfrac7{55}

\dfrac6{55}

Answer and worked solution

Official answer: D

Both $x+y$ and $x-y$ divisible by 4 means $x\equiv y\pmod4$ and $x$ even. The pairs come from $\{0,4,8\}$ (3 pairs) and $\{2,6,10\}$ (3 pairs). Out of $\binom{11}2=55$ pairs: $\frac6{55}$ .

Topics:Classical probability

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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 87