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Question #41833

Difficulty: 8/10 | 🟢 Free

The Question

Let $A = \{x \in \mathbb{Z} : 2x^2 - 17x + 21 \le 0\}$ and $B = \{y \in \mathbb{Z} : y^2 - 9y + 8 \le 0\}$ . If a function $f: A \to B$ is chosen at random, what is the probability that $f$ is an injective mapping?

Options

A.
$\frac{315}{4096}$
B.
$\frac{105}{512}$
C.
$\frac{315}{16384}$
D.
$\frac{105}{256}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Combinatorial Probability|Injective Mapping (One-One)|Domain Restrictions

Why This Question Is Tricky

Common Mistakes

This question tests combinatorial probability intertwined with domain restrictions.

The primary trap lies in correctly identifying the cardinality of set A.

The quadratic inequality yields the interval [1.5, 7].

Students frequently make boundary errors here: either incorrectly rounding 1.5 down to 1 (resulting in |A|=7 and leading to the trap option C), or simply subtracting the integer endpoints (7 - 2 = 5) without adding 1 for inclusive counting (resulting in |A|=5 and leading to the trap option B).

By embedding the domain within a non-integer bounded inequality, the question forces precise discrete counting before any probability can be calculated.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Probability - Class 12
Concept	Combinatorial Probability
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free