સંખ્યા \(x\) ને ગણ \(\{1, 2, 3, 4, .... , 100\}\) માંથી યાર્દચ્છિક રીતે પસંદ કરવામાં આવે છે . ઘટના: \(A =\) સંખ્યા \(x\) એ \(\frac{{(x - 10)(x - 50)}}{{(x - 30)}} \ge 0\) નું સમાધાન કરે છે તો \(P(A)\) મેળવો.

A \(0.71\)
B \(0.70\)
C \(0.51\)
D \(0.20\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(0.71\)

Step-by-step Solution

Detailed explanation

Given \(\frac{(x-10)(x-50)}{(x-30)} \geq 0\) Let \(x \geq 10, x \geq 50\) equation will be true \(\forall x \geq 50\) as \(\left(\frac{x-50}{x-30}\right) \geq 0, \forall x \in[10,30)\) \(\begin{array}{c}{(x-10)(x-50)} \\ {x-30}\end{array} \geq 0 \forall x \in[10,30)\) Total…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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વર્ગ	\(10-20\)	\(20-30\)	\(30-40\)	\(40-50\)	\(50-60\)
આવૃતિ	\(\alpha\)	\(110\)	\(54\)	\(30\)	\(\beta\)