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JEE Mains · Maths · STD 12 - 1. relation and function
Statement \(-1\) : The equation \(x\, log\, x = 2 - x\) is satisfied by at least one value of \(x\) lying between \(1\) and \(2\) Statement \(-2\) : The function \(f(x) = x\, log\, x\) is an increasing function in \([1, 2]\) and \(g (x) = 2 -x\) is a decreasing function in \([ 1 , 2]\) and the graphs represented by these functions intersect at a point in \([ 1 , 2]\)
- A Statement \(-1\) is true; Statement \(-2\) is true;Statement \(-2\) is a correct explanation for Statement \(-1\)
- B Statement \(-1\) is true; Statement \(-2\) is true;Statement \(-2\) is not correct explanation for Statement \(-1\)
- C Statement \(-1\) is false, Statement \(-2\) is true
- D Statement \(- 1\) is true, Statement \(-2\) is false
Answer & Solution
Correct Answer
(A) Statement \(-1\) is true; Statement \(-2\) is true;Statement \(-2\) is a correct explanation for Statement \(-1\)
Step-by-step Solution
Detailed explanation
\(f\left( x \right) = x\log x,f\left( 1 \right) = 0,f\left( 2 \right) = 4\) \(g\left( x \right) = 2 - x,g\left( 1 \right) = 1,g\left( 2 \right) = 0\) \(\log \,10 > \log \,4 \Rightarrow 1 > \log \,4\) Thus statement- \(1\) and \(2\) both are true and sataement- \(2\) is a correct…
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