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Let \( f(x) \) be a continuously differentiable function on the interval \( (0, \infty) \) such that \( f(1) = 2 \) and \[ \lim_{t \to x} \frac{t^{10} f(x) - x^{10} f(t)}{t^9 - x^9} = 1 \] for each \( x > 0 \). Then, for all \( x > ...
2 months ago
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IIT-JEE
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A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a q
2 months ago
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IIT-JEE
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Let 𝑓 ( 𝑥 ) f(x) be a continuously differentiable function on the interval ( 0 , ∞ ) (0,∞) such that 𝑓 ( 1 ) = 2 f(1)=2 and lim ⁡ 𝑡 → 𝑥 𝑡 10 𝑓 ( 𝑥 ) − 𝑥 10 𝑓 ( 𝑡 ) 𝑡 9 − 𝑥 9 = 1 t→x lim ​ t 9 −x 9 t 10 f(x)−x 10 f(t) ​ =
2 months ago
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IIT-JEE
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A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed in this circle and 𝑚 𝑎𝑛𝑑 𝑛, respectively, then 𝑚+𝑛^2 is equal to
2 months ago
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IIT-JEE
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If 𝑃(6,1) be the orthocenter of the triangle whose vertices are 𝐴(5,−2), 𝐵(8, 3) 𝑎𝑛𝑑 𝐶(ℎ, 𝑘), then the point C lies on the circle:
2 months ago
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IIT-JEE
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