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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 > ...
By admin, Sep 23 
Topic Tags:  iit jee , 2024 ,
  IIT-JEE
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By admin
2 months ago
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
By admin, Sep 23 
Topic Tags:  iit jee , probability ,
  IIT-JEE
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0
By admin
2 months ago
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) ​ =
By admin, Sep 23 
Topic Tags:  iit jee , advanced 2024 ,
  IIT-JEE
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0
By admin
2 months ago
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
By admin, Sep 23 
Topic Tags:  circle ,
  IIT-JEE
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By admin
2 months ago
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:
By admin, Sep 23 
Topic Tags:  circle ,
  IIT-JEE
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By admin
2 months ago
Find the value of \[ \int_0^4 \lfloor x \rfloor \, dx \], where [.] represent the greatest integer function.
By rituwitu, Sep 17 
  Class 11th
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By rituwitu
2 months ago
The equation \(E = mc^2\) is very famous.
By rituwitu, Sep 17 
  Class 11th
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By rituwitu
2 months ago
What is Computer Application?
By rituwitu, Sep 17 
  BTech
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By rituwitu
2 months ago
What is example?
By rituwitu, Sep 17 
  IIT-JEE
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By rituwitu
2 months ago

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