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Let E be the ellipse x^2/16+y^2/9=1. For...

Let `E` be the ellipse `x^2/16+y^2/9=1`. For For any three distinct points `P,Q and Q'` on `E`, let `M(P,Q)` be the mid-point of the line segment joining P and Q, and `M(P, Q')` be the mid-point of the line segment joining P and Q'. Then the maximum possible value of the distance between `M(P,Q) and M(P,Q')`, as `P , Q and Q'` vary on `E`, is ___ .

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JEE ADVANCED PREVIOUS YEAR-JEE ADVANCED 2021-QUESTION
  1. Let vecu , vecv and vecw be vectors in three-dimensional space, where ...

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  2. Let s1 = {(i,j, k) ∶ i,j, k ∈ {1,2, … ,10}} ,s2 = {(i,j) ∶ 1 ≤ i < j +...

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  3. Consider a triangle PQR having sides of lengths p,q,r opposite to the ...

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  4. Let f:[-pi/2,pi/2] to R be a continuous function such that f(0)=1 and ...

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  5. For any real number alpha and beta , let y(alpha,beta)(x): alpha,beta ...

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  6. Let O be the origin and vec(OA)=2hati+2hatj+hatk , vec(OB)=hati-2hatj+...

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  7. Let E denote the parabola y^2 = 8x. Let P = (-2,4), and let Q and Q' b...

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  8. Consider the region R = {(x, y) in R xx R : x ge 0 and y^2 le (4 − x)}...

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  9. Consider the region R = {(x, y) in R xx R : x ge 0 and y^2 le (4 − x)}...

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  10. Let f1 : (0, oo) to R and f2 : (0, oo) to R be defined by f1(x) = int0...

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  11. Let f1 : (0, oo) to R and f2 : (0, oo) to R be defined by f1(x) = int0...

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  12. Let gi:[pi/8,(3pi)/8] to R , i=1,2 , and f:[pi/8,(3pi)/8] to R be func...

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  13. Let gi:[pi/8,(3pi)/8] to R , i=1,2 , and f:[pi/8,(3pi)/8] to R be func...

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  14. Consider M with r=1025/513. Let k be the number of all those circle Cn...

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  15. Consider M with r=((2^199-1)sqrt2)/2^198. The number of all those circ...

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  16. Let psi1:[0,oo] to R , psi2:[0,oo) to R , f:[0,oo) to R and g :[0,oo) ...

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  17. Let psi1:[0,oo] to R , psi2:[0,oo) to R , f:[0,oo) to R and g :[0,oo) ...

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  18. A number is chosen at random from the set {1,2,3, . . . 2000} Let p be...

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  19. Let E be the ellipse x^2/16+y^2/9=1. For For any three distinct points...

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  20. For any real number x, let [x] denote the largest integer less than or...

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