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Consider the following statements : I....

Consider the following statements :
I. `lim_(n rarr infty) (2^(n)+(-2)^(n))/(2^(n))` does not exist
II. `lim_(n rarr infty)(3^(n)+(-3)^(n))/(4^(n))` does not exist
Then

A

I is true and II is false

B

I is false and II is true

C

I and II are true

D

neither I nor II is true

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KVPY PREVIOUS YEAR-KVPY 2021-PART-I Mathematics
  1. Consider the following statements : I. lim(n rarr infty) (2^(n)+(-2)...

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  2. Consider a regular 10-gon with its vertices on the unit circle. With o...

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  3. The value of the integral int(-pi//2)^(pi//2)(sin^(2)x)/(1+e^(x))dx ...

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  4. Let RR be the set of all real numbers and f(x) = sin^(10)x(cos^(8) x...

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  5. A person standing on the top of a building of height 60sqrt(3) feel ob...

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  6. Assume that 3.313 le pi le 3.15. The integer closest to the value of s...

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  7. The maximum value of the function ƒ(x) = e^x + x ln x on the interval ...

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  8. Let A be a 2 xx 2 matrix of the form A = [[a,b],[1,1]], where a, b are...

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  9. Let A = (a(ij))(1 le I, j le 3) be a 3 xx 3 invertible matrix where ea...

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  10. Let x, y be real numbers such that x gt 2y gt 0 and 2log (x-2y) = lo...

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  11. Let (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1(b lt a). Be an ellipse with ...

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  12. Let A denote the set of all real numbers x such that x^(3) - [x]^(3) =...

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  13. Define a sequence {S(n)} of real numbers by S(n) = sum(k=0)^(n) (1)/...

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  14. Let f(x) = {{:((x)/(sin x) ",",x in "(0,1)"),(1",",x=0):} Consider...

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  15. The value of the integral int(1)^(3)((x-2)^(4)sin^(3)(x-2)+(x-2)^(20...

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  16. In a 15 sidead polygon a diagnol is chosen at random. Find the probabi...

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  17. Let M = 2^(30)-2^(15)+1, and M^(2) be expressed in base 2. The number ...

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  18. Let ABC be a triangle such that AB = 15 and AC = 9. The bisector of an...

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  19. The figur in the complex plane given by 10zbar(z) - 3(z^(2)+bar(z)^(...

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