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KVPY PREVIOUS YEAR-KVPY 2021-PART-I Mathematics
- Consider the following statements : I. lim(n rarr infty) (2^(n)+(-2)...
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- Consider a regular 10-gon with its vertices on the unit circle. With o...
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- The value of the integral int(-pi//2)^(pi//2)(sin^(2)x)/(1+e^(x))dx ...
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- Let RR be the set of all real numbers and f(x) = sin^(10)x(cos^(8) x...
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- A person standing on the top of a building of height 60sqrt(3) feel ob...
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- Assume that 3.313 le pi le 3.15. The integer closest to the value of s...
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- The maximum value of the function ƒ(x) = e^x + x ln x on the interval ...
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- Let A be a 2 xx 2 matrix of the form A = [[a,b],[1,1]], where a, b are...
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- Let A = (a(ij))(1 le I, j le 3) be a 3 xx 3 invertible matrix where ea...
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- Let x, y be real numbers such that x gt 2y gt 0 and 2log (x-2y) = lo...
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- Let (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1(b lt a). Be an ellipse with ...
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- Let A denote the set of all real numbers x such that x^(3) - [x]^(3) =...
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- Define a sequence {S(n)} of real numbers by S(n) = sum(k=0)^(n) (1)/...
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- Let f(x) = {{:((x)/(sin x) ",",x in "(0,1)"),(1",",x=0):} Consider...
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- The value of the integral int(1)^(3)((x-2)^(4)sin^(3)(x-2)+(x-2)^(20...
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- In a 15 sidead polygon a diagnol is chosen at random. Find the probabi...
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- Let M = 2^(30)-2^(15)+1, and M^(2) be expressed in base 2. The number ...
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- Let ABC be a triangle such that AB = 15 and AC = 9. The bisector of an...
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- The figur in the complex plane given by 10zbar(z) - 3(z^(2)+bar(z)^(...
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