KVPY Government Jobs Exams

Let [x] and {x} be the integer part and fractional part of a real number x respectively. The value of the integral [x]{x}dx is

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KVPY Other Question

Let f : R → R be the function f(x) = (x – a1)(x–a2)+(x–a2)(x–a3) + (x– a3) (x–a1) with a1, a2, a3 ∈ R. Then f(x) > 0 if
and only if –
(A) At least two of a1, a2, a3 are equal (B) a1 = a2 = a3
(C) a1, a2, a3 are all distinct (D) a1, a2, a3 , are all positive and distinct Let Σ=
=
n
k 1
Sn k denote the sum of the first n positive integers. The numbers S1, S2, S3,…S99 are written on 99
cards. The probability of drawing a card with an even number written on it is