KVPY Government Jobs Exams

The minimum distance between a point on the curve y = e^x and a point on the curve y = logex is

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KVPY Other Question

Which of the following intervals is a possible domain of the function f (x) = log{x} [x] + log[x] {x}, where [x]
is the greatest integer not exceeding x and {x} = x – [x] ?
(A) (0, 1) (B) (1, 2) (C) (2, 3) (D) (3, 5) Two players play the following game : A writes 3, 5, 6 on three different cards ; B writes 8, 9, 10 on three
different cards. Both draw randomly two cards from their collections. Then A computes the product of two
numbers he/she has drawn, and B computes the sum of two numbers he/she has drawn. The player getting the
larger number wins. What is the probability that A wins ?