KVPY Government Jobs Exams

Suppose logab + logba = c. The smallest possible integer value of c for all a, b > 1 is

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KVPY Other Question

A standing wave in a pipe with a length L = 1.2 m is described by
y (x,t)= y0 sin [(2π/L)x] sin [(2π/L)x + π/4]
Based on above information, which one of the following statements is incorrect.
(Speed of sound in air is 300 m s–1)–
(A) The pipe is closed at both ends
(B) The wavelength of the wave could be 1.2 m
(C) There could be a node at x = 0 and antinode at x = L/2
(D) The frequency of the fundamental mode of vibrations is 137.5 Hz Suppose n is a natural number such that| i + 2i2 + 3i3 + ... + nin |=18 2 , where i is the square root of – 1.
Then n is