A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let R be
the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency v about
its equilibrium shape. By dimensional analysis the ratio
3
v
σ / ρR
can be (Here σ is surface tension, ρ is density,
g is acceleration due to gravity, and k is arbitrary dimensionless constant)
Let S = {1, 2, 3, …..,n} and A = {(a, b) |1< a, b < n} = S x S. A subset B of A is said to be a good subset if
(x, x) ∈ B for every x ∈ S. Then the number of good subsets of A is
Suppose a1, a2, a3, …….,a2012 are integers arranged on a circle. Each number is equal to the average of its two
adjacent numbers. If the sum of all even indexed numbers is 3018, what is the sum of all numbers ?
(A) 0 (B) 1509 (C) 3018 (D) 6036
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
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
Six is a number perfect in itself, and not because God created the world in six days; rather the contrary is true. God created the world in six days because this number is perfect, and it would remain perfect, even if the work of the six days did not exis