Integers 1, 2, 3, ...., n, where n > 2, are
written on a board. Two numbers m, k
such that 1 < m < n, 1 < k < n are
removed and the average of the
remaining numbers is found to be 17.
What is the maximum sum of the two
removed numbers?
A 5 kg block B is suspended from a
cord attached to a 40 kg cart A. Find
the accelerations of both the block and
cart. (All surfaces are frictionless)
(g = 10 m/s^2 )
Suppose x is a positive real number
such that {x}, [x] and x are in a
geometric progression. Find the least
positive integer n such that x^n > 100.
(Here [x] denotes the integer part of x
and {x} = x − [x].)
In a rectangle ABCD, E is the midpoint
of AB; F is a point on AC such that BF
is perpendicular to AC; and FE
perpendicular to BD. Suppose BC = 8(√3).
Find AB.
The surface between wedge and block
is rough (Coefficient of friction μ).
Find out the range of F such that,
there is no relative motion between
wedge and block. The wedge can move
freely on smooth ground.