A block of mass m is connected with
another block of mass 2m by a light
spring. 2m is connected with a hanging
mass 3m by an inextensible light string.
At the time of release of block 3m, find
tension in the string and acceleration
of all the masses.
Balls are dropped from the roof of a
tower at a fixed interval of time. At the
moment when 9th ball reaches the
ground the nth ball is (3/4)th height
of the tower. What is the value of n?
If x, y, z are three real numbers such
that x + y + z = 4 and x^2 + y^2 + z^2 = 6,
then
(1) (2/3) ≤ x, y, z ≤ 2
(2) 0 ≤ x, y, z ≤ 2
(3) 1 ≤ x, y, z ≤ 3
(4) 2 ≤ x, y, z ≤ 3
Let p = (x_1 − x_2 )^2 + (x_1 − x_3 )^2 + .... +
(x_1 − x_6 )^2 + (x_2 − x_3 )^2 + (x_2 − x_4 )^2 +
.... + (x_2 − x_6 )^2 + .... + (x_5 − x_6 )^2 =
Σ_(1≤i<j≤6) ^6 (x_i − x_j )^2 .
Then the maximum value of p if each
x_i (i = 1, 2, ....., 6) has the value 0 and
1 is
Suppose p is a polynomial with complex
coefficients and an even degree. If all
the roots of p are complex non-real
numbers with modulus 1, prove that
p(1) ∈ R iff p(−1) ∈ R.