The sum of four consecutive
2−digit numbers when divided by
10 becomes a perfect square.Which
of the following can possibly be
one of these four numbers?
(a)21(b)25(c)41(d)67(e)73
please show workings
Two blocks of masses M and 2M are
connected to each other through a light
spring as shown in figure. If we push the
mass M with a force F which cause
acceleration a in mass M, what will the
acceleration in 2M?
Two blocks A and B each of mass 1 kg
are placed on a smooth horizontal
surface. Two horizontal forces 5 N and
10 N are applied on the blocks A and B
respectively as shown in figure. The
block A does not slide on block B. Then
the normal reaction between the two
block is
A point ′A′ is randomly chosen in a
square of side length 1 unit. Find the
probability the distance from A to the
centre of the square does not exceed x.
A spring of force constant k is cut into
two pieces such that one piece is twice
as long as the other. Then the longer
piece will have a force constant of
Consider a block sliding over a smooth
inclined surface of inclination θ. Relating
to Newton′s second law applied on the
block, select the incorrect alternative.
(1) ΣF_(y′) ≠ 0
(2) ΣF_y = 0
(3) ΣF_x = −mg sin θ
(4) ΣF_(x′) < 0
A bird sits on a stretched telegraph
wire. The additional tension produced
in the wire is
(1) Zero
(2) Greater than weight of the bird
(3) Less than the weight of the bird
(4) Equal to the weight of the bird
A light rope is passed over a pulley such
that at its one end a block is attached,
and on the other end a boy is climbing
up with acceleration (g/2) relative to rope.
Mass of the block is 30 kg and that of
the boy is 40 kg. Find the tension and
acceleration of the rope.
If the equation sin6x + cos4x = −2 have
a family of nonnegative solutions x_k ′s,
where 0 ≤ x_1 < x_2 < x_3 < .... < x_k < x_(k+1)
....., then the value of (1/π)Σ_(k=1) ^(1000) ∣x_(k+1) − x_k ∣ is