Given any positive integer n show
that there are two positive rational
numbers a and b, a ≠ b, which are not
integers and which are such that a − b,
a^2 − b^2 , a^3 − b^3 , ....., a^n − b^n are all
integers.
Let ABC be a triangle and h_a the
altitude through A. Prove that
(b + c)^2 ≥ a^2 + 4h_a ^2 .
(As usual a, b, c denote the sides BC,
CA, AB respectively.)
The students were asked whether
they had dictionary(D) or thesau
rus(T) in their room.the results
showed that 650 students had dict
ionary,150 did not had dictionary,
175 had a thesaurus,and 50 had
neither a dictionary nor a thesaur
us,fimd the number of student who
(i)live in domitory
( ii)have both dictionary and thesaurus
(iii)have only thesaurus
STATEMENT-1 : If an object is at
rest then there should not be any friction
on it.
STATEMENT-2 : If an object is moving
then the friction acting on it has to be
kinetic.
STATEMENT-3 : If an object is at rest
then kinetic friction cannot act on it.
Two balls of mass 500g and 750g moving with 15m/s and
10m/s towards each other collides. Find the velocities of the ball after
collision, if the coefficient of restitution is 0.8
A hockey player is moving northward
and suddenly turns westward with
the same speed to avoid an opponent.
The force that acts on the player is
(a) frictional force along westward
(b) muscle force along southward
(c) frictional force along south-west
(d) muscle force along south-west
Calculate the energy emitted when
electrons of 1 g atom of hydrogen
undergo transition giving the spectral
line of lowest energy in the visible
region of its atomic spectrum
(R_H = 1.1 × 10^7 m^(−1) , c = 3 × 10^8 ms^(−1) ,
h = 6.62 × 10^(−34) Js)
Let A = {1, 2, 3, ....., n}, if a_i is the
minimum element of the set A; (where
A; denotes the subset of A containing
exactly three elements) and X denotes
the set of A_i ′s, then evaluate Σ_(A_i ∈X) a.
On the modified chess board 10 × 10,
Amit and Suresh two persons which
start moving towards each other. Each
person moving with same constant
speed. Amit can move only to the
right and upwards along the lines
while Suresh can move only to the left
or downwards along the lines of the
chess boards. The total number of
ways in which Amit and Suresh can
meet at same point during their trip.
How many 5-digit numbers from the
digits {0, 1, ....., 9} have?
(i) Strictly increasing digits
(ii) Strictly increasing or decreasing
digits
(iii) Increasing digits
(iv) Increasing or decreasing digits
The line of action of the resultant of
two like parallel forces shifts by one
fourth of the distance between the
forces when the two forces are
interchanged. The ratio of the two
forces is