Men are running in a line along a road
with velocity 9 km/hr behind one
another at equal distances of 20 m.
Cyclists are also riding along the same
line in the same direction at 18 km/hr
at equal intervals of 30 m. The speed
with which an observer must travel
along the road in opposite direction of
so that whenever he meets a runner he
also meets a cyclist is
(1) 9 km/h
(2) 12 km/h
(3) 18 km/h
(4) 6 km/h
Two particles are revolving on two
coplanar circles with constant angular
velocities ω_1 and ω_2 respectively. Their
time periods are T_1 and T_2 then prove
that the time taken by second particle
to complete one revolution more than
the first particle, T, is given by
T = ((T_1 T_2 )/(T_1 − T_2 ))
Rain is falling vertically with a speed
of 4 m/s. After some time, wind starts
blowing with a speed of 3 m/s in the
north to south direction. In order to
protect himself from rain, a man
standing on the ground should hold his
umbrella at an angle θ given by
(1) θ = tan^(−1) 3/4 with the vertical
towards south
(2) θ = tan^(−1) 3/4 with the vertical
towards north
(3) θ = cot^(−1) 3/4 with the vertical
towards south
(1) θ = cot^(−1) 3/4 with the vertical
towards north
The sixth term of an AP is 2, and its
common difference is greater than one.
The value of the common difference of
the progression so that the product of the
first, fourth and fifth terms is greatest is
ABC is a triangular park with AB =
AC = 100 m. A clock tower is situated
at the midpoint of BC. The angles of
elevation of top of the tower at A and
B are cot^(−1) (3.2) and cosec^(−1) (2.6)
respectively. The height of tower is
3 cubes of metal whose edges are 3,4
and 5 respectively are melted and
formed into a single cube. If there be
no loss of metal in the process find
the side of the new cube.