SCHOLASTIC APTITUDE TEST 1999
|Time: ONE Hour
Max. Marks: 60
- Answers must be written either in
English or the medium of instruction of the candidate in
- Answer all the questions in the
booklets provided for the purpose.
- There will be no negative marking.
- The relevant working in arriving at
an answer has to be shown wherever required. However if
the answer can be arrived at without detailed working,
write only the answer
- Use of calculators or graph papers
is not permitted.
- All questions carry equal marks
- At a certain moment of
time a particle moving along a straight line is located
at a distance of 5 m from a point and at a
subsequent moment it is at a distance of 10 m from
the same point. The minimum and maximum distances the
particle could have moved are .
- A particle is going round
a circular path with a constant speed. The angle between
its acceleration and velocity vectors is .
- An object placed on an
equal arm balance requires 12 kg to balance it. When
placed on a spring scale, the scale reads 120 N.
Everything (balance, scale, set of masses, and the object)
is now transported to the moon where the gravitational
force is one-sixth that on Earth. The new readings of the
balance and the spring scale are
- A body is thrown up from
a certain height and another thrown down from the same
point with the same speed at the same time. If they hit
the ground with a time gap of 4 s, the speed of
projection is .
- On applying brakes a car
slows down from v1 to v2 as it
travels a certain distance and from v2 to v3
as it travels an equal distance. the relation between the
velocities is .
- A ball of mass m is
thrown vertically upward. Air resistance is not
negligible. Assume the force of air resistance has
magnitude proportional to the velocity, and direction
opposite to the velocity's. At the highest point, the
ball's acceleration is
(greater than /less than /equal to) acceleration due
- A converging lens with
focal length +10 cm would produce a twice magnified image
of an object, if the object is placed at a distance of
- Two small identical
conducting spheres are separated by a distance much
larger than their diameter. They are initially given
charges of -2.00 m C and +4.00 m C,
and are found to exert a force on each other of magnitude
1 N. Without changing their position, they are connected
by a conducting wire. When the wire is removed, the
magnitude of the force between them is .
- Three 60 W light bulbs
are mistakenly wired in series and connected to a 120 V
power supply. Assume the light bulbs are rated for single
connection to 120 V. With the mistaken connection, the
power dissipated by each bulb is .
- In the
circuit shown the resistance R1, R2,
R3, R4 and R5
are 80 W , 20 W 60 W 25 W and 20 W respectively. A
current of 0.10 A flows through the 25 W resistor shown in the
diagram. The current through the 80 W resistor is .
- A wire of a
certain radius has a resistance R. Another wire of same
length, same material has one end of same radius and the
other end of twice greater radius, the radius increasing
linearly from the narrower end. If the resistance R' of
the second wire is less than nR where n is an integer, n
would be .
- Angular momentum of a
particle about a point is defined as the product of its
mass, velocity and perpendicular distance from the given
point. A particle of mass m is moving in the xy plane
parallel to x- axis at a distance d from it with a speed
v. Its angular momentum about the origin would be
- An alloy consists of a
metal A of density 3.1 gm/cc and a metal B of density 8.8 gm/cc
mixed in the ratio 2:1. A hollow ball made of this
material has an external volume of 80 cc and a mass of
100 g. The volume of the cavity is .
- A body is dropped from a
height of 20 m above the ground. If gravity disappears 1
second after it starts falling , the time it takes to hit
the ground is ( Assume acceleration due to gravity =
10 ms2 ) .
diagram to the right shows the velocity-time
graph for two masses A and B that collided
Consider the following statements.
I. A and B moved in the same direction after the
II. The velocities of A and B were equal at the
mid-time of the collision
III. The mass of A was greater than the mass of B.
The true statements from these are .
difference between A and B is
and the current flowing from C to D is .
- Parallel beam
of light parallel to the principal axis of a lens falls
on a lens of focal length 50 cm. After passing through
the first lens they pass through another coaxially
mounted convex lens of focal length 50 cm placed 150 cm
from the first lens. After passing through the second
lens, the rays converge at a distance of __________ from
the first lens.
- If velocity of light in
medium A is 2.25 ´ 108 m/s. Refractive
index of medium B with respect to medium C is 1.2.
Velocity of light in a medium C is 1.5 ´
108 m/s. Refractive index of A with
respect to B is
. ( You should not use the value of velocity of
light in vaccum or air ).
- Particles A and B are
free to move along parallel paths. B is moving at a
constant velocity of 10 m/s and A starts moving at
the moment B passes it. If A accelerates at 1 m/s2
for 5 s and then travels at a constant velocity, the
distance between A and B 10 s after B passes A is .
- Dust particles are
uniformly distributed in space with a mass per unit
volume r . A circular plate of area A
is moving in this space at v. The dust particles that
come in to contact with the plate stick to it. The mass
of dust that collects on the plate in a time t is .
equal resistances (AB,BC,CD,
connected to form a star as shown. When the
resistances JB and JH are removed the equivalent
resistance between terminals A and I is R. The
equivalent resistance between A and I when the
resistances AJ and JI are removed would be .
- A point object
is located 5 cm above the principal axis of a lens of
focal length 20 cm. If the distance of the object
measured parallel to the principal axis is 30 cm, the
distance of the image of the object from the principal
axis would be .
- The orbital radius of a
certain satellite is R and it takes two hours to complete
one revolution. The radius of the orbit of a satellite
that would take 16 hours to complete one revolution would
- A longitudinal wave is
normally incident on a wall and is reflected. The
incident and the reflected waves interfere producing a
stationary wave. If the nearest node to the wall is 25 cm
from it and the velocity of longitudinal waves in air is
350 m/s, the frequency of the wave is .
- An solid object A has a
mass m and is made of a material of density r .
One fourth of its mass is removed and another material of
density r /2 is added to it and a new
solid object B is formed. The mass of B is 5/4 times the
mass of A. The difference in the volumes of the two
spheres is .
- A sealed evacuated vessel
of volume 1500 m3 and mass 3 ´
105 kg is floating on water. The downward
force that should be exerted on the vessel to just
submerge it is .(
Density of water is 1 gm/cc, assume g =10 m/s2)
- A wagon of mass M is free
to roll on frictionless rails and is located on a
straight track. A man of mass m is standing at one end of
the wagon. The man runs parallel to the rails towards the
other end and jumps off. If the speed of the man at the
moment he jumps off is v, the speed of the wagon is .
- Gravity at a height h
above the earth is
for h<<R and for any h.
and gravity at a depth d below the earth is
for all d.
( R= 6400 km, g is the gravity on the earth and g'
gravity at the specified position)
Use these equations in filling the following blanks.
The height where the gravity is same as at a depth of 10
The height where the gravity is same as at a depth of
3200 km is .
- The fundamental frequency
of vibration of a string stretched between two supports
is given by the expression , where n, l, T and
m are the frequency, length of
the string, tension in the string and mass per unit
length respectively. Use this equation in filling the
A string stretched between
two supports has a frequency n. This string is then stretched
to twice its original length and fixed between two new
supports with same tension as earlier. The new fundamental
frequency is .
- A charged
particle moving northward at right angles to a magnetic
field experiences a force directed eastward. Another
charged particle of opposite charge is moving towards
southeast in the same magnetic field. The force
experienced by it is directed towards .