. An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :
8 : 27
4 : 9
3 : 2
2 : 3
Option 1)
8 : 27
Option 2)
4 : 9
Option 3)
3 : 2
Option 4)
2 : 3
Which of the following arrangements shows the schematic alignment of magnetic moments of antiferromagnetic substance?
As we learned
The substances which are expected to passes paramagnetism or ferromagnetism on the basis of unpaired electrons but actually, they possess zero net magnetic moments are called anti ferromagnetic substance.
Option 1)
Option 2)
Option 3)
Option 4)
A man on the top of a vertical tower observes a car moving at a uniform speed
towards the tower on a horizontal road. If it takes 18 min. for the angle of
depression of the car to change from to
; then after this, the time taken
(in min.) by the car to reach the foot of the
tower, is :
As we have learned
Angle of Elevation 
If an object is above the horizontal line from the eye, we have to raise our head to view the object.
 wherein
Option 1)
This is correct
Option 2)
This is incorrect
Option 3)
This is incorrect
Option 4)
This is incorrect
If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2) of this cone is :
As we learned
Method for maxima or minima 
First and second derivative method :
 wherein
r,h be the radius and height of sphere
in ,using pythagorus theorem
So at ; we get max r=3 h = 4
thus
Option 1)
Option 2)
Option 3)
Option 4)
An ideal capacitor of capacitance 0.2 μF is charged to a potential difference of 10 V. The charging battery is then
disconnected. The capacitor is then connected to an ideal inductor of self inductance 0.5 mH. The current at a time
when the potential difference across the capacitor is 5 V, is :
0.34 A
0.25 A
0.17 A
0.15 A
A force of 40 N acts on a point B at the
end of an Lshaped object, as shown in
the figure. The angle θ that will produce
maximum moment of the force about
point A is given by :
As we learned
Torque 
 wherein
This can be calculated by using either
= perpendicular distance from origin to the line of force.
= component of force perpendicular to line joining force.
torque about A=
for maximum torque
Option 1)
Option 2)
Option 3)
Option 4)
If , then the value of at the point (2,0) is :
As we learned
Derivative at a point 
The value of f'(x) obtained by putting x = a is called the derivative of f(x) at x = a and it is denoted by f'(a) or
at x = a.

On Differentiating , we get
at (2,0)
at (2,0)
Option 1)
Option 2)
Option 3)
Option 4)
It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is p_{d} ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is p_{c}. The values of p_{d} and p_{c} are respectively :
(0, 1)
(⋅89, ⋅28)
(⋅28, ⋅89)
(0, 0)
Perfectly Elastic Collision 
Law of conservation of momentum and that of Kinetic Energy hold good.
 wherein
Before Collision
for elastic collision :
For collision with carbon
Fraction Loss =
Option 1)
(0, 1)
Option 2)
(⋅89, ⋅28)
Option 3)
(⋅28, ⋅89)
Option 4)
(0, 0)
If , then equals :
As we learned,
Option 1)
Option 2)
Option 3)
Option 4)
Let and Then,
the least odd natural number p, so that , for all , is:
9
7
11
5
Let be a function defined as where and . Then f is :
invertible and
invertible and
invertible and
not invertible
As we learned,
The function is invertible and
Option 1)
invertible and
Option 2)
invertible and
Option 3)
invertible and
Option 4)
not invertible
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c. Which of the following correctly gives the Planck length ?
As we have learnt @1035
let planck length is
Planck Length =
Option 1)
Option 2)
Option 3)
Option 4)
In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scale
divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is :
0.4300 cm
0.2150 cm
0.3150 cm
0.0430 cm
As we learned
To measure the diameter of small spherical cylindrical body using Vernier Callipers 
Vernier Constant
= 1 Main scale division  1 V.S. Division
V.C= 1 M.S.D  1 V.S.D
M.S.D= Main Scale Reading
V.S.D= Vernier Scale Reading
 wherein
Total observed reading =
N= N^{th} division
Observations:
1. Vernier constant (least count) of the Vernier Callipers:
1 M.S.D. = 1 mm
10 vernier scale divisions = 9 main scale divisions
i.e. 10 V.S.D. = 9 M.S.D.
1 V.S.D. = M.S.D.
Vernier Constant (L.C.) = 1 M.S.D.  1 V.S.D. = 1 M.S.D. M.S.D.
2. Zero error: (i) ........ cm (ii) ............cm (iii) ..........cm
Mean Zero Error (e) = ............ cm
Mean Zero Correction (c) =  (Mean Zero Error)
= .......... cm
= 0.2150cm
Option 1)
0.4300 cm
Option 2)
0.2150 cm
Option 3)
0.3150 cm
Option 4)
0.0430 cm
A uniform rod AB is suspended from a point X, at a variable distance x from A, as shown. To make the rod horizontal, a mass m is suspended from its end A. A set of (m, x) values is recorded. The appropriate variables that give a straight line, when plotted, are :
m, x
As we learned
Torque 
 wherein
This can be calculated by using either
= perpendicular distance from origin to the line of force.
= component of force perpendicular to line joining force.
Balancing Torque w.r.t point of suspension
This represents a straight line
Option 1)
m, x
Option 2)
Option 3)
Option 4)
The number of amplitude modulated broadcast stations that can be accomodated in a 300 kHz band width for the highest modulating frequency 15 kHz will be :
20
15
10
8
As we learned
Band width 
It is frequency range over which an equipment operate or the portion of the spectrum occupied by the signal.

Frequency required for one station
Number of channel = 10
Option 1)
20
Option 2)
15
Option 3)
10
Option 4)
8
In a common emitter configuration with suitable bias, it is given that is the load resistance and is small signal dynamic
resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by : β is current gain, , and arerespectively base, collector and emitter currents.
As we learned
Relation between α and β 
 wherein
(current gain )
Current Gain
Vol + age Gain =
power gain = (voltage gain) (Current gain)
Option 1)
Option 2)
Option 3)
Option 4)