Problems 46-50
(50) Persons A and B communicate with each other on a regular basis. Each person has two independent telephone landlines, one fax line, one mobile and an email ID to deliver the messages. At a particular point of time, it was found that each person was sending out one message to the other. In how many ways can this happen?
Submission: Closed
This problem could not be completely cracked by any student. However attempt made by Niveditha Samudrala, Class XI, Visakhapatnam is worth mentioning.
Solution:
Assumptions: (other assumptions made by the students have also been considered)
- A person can be engaged in one activity at a time.
- A mobile phone can send text message (sms) and email.
- An email can send email, mobile text message (sms) and fax.
Case (i) - Voice Conversations
When a person talks on the phone, the other person must listen to him to receive his message. Hence, it is not possible for a person to send and receive a message simultaneously using voice conversation.
Case (ii)
mobile sms to mobile sms
mobile sms to email
email to email
email to mobile sms
There are 4 X 4 = 16 ways (note that the events are independent)
Case (iii)
A fax machine can either send or receive a message at a time.
No. of ways = 1(person A sends message from email to fax to B) X (4+1 person B can also send message from email to fax to A) = 5
+ 1(person B sends message from email to fax to A) X (4+1 person A can also send message from email to fax to B) = 5
- 1(since one way in which both A and B send email to fax messages has been counted twice) = -1
+ 1 (person A sends fax to B from fax machine) X 4 = 4
+ 1 (person B sends fax to A from fax) X 4 = 4
= 17
Total no. of ways = 33
(49) Radiation falls on the slits in a Young's Double Slit Experiment due to the de-excitation of Bohr ions of atomic number Z from n2 ----> n1 quantum state. The ions are located very far away from the slits. The distance between the slits is d. The detector screen is placed parallel to the slits which records minima at the centre. Find the angle that the incident beam makes with the normal to the plane of the slits.
Submission: Closed
Hint:
The waves reaching the slits can be considered to be parallel as the source is far away. The phase difference takes place when the waves reach the slits (not afterwards which usually happens in YDSE) which is equal to d.sinq where q is the angle that has been asked (you are expected to prove this by drawing a diagram).
Now, \(dsin\theta=(2n+1)\frac{\lambda}{2},n\in I\)
Use the formula valid for Bohr atom/ion to find \(\lambda\) in terms of n1, n2, Z and R.
The final answer comes in terms of n1, n2, Z, R, n and d. The values of n should be such that sin inverse is defined.
Cracked by:
1.Nachiket Vasant Vaidya, 12'th, Sathaye College, Vile Parle, Mumbai.
2.Anurag Dhingra, 12'th, Thakur College, Kandivali, Mumbai.
(48) A, C6H13N reacts with 2 moles of CH3I and Ag2O/D giving B, C8H17N. On further reaction with CH3I and Hofmann degradation, B yields a conjugated di-ene C along with N(CH3)3. Identify A and B. The structure of C is shown below.
C: 
Submission: Closed
Solutions by Nachiket and Vivek Edited by INDIANET (.pdf)
Cracked by:
1.Nachiket Vasant Vaidya, 12'th, Sathaye College, Vile Parle, Mumbai.
2.Vivek Saxena, 12'th pass, Dr Virendra Swarup Education Centre, Kanpur.
(47) Bull's Eye: In the finals of a shooting competition, a specially designed target is used. The equation of the boundary of the target which is a planar is given by Abs(x)+Abs(y)=10. All the shooters have passed various levels of screening stages and one can expect that none of the shots would go beyond the target. Inside the target, there are various regions. Certain point is given if the bullet hits a particular region. However, one gets maximum points by hitting the bull's eye. The bull's eye is the region bounded by x2/3+y2/3=22/3, Abs(x)=1 and Abs(y)=1. Find the probability of hitting the bull's eye without assigning any weight age to the skill of a shooter. Abs denotes the absolute value function.
Submission: Closed
Cracked by:
1.Royan John D' Mello, 1'st Year B.Tech., NIT(K), Surathkal.
2.Nachiket Vasant Vaidya, 12'th, Sathaye College, Vile Parle, Mumbai.
(46) Dr H.C. Verma's statement of the Gauss's law in his book, "Concepts of Physics II" is as follows:
"The flux of the net electric field through a closed surface equals the net charge enclosed by the surface divided by \(\epsilon_0\)."
Is the above statement applicable in the presence of changing magnetic field? Explain.
Submission: Closed
Solution:
Changing magnetic field creates electric field flux of its own in the shape of closed lines. However, Gaussian surface is a closed surface and any closed line going out of the surface must reenter it as well. And therefore, the statement is still valid. Had magnetic field created diverging/converging flux, the statement would be invalid which is not the case.