Download Applied Mathematics

Sub Name:
Chemistry
Faculty Name:Dr.Preetinand Kumar
Group:P
Sem: 1st
1. (a) Define hardness? Write the different types of hardness?
b) Give the relationship between various units of hardness.
c) What is degree of Hardness?
2. A) what are the major boiler problems caused by the use of hard water? What are the
Disadvantages, how they can be minimized? Write any one of the boiler problem in
Detail?
b). Write notes on: - Caustic Embrittlement and Boiler Corrosion
3. What do you mean by internal conditioning of boiler feed water?
4. Describe lime soda process. How water is conditioned by this process. Explain
Diagrammatic set up, its principle & working.
5. What is zeolite? How they function in removing hardness of water. Explain in detail with
Diagram?
6. What is ion exchange process ? How demineralization of water is carried out?
7. What is alkalinity? How it is determined experimentally?
8. Write notes on Break point chlorination?
PROFESSIONAL Faculty Name:Dr.Bindu Jacob
COMMUNICATION IN ENGLISH Group: P
Sub Name:
1. Define communication with the help of diagram?
2. What are the objectives of communication?
3. What are the 7’Cs of communication?
4. What are the steps to be kept in mind to make communication effective?
5. What is Non-Verbal communication? Mention its types.
6. Explain the barriers to effective communication?
7. What is Semantic Gap?
8. Describe Grapevine communication?
9. Explain Upward &Downward communication with its merits &demerits.
Sem:1st
Sub Name:
EEE
Faculty Name:Mrs.Payal Roy
Group: P
Sem: 1st
1.a) State kirchhoff’s law.
b) Solve the network given for the following:
(i) unknown resistance R1 and R2
(ii) unknown currents in various branches of the circuit.
2. Find current through branch ab in the circuit shown in fig. by using loop current method.
3. Find resistance between point A & C of the circuit shown in fig. using star delta
transformation.
4. (a)State and explain Thevenin theorem .
(b)The circuit shown in fig conatains two voltage source and two current sources. Calculate (i)
Voc (ii) Rth, between the open terminal A & B of the circuit
5.State Maximum Power Transfer theorem , how we solve the network using Maximum Power
Transfer theorem
(b)Using Norton's Theorem find the current which would flow in a 15Ω resistor connected
between Pt. A & b in following Fig.
Sub Name:
ENGG. GRAPHICS
Faculty Name:Mr.Sanjay Gupta
Group: P
Sem: 1st
1. A room of 1728 m3 volume is shown by a cube of 216 cm3 volumes. Find RF and
construct a plain scale to measure up to 42m. Mark a distance of 22m on the scale.
2. Distance between Delhi and Agra is 200km. In a railway map it is represented by a line
5cm long. Find its RF. Draw diagonal scale to show single kilometer and maximum 600
km. Indicate on it following distance 1) 222km. 2) 336km. 3) 459km. 4) 569km.
3. On a map the distance between two points is 14cm. The real distance between them is
20km. draw a diagonal scale of this map to read kilometer and hectometers and to
measure up to 25km. Show a distance of 17.6 km on this scale.
4. A rectangular plot of land measuring 1.28 hectors is represented on a map by a similar
rectangle of 8 sq cm. Calculate RF of the scale. Draw a diagonal scale to read single
meter. Show a distance of 438 m on it. (Hint: - 1 hector = 10,000 sq meter).
5. A point A is situated in the first quadrant. Its shortest distance from the intersection point
of H.P., V.P. and auxiliary plane is 60mm and it is equidistant from the principle planes.
Draw the projections of the point and determine its distance from principle planes.
6. Two points A and B are in the H.P. The point A is 30mm in front of the V.P. while B is
behind the V.P. The distance between their projectors is 75mm and the line joining their
top views makes an angle of 45º with xy. Find distance of the point B from the V.P.
Faculty Name:Dr.Biswas
Group: P
Sub Name:
Applied Mathematics
Sem 1st
1. Find the rank of matrix by reducing to normal form:
 8 1 3 6
A   0 3 2 2
 8  1  3 4
2. Find the rank of the following matrix:
1
1 
 1

A  b  c c  a
a  b
 bc
ca
ab 
3. Find the non-singular matrices P and Q such that PAQ is in the normal form for the
matrix:
1
1
A   1
2
 0  1
2
3  and hence find the rank of A.
 1
4. Test for consistency and solve:
x  2y  z  3
2x  3 y  2z  5
3x  5 y  5 z  2
3x  9 y  z  4
5. Investigate the values of  and  so that the equation:
2 x  3 y  5z  9
7x  3y  2z  8
2 x  3 y  z  
have (i) no solution (ii) a unique solution and (iii) infinite number of solutions.
6. show that the equation
3𝑥 + 4𝑦 + 5𝑧 = 𝑎 , 4𝑥 + 5𝑦 + 6𝑧 = 𝑏, 5𝑥 + 6𝑦 + 7𝑧 = 𝑐do not have a
solution unless 𝑎 + 𝑐 = 2𝑏
7. for what value of 𝑘 the equations 𝑥 + 𝑦 + 𝑧 = 1, 2𝑥 + 𝑦 + 4𝑧 = 𝑘, 4𝑥 + 𝑦 + 10𝑧 = 𝑘 2
have a solution and solve them completely in each case.
8. Find the Eigen values and Eigen vectors of the matrix
3 1 4
A  0 2 6
0 0 5
9.Verify the Cayley Hamilton theorem and hence find A-1for the matrix
 2  1 1
A    1 2  1
 1  1 2
10Find the matrix represented by the polynomial
2 1 1 
A  5 A  7 A  3 A  A  5 A  8 A  2 A  I  0 where matrix A  0 1 0.


1 1 2
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