l-2/t-2/wre date: 17/02/2018

s .~

L-2/T-2/WRE Date: 17/02/2018BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA

L-2/T-2 B. Sc. Engineering Examinations 2016-2017

Sub: WRE 201 (Mechanics of Solids)

Full Marks: 280 Time: 3 HoursThe figures in the margin indicate full marks.

USE SEPARATE SCRIPTS FOR EACH SECTION

SECTION-AThere are FOUR questions in this section. Answer any THREE.

Assume reasonable value if data is not given.

1. (a) Distinguish between(i) Newtonian and Non-Newtonian fluid(ii) Poise and Stokes(iii) Surface Tension and Capillarity

(b) In Fig. 1, oil of viscosity I..l fills the small gap of thickness Y. Determine expression

for the torque T required to rotate the truncated cone at constant speed roo Neglect the

fluid stress exerted on the circular bottom. Also calculate the viscosity of the fluid I..l if

T = 3 x 105 N.m, ro = 0.5 rad/s, a = 10 cm and b = 3 cm, Y = 0.2 cm and a = 40.----------~"---------:-., ,

!,.

Fig. 1 for question I(b)

(c) A U-tube manometer shown in Fig. 2, the tube length AB = y is filled with waterand, tube length BCD if filled with mercury. When the funnel is empty the manometerreading CD = 0.27 m. Calculate the manometer reading when the funnel is filled with

oil of Sp. gr. 0.8.

1m~ .

(6)

(26)

(147j )

0.27m

A

ercury (sp.gr.13.55)

. Fig.-2 for question No. 1(e)

2.0m

y

. ~.

Contd P/2

=2=WRE201

2. (a) The gate in Fig. 3 is 5 m wide, is hinged at point B, and rests against a smooth wall"

at point A. Compute, (i) The force on the gate due to the water pressure, (ii) The

horizontal force P exerted by the wall at point A, (iii) The reactions at hinge B.

P~l

Water

Figure 3 for question No.2(a)

(b) Find the horizontal and vertical forces per meter width on the Tainter gate shown in

Fig. 4. Locate the horizontal force and indicate the line of action of the vertical force

without actually computing the location. Also repeat the calculations when water depth

(24)

h=3m.

Fig.- 4 for question No.2(b)

(12+10%)

3. (a)(i) Sketches for floating bodies when, (A) neutral equilibrium and (B) unstable

equilibrium. (ii) A wooden pole 3 m long, weighing 30 N/m has a cross~sectional area

45 cm2 and is supported as shown in Fig. 5. The hinge is frictionless. Find angle e. (6+ 10)

Contd P/3

WRE201Contd ... Q. NO.3

Hinge

Oil, y= 9.10 kN/m2.

Fig. 5 for question No 3(a)

(b) A pipe line is 50 m long is connected to water at one end as shown in Fig. 6 wherethe pipe 1 is 25 m long and diameter is 25 cm and suddenly enlarged to 50 cm up tolength of another 25 m. A nozzle of 25 cm dia. is attached at the end. The head ofwater at the tank is 8 m, considering all losses; determine the rate of flow (Q). Take

f= 0.015 for both pipes. Assume reasonable value ifnot given. (20)

8mNozzle

Gate valve

gpe-I

Fig.-6 for question No.3(b)-------------------'----- ---.:.-.!i

(c) Deduce the expression of equivalent length of three different pipes flow in seriesand then calculate the equivalent length of the following pipes in series in terms of

pipe size of pipe-2. Take f = 0.02 for all the pipes. (10% )

Pipe No. Length (m) Diameter (mm)1 200 200

2 400 150

3 300 100

4. (a) Using the Hardy-cross method distribute the flow through pipe network. (Fig. 7) (20)

100 litis

10 litis

K=1

K=1

1('=2Fig.-7 for question No.4(a)

20 litis

110 litis

i

~... P/4

=4=

WRE201Contd ... Q. No.4

(b) Drag force on rough sphere is function of D, p, J.1, V and k, using dimensional

analysis express these in the form of 1t3 = (1tb 1t2)'

(c) (i) Define the types of similarity with examples.

(10)

(6+10%)

(ii) For satisfying dynamic similarity, Remold Number ratio = 1 gives the scale

rati~ Lr = 30. If the density scale ratio Pr = 800, absolute viscosity ratio

j..tr = 50, what will be the scale ratio Lr satisfying the Froudian criteria?

SECTION-B

There are FOUR questions in this section. Answer any THREE.

5. (a) Define (i) Piezometric head, (ii) Streak line, (iii) Eddies and (iv) Hydraulic grade

line.

(b) Derive the general relationship between a fluid system and a control volume. Using

that relationship, derive the equation of continuity.

(c) Velocities in a 300 mm diameter circular conduit, measured at radius of 0, 40, 80

and 120 mm were 8 mis, 7 mls and 5 mls. Find the approximate values of volume flow

rate and mean velocity.

(d) In a fire fighting system as shown in Fig. 8, a pipeline with a pump leads to a

nozzle. Find the flow rate when pump (at K) develops a head of 75 m. The head losses

in the 250 mm dia pipe and 150 mm dia pipe are 7(V250i12g and 15(V150)2/2g

respectively. Sketch the energy line and hydraulic grade line.-------, J

Water

_. _. _. _. -' - Elev" = 45 m

Fig; 8 for Q 5(<1)

100 mm.::.:::.::::.:::.:::,:.::_. _. _. 'Elev. = 40 m

diajet

Elev. = 10 m

(10)

(12)

(18)

,iI. IiJ!i

J

(6% )

(10)

(a) Explain the phenomenon (i) Loss of head at submerged discharge, (ii) Jet reaction.

(b) Derive the energy equation for steady flow of a real fluid along a streamline.

(c) A large tank contains ideal fluid which flows out of the bottom through a 1.2 cm

diameter hole. The outflow rate is Q = 1.1 - 0.075 to.6, where Q is in m3/s and t is in

sec. Assume the liquid approached the hole radially. Find the local convective and total

accelerations at a point 0.75 m from the center of the hole at t = 8 sec and t = 12 sec. (12)

6.

Contd P/5

•

=5=

WRE201Contd ... Q. NO.6

(d) The pipe MNP is in a vertical plane as shown in Fig. 9. A liquid (S=0.9) flows up

the pipe MN (8 m long, 70 mm dia) and along NP (5 m long, 90 mm dia) at a rate of

3.5 Lis. If the measured pressure at M is 380 kPa and pipe friction head loss between

M and Pis 0.65 m, find the pressure at P. Neglect losses at bend. (18)

...........{i::.:::;.~~ .

........ N

Fig. 9 for Q 6{d)

P

. I

I

7. (a) Define Computational Fluid Dynamics (CFD). Derive the momentum principle for

a fluid flow.

(b) Write down the basic assumptions involved in the derivation Bernoulli's equation.

Derive the expression of viscosity measurement of a fluid using Saybolt viscometer.

(c) Find the water depth just upstream ofa 0.95 m high broad crested weir in a channel

3.5 m wide. The flow rate is 3.6 m3 Is.

(d) Water flows through a triple nozzle (6 inch and 4 inch dia) as shown in Fig. 10. The

velocity of 6 inch dia jet, 5 inch dia jet and 4 inch dia jet are 20 fps, 25 fps and 30 fps.

The axis of the pipe and the nozzles lie in a horizontal plane. Neglecting friction

losses, determine the magnitude and direction of resultant force the water exerts on the

nozzle.

...........6 inch dia jet.,.,'

.........:.....5 inch dia jet .

12 inchdia

...:~:~:.:~::~~:.::..4 inch. dia jet

Fig. 10 for Q7(d)

Contd P/6

(6%)

(51:"5)

(12)

(18)

•

=6=WRE201

8. (a) What is pitot tube? Explain the working principle of pitot-static tube.

(b) Derive the equations of measuring discharge in a channel using (i) suppressed

rectangular weir, (ii) broad-crested rectangular weir.

(c) Water flows through a 60 m long pipe at 600 Lis. At the entry point the pipe dia 40

cm and the pressure is 220 kPa. At the exit point (which is 10m higher than the entry

point) the pipe dia is 30 cm and the pressure is 160 kPa. Calculate the magnitude of

friction force on the pipe.

(d) The flow through an open channel of rectangular cross-section is given as shown in

Fig. 11 below. The width of the channel is 10m. The flow depths at upstream and

downstream of the gate are 7.6 m and 4.2 m respectively. Assume a frictional loss

between these two sections as 0.35 m and the value of energy correction factor and

. momentum correction factor are 1.1 and 1.05 respectively. Calculate the flow rate and

the horizontal force exerted by water on the gate.

gate

7.6m

4.2mII

I

1 .

I

(5+5)

(12)

(18)

Fig. 11 for Q 8(d)

I

[\' .

L-2/T -2/WRE Date: 22/02/2018

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA


Sub: CE 223 (Mechanics of Solids-II)

Full Marks: 210 Time: 3 Hours

The figures in the margin indicate full marks.

USE SEPARA TE SCRIPTS FOR EACH SECTION

SECTION-AThere are FOUR questions in this section. Answer any THREE.

1.

2.

(a) An element of a ductile material (Poisson's ratio = 0.30 and yield stress under uni-

axial tension, O"yp = 60 ksi) is subjected to the state of stress as shown in Figure 1.

Check whether yielding will occur or not on the basis of Saint Venant principal strain

theory.

(b) Determine the strain energy absorbed by a soJid shaft subjected to a end twisting

moment as shown in Figure 2(a). Suppose, a groove is cut from another solid shaft to a

distance of'L' and the remaining portion is kept solid as shown in Figure 2(b). If strain

energy in both cases remains same under the application of same end torque, then

determine the length 'L' of the hollow portion. Given, modulus of rigidity, G = 12000

ksi.

(c) A % inch thick bracket plate is fastened to a linch thick main plate as shown in

Figure 3. Determine the required, size of rivets. Rivet sizes available are from ~ inch

to 1t with t inch increments. Given, allowable shear stress in rivet = 18 ksi,

allowable bearing stress between rivet and plates = 32 ksi.

(a) A flexible cable whose ends are supported at different elevation (see Figure 4)

subjected to a uniformly distributed load of 0.21 0 kip per horizontal foot. Determine,

(i) horizontal component of cable tension (H), (ii) mid-span sag (t), (iii) equation of the

cable having origin at left support, (iv) maximum cable tension (Tmaximum), (V) cross-

sectional area of the cable (A), (vi) stretched length (S), elongation (b.S) and

unstretched length (So) of the cable.

Given, allowable tensile stress in cable (O"allowable) = 45 ksi and modulus of elasticity

(E) = 30000 ksi.

(b) A cantilever solid shaft is subjected to bending moment of 20 kip-inch (about X-

axis) and a twisting moment of 15 kip-inch (in XY plane) at free end as shown in

Figure 5. Determine the state of stress of an element 'A' near the free surface at top of

the shaft and hence determine diameter of shaft 'd' according to distortion energy

theory (Von-Mises yield criterion). Given, yield stress under uni-axial tension (O"yp) =

30 ksi.

Contd P/2

(5)

(5)

(25)

(25)

(10)

=2=

CE223/WRE

3.

4.

5.

(a) A cylindrical pressure vessel with internal diameter of 30 inch and wall thickness of

0.10 inch is subjected an internal pressure 'p' (psi) as shown in Figure 6. Determine the

value of safe internal pressure 'p' (psi) if maximum total strain energy theory (Beltromi

yield criterion) of failure is considered.

Given, yield stress under uni-axial tension (O'yp) = 45000 psi, Poisson's ratio = 0.30 and

modulus of elasticity = 30000 ksi.

(b) Determine the fillet weld size ('s') required to support the external loads acting at

free end of a bracket which is connected to steel column as shown in Figure 7. Use E80

electrode. Weld sizes are available with 1~ inch increments.

(a) Using direct integration method, determine the vertical reaction and moment at

support 'A' of the symmetric indeterminate beam as shown in Figure 8 and hence

compute vertical deflection at '0'. Given, bending stiffness (EI) = 45,000 kip-feet2•

(b) Using moment-area method, determine the vertical reaction at support 'A' of the

indeterminate beam as shown in Figure 9 and hence compute angular rotation at

support 'A'. Given, bending stiffness (EI) == 45,000 kip-feet2•

SECTION -B,


Assume reasonable values for missing data.

(a) Determine the critical load of a steel column of 20 ft height having a cross-section

WI0x45 (properties are attached in Annexure-I). The column is fixed supported at the

both ends and a lateral support is provided at mid-height to resist the buckling about

minor axis. E = 29x 106 psi.

(b) Using AISCIASD column formulas, select the lightest W section of a 15 ft long pin

ended column to carry a axial load of 150 kips. The structural steel is to be A36,

having O'yp = 36 ksi. American standard steel W shapes are attached in Annexure-l and

the formula are also given there.

(10)

(25)

(10)

(25)

(15)

(20)

6. (a) Draw state of stress of infinitesimal elements A, B and C of the beam shown in

Figure 10.

-1'~/6;----_.-_._---I6'L_--------~

~'1 ;f-----_=~--~~t~\l~-l~ /_..---_. 6.1 ~---*-. -. ~_._------------._-.-1

-.-----~.-. ~.---.-- ..__ .----~---.,~-.----------~-----.~~"~.-~--,--_._-».-i" H' tIA.VL.e. - to :

--~._-'--'--------,--_._-~---_._--;---_. "(\....:. "-. .."'- ..- .._-- . - J

Contd P13

(15)

=3=CE223/WREContd ... Q. NO.6

(b) For the state of stress as shown in Figure 11, determine (i) the principle stresses and

(ii) the maximum shear stress and the corresponding normal stress. Draw Mohr's circle

in plain graph paper and show the results on properly oriented elements7(20)

--5-10*---------'----11.

,__ ~N~" __ ••• ~ • __ ~,

,;---------.--.----- ...-. ---- ..-. \-tf--~*------------- ..---- ...;

7. (a) A riveted lap joint is shown in Figure 12, calculate the maximum safe load P that

can be applied in the connection. Given:

allowable shearing stress of rivet = 15 ksi

allowable bearing stress = 30 ksi

allowable tearing stress = 25 ksi

(17)

-_.---.-_. --- _ ..-----._eJ- - ---------'--.-------...---...-..----- _'P 0 0 I--, --'--, ---- -'--()~o-e--e--o€>-'---:----'_"--------' ~--I

--.------------ ...-------...--.-0-~.- ..-.---._-.f-----.--------- -- +G.!L----_I

, If . . ..........-_.- .. :

,------------------------. -'~3jzrcf-fl;fi.~V~---,-"--------~--'-----------" , _ .._--_.__ ._-_: --~-~~--.l

mm. ... \Ir ?(iti...----.;

--.,--------]. Ii .'.,' " _._', ~ .. " . ;.. ..., . ..... (: !.=.:i:__._p._~__._-'~.-..~:p3 ' - ~ >-- "'--, : ',- -I:07£-P!:J;e---,"--,,---,.-----------.------r:~-\ -....-c-~-------..-.- ...--.-_. ._ .. _:

'..----------. --------~__t1_~-~ /.~ •.:-.-.---- ,n--- I~ ---.' ...--.-.------ ...

(b) A frame for a punch press has the properties shown in Figure 13. What force P can

be applied to this frame controlled by the stresses in the section a-a, if the allowable

stresses are 6,000 psi in tension and 10,000 psi in compression. (18)

Contd P/4

CE223/WREContd ... Q. No. 7(b)

------..• ""', .•••••~~'n'.__ ~.- ,

=4=

. 1" 11"2"~ ~6jl1t .4T[k' " *=b7~./1. . '. ~ ......3....••...'1 i-

/J TT•1" t.1"

4

5e{;tion a-a

8. (a) Calculate the deflection and rotation of point B and the free end D of the beam

shown in Figure 14. (18)

(b) A horizontal load of 10 kips is applied at the top of a column. The cross-section ofthe column is rectangular and the force is applied along the diagonal of the section asshown in Figure 15. Determine the stresses at four corners of the column section at

cross-section 36 inch from the top. Also locate the neutral axis of the cross-section. (17)

~,'-"-.-- ------T-- ---------.-.~

..._-.--- ------1--.---.-- .-------., I. 77----- ----- - -..----..-- ..~---.-~

I-.~-'-----'-l-' --.- -.-.----.--:

--_ ..._-------1-.. ----------.-----,, ,/'-- .

_._---- ..._._-/.-:.-:....._. ",---"._._---_._._. ..,/', I/ ~. ,~-=-~--~~=--==---,

,..----..__. ~--. -_. ---_.- .....---_._._,---1

140 ksi

16kSi~ .---:-------,

20bi4 rZObi

L----'-~---l:r 16ksi

40 ksi . Figure I

m~ T = 200 kip-inchT ~

4 inch solid shaft

1 Figure 2(a)~,

100 inch

T= 200.kip'-inchT4 inch

1i

II

Figure 2(b) 'I

40 inch 'L' inchsolid portion hollow portion I

_--':"'~=~~-----------------------~T--j

:::::~---rrl"<l).•...CI:l

611....;0..0.....CI:lS 511

611

.~ .

..dD ...~ .

...~ ...

..~ ...

I

I

I••••.. '1" .•••••••••••

15 kips

bracket=5/SI1

+ 4.5011 + Figure 3

"Cable chordt.., .................................

r20 feet

115 feet

............

. 20 feet 60 feet

~ Figure 4

•

d

wall thickness,t = 1/10 inch

--='-

A

x

30 inch'-----t

y

Figure 6

z

Figure 5

I.column

fillet weld.8,000 lb.

Figure 7

4,000 lb.

.~-

cFigure 8

4 feet 4 feet

B

Figure 9

Aiulexure-I

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11'.16 x 100)( SOx 36)( 26

11'14 x' 730x' 455x 311X 193~ 159

_ ",)< .90

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11'14 X 36x Hx 30'

Wl2 x 87)( 65X 5)X 40

WI2 x IIX 30X 26

11'10)( 112x'IOO" 68" 77')( 60X 49

,11'10 X 45x 39x )J.

WIO X 30X 22

II' 8 x' 67x ,18

,x 48',x 40

X )5x )1

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ItI

!I.~

fl. kL 'or ---- r -. < '-""c' 0 a 110 kI.r

(kL)2 . 21] ---... /2C d\. r C yp

__ R ~. .=_:__

1".5.

Where, F.S. ~. _.3(kf, I r) (Ie! / r l-j' _ ..._--- -- --,,----

3 8Cc 8C}

L-2/T-2/WRE Date: 27/0212018



Sub: WRE 205 (Numerical Methods)Full Marks: 140 Time: 3 Hours



SECTION-A


1. (a) What do you mean by finite difference method? What is the difference between

explicit and implicit finite difference schemes?

(b) A function is given by f(x) = 1+ 2x + 3x2 + 4x3 . (i) Using the values of the

function and its derivatives at x = 1, determine the values of the function at x = 1.01,

1.10 and 1.50 with the help of Taylor series expansion and compare these values with

the actual values of the function. (ii) Taking 6x = 0.01, 0.10 and 0.50, determine the %

of error of forward, backward and central differences of the first order derivative and

of the second order derivative with respect to the point where x = 1. (iii) State the

effect of 6x on the % of error.

(10)

(13}j)

2.

3.

(a) Derive the Lagrange's interpolation formula for unequal intervals.

(b) Using the following table, find fix) as a polynomial in terms of x by using the

Newton's divided difference interpolation polynomial.

x -1 a 3 6 7

f(x) 3 -6 39 822 1611

(a) Fit the power equation y = axb to the following data by the least squares technique:

I ~ I J.~413.:0 15.~O17.~1 I

(b) Using the multiple linear regression of the form Z = a + bx + cy to fit the following

data:

x 1 2 3 4 5

y 5 4 3 2 1

Z 14 9 4 -1 -6

(10)

(13}j)

(10)

(13}j)

4. (a) What is numerical differentiation and integration? Why and when do we use

numerical differentiation and integration?

Contd P/2

(3}j)

t,

"

=2=WRE205/WREContd ... Q. No.4

(b) The table below gives the values of distances traveled by a car at various time

intervals during the initial running. (10)

Time, t(s) 5 6 7 8 9

Distance, s (kIn) 10.0 14.5 .19.5 25.5 32.0

Estimate the velocity of the car at time, t = 5, 7 and 9 s. Also, calculate the acceleration

at t = 7 s.

(c) The table below shows the temperature f(t) as a function oftime:

Time, t 1 2 3 4 5 6 7

Temperature, f(t) 81 75 80 83 78 70 60

7Use Simpson's 1/3 rule to estimate ff(t)dt and use the result to estimate the average

1term.

SECTION-BThere are FOUR questions in this section. Answer any THREE.

Assume any reasonable value where necessary.

(10)

5. (a) Define: (i) Rounding of numbers (ii) Numerical stability (iii) Rate of convergence. (3x2=6)(b) Develop the recurrence formula for cube root of a number "a" using Newton-

Raphson method. Then find the value of 'JJ2.94 , correct to three decimal places. (7 X)(c) Find a positive root of the equation x - cos(x )-1= 0; by Regular Falsi method.

Start with the values xl = 1,x2 = 2. (Do only five iterations.)

6. (a) What are the different methods for finding roots of a non-linear equation of the

form f(x)=O?

(b) During an experiment in a flume at Hydraulics and River Engineering Laboratory

of BUET, discharge over a right angled notch (V-notch) was found 0.01462 m3/s.

Discharge formula over the v-notch is given by,

Q = ~*Cd *-J2i *tan~* H2.5. 15 2

1------,,---:-----:- _) 2Htan!' I ;.:tk 2 .

,IrI

H

Contd P13

(10)

(3}j) .

(10)

•,

=3=

WRE205/WREContd ... Q. No. 6(b)

Determine the water depth (H) over the v-notch, corrected to 2nd decimal places

assuming Cd=0.6. Use Newton-Raphson method.

(c) Solve the following system of equations by Gauss Elimination method.

-3xl +x2 + I2x3 = 50

6xl - x2 - x3 = 36xl +9x2 +x3 =40

7. (a) Determine the accuracy of the result obtained by taking the first 3 terms of the

logarithmic series, loge (1+ x) at x = 0.01.

(b) Solve the following system of equations by the method of Triangularization.

2xl +x2 +x3 = 53xl + 5x2 + 2x3 = 152xl +x2 +4x3 =8

(c) The following system of equations is designed to determine discharge in a series of

coupled flume.

2ql + 3q2 + q3 = 9ql +2q2 +3q3 = 63ql +q2 + 2q3 = 8

Now, using Cramer's rule determine the flow rate in each flume i.e. the values of ql, q2

and q3.

(10)

(4X)

(12)

(7)

8. (a) What do you mean by (i) initial value problems and (ii) boundary value problems?

(b) Given the ~quation : = x2 + y2 with y(O)=I, estimate y(0.5) using the fourth

. order Runge- Kutta method.

(c) Determine the roots of the simultaneous nonlinear equations with the Newton-

Raphson method.

j(x,y)=x2 - y+I = 0g(x,y)= 2cosx- y = 0

In your solution pick the initial values as x=I.O and y=0.5. Do at least two iterations.

(4)

(10)

L-2/T-2/WRE Date: 05/03/2018BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY, DHAKA


Sub: MATH 235 (Vector Analysis and Statistics)



Symbols used have their usual meaning.

USE SEPARATE SCRIPTS FOR EACH SECTION-------_.-._ .._--_ ..--------~-----_ ..__._------_.

SECTION -A


1. (a) If the vector set {VI, V2, V3} is independent, then determine whether the set

{VI + V2 - 3V3, VI + 3V2- V3, V2 + V3} is independent or not.

(b) The accompanying figure shows a force F of 10 lb applied in the positive y-

direction to the point Q( 1,1,1) of a cube whose sides have a length of 1 ft. In each part,

find the scalar moment of F about the point P and describe the direction of rotation, if

any, if the cube is free to rotate about P. (i) P is the point (1,0,0), (ii) P is the point

(1,0,1).--~- ...

,..x----- --"

(12)

(12)

(c) Find the area of the triangle that is determined by the points P1(2,2,0), P2(-1,0,2)

and P3(0,4,3). (11)

2. (a) In what direction has cp = 3xy2 + 12yz - 4X3Z2 the maximum derivative at the point

(1,2,-1)? Find also the value of this maximum derivative.

(b) Prove that curl (cpF) =cp curl F + Vcp x F, where F= F (x,y,z), cp = cp(x,y,z).

(c) Suppose that a particle moves through 3-space so that it's position vector at time tis

r(t) = t1+ t21 + t3k(i) Find the vector tangential and normal components of acceleration at time

t = 1.

(ii) Find the curvature of the path at the point where the particle is located at

time t = 1.

Contd P/2

(13)

(10)

(5+7)

=2=

MATH 235/WRE

3. (a) Evaluate fx2zdx- yx2dy +3dz along the curve C shown in the figure.C

(12)

(b) Evaluate 1(ex + y2 }tx + (eY + x2 ~y , where C IS the boundary of the regionC

betweeny = x2 andy = x. (12)(c) Find the volume of the parallelepiped that has u, v and w as adjacent edges.

u = 31+ J + 2k, v = 41 + 5J + k, W = 1+ 2J + 4k . (11)

4. (a) Use Divergence theorem to find the outward flux of the vector field

F(x, y, z) = x31 + y3J + z3k across the surface of the region that is enclosed by the

hemisphere z = ) a2 - x2 - y2 and the plane z =O.

(b) Use Stoke's theorem to evaluate 1F .dr where F(x,y,z)= (x- y)1 + (y-z)J +C

(z - x)k , C is the circle x2 +y2 = a2 in the xy-plane with counterclockwise

orientation looking down the positive z-axis.

SECTION-BThere are FOUR questions in this section. Answer any THREE.

5. (a) The median and mode of the following wage distribution are Tk. 33.5 and Tk. 34

respectively. However three frequencies are missing. Determine their values:

Wages 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Total

Frequencies 4 16 ? ? ? 6 4 230

(b) In a survey, data on daily wages paid to workers of two factories A and B are as

follows:

Daily 20-30 30-40 40-50 50-60 60-70 70-80 80-90WagesFactory A 15 30 44 60 30 14 7

Factory B 25 40 60 35 20 15 5

Find out:

(i) Which factory pays higher average wages?

(ii) Which factory has greater variability about paying wages?

Contd P/3

(15)

(20)

(17)

(18)

=3=MATH 235/WRE

6. (a) To study the tensile strength of a certain type of wire, the following pairs of

observations were recorded, where X is the diameter in cm and Y is the mass supported

inkg/cm.

X 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Y 14 26 50 56 42 98 82 88 134 124

(i) Fit a linear regression model Y on X.

(ii) Is the linear model appropriate for given data? Justify your result.

(b) A survey was conducted by a manufacturing company to enquire the maximum

price at which persons would be willing to buy their product. The following table gives

the stated price (in Taka) by persons:

Price (in Tk.) 89-90 90-100 100-110 110-120 120-130

No. of persons 11 29 18 27 15

Measure kurtosis and skewness and interpret.

(18)

(17)

7. (a) The proportion of the budget for a certain type of industrial company that is allotted

to environmental and pollution control is coming under scrutiny. A data collection

project determines that the distribution of these proportions is given by (12)

f(x) = {5(1- x )4, 0 ::;x ::;10, elsewhere

(i) Verify that the above is a valid density function.

(ii) What is the probability that a company chosen at random expends less than

10% of its budget on environmental and pollution controls?

(iii) What is the mean proportion of the budget allocated to environmental and

pollution control?

(iv) What is the probability that a company selected at random will have

allocated to environmental and pollution control a proportion that exceeds

the population mean given in (iii)?

(b) If X is a binomial random variable with probability distribution b(x; n, p). When

n ~ 00, p ~ 0, and np ~ I-t remains constant then prove that b(x; n, p) ~ p(x, I-t). (17)(c) An electronic switching device occasionally malfunctions, but the device is

considered satisfactory if it makes, on average, no more than 0.20 errors per hour. A

particular 5-hour period is chosen for testing the device. If no more than 1 error occurs

during the time period, the device will be considered satisfactory. (6)(i) What is the probability that a satisfactory device will be considered

unsatisfactory on the basis of the test? Assume a Poisson process.

(ii) What is the probability that a device will be accepted as satisfactory when,

in fact, the mean number of errors is 0.25? Again, assume a Poisson

process.Contd P/4

(10)

•

=4=

MATH 235/WRE

8. (a) A soft-drink machine is regulated so that it discharges an average of 200 milliliters

per cup. If the amount of drink is normally distributed with a standard deviation equal

to 15 milliliters, (15)

(i) What fraction of the cups will contain more than 224 milliliters?

(ii) What is the probability that a cup contains between 191 and 209 milliliters?

(iii) How many cups will probably overflow if 230 milliliter cups are used for

the next 1000 drinks? (Necessary table attached)

(b) The Edison Electric Institute has published figures on the annual number of

kilowatt-hours expended by various home appliances. It is claimed that a vacuum

cleaner expends an average of 46 kilowatt-hours per year. If a random sample of 12

homes included in a planned study indicates that vacuum cleaners expend an average

of 42 kilowatt-hours per year with a standard deviation of 11.9 kilowatt-hours, does

this suggest at the 0.05 level of significance that vacuum cleaners expend, on the

average, less than 46 kilowatt-hours annually? (Given that v = 11, to.05 = 1.796). (10)

(c) A commonly prescribed drug for relieving nervous tension is believed to be only

60% effective. Experimental results with a new drug administered to a random sample

of 100 adults who were suffering from nervous tension show that 70 received relief. Is

this sufficient evidence to conclude that the new drug is superior to the one commonly

prescribed? Use a 0.01 level of significance. (Given that z = 2.33)

••

Appendix LAreas

Under theStandard

Normal Curvefrom 0 to z

z 0 ] 2 3 4 5 6 7 -8 9, '

0.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 ;0279 .0319 ' .0359

0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 ol)7l4 .0754

0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141

0.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517

0.4 .1554 .1591 .1628 .1664 .1700 .1736 .1772 .1808 .1844 .1879

0.5 .1915 .1950 .1985 .2(1l9 .2054 .2088 .2123 .2157 .2190 .2224

0.6 .2258 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2518 .2549

0.7 .2580 .2612 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852

0.8 .2881 .2910 .2939 .2967 .2996 .3023 .3051 .3078 .3106 .3133

0.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389

1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621

l.l .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830

1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015

1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177

1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319

1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441

1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545

1.7 .4554 . .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633

1.8 .4641" .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706

1.9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767

2.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .481.7

2.1 .4821 .4826 . .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857

2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890

23 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .4916

2.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .4936

2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952

2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964

2.7 .4965 .4966 . .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974

2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981

2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 4986

3.0 .4987 .4987 .4987 .4988 .4988 .4989 .4989 . .4989 .4990 .4990

3.1 .4990 .4991 .4991 .4991 .4992 .4992 .4992 .4992 .4993 .4993

3.2 .4993 .4993 .4994 .4994 .4994 .4994 .4994 .4995 .4995 .4995

3.3 .4995 .4995 .4995 .4996 .4996 .4996 .4996 .4996 .4996 .4997

3.4 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4997 .4998,

3.5 .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998 .4998

3.6 .4998 .4998 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999

3.7 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999

3.8 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999 .4999

3.9 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000_d_:"' _ ..

~.

L-21T-2/WRE Date: 11/03/2018



Sub: HUM 313 (Principles of Accounting)

Full Marks: lAO Time : 3 Hours



SECTION -AThere are FOUR questions in this section. Answer any THREE.

1. (a) What is the difference between expense and loss? Differentiate with example. (3lj)(b) Mr. Tomson has started his compute~ service business on April 1st of 2017. The

following transactions occurred during the month. (20)April- 1: Invested cash in the business Tk. 30,000.April- 2: Purchased computer terminals for Tk. 20,000 on account.April - 3: Purchased supplies for Tk. 1500 cash.April- 6: Performed computer services Tk. 8000 cash.April- 8: Paid dues for purchase on account in April 2.April- 19: Provide services on credit to a customer Tk. 5000April- 25: Paid expenses for the month Tk. 2000. It is for utility bill.April- 30: Received dues from customer Tk. 5000 billed in April 19.Required: (i) Show the effects of transaction or prepare the tabular summary onaccounting equation.

(ii) From the summary prepare an Income Statement for April 30, 2017.

2. (a) What is accrual basis and cash basis of accounting? Explain with examples.

(b) Mrs. Riana opened a consultancy firm on May 1, 2017. Following transactions

~appened for the month of May. (18)May- 1: Initially invested Tk. 200,000 cash in the business.May - 3: Purchased decorated office room for Tk. 150,000 cash.May - 5: Paid advertisement expense ofTk. 7000.May - 10: Received Tk. 30,000 as consultancy fees.May - 18: Billed a client for services performed on account Tk. 8500.May - 25: Withdraw Tk. 5000 for personal use.May - 28: received dues on services provided on credit.May - 29: Purchase supplies for office Tk. 2000 in cashMay - 30: Paid salary to the office staffTk. 10,000.Required: Journalize the transactions in a good form, for the month May, 2017.

3. (a) Following transactions are other information of adjustments. Prepare appropriate

adjusting journal entries from the information below:(i) Services provided but not yet recorded and received in cash Tk. 2000.(ii) Depreciation expense @ Tk. 500 per month.(iii) Expense of rent expired Tk. 10,000 per month (Prepaid rent Tk. 30,000).(iv) Utility expense is accrued Tk. 1000.(v) Unearned revenue is earned Tk. 2000 (Unearned revenue Account Tk. 3000).(vi) Accrued revenue Tk. 1000.

Contd P/2

(12)

=2=HUM 313Contd ... Q. No. 3(a)

(b) Selected comparative data for Qubic Products Company are presented below:

2016 (Tk.) 2017(Tk.)Net Sales (all in credit) 720,000 750,000Cost of Goods Sold 440,000 480,000Interest Expense 5000 7000Net Income 42,000 45,000Accounts receivable 100,000 120,000Inventory 75,000 85,000Total Assets 500,000 580,000Total Stockholders' Equity 325,000 430,000

Required: Compute the following ratios for 2017.(i) Profit Margin.(ii) Asset Turnover.(iii) Return on Assets.(iv) Return on Shareholder's Equity.(v) Inventory turnover.(vi) Accounts Receivable turnover.

4. Following is the trial balance of Rexon Company.

Rexon CompanyTrial Balance

December 31, 2017Account Title Debit (Tk.) Credit (Tk.)Cash 5300 -Accounts Receivable 10,800 -Supplies 1500 -Prepaid Insurance 2000 -Equipment 27,000 -Accumulated Depreciation - 5600Notes Payable - 15,000Accounts Payable - 6100Salaries payable - 2400Intetest payable - 600Owner's Capital - 13,000Owner's Drawings 7000Service Revenue - 61,000Advertising Expense 8400 -Supplies Expense 4000 -Depreciation Expense 5600 -Insurance Expense 3500 -Salaries expense 28000 -Interest expense 600

103700 103700

Tk. 1000 of prepaid insurance expired during the year.

Required:

(i) Prepare an Income Statement and owner's equity statement.

(ii) Prepare a Balance Sheet.

Contd P/3

(23X)

.,

=3=HUM 313

SECTION-B

There are FOUR questions in this section. Answer any THREE questions.

5. (a) Write down the classification of fixed cost.

(b) What is "Relevant range" and "Non manufacturing cost"? Explain with example.

(c) The following information has been taken from the accounting records of Edward

Corporation for the last year, 2017 -

Im'entories January 1,2017 31st December, 2017Direct materials Tk.15,000 Tk.l0,000

Work in process 12,000 8,000

Finished goods 11,000 9,000

Particulars Amount (Tk.)Material purchased 650,000Direct labor 100,000Indirect labor 13,000Marketing expenses 8,000Sales mans salary 20,000Miscellaneous factory expense 6,000Fuel for the factory equipment 2,000Factory insurance 8,000Depreciation, factory plant 40,000Depreciation, office equipment 12,000Power and electricity, factory 10,000Sales 1500,000Advertisement 17,000Office Salaries 25,000Office Rent 20,000Utility (20% factory, 80% office) 15,000

Required:(i) Prepare a cost of goods sold statement.(ii) Prepare an income statement.

(4/j)(4)

(15)

6. (a) What is meant by products contribution margin ratio? How is this ratio useful in

planning business operation? (S/j)(b) Samsung company manufactures and sales a specialized cordless telephone for themost electromagnetic radiation environments. The company's contribution format

income statement for recent year is given below: (18)

Total (Tk.) Per unit (Tk.) Percentage (%)Sales 10,00,000 50 100Less: variable expenses 800,000 40 ?Contribution margin 200,000 lQ ?Less: fixed cost 150,000Net profit 50,000

Contd P/4

.~

=4=

HUM3!3Contd ... Q. No. 6(b)

Management is anxious to increase company's profit and has asked for an analysis of anumber of items.Required:

(i) Compute the company's CM ratio and variable expense ratio.(ii) Compute the company's break-even-points in units and Tk.(iii) Assume that in next year company wants to sell 70,000 units; if selling priceincreased by Tk. 2 per unit and if fixed expenses increased by Tk. 20,000 then

calculate the profit or loss.(iv) Refer the original data. Assume that next year management wants the

company to earn a profit of at least Tk. 100,000. How many units will have to be

sold to meet this target profit?(v) If selling price decreased by Tk. 2 per unit and variable expense increased byTk. 1 per unit what will be the new breakeven point in units and amounts? (Other

information remaining same as original data)(vi) Calculate margin of safety and operating leverage. (Based on original data).

7. (a) In wh~t situation, absorption costing will result higher net income than variable

costing? Why?

(b) For the income year ended on December 31, 2017 ; you have been given the

information below-

Selling price per unit Tk. 50

Manufacturing cost (Tk.):

Direct material cost per unit 8

Direct labor cost per unit 7

Variable manufacturing cost per unit 5

Fixed manufacturing cost for the period Tk.l00,000

Selling and administrative cost (Tk.)Variable cost per unit 2

Fixed cost for the period Tk.80,000

During the year, a total 10,000 units produced but only 8,500 units sold.

Required:(i) Calculate the product cost per unit under absorption costing system andvariable costing system.(ii) Prepare income statement using under absorption costing system and variablecosting system.(iii) Reconcile the amount of profits under two costing systems.

(5 ~)

(18)

8. (a) What is the major disadvantage of high and 1'owpoint method?

Contd PIS

(4 ~)

=5=

HUM3!3eonid ... Q. No. 8(b)

(b) The following data were available for PXL Company- (9)

Month Unit Processed Total cost (Tk.)January 8,000 15,000February 4,500 6,500March 7,000 7,900April 9,000 16,000May 3,750 5,400June 6,000 7,200July 6,200 7,500

Required:(i) Using high low method find out variable and fixed cost for the company.(ii) Express the fixed and variable components of cost as a cost formula in the

form Y = a + bX.(iii) What will be the total cost, if the company will produce 20,000 units?

(c) Lenovo Computer has two supports departments and two operating departments.

Following information were given below- (10)

Support Dept. Operating Dept. TotalBudgeted Work

Personnel Laptopoverhead Legal Dept. station

Dept. divisionbefore Division

Allocation1100,000

(Tk.) 5000,00 100,000 300,000 200,000

By legaldepartments

1200 3200 4000 8400-Budgeted laborhours

By PersonneldepartmentsBudgeted 400 - 1200 300 1900personnelhours

Required:Allocate two supports departments cost to the two operating departments by using-

(i) Direct method.(ii) Step-down method.

"

L-2/T-2/WRE Date: 11/03/2018


L-2/T-2 B. Sc, Engineering Examinations 2016-2017

Sub: HUM 211 (Sociology)




SECTION -A


1. (a) Define urban sociology, How can sociology help us to understand environmental.

issues?

(b) Discuss why technology cam10t solve all the problems of diminishing resources and

environmental pollution.

(c) Briefly describe how the socio-economic development depends on physical

environment.

(7 X)

(8)

(8)

2.

3.

4.

(a) Critically discuss how the technological developments have changed our social and

economic life.

(b) What are the socio-cultural factors that influence population growth? Describe in

detail.

(c) What do you .know about optimum population theory? Add a brief criticism to your

answer.

(a) 'A large population means a low standard of living.' Do you agree? What is the

relation between standard of living and population?

(b) What do you mean by social change? Discuss the characteristics of social change.

(c) Write down different sources of social change in the context of Bangladesh.

(a) Define Human migration. Explain push-pull theory as a factor of migration.

(b) Briefly discuss what are the main forces of human migration.

Contd P/2

(8)

(8)

(7 X)(8)

(8)

(10)

(13 X)

••

=2=HUM 211

SECTION -B


5.

6.

7.

8.

(a) How did industrial revolution fabricate changes in culture and society?

(b) Explain how globalization is affecting our culture.

(a) What is human migration? Explain the forces of human migration.

(b) Show the key differences between 'urban ecology' and 'new urban sociology',

(a) Discus show modern technology is inducing social change.

(b) Critically discuss the transition theory of population.

Write short notes on any THREE of the following:

(a) Megalopoliser

(b) Water pollution

(c) Natural disaster

(d) Capitalism

(13 X)(10)

(13 X)(10)

(13 X). (10)

(23X)

l-2/t-2/wre date: 17/02/2018

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