Maharashtra State Board of Technical Education 2008-2nd Sem Diploma in Hospital Management Engineering Mathematics- All Branches - Question Paper

Sample Question Paper - I

Course Code : All Branches of Diploma in Engineering and Technology OMMA Course Code : AE/ME/PG/PT/FE/CE/CV/CS/CR/CH/CO/CM/CD/IF/EV/ET ⁹⁰⁰⁶ EN/DE/EJ/EX/EI/IE/IU/IS/IC/MU Semester : Second Subject : Engineering Mathematics

Max Marks : 80    Duration: 3 Hours

Instructions:

   All Questions are compulsory.

   Figures to the right indicate full marks.

   Assume suitable additional data if necessary.

   Non Programmable pocket calculator is allowed.

Q1. Attempt any Eight

a)    If f(x)=3x²-5x+7 Show that f(-1)=3f(1)

b)    Test the function for odd or even if

F(x)=3x⁴-2x²+cosx

3x

c)    Evaluate

dy

d)    Find if y= sin(logx)

dx

dy

e)    Find ^dx if y= (a^x+e^x)

f)    Find if y=e^xtanx

dx

. , dy tan^-1( x)

g)    Find if y= -

dx 1 + x

h)    Find the mean of the following data

x	4	7	10	13	16	19
f	7	10	15	20	25	30

i) The daily earning (in Rs) of 12 workers in a Workshop are 16,19,12,14,13,17,16,19,20,15,16,13 Find Mode and Median

o    O    A

j) If P( A) = 5 P(B') = 4 and P( %) = 5 Find P (A n B) and P (B/A)

Q2. Attempt any Three    12 Marks

a) If f(x)= Show that f[f[f(x)]] = x

1 - x

Q3. Attempt any three

a) If y=a cos(logx) + bsin(logx) then Prove that

₂ d 2 v dy _ x²f+x +y=0

dx ² dx

b) Evaluate

x a x - a c) Calculate the Mean Deviation (M.D) about mean for the following data

Weight in (gm) 10-15 15-20 20-25 25-30 30-35 35-40 40-45 No. of items 7 12 16 25 19 15 06

d) A room has 3 electric lamps. From a collection of 15 electric bulbs of which only 10 are good,3 are selected at random and put in the lamps. Find the probability that the room is lighted by at least one of the bulbs.

Q4. Attempt any three

a)    If x=a(cos 0 + 0 sin 0), y=a(sin 0 - 0 cos 0)

Find -IV

dx

b)    Find if y=Cos^-1(2x²-1)

dx

c)    Find if x⁴+y⁴=4xy

dx

d) If x^y=e ^y Show that

dx (1 + log x)²

Q5. Attempt any three a) Find Median of the Following distribution 12 Marks

x 31-35 36-40 41-45 46-50 51-55 56-60 61-65 f 10 25 30 40 28 16 07

b) Find Mode graphically and Analytically for the following data

Expenditure in (Rs) 0-10 10-20 20-30 30-40 40-50 Frequency 14 23 27 21 15

Calculate the mean anc		Standard Deviation (S.D) of t			ie following data
Class Marks	7	8	9	10	11	12	13
Frequency	4	6	9	12	9	6	4

d) A card is drawn at random from a pack of 52 cards. Find the probability that the card is an ace or a spade

Note : Q6. For Civil Electrical, Electronics, Mechanical groups

Q6. Attempt any Four    16 Marks

a)    If the distance traveled by the particle is given by s=2t³-9t¹+12t.Calculate the acceleration when it stops.

b)    Find maximum and minimum value of

3 2

x +6x -15x+5

c)    A telegraphic wire hangs in the form of a curve y=alogsec(x/a) where a is constant.

1 x

Show that the curvature at any point is cos()

a a

2 + 3i

d)    Express -in the form A+iB Find its modulus and amplitude

1 - i

e)    By using De-Moivres theorem Simplify

(Cos2d + i sin 29)(Cosd - i sin d)^A (Cos3d + iSin3d)(Cos5d - i sin 5B)³

f)    If cos(x-iy)=A+iB then prove that

A²

Note : Q6. For Computer/Information Technology Group

Q6. Attempt any four

a)    Using Bisection method find approximate root of x²-12=0[carry out three iterations only]

b)    Using Regula Falsi method solve x -9x+1=0 [carry out three iterations only]

c) Using Newton-Raphson method solve x -5x+3=0 [Carry out three iterations only]

d) Using Gauss Elimination method solve 2x+3y+2z=2 10x+3y+4z=16 3x+6y+z=-6

e)    Using Jacobis Method solve 10x+2y+z=9 2x+20y-2z=-44

-2x+3y+10z=22 [carry out two iterations only]

f)    Using Gauss -Seidal Method solve 25x+6y-z=82 6x+15y+5z=75

x+y+40z=66 [carry out two iterations only]

1

2 cos x sin x

Attachment: maharashtra-state-board-of-technical-education-2008-diploma-in-hospital-management-31168-1.pdf

Earning:   Approval pending.