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
16 Marks
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
lim
x
1+1
x
c) Evaluate
dy
d) Find if y= sin(logx)
dx
dy
e) Find dx if y= (ax+ex)
f) Find if y=extanx
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
lim
x 0 lim x 0 lim x
b) Evaluate
c) Evaluate
d) Evaluate
x sin x
1 - cos x
sin (x)
V
x + x - 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
lim
sin x - sin a
x a x - a c) Calculate the Mean Deviation (M.D) about mean for the following data | ||||||||||||||||
|
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
12 Marks
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 xy=e y Show that
dy
log x
dx (1 + log x)2
Q5. Attempt any three a) Find Median of the Following distribution 12 Marks | ||||||||||||||||
|
b) Find Mode graphically and Analytically for the following data | ||||||||||||
|
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
1]
=1
cosh (y) sinh (y)
B2
+
A2
B2
2]
Note : Q6. For Computer/Information Technology Group
Q6. Attempt any four
16 Marks
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]
2 cos x sin x
Attachment: |
Earning: Approval pending. |