Maharashtra State Board of Technical Education 2008 Diploma Mechanical Engineering Applied Mathematics Mechanical Group - Question Paper
Sample Question Paper - I
9018Mechanical Engineering Group
Course Name Course code Semester Subject Duration
CE/CS/CR/CV/ME/FE/CH
Third
Applied Mathematics
3 hours Marks: 80
Instructions: 1) All the questions are compulsory
2) Figures to the right indicate full marks
3) Assume suitable additional data if necessary Q. 1 Attempt any eight of the following (16)
(x +1)( x + 2)
3) JV1 + cos 2x dx
4) J x2 exdx
dx
(x +1)( x + 2)
dy dx2
6) Verify that y= e x is a solution of - y = 0
7) Solve the following differential equation xdy-ydx=0
8) A body released from a height of 490m find the time by the body to reach the ground (g=9.8m/s2)
9) A cubic die is thrown 4 times. What is the probability of obtaining at least one six.
10) On a final examination in maths the mean was 72 and the standard deviation was 15. Determine the standard scores of students receiving grades a) 60 b) 93
Q. 2 Attempt any three (12)
dx
x log x log(log x) dx
b) J
5 - 4cos x
5 V9 - x
f V9 - x
I .--. dx
c) 0 v 9 - x + %/x + 4 n / 2
a) |log(sin x)dx
0
b) find the volume of sphere of radius r
c) find the MI of a uniform rod of length 2l about an axis through the mid pt perpendicular to it
d) Find C.G of the area in the first quadrant bounded by the parabola y2=4ax and the ordinate x=h
2 2 2 2
a) solve the differential equation (3x +6xy )dx+(6x y+4y )dy=0
b) Solve the differential equation
(1 + x2) + y = e tan"x dx
dy
c) Solve the diferential equation (x + y +1) = 1
dx
a) Solve by Gauss-elimination method 2x+y+z=10, 3x+2y+3z=18, x+4y+9z=16
b) Solve by jacobis method
5x-y+z=10 2x+4y=12 x+y+5z = - 1
c) Solve the following equation by Gauss-seidal method
10x+y+z=12
x+10y+z=12
x+y+10z=12
d2 y
a) The SHM is executed by the particle according to the law 2 = 3x if y=3/4
dx
when x=0 and y= 2 when x=1 find y
b) The velocity of a particle at time t seconds from the commecement of motion is given by v=5t-t2+4 How much distance does it cover in 3 seconds if it was intially at rest.
c) find roots of x2-logx-12 over (3,4)
d) Evaluate V7 using Newton-Raphson method
3
a) Find the approximate root of x -9x+1=0 in (2.5,3)
b) Using Poissons distribution find the probability that the ace of spades will be drawn from a pack of well shuffled cards at least once in 104 consecutive trials
c) The mean intelligence level of a group of children is go with a standard deviation of 20. Assuming that intelligence level is normally distributed.
Find the percentage of children with intelligence level over 100
d) If 20% of the bolts produce by a machine are defective, determine the probability that out of 4 bolts drawn a) one is defective b) at the most two are defective.
d) find area enclosed by the curve y=4-x and the lines x=0,x=2,y=0
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| Earning: Approval pending. |
