7/31/2019 Winter 1010 Maths III
1/1
Q.1.Solve any TEN of the Following (20)
a) Evaluate 1
3x24dx
b) Evaluate
sin2x
2dx
c) Evaluate 1
x23x2dx
d) Evaluate 1
2
dx3x2
e) Evaluate 0
/2
esinx
cosx dx
f) Verify that y=cosx is a solution of
d2y
dx2y=0
g) Show that 3x2y dxxdy=0 ,is an exact D.E.h) From a pack of 52
card, one is drawn at random.Find a
probability of getting a king.
i) An urn contains 10 black and 10 white ball. Find
theprobability of drawing two balls of the same colour.
j) Find the probability of getting 9 with two dice.
k) If the probability of a defective bolt is 0.1,find a)
Mean
b)Std.dev. for the distribution bolts in a total of 400.
l) Find the area between the lines y=2x ,x axis and
ordinates at x=1 and x=3.
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Q.2. Solve any four of the following: (16)
a) Evaluate 1tanx
1tanxdx
b) Evaluate dx54cosx
c)Evaluate 0
59x
9xx4dx
d) Evaluate 0
/4
log 1tanx dx
e)Find area bounded by the y=4x2 & the x axis.
f) If the slope curve passing through the point (2,3) is
x+3 find the equation of the curve.
Subject: Maths III {Mech/Auto/Civil}
Exam:Model question paper
Q.3. Solve any four of the following: (16)
a) Evaluate : 0
xsinx
1cos2x dx
b) Find the volume of right circular cone generated by
revolving the line y=3
4x about x axis between the
ordinate x=0 to x=4.c)The particle starts from rest. Its
acceleration at any
time 't' is (t+3) m/sec2 . Find the distance traveled in
4 sec.
d) Evaluate . xsin1x
1x2dx
e) Find the area bounded by the curve y2=4x and
x2=4y .
f)Find the center of gravity of the area under the
parabola y=4ax2 from x=0 to
x=C.===========================================
Prepared By :
Shaikh sir's RELIANCE ACADEMY
Q.4. Solve any four of the following: (16)
a) Solvedy
dx=sinxy
b) solve
ex2xy
2y
3dxa
y2x
2y3xy
2dy=0
c) Solve x1dy
dxy=ex x12.
d) Solve by Gauss elimination Method,
2x+y+z=10, 3x+2y+3z=18 ,x+4y+9z=16.
e) Solve by using Jacobi's Method,(three iterations only)
20x+y-2z=17, 3x+20y-z=-18, 2x-3y+20z=25.
f) Solve using Gauss -seidal Method,(three iterations
only)
10x+y+z=12, x+10y+z=12, x+y+10z=12.
Q.5. Solve any four of the following: (16)a)The SHM is executed
by the particle according to the
law d2x / dt
2=4e
2t and if dx /dy=10. and x=3when t=0,find the displacement x at
any time t.
b) A train moves with uniform velocity 50 km/ hr and its brakes
produces retardation 400 km/ hr2. .How much time will it take to
rest?
c) Find a real root of the equation
fx =x3x1=0 using bisection method. (three
iteration only).d)Using Newton's-Raphson method,to evaluate 10
upto three iterations only.
e) Solve the differential equationdy
dx=x2y22xy
f) solve the differential equationdy
dxy
x=y
2.
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Q.6. Solve any four of the following: (16)
a) Find real root of the equation xex3=0 by
Regular falsi method.(three iterations only)
b) Fit a poisson distribution to set of observation.
x 0 1 2 3 4
f 122 60 15 2 1
c) If 20% of 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)In a sample of 1000 cases, the mean of a certain test is
14 and standard devition is 2.5. Assuming the
distribution is to be normal ,finda) How many student
score between 12 and 15? b) How many student score
above 18?{ Area 0 .to 0.8 = 0.2881 area 0 to 0.4 =0.1554
area 0 to1.6 =0.4452e) An urn contains 10 red , 5 white and 5
black balls. Two
balls are drawn at random .Find the probability that they
are not of the same colour.
f) A husband and wife appeared in an interview for two
vacancies in office. The probability of husband's
selection is 1/5 and that of wife's selection is 1/7 Find the
probability that
a) both of them are selected, and
b)only one of them is selected.
