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I test/6 th weak of sem 10-11 Am |
I/II SEM |
ENGINEERING MATHEMATICS –II |
20 |
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Course code: 15SC02M |
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Model Question Paper:
Code: 15SC02M
I
Semester Diploma Examination
ENGINEERING
MATHEMATICS –II
(For
All Engineering Diploma Programmes) Time: 3 Hours][Max. Marks: 100
NOTE: i)Answer any 10 questions from section A, 8 questions
from section B and 5 questions from section-C
i)
Each question carries 3 marks in section A.
ii) Each
question carries 5 marks in section B.
iii) Each
question carries 6 marks in section C.
SECTION-A
1. Find
the equation of the line passing through the point (2,-3) with slope 1/3.
2. Find
the equation of parabola with vertex (2,0) and focus (5,0)
3. Differentiate:
(3x + 8)7
with respect to x.
4.
If y = cos–1
x show that dy = –1 .
dx √1–x2
5.
If y =
xx, find dy .
dx
6.
If y = 1+sinx find dy .
1–sinx dx
7. Find the equation to the tangent
to the curve 2x3 + 5y −
4 = 0 at (-2,4).
8.
The volume of the sphere is increasing at the rate of 6cc/sec. Find the rate of change of
radius when the radius is 3 cm.
9.
Integrate: (2x + 1)(x +
5) with respect
to x
10. Evaluate: ∫ tan2 xdx
11.
∫
Evaluate: cosx dx
1+sinx
12.
0
Evaluate: ∫g/4(sec2x + 1)dx.
13. Find area bounded by the line
x + 2y =
0 , x- axis, and ordinates x = 0, andx =
4 by
integration.
14. Form
differential equation for curve y2 = 4ax
SECTION – B
1.
Find the equation of line passing through the point (2,5) and (-3,2).
2. Differentiate √x + logx + sin–1 x + etan x − ax with
respect to x.
3. Differentiate tan x with respect
to x using first principal method.
4.
If y = sinh 3x cosh 2x then find dy .
dx
5.
If S = t3 − t2 + 9t + 8, where S is distance
travelled by particle
in t seconds. Find the velocity and acceleration at t = 2 sec.
6.
Integrate: 1 − tanx + e–3x + 1
+
5 with respect to x.
x
7. ∫
Evaluate: (1+log x)2 dx
x
8. Evaluate:
∫ xsinxdx
1+x2
9.
0
Evaluate: ∫g/2 cos 5x cos 3x dx
10.
0
Evaluate: ∫g/2 cos3 x dx
11. Solve the
differential equation sin2ydx − cos2xdy =0
SECTION – C
1.
Find the equation
of median through B in a triangle with vertices A(-1 ,3), B(-3, 5) and C(7,-9)
2. Find the equation of hyperbola, given
that vertices are (±7,
0) and eccentricity, е=4/3
3.
If xy = ax , show that
dy = x loge a–y.
dx x loge x
4.
If y = etan—1 x then show that (1 + x2) d2y + (2x − 1) dy = 0.
dx2 dx
5. Find
the maximum and minimum values of the function
f(x) = 2x3 − 21x2 + 36x − 20.
6. Evaluate: ∫ tan–1 x dx
7.
Find the volume of solid generated by revolving the curve
y
= √x2 + 5x between
x=1 & x=2.
8.
Solve
the differential equation
x dy − 2y =
2x