### FORMAT OF I A TEST QUESTION PAPER (CIE) | ENGINEERING MATHEMATICS –II | Diploma 2020

 Test/Date and Time Semester/year Course/Course Code Max Marks Ex: I test/6 th weak of sem 10-11 Am I/II SEM ENGINEERING MATHEMATICS –II 20 Year: Course code: 15SC02M Name of Course coordinator :                                                                                             Units:  CO’s: Question no Question MARKS CL CO PO 1 2 3 4

### 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