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 = x^x, 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 + e^{tan x} − a^x 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 = e^{tan—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