Solved question paper for MATH-2 Dec-2018 (DIPLOMA Electrical and Electronics Engineering 1st-2nd)

Applied mathematics-2

Previous year question paper with solutions for Applied mathematics-2 Dec-2018

Our website provides solved previous year question paper for Applied mathematics-2 Dec-2018. Doing preparation from the previous year question paper helps you to get good marks in exams. From our MATH-2 question paper bank, students can download solved previous year question paper. The solutions to these previous year question paper are very easy to understand.

These Questions are downloaded from www.brpaper.com You can also download previous years question papers of 10th and 12th (PSEB & CBSE), B-Tech, Diploma, BBA, BCA, MBA, MCA, M-Tech, PGDCA, B-Com, BSc-IT, MSC-IT.

Print this page

Question paper 1

  1. SECTION-A
    Q1. a) Choose the correct answer.
    i. If A is a non singular matrix, then A-1 is
    a) |A| adj A      b)      
    c) (adj A)T            d) 

    Answer:

    (b)

  2. ii.  
    a) π      b) 
    c)       d)  

    Answer:

    (c)

  3. (iii) limx->0   

    a) 1      b) π
    c)       d)  -π

    Answer:

    (a)

  4. iv. Order of differential equation (y''') + 2y'' + 3y = x is
    a) 3       b)         4       c) 1        d) 2
     

    Answer:

    (a)

  5. v. The differential coefficient of sinx2 w.r.t  cosx2 is
    a) -tan x2 b) -cot x2 c) 2x  d) -2x

    Answer:

    (b)

  6. b) State True or False.
    vi. The differential coefficient of a constant is one.

    Answer:

    False

  7. (vii)    if    is even.

    Answer:

    False

  8. viii. Mean Deviation =   Standard Deviation

    Answer:

    True

  9. ix. Volume of a sphere of radius 'a' is   π   

    Answer:

    True

  10. x. cos 2A = cos2A - sin2A

    Answer:

    True

  11. c) Fill in the blanks
    xi. The angles in trigonometric functions are supposed to be measured in ______.
     

    Answer:

    Degree or radian

  12. xii. A square matrix is said to be a diagonal matrix if all its non-diagonal elements are______.

    Answer:

    Zero

  13. xiii.  is equal to______.

    Answer:

    Log(g(x)) + constant

  14. xiv. Central value of the set of observation is called_______.

    Answer:

    Central Tendency

  15. xv. The derivative of ?ex is equal to________.

    Answer:

    ex

  16.                                            SECTION-B
    Q2. Attempt any six questions.
    a. In a class of 30 students with roll no. 1 to 30, a student is picked up at random to answer a question. Find the probability that the roll number of selected students is either a multiple of 4 or 7.

    Answer:

    = 4,8, 12,16,20,24, 28

      &    

  17. b. If ?y = ex+y prove that    = 

    Answer:

     

  18. c. Calculate by Simpson’s rule an approximate value of     by taking seven equidistant ordinates.

    Answer:

    7  equidistant co-ordinate                   

     

    Equation..  

     

     

  19. d. Find the equation of the tangent to the curve y = x2 whose slope is  . 

    Answer:

    Y =                  -------------  1

    The slope of tangent to 1 at point ( is

    Y = 

    Slope = 

    Also  lies on curve 1

    ∴Requrid equation of tangent is 

    Y =  

    16y= 8x-1

    8x -16y =1

  20. e. Evaluate  .

    Answer:

    I =  

    Put

    Dx =

     =  

    =

    = 2 

    = 2 tan 

  21. f. Find the area bounded by the curve y = log x between the x-axis and the ordinates x = 2 and x = 3.

    Answer:

    Y =logx

     = 

    = log   -1

  22. g. If y = tan-1x , prove that (1 +x2) y2 + 2xy1 = 0

    Answer:

    Y =

    = 

    = (1+    = -2x.    

  23. h. Solve the equations by Crammer’s rule.

    Answer:

    A=

    =   

    X =                     y =

    X= -1                                                     y = 4

  24. i. 5x + 2y = 3


     

    Answer:

  25. j. 3x + 2y = 5

    Answer:

  26. k. Evaluate  

    Answer:

    I =

      Put logx  = t

            =

     

     =

     =

  27. SECTION-C

    Q3. Attempt any three questions.
    i. Solve the following equations by matrix method
    3x + y + 2z = 3

    2x - 3y - z = -3

    x + 2y + z = 4

    Answer:

    3x+ y+2z=3

    2x-3y-z=-3

    X+2y+z=4

    Ax=B

    X = 

    Where

    A= 

          = -3-3+14= 8  0

    (adj.A)=  = 

    Ax = B

    X=

    X =  

      =

    X = 1       ,    y= -2 ,   x=1

  28. ii. Find the maximum and minimum values of the function x3 - 6x2 + 9x + 15

    Answer:

      

    = 6(3) -12>0

    ∴x=3 is Point of minima

    Maximum value is

        = 1-6 + 9 + 15 = 19

    Min.  value is =

                             = 27-54+27+15

                             =  15

  29. iii. Find the standard deviation from the following data

    Wages

    0-10

    10-20

    20-30

    30-40

    40-50

    50-60

    60-70

    70-80

    Frequency

    12

    18

    35

    42

    50

    45

    20

    8

    Answer:

    Wages

    0-10

    10-20

    20-30

    30-40

    40-50

    50-60

    60-70

    70-80

    F

    12

    18

    35

    42

    50

    45

    20

    8

    N= 230

    X

    5

    15

    25

    35=a

    45

    55

    65

    75

    D=x-35

    -30

    -20

    -10

     0

    10

    20

    30

    40

    Fd

    -360

    -360

    -350

    0

    500

    900

    600

    320

    10800

    7200

    3500

    0

    5000

    18000

    12800

     

     

    Standard  deviation =

    = =

    =  = 17.25

  30. iv. Solve the differential equation
    y2(x2 - 1)   - x2 (y2 - 1) = 0

    Answer:

    =

    =

  31. v. Integrate x2 sin2x dx

    Answer:

    I = 

    =

    =

    =

    =