Solved question paper for MATH-2 May-2018 (DIPLOMA civil enginerring 1st-2nd)

Applied mathematics-2

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Question paper 1

  1. SECTION-A

    Q1. Choose the correct answer

    i) If a square matrix A has two identical rows or columns, then det A =

    a) 0 b) 1 c) -1 d) none

    Answer:

  2. ii)  \(d \over dx \) \((tan^{-1} (cot x)) = \)

    a) -cosec2x   b) -1    c) sin2x    d)1

    Answer:

  3. iii) ∫ log x dx is equal to

    a) \({1 \over 2} (log x )^2\)    b) \(1 \over x\)     c) x (log x- x)    d) 2log x

    Answer:

  4. iv) if x = a cos3 t, y = a sint , then \(dy \over dx\)  is equal to 

    a) cot t    b) cos t    c) cosec t    d) – tan t

    Answer:

  5. v) Degree of \(({d^2y \over dx^2})^2 = ({1+dy \over dx})^3\)  is 

    a) 2 b) 3 c) 1 d) 4

    Answer:

  6. Q2. State True or False.

    a) \({d \over dx} (x sin x) = x cos x\)

     

    Answer:

  7. b. If D = D1 = D2  D3= 0, system has infinite solution

    Answer:

  8. c)  \({d \over dx} ({1 \over x }) = log x\)

    Answer:

  9. d. If tangent is parallel to x axis, then slope of curve is zero.

    Answer:

  10. e. ∫ emx dx = memx

    Answer:

  11. Q3. Fill in the blanks.

    i. If S = cos2t, then velocity is ……………

    Answer:

  12. ii. The anti derivative of xn is ……………

    Answer:

  13. iv. Relationship between mean, median, and mode is ……………. .

    Answer:

  14. v. The probability of an impossible event is …………. .

    Answer:

  15. SECTION-B

    Q4. Attempt any six questions.

    i) Solve by means of determinants the following equations

    3x + 2y = 7

    11x - 4y = 3

     

    Answer:

  16. ii) The velocity of a body moving in a straight line at different times is given below

    t(sec) 0 1 2 3 4 5
    v(m/sec) 4 3.98 3.87 3.55 2.83 0.61

     

    Answer:

  17. iii) Evaluate \(\int_0^{\pi \over 6}\) Cos 5 3x dx

     

    Answer:

  18. iv) Solve 3݁ex tan y dx + (1 + ex)  Sec2y dy = 0

    Answer:

  19. v) Find the equation of the normal to the curve y = 6x2 - 5y + 3 at (1,4)

    Answer:

  20. vi) If y = tan(x+ y),  prove that \(dy \over dx\) = \({1- y^2 \over y^2}\)

    Answer:

  21. vii) Find \({ d^4 y \over dx^2 } \) if \(y = x^3\) log x

    Answer:

  22. viii) Evaluate \(\int { e^x \over e^{2x} + 6e^x + 5}\)

    Answer:

  23. ix) A card is drawn from a well shuffled pack of playing cards. What is the probability that it is either a spade or an ace?

    Answer:

  24. SECTION-C

    Q5. Attempt any three questions.

    i) Find the maximum or minimum values of the function

    2 x3 - 21 x2 + 36 - 20 

     

    Answer:

  25. ii) a) Evaluate \(\int {cos x \over cos 3x}\)

    b) Differentiate  Sinxn  wrt x

    Answer:

  26. iii) Solve the following equations by matrix method

    10x + 10y - z = -2

    x + 5y + 2z = 0

    x - 5y - z = 4

    Answer:

  27. iv) Evaluate \(\int {(x^2 + 4) \over (x^2 + 1) ( x^2 + 3) } dx\)

    Answer:

  28. v) Calculate the median and standard deviation from the following data

    class interval  1-10 11-20 21-30 31-40 41-50 51-60
    frequency 3 16 26 31 16 8

     

    Answer: