Solved question paper for MATH-2 May-2017 (DIPLOMA 1st-2nd)

Applied mathematics-2

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Question paper 1

  1. SECTION – A

    Q1. (A) Choose the correct answer:

    (i) If D ≠ 0, then system has

    (a) Infinite Solution (b) Unique Solution (c) Not a Solution (d) None of the above

    Answer:

  2. (ii) limx->0  \(sin x - x \over x\)

    (a) 1 (b) -1 (c) 0 (d) ∞

    Answer:

  3. (iii) \(\int_o^1 {1 \over 1+x^2}\) dx = 

    (a) \(\pi/2\) (b)\(\pi \over 4\)   (c) 1 (d) 0

    Answer:

  4. (iv) The order of differential equation  \( ({d^4 y \over dx^4})^2 + 3 ({d^2 y \over dx^2})^4 + y = 0\) is

    (a) 4 (b) 2 (c) 8 (d) 1

    Answer:

  5. (v) If  f(-x) = f(x)  then the function is

    (a) odd (b) even (c) both (d) none

    Answer:

  6. (B) State true or false.

    i. \(\int log x dx = {1 \over x}\)

    Answer:

  7. (ii) The differential coefficient of a constant is one.

    Answer:

  8. iii. Tossing of a coin is an event and the turning up of head and tail is a trial

    Answer:

  9. iv. Median is a measure of central tendency

    Answer:

  10. (C) Fill in the blanks.

    i. Derivative of x6 w.r.t  x3 is ………….

    Answer:

  11. ii. A matrix is said to be singular if its ………….

    Answer:

  12. iii. The square of …………… is called variance.

    Answer:

  13. iv. Arithmetic mean of 10 terms is 7. If each term is decreased by 3, then the new mean is ………..

    Answer:

  14. v. Area bounded by the curve, y = 4 x - x2  and x-axis and the ordinates x=1 and x= 3 is …………..

    Answer:

  15. SECTION – B

    Q2. Attempt any six questions.

    Answer:

  16. (i) If xy = ex-y Prove that \({dy \over dx} = {logx \over(1+logx^2)}\)

    Answer:

  17. (ii) Evalluate \(x \int cos^2 x dx\)

    Answer:

  18. (iii) Using Cramer’s rule find the value of x and y for

    6x - 4y = -24

    5x - 11y = -43

     

    Answer:

  19. (iv) if y = (tan-1 x)2 Prove that (1 + x2)y2 + 2x (1+ x2) y1 = 2

    Answer:

  20. (v) Find the equation of tangent to the curve y = 9x- 12x + 9   which is parallel to x-axis

    Answer:

  21. (vi) Find the approximate area under the smooth curve whose ordinates are given below by the method of trapezoidal rule

    x 1 2 3 4 5 6 7 8
    y 2 2.6 3 3.2 2.8 2 1.5 1

     

     

     

    Answer:

  22. (vii) Evaluate \(\int { cosx dx \over 2cosx +son x}\)

    Answer:

  23. (viii) The students work independently on a problem. The probability that the first will solve it is 2/3 and probability that the second one will solve is 2/9 . Find the probability that the problem will be solved.

    Answer:

  24. (ix) Solve \((xy^2 + x )dx/dy = yx^2 - y\)

    Answer:

  25. SECTION – C

    Q3. Attempt any three questions.

    (i) Solve the following equations by matrix method

    x + y - z = -2

    2x - y - z = -7 

    4x + y + 2z = 4

    Answer:

  26. (ii) Find the maximum and minimum values of the function 

    2x3 -15x2 + 36x +10 

    Answer:

  27. (iii) Calculate the standard deviation from the following data

    x 25 35 45 55 65 75 85
    f 3 61 132 153 140 51 2

     

    Answer:

  28. (iv) Show that 

    \(\int_0^{\pi \over 4} log (1 + tan Q) dQ = {\pi \over 8 }log 2\)

    Answer:

  29. (v) Solve

    \(x^2 {dy \over dx} - x^2 - 2y^2 + xy\)

    Answer: