Solved question paper for MATH-2 Dec-2017 (DIPLOMA automobile engineering 1st-2nd)

Applied mathematics-2

Previous year question paper with solutions for Applied mathematics-2 Dec-2017

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Question paper 1

  1. SECTION-A

    Q1. Choose the correct answer.

    i. Which one is a measure of dispersion?

    a) Mean b) Median c) Mode d) Range

    Answer:

  2. ii. Order of differential equation (y''')2 + 2y'' + 3y = x

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

    Answer:

  3. iii. A square matrix A is singular if |ܣ |is

    a) 0 b) 1 c) 2 d) 3

    Answer:

  4. iv. If x = sin3t ,then acceleration at \(\pi \over 2\) ଶ is (x stands for displacement at time t)

    a) -9 b) -3 c) 3 d) 9

    Answer:

  5. v. The equation of the normal to the curve y = sinx at (0, 0) is

    a) x = 0 b) y = 0 c) x + y = 0  d) x - y = 0

    Answer:

  6. Q2. State True or False.

    a. limQ->0 sinQ/Q is equal to 1

    Answer:

  7. b. \(\int sin 4x dx = cos 4x\)

    Answer:

  8. c. If D≠0, then system has unique solution

    Answer:

  9. d. If the mean of 4, 3, 7, x, 10  is 6 then x = 6 

    Answer:

  10. e. The integral of log x w.r.t x is 1/x

    Answer:

  11. Q3. Fill in the blanks.

    \(\int e ^{mx}\) ݀ is equal to -------

    Answer:

  12. ii. Area of trapezoid = 1/2 (sum of parallel side) x -------.

    Answer:

  13. iii. If AB is defined then (AB)t = -------------

    Answer:

  14. iv. Integration is defined as the ------ of differentiation.

    Answer:

  15. v. The differential co-efficient of a constant is ------.

    Answer:

  16. SECTION-B

    Q4. Attempt any six questions.

    (i) If = a(t + 1/t), y = a(t - 1/t) where “a” is constant. Then prove that dy/dx = x/y

    Answer:

  17. (ii) If ݇ kx + y - z = 0  and  x-  2y + z = 3, and 4x - 3y + z = 5 system is inconsistent, then find the value of ݇k

    Answer:

  18. (iii) Evaluate ∫ dx/1+cotx

    Answer:

  19. (iv) If y = (sin-1 x)2  prove that (1+ x2) y2 - xy1 = 2

    Answer:

  20. (v) Evaluate \(\int\)cos4 x dx

    Answer:

  21. (vi) The probability of the horse A winning the race is 1/4 and the probability of horse B winning the race is 1/3, find the probability that one of the horse wins the race.

    Answer:

  22. (vii) Calculate the median of the following data:-

    Class interval 0-5 5-10 10-15 15-20 20-25 25-30 30-35
    Frequency 12 15 25 40 42 14 8

     

    Answer:

  23. (viii) Find the point on the curve y = 10 + 2x - x2 the curve has slope unity.

    Answer:

  24. SECTION-C

    Q5. Attempt any three questions.

    (i) Solve the following equations by matrix method

    x - y + z = 4 , x - 2y - 2z = 9 , 2x + y + 3z = 1 

    Answer:

  25. (ii) Using Simpson’s Rule, calculate the approximate value of  \(\int_0^1 {1 \over 1 +x^2}\) by dividing the interval 0 to 1 into four equal parts. Hence obtain the value of π correct to four places of decimals.

    Answer:

  26. (iii) Solve the differential equation 

    \(y^2 (x^2 - 1){dy \over dx} - x^2 (y^2 - 1) = 0\)

    Answer:

  27. (iv) a) Differentiate etan x w.r.t sin x

    b) Determine the point of maxima of f(x) = sin x + cos x in 0<= x pi/2

    Answer:

  28. (v) Find S.D and coefficient of variation of following data

    Marks  0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
    No of student 5 10 20 40 30 20 10 4

     

    Answer: