applied mathematics 2 diploma question papers 2017

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Applied Mathematics-II Exam
S.B. Roll No…………………………………
APPLIED MATHEMATICS-II
2nd Exam/Common/2354/2251/5422/Nov’17
Duration: 3Hrs. M.Marks:75
SECTION-A
Q1. Choose the correct answer. 5×1=5
  • i. Which one is a measure of dispersion?
    a) Mean b) Median c) Mode d) Range
  • ii. Order of differential equation (y”’)2 + 2y” + 3y = x
    a) 1 b) 2 c) 3 d) 4
  • iii. A square matrix A is singular if |A| is
    a) 0 b) 1 c) 2 d) 3
  • iv. If x = sin 3t, then acceleration at
    π2
    is (x stands for displacement at time t)
    a) -9 b) -3 c) 3 d) 9
  • v. The equation of the normal to the curve y = sin x at (0, 0) is
    a) x = 0 b) y = 0 c) x + y = 0 d) x − y = 0
Q2. State True or False. 5×1=5
  • a. limθ→0
    Sinθ°θ
    is equal to 1
  • b. ∫ sin 4x dx = cos 4x
  • c. If D≠0, then system has unique solution
  • d. If the mean of 4, 3, 7, x, 10 is 6 then x = 6
  • e. The integral of log x w.r.t x is
    1x
Q3. Fill in the blanks. 5×1=5
  • i. ∫ emx dx is equal to ——-.
  • ii. Area of trapezoid =
    12
    (sum of parallel side) x ——-.
  • iii. If AB is defined then (AB)t = ——-.
  • iv. Integration is defined as the —— of differentiation.
  • v. The differential co-efficient of a constant is ——.
Applied Mathematics-II Section B
SECTION-B
Q4. Attempt any six questions. 6×5=30
  • (i) If x = a(t +
    1t
    ),  y = a(t −
    1t
    ) where “a” is constant. Then prove that  
    dydx
    =
    xy
  • (ii) If kx + y − z = 0;  x − 2y + z = 3 and 4x − 3y + z = 5, and system is inconsistent, then find the value of k.
  • (iii) Evaluate ∫π/20
    dx1 + cot x
  • (iv) If y = (sin−1 x)2 , prove that (1 − x2)y2 − xy1 = 2
  • (v) Evaluate ∫ cos4 x dx
  • (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.
Applied Mathematics-II Section B Cont & Section C
  • (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
  • (viii) Evaluate ∫ x tan−1 x dx
  • (ix) Find the point on the curve y = 10 + 2x − x2 where the curve has slope unity.
SECTION-C
Q5. Attempt any three questions. 3×10=30
  • (i) Solve the following equations by matrix method
    x − y + z = 4,  x − 2y − 2z = 9,  2x + y + 3z = 1
  • (ii) Using Simpson’s Rule, calculate the approximate value of ∫10
    11 + x2
    dx      by dividing the interval 0 to 1 into four equal parts. Hence obtain the value of π correct to four places of decimals.
  • (iii) Solve the differential equation
    y2(x2 − 1)
    dydx
    − x2(y2 − 1) = 0
  • (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 ≤
    π2
  • (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 students 5 10 20 40 30 20 10 4

MATHEMATICS-2-NOV-2017

Applied Mathematics-II Exam Paper
S.B. Roll No…………………………………
APPLIED MATHEMATICS – II
2nd Exam/Common/2354/2251/5422/May’17
Duration: 3 Hours M. Marks:75
SECTION – A
Q1. (A) Choose the correct answer: 5×1=5
  • (i)   If D ≠ 0, then system has
    (a) Infinite Solution (b) Unique Solution (c) Not a Solution (d) None of the above
  • (ii)   limx→0
    sin x − xx
    =
    (a) 1 (b) -1 (c) 0 (d) ∞
  • (iii)   ∫10
    11 + x2
    dx =
    (a)
    π2
     (b)
    π4
     (c) 1 (d) 0
  • (iv)   The order of differential equation (
    d4ydx4
    )2 + 3(
    d2ydx2
    )4 + y = 0 is
    (a) 4 (b) 2 (c) 8 (d) 1
  • (v)   If f(-x) = f(x) then the function is
    (a) odd (b) even (c) both (d) none
(B)   State true or false. 5×1=5
  • i.   ∫ log x dx =
    1x
  • ii.   If A =
    [
    cos α − sin α sin α cos α
    ]
    then |A| = 1
  • iii.   The differential coefficient of a constant is one.
  • iv.   Tossing of a coin is an event and the turning up of head and tail is a trial.
  • v.   Median is a measure of central tendency.
Applied Mathematics-II Section A(C) & Section B
(C)   Fill in the blanks. 5×1=5
  • i. Derivative of x6 w.r.t  x3 is …………
  • ii. A matrix is said to be singular if its …………
  • iii. The square of ………… is called variance.
  • iv. Arithmetic mean of 10 terms is 7. If each term is decreased by 3, then the new mean is …………
  • v. Area bounded by the curve, y = 4 x – x2 and x-axis and the ordinates x=1 and x=3 is …………
SECTION – B
Q2. Attempt any six questions. 6×5=30
  • (i) If xy = ex−y  Prove that  
    dydx
    =
    log x(1 + log x)2
  • (ii) Evaluate ∫ x cos2 x dx
  • (iii) Using Cramer’s rule find the value of x and y for
    6 x − 4y = −24
    5 x − 11y = −43
  • (iv) If y = (tan−1 x)2  Prove that (1 + x2)2y2 + 2x(1 + x2)y1 = 2
  • (v) Find the equation of tangent to the curve y = 9x2 − 12x + 9 which is parallel to x-axis
Applied Mathematics-II Section B Cont & Section C
  • (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
  • (vii) Evaluate ∫
    cos x dx2 cos x + sin x
  • (viii) The students work independently on a problem. The probability that the first will solve it is
    23
    and probability that the second one will solve is
    29
    . Find the probability that the problem will be solved.
  • (ix) Solve  (xy2 + x) dx/ dy = yx2 − y
SECTION – C
Q3. Attempt any three questions. 3×10=30
  • (i) Solve the following equations by matrix method
    x + y − z = −2
    2x − y − z = −7
    4x + y + 2z = 4
  • (ii) Find the maximum and minimum values of the function
    2x3 − 15x2 + 36 x + 10
  • (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
  • (iv) Show that
    ∫π/40 log (1 + tan θ) dθ =
    π8
    log 2
  • (v) Solve
    x2
    dydx
    = x2 − 2y2 + xy

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