Applied mathematics-2
Previous year question paper with solutions for Applied mathematics-2 May-2017
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Question paper 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:
(ii) limx->0 \(sin x - x \over x\)
(a) 1 (b) -1 (c) 0 (d) ∞
Answer:
(iii) \(\int_o^1 {1 \over 1+x^2}\) dx =
(a) \(\pi/2\) (b)\(\pi \over 4\) (c) 1 (d) 0
Answer:
(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:
(v) If f(-x) = f(x) then the function is
(a) odd (b) even (c) both (d) none
Answer:
(B) State true or false.
i. \(\int log x dx = {1 \over x}\)
Answer:
(ii) The differential coefficient of a constant is one.
Answer:
iii. Tossing of a coin is an event and the turning up of head and tail is a trial
Answer:
iv. Median is a measure of central tendency
Answer:
(C) Fill in the blanks.
i. Derivative of x6 w.r.t x3 is ………….
Answer:
ii. A matrix is said to be singular if its ………….
Answer:
iii. The square of …………… is called variance.
Answer:
iv. Arithmetic mean of 10 terms is 7. If each term is decreased by 3, then the new mean is ………..
Answer:
v. Area bounded by the curve, y = 4 x - x2 and x-axis and the ordinates x=1 and x= 3 is …………..
Answer:
SECTION – B
Q2. Attempt any six questions.
Answer:
(i) If xy = ex-y Prove that \({dy \over dx} = {logx \over(1+logx^2)}\)
Answer:
(ii) Evalluate \(x \int cos^2 x dx\)
Answer:
(iii) Using Cramer’s rule find the value of x and y for
6x - 4y = -24
5x - 11y = -43
Answer:
(iv) if y = (tan-1 x)2 Prove that (1 + x2)2 y2 + 2x (1+ x2) y1 = 2
Answer:
(v) Find the equation of tangent to the curve y = 9x2 - 12x + 9 which is parallel to x-axis
Answer:
(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:
(vii) Evaluate \(\int { cosx dx \over 2cosx +son x}\)
Answer:
(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:
(ix) Solve \((xy^2 + x )dx/dy = yx^2 - y\)
Answer:
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:
(ii) Find the maximum and minimum values of the function
2x3 -15x2 + 36x +10
Answer:
(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:
(iv) Show that
\(\int_0^{\pi \over 4} log (1 + tan Q) dQ = {\pi \over 8 }log 2\)
Answer:
(v) Solve
\(x^2 {dy \over dx} - x^2 - 2y^2 + xy\)
Answer: