Applied mathematics-2
Previous year question paper with solutions for Applied mathematics-2 May-2018
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Question paper 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:
ii) \(d \over dx \) \((tan^{-1} (cot x)) = \)
a) -cosec2x b) -1 c) sin2x d)1
Answer:
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:
iv) if x = a cos3 t, y = a sin3 t , then \(dy \over dx\) is equal to
a) cot t b) cos t c) cosec t d) – tan t
Answer:
v) Degree of \(({d^2y \over dx^2})^2 = ({1+dy \over dx})^3\) is
a) 2 b) 3 c) 1 d) 4
Answer:
Q2. State True or False.
a) \({d \over dx} (x sin x) = x cos x\)
Answer:
b. If D = D1 = D2 D3= 0, system has infinite solution
Answer:
c) \({d \over dx} ({1 \over x }) = log x\)
Answer:
d. If tangent is parallel to x axis, then slope of curve is zero.
Answer:
e. ∫ emx dx = memx
Answer:
Q3. Fill in the blanks.
i. If S = cos2t, then velocity is ……………
Answer:
ii. The anti derivative of xn is ……………
Answer:
iv. Relationship between mean, median, and mode is ……………. .
Answer:
v. The probability of an impossible event is …………. .
Answer:
SECTION-B
Q4. Attempt any six questions.
i) Solve by means of determinants the following equations
3x + 2y = 7
11x - 4y = 3
Answer:
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:
iii) Evaluate \(\int_0^{\pi \over 6}\) Cos 5 3x dx
Answer:
iv) Solve 3݁ex tan y dx + (1 + ex) Sec2y dy = 0
Answer:
v) Find the equation of the normal to the curve y = 6x2 - 5y + 3 at (1,4)
Answer:
vi) If y = tan(x+ y), prove that \(dy \over dx\) = \({1- y^2 \over y^2}\)
Answer:
vii) Find \({ d^4 y \over dx^2 } \) if \(y = x^3\) log x
Answer:
viii) Evaluate \(\int { e^x \over e^{2x} + 6e^x + 5}\)
Answer:
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:
SECTION-C
Q5. Attempt any three questions.
i) Find the maximum or minimum values of the function
2 x3 - 21 x2 + 36 - 20
Answer:
ii) a) Evaluate \(\int {cos x \over cos 3x}\)
b) Differentiate Sinn xn wrt x
Answer:
iii) Solve the following equations by matrix method
10x + 10y - z = -2
x + 5y + 2z = 0
x - 5y - z = 4
Answer:
iv) Evaluate \(\int {(x^2 + 4) \over (x^2 + 1) ( x^2 + 3) } dx\)
Answer:
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: