Applied mathematics-2
Previous year question paper with solutions for Applied mathematics-2 Dec-2017
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Question paper 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:
ii. Order of differential equation (y''')2 + 2y'' + 3y = x
a) 1 b) 2 c) 3 d) 4
Answer:
iii. A square matrix A is singular if |ܣ |is
a) 0 b) 1 c) 2 d) 3
Answer:
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:
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:
Q2. State True or False.
a. limQ->0 sinQ/Q is equal to 1
Answer:
b. \(\int sin 4x dx = cos 4x\)
Answer:
c. If D≠0, then system has unique solution
Answer:
d. If the mean of 4, 3, 7, x, 10 is 6 then x = 6
Answer:
e. The integral of log x w.r.t x is 1/x
Answer:
Q3. Fill in the blanks.
\(\int e ^{mx}\) ݀ is equal to -------
Answer:
ii. Area of trapezoid = 1/2 (sum of parallel side) x -------.
Answer:
iii. If AB is defined then (AB)t = -------------
Answer:
iv. Integration is defined as the ------ of differentiation.
Answer:
v. The differential co-efficient of a constant is ------.
Answer:
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:
(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:
(iii) Evaluate ∫ dx/1+cotx
Answer:
(iv) If y = (sin-1 x)2 prove that (1+ x2) y2 - xy1 = 2
Answer:
(v) Evaluate \(\int\)cos4 x dx
Answer:
(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:
(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:
(viii) Find the point on the curve y = 10 + 2x - x2 the curve has slope unity.
Answer:
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:
(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:
(iii) Solve the differential equation
\(y^2 (x^2 - 1){dy \over dx} - x^2 (y^2 - 1) = 0\)
Answer:
(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:
(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: