JNTU

JNTU B.Tech I Year MATHEMATICS - III Previous Question Paper (May - 2019 - R16)

B.Tech | I Year | I-II | R16 | May - 2019

Answer PaperPaper Code: 132ACMaximum Marks: 75Time: 3 hours

Part A is compulsory. Answer any one full question from each unit in Part B.

Part A

125 marks
a
Let X denotes the number of heads in a single toss of 4 fair coins. Determine P(1 < X ≤ 3).
2 marks

Answer

The number of heads X in 4 tosses of a fair coin follows a Binomial Distribution with parameters n = 4 and p = 0.5. The probability mass function is given by P(X = k) = 4Ck (0.5)4.

  • P(X=2) = 4C2 (0.5)4 = 6/16 = 0.375
  • P(X=3) = 4C3 (0.5)4 = 4/16 = 0.25

We need P(1 < X ≤ 3) = P(X=2) + P(X=3) = 0.375 + 0.25 = 0.625.

b
Define moment generating function of a random variable.
3 marks

Answer

The Moment Generating Function (MGF) of a random variable X, denoted by MX(t), is defined as the expected value of etX, provided the expectation exists for all t in some neighborhood of zero:

MX(t) = E[etX] = ∑ etx P(x) (for discrete) or ∫ etx f(x) dx (for continuous).

c
Define central limit theorem.
2 marks

Answer

Sign in to view the complete answer paper.

d
A random sample of size 100 has a standard deviation of 5. What can you say about maximum error with 95% confidence?
3 marks

Answer

Sign in to view the complete answer paper.

e
Define Type I and Type II errors.
2 marks

Answer

Sign in to view the complete answer paper.

f
Explain one way classification of ANOVA.
3 marks

Answer

Sign in to view the complete answer paper.

g
Establish an iterative formula for computing √N by Newton Raphson method.
2 marks

Answer

Sign in to view the complete answer paper.

h
Construct normal equations for fit a straight line by method of least squares.
3 marks

Answer

Sign in to view the complete answer paper.

i
Write Simpsons 1/3rd and 3/8th rule formulas.
2 marks

Answer

Sign in to view the complete answer paper.

j
Given y' = xy with y(0)=1. Find y(0.2) with h=0.1 by Euler's method.
3 marks

Answer

Sign in to view the complete answer paper.

Part B

210 marks
a
A sample of 4 items is selected at random from a box containing 12 items of which 5 are defective. Find the expected number of defective items.
5 marks

Answer

Sign in to view the complete answer paper.

b
In a normal distribution, 7% of the items are under 35 and 89% are under 63. Determine the mean and variance of the distribution.
5 marks

Answer

Sign in to view the complete answer paper.

OR
310 marks
a
Let the continuous random variable X have the pdf f(x) = 3/x^4, x > 1. Find F(x).
5 marks

Answer

Sign in to view the complete answer paper.

b
A discrete random variable X has mean 6 and variance 2. If it is Binomial, find P(5 ≤ X ≤ 7).
5 marks

Answer

Sign in to view the complete answer paper.

410 marks
a
A sample of size 100 is taken from a population with mean μ=76 and σ=16. Find the probability that the sample mean is between 75 and 78.
5 marks

Answer

Sign in to view the complete answer paper.

b
Assuming σ=20, how large a sample is needed to assert with 0.95 probability that the sample mean differs from the true mean by at most 3.0?
5 marks

Answer

Sign in to view the complete answer paper.

OR
510 marks
a
A normal population has mean 0.1 and σ=2.1. Find the probability that the mean of a sample of size 900 will be negative.
5 marks

Answer

Sign in to view the complete answer paper.

b
Find 95% confidence limits for the mean given sample: 15, 17, 10, 18, 16, 9, 7, 11, 13, 14.
5 marks

Answer

Sign in to view the complete answer paper.

610 marks
a
In a sample of 60 workers, average time is 33.8 mins, σ=6.1. Can we reject μ=32.6 in favour of μ > 32.6 at α=0.025?
5 marks

Answer

Sign in to view the complete answer paper.

b
Two samples (n1=10, x1=1456, s1=423; n2=17, x2=1280, s2=398). Is there a significant difference between means?
5 marks

Answer

Sign in to view the complete answer paper.

OR
7
The following are typing mistakes in four weeks by four typists (Data Table). Using ANOVA, test at 0.05 level whether the difference among means is significant.
10 marks

Answer

Sign in to view the complete answer paper.

810 marks
a
Find a real root of xe^x - cos(x) = 0 using Newton-Raphson method.
5 marks

Answer

Sign in to view the complete answer paper.

b
Fit a least square parabola to the given data.
5 marks

Answer

Sign in to view the complete answer paper.

OR
910 marks
a
Find the root of x log(x) - 7 = 0 between 3.5 and 4 by Regula-Falsi method.
5 marks

Answer

Sign in to view the complete answer paper.

b
Solve the system: 8x+y+z=8, x+8y+z=12, x+y+7z=4 by Gauss-Seidel method.
5 marks

Answer

Sign in to view the complete answer paper.

10
Find y(0.1) and y(0.2) using 4th order Runge-Kutta method given y' = xy + y^2, y(0)=1.
10 marks

Answer

Sign in to view the complete answer paper.

OR
11
Solve y' = x + y^2 subject to y(0)=1 by Picard's method.
10 marks

Answer

Sign in to view the complete answer paper.

About this paper

This page contains the question paper of MATHEMATICS - III from JNTU for B.Tech ME I Year I-II, May - 2019, R16.

For the solved question paper with answers, switch to the Answer Paper tab.

Other papers in MATHEMATICS - III

Loading Question Papers

Fetching data from database...