Math Answers

Solve the following differential equation by using the method of undetermined

coefficients:

𝑦"+4𝑦=3𝑥+𝑐𝑜𝑠(2𝑥)

The random variable Y is normally distributed with expectation a=75 and standard deviation equal to 28. Use the Laplace function to find the probability that the test result will be assigned to a random value within the interval [147, 231]

15.Determine whether f: R to R, defined as f (x) = −3x + 4 is a bijection. Is f invertible, and if it is, 

what is its inverse?

16.Find the inverse of f (x) =

𝑥+1

𝑥+2

, on a suitable subset of R.

Find mean, median, mean deviation about mean, mean deviation about median for the

following data

Age in Years 20 – 22 22 – 24 24 – 26 26 – 28 28 – 30 30 – 32 32 – 34

No. of Employees 70 90 110 140 130 80 80

15. Find mean deviation from mode and its coefficient for the following data

Class – Interval 14 – 18 18 – 22 22 – 26 26 – 30 30 – 34

Frequencies 5 12 14 12 7

Find the mean deviation from mean and median for the following data

13, 17, 9, 21, 15, 25, 30, 35, 31

12. Find the mean deviation from mean and its coefficient for the following data representing

age distribution of 50 boys.

Age (in years): 17 18 19 20 21 22 23

No. of Boys 8 12 15 8 4 2 1

13. Find the mean deviation from median and its coefficient for the following data:

Height (in cm) 160 164 168 172 176 180

Number of students 3 7 12 15 6 2

Find the coefficient of quartile deviation from the following:

Class 5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40

Frequency 6 8 17 21 15 11 2

9. Find the semi-inter-quartile range for the following data:

Marks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50

No. of students 22 38 46 35 19

10. Find which of the following industry has less variation if the salaries paid to the employees

are as given below:

Salary (Rs. in

1000’s)

Below

4500

4500 –

4700

4700 –

4900

47900 –

5100

5100 &

above

Industry A 6 13 20 7 6

Industry B 4 9 16 7 0

Find the quartile deviation for the following set of 11 bottles of 1 litre of emery milk for

11 days by a dealer.

34, 37, 32, 25, 40, 45, 50, 42, 39, 47, 55

7. Calculate the quartile deviation and its coefficient from the following:

x 43 44 45 46 47 48 49

f 10 18 21 18 15 10 8

Calculate range and its coefficient from the following data:

Price of sold per 1 gm from Monday to Saturday

Monday Tuesday Wednesday Thursday Friday Saturday

902 910 914 908 922 920

The students of two groups A and B obtained following marks in a test of Mathematics.

Find which group gave more consistent performance, based on coefficient of range.

Marks of Group A 35 47 42 45 40 39 38 46 41 43

Marks of Group B 35 70 55 65 60 42 73 80 53 57

4. The temperatures recorded at the end of every 4 hours during a day at two cities Mumbai

and Pune are given below:

Mumbai 28 30 34 31 28 27

Pune 25 28 34 40 32 26

Use appropriate measure of dispersion and comment on variation.

Labelled and Unlabelled trees.

(a) How many labelled trees of order 5 are there?

(b) Draw all unlabeled tree of order 5 (under isomorphism). Hint: make cases on the diameter size.