Scribd
Upload
2K views14 pages

General Mathematics and Statistics (6401)

The document is a mathematics assignment containing 5 questions. It asks to: 1) Calculate additional workers needed to complete a job on time. 2) Calculate income tax owed after exemptions, rebates and deductions. 3) Prove De Morgan's laws using Venn diagrams with sets A and B. 4) Find the number of real solutions for two quadratic equations by calculating the discriminant. 5) Eliminate the variable x from two equations containing x, P, and Q.

Uploaded by

Chemo Phobia
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
2K views14 pages

General Mathematics and Statistics (6401)

The document is a mathematics assignment containing 5 questions. It asks to: 1) Calculate additional workers needed to complete a job on time. 2) Calculate income tax owed after exemptions, rebates and deductions. 3) Prove De Morgan's laws using Venn diagrams with sets A and B. 4) Find the number of real solutions for two quadratic equations by calculating the discriminant. 5) Eliminate the variable x from two equations containing x, P, and Q.

Uploaded by

Chemo Phobia
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
You are on page 1/ 14

General Mathematics and Statistics (6401)

ASSIGNMENT NO.1

SEMESTER
SPRING 2022

PROGRAMME
B. ED (1.5)

TUTOR NAME
--------------------------------------

SUBMITTED BY
------------------

ROLL NO#
-------------------

SUMBISSION DATE
-------------
Q.1

a. A contractor contract to build house in 3 days. He employed

10 men to build the house. After 20 days, they completed

only 1/ 3 of the total work. How many more men will be

required to finish the remaining work within due time.

Solution :

Find the number of man-hrs. to complete 1/4 of the job


20 * 10 = 200 man-days
therefore
3 * 200 = 600 man-days required to complete the job.
Let m, = no. of additional men required to complete the job in the
remaining 20 days
10(m + 10) = 600
10m + 100 = 600
10m = 600 - 100
10m = 500
m = 500/10
m = 50 additional men required to finish the job.
Answer

b. The total annual income of Mrs. Marium is Rs.555000.


The exempted amount of her income tax is Rs. 190,000.
Calculate her income tax @ 5%. If she is given rebate Rs,
4500 and Rs. 500 has already been deducted at some sources
as income tax.

Solution :

Total income = 555000


Exemption = 190000
Income tax = 5%
Rebate = 4500
Deducted = 500
Taxable income = 555000 – 190000 = 365000
Tax @ 5% = 5 / 100 * 365000 = Rs. 18250
Deduction = 18250 – 4500 – 500 = 13250
Tax Payable = Rs. 13250
Answer

Q.2 A= {1,2,3,4,5} B= {6,7,8,9,10} and U=

{1,2,3………….10}. Prove De Morgan’s law and

verify them by using Venn diagrams.

Solution :

(AUB)’ = A’ ∩B’

AUB = {1,2,3….10}

U – (AUB) = Empty………………1

A’ = U-A = {6,7,8,9,10}

B’ = U-B = {1,23,4,5}

A’∩B’ = Empty……………….2

From 1 and 2 (AUB)’ = A’ ∩B’


(A∩B)’ = A’ UB’

A∩B = Empty

U- (A∩B)) = {1,2,3…………,10} ………………….1

A’ UB’ = {1,2,3….10} ………………….2

From 1 and 2 (A∩B)’ = A’ UB’


Q.3 Solve the following linear equations using both matrix
equation and Cremer rule and compare the results.

x+8y = -3
2x-6y =-17

Matrix Equation
Q.4 Find the value of discriminate, and state has many

real solutions there are to each quadric equation.

a. - 5t2 – t +9=0
b. x(6x-7) = - 4

Q.5 Eliminate x from the following equations


Solution :

1+x 2
2ax
P=

2axP = 1 + x2 2axP-x2-1=0

x2-2axP+1=0 x2-2axP+1=0

x2-axP-axP+1=0

1−x2
2bx
Q=

Solution :

You might also like