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Test 3

1. The document is a mathematics exam for a 1st year class containing multiple choice questions, short answer questions, and long answer questions testing concepts from chapters 1-4. 2. The multiple choice section contains 5 questions testing topics like products of rational and irrational numbers, properties of sets, and properties of groups. 3. The short answer section contains 10 questions asking students to prove rules, perform operations on complex numbers, simplify expressions using properties, describe sets, and solve equations. 4. The long answer section contains 3 questions asking students to expand expressions, solve equations, and use synthetic division and factoring.

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abdul majeed
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32 views1 page

Test 3

1. The document is a mathematics exam for a 1st year class containing multiple choice questions, short answer questions, and long answer questions testing concepts from chapters 1-4. 2. The multiple choice section contains 5 questions testing topics like products of rational and irrational numbers, properties of sets, and properties of groups. 3. The short answer section contains 10 questions asking students to prove rules, perform operations on complex numbers, simplify expressions using properties, describe sets, and solve equations. 4. The long answer section contains 3 questions asking students to expand expressions, solve equations, and use synthetic division and factoring.

Uploaded by

abdul majeed
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Smart Guess & Test Papers

Student Name ______________________ Father Name ______________________ Roll Number _______


Class: 1st /year - Mathematics Marks : 40 Exam Format : 1st Term Exam 2022
Time : notespk.com_Nauman Sadaf | Date _________________ Examiner Sig __________ Chapter#: 1, 2, 3, 4

MCQ's S/Q L/Q Total

Objective Type

‫تس‬
1. Encircle the Correct Option. (1 x 5 = 5) ‫وجاب ےک رگد دارئہ اگلںیئ۔‬ ‫در‬ .1
1) The product of rational and irrational number is
a) Rational number b) Irrational number c) Integer d) All

2) The set of {0,1} is closed under


a) addition b) subtraction c) multiplication d) Division

3) (A-B)UB =
a) A U B b) A B c) A - B d) B - A

4) If a,b are elements of a group G and ax=b then x=


a) a-1 b b) ab-1 c) a-1 b d) a-b

5) The power Set P(S) of a set S w.r.t union with identity element
a) S b) 1 c) ϕ

Subjective Type

2 Answer the following short questions [Any TEN] (2 x 10 = 20)


]10 ‫رکںی۔[وکیئ ےس‬ ‫دنمرہج ذلی وساالت ےک رصتخم وجاابت رحتری‬ 2
i) Prove the rules of addition.

ii) Find the sum, difference and product of the complex numbers
(8, 9) and (5, -6) iii) Simplify:
iv) For real numbers a, b show the following by stating the
properties used. v) Write the set in the descriptive and tabular forms:
(-a) (-b) = ab
vi) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {2, 4, 6, 8, 10}, B = {1,
2, 3, 4, 5} and C = {1, 3, 5, 7, 9} List the members of each of vii) Show that = +
the following sets:
i) A B ii) A - B

viii) If A = and B = then show that

A + B is symmetric. ix) If A = , evaluate |A|

x) Use Synthetic division to show that x is the solution of the


polynomial and use the result to factorize the polynomial
completely. 2x4+7x3 - 4x2 - 27x - 18 , x = 2, x = -3

3 Answer the Following Long Questions [Any THREE] (5 x 3 = 15)


]3 ‫دںی۔[وکیئ ےس‬ ‫درج ذلی وساالت ےک ًالیصفت وجاابت‬ 3
i) Show that = a3 + b3 + c3 - 3abc

ii) Solve the equation:

iii) Find the numerical value of k if the polynomial x3 + kx2 - 7x +


6 has a remainder of -4, when divided by x + 2.

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