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Azaan Academy of Sciences: Circular Road, Samundri 0301-6064502

This document is an examination paper for 1st Year Math students at Azaan Academy of Sciences, covering Chapter 4 with a total of 35 marks. It includes multiple-choice questions, short questions, and subjective questions related to mathematical concepts such as cube roots, equations, and polynomial division. The exam is designed to assess students' understanding of the syllabus through various problem-solving techniques.

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13 views1 page

Azaan Academy of Sciences: Circular Road, Samundri 0301-6064502

This document is an examination paper for 1st Year Math students at Azaan Academy of Sciences, covering Chapter 4 with a total of 35 marks. It includes multiple-choice questions, short questions, and subjective questions related to mathematical concepts such as cube roots, equations, and polynomial division. The exam is designed to assess students' understanding of the syllabus through various problem-solving techniques.

Uploaded by

Adnan
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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AZAAN ACADEMY OF SCIENCES

Circular Road, Samundri 0301-6064502

Name of Student_____________________ Father Name________________________ Roll No.________


Class: 1st Year Subject: Math (T-11) Time: 50 Minutes Total Marks: 35

Syllabus: Ch#04(Ex#4.1-4.5)
OBJECTIVE
Q. No. 01: Attempt the following Multiple Choice and tick the correct answer. (5)
Sr # MCQs A B C D
1 The sum of the cube roots of unity is ----- 2 3 1 0
An equation, which remains unchanged Homogeneous
2 1
when x is replaced by 𝑥 is called equation
Quadratic Reciprocal None

Roots of this equations are 𝑥 2 − 7𝑥 + 10 = (2, 4) (5,3) (5,3) (2,5)


3 0
4 Solutions of the equation are also called Roots Number set None
The real 4th roots of unity are ------------of Multiplicative Additive
5 each other inverse inverse
Both a and b None

SUBJECTIVE

Q. No. 02: Attempt the following Short Questions. (2 x 9 = 18)


i. Solve the equation 41+𝑥 + 41−𝑥 = 10
𝑎 𝑏 1 1
ii. Solve the equation by factorization + 𝑏𝑥−1 = 𝑎 + 𝑏 ; 𝑥 ≠ 𝑎 , 𝑏
𝑎𝑥−1

iii. Solve the equation 2𝑥 + 2−𝑥+6 − 20 = 0


iv. Evaluate (1 + 𝜔 − 𝜔2 )8
v. Solve by completing square 𝑥 2 − 2𝑥 − 899 = 0
vi. Find four fourth roots of 16.
vii. Define reminder and factor theorem.
viii. When the polynomial 𝑥 3 + 2𝑥 2 + 𝑘𝑥 + 4 is divided by 𝑥 − 2, the reminder is 14. find the value of k.
ix. Show that (1 + 𝜔)(1 + 𝜔2 )(1 + 𝜔4 )(1 + 𝜔8 ) … … … 2𝑛 𝑓𝑎𝑐𝑡𝑜𝑟𝑠 = 1

Q. No. 03: Attempt the following Subjective Questions. (3x 4 = 12)


1+√3𝑖 1−√3𝑖
a) Prove that complex cube roots of −1 are and ; and hence prove that
2 2
9 9
1+√−3 1−√−3
( ) +( ) = −2.
2 2
1 1
b) Solve the equation 𝑥 2 + 𝑥 − 4 + 𝑥 + 𝑥 2 = 0

Use synthetic division to find the values of 𝑝 and 𝑞 if 𝑥 + 1 and 𝑥 − 2 are the factors of the
polynomial 𝑥 3 + 𝑝𝑥 2 + 𝑞𝑥 + 6.

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