RS Aggarwal Solutions: Exercise 1G - Number System

RS Aggarwal Solutions: Exercise 1G - Number System | Extra Documents & Tests for Class 9 PDF Download

Q.1. Simplify
(i)
(ii)
(iii)
(iv)
Ans.
(i)

=21
= 2
(ii)

(iii)

(iv)

= (6)3
= 216

Q.2. Simplify:
(i)
(ii)
(iii)
Ans.

Q.3. Simplify:
(i) 31/4 × 51/4
(ii) 25/8 × 35/8
(iii) 61/2 × 71/2
Ans.

Q.4. Simplify:
(i) (34)1/4
(ii) (31/3)4
(iii)
Ans.

Q.5. Evaluate
(i)
(ii)
(iii)
(iv)
(v)

(vi)
Ans.
(i)
(ii)
(iii)
(iv)
(v)
(vi)

Q.6. If a = 2, b = 3, find the values of
(i) (ab + ba)–1

(ii) (aa + bb)–1
Ans.

(i) (ab + ba)–1

(a+ ba) −1 = (2+ 32) −1
= (8 + 9)−1

= (17)−1
= 1/17
(ii) (aa + bb)–1

(a+ bb)−1 = (2+ 33)−1
= (4 + 27)−1
= (31)−1
=1/31

Q.7. Simplify

(i)
(ii) (14641)0.25
(iii)
(iv)
Ans.

(ii) (14641)0.25

(iii)

(iv)

Q.8. Evaluate
(i)
(ii)
(iii)
(iv)
Ans.
(i)

=4(6)2 + (4)3 + 2(3)
=144 + 64 + 6
=214
(ii)

(iii)

(iv)

Q.9. Evaluate
(i)
(ii)
(iii)
(iv)
Ans.
(i)

(ii)

(iii)

= 2
(iv)

Q.10. Prove that
(i)
(ii)
(iii)
Ans.
(i)
LHS =

= √2
= RHS

(ii)

= RHS

(iii)

Q.11. Simplify and express the result in the exponential form of x.
Ans.

Hence, the result in the exponential form is

Q.12. Simplify the product
Ans.

Q.13. Simplify
(i)
(ii)
(iii)
Ans.
(i)

(ii)

(iii)

Q.14. Find the value of x in each of the following.
(i)
(ii)
(iii)
(iv)5x−3 × 32x−8 = 225
(v)
Ans.
(i)

Hence, the value of x is 6.
(ii)

Hence, the value of x is 22.
(iii)

Hence, the value of x is 5.

(iv) 5x−3×32x−8 = 225
⇒5x−3 × 32x−8 = (15)2
⇒5x−3 × 32x − 8 = 52 × 32
⇒x − 3 = 2 and 2x − 8 = 2
⇒x = 2 + 3 and 2x = 2 + 8
⇒x = 5 and 2x = 10

⇒ x = 5 and x = 5
⇒ x = 5
Hence, the value of x is 5.

(v)

Hence, the value of x is

Q.15.
Prove that
(i)
(ii)
(iii)
(iv)
Ans.
(i)

Hence,
(ii)

=x0
=1
= RHS
Hence,
(iii)

=xab−ac−ba+bc.xac−bc
=x−ac+bc.xac−bc
=x−ac+bc+ac−bc
=x0
= 1
= RHS
Hence,
(iv)

= 1
= RHS

Q.16. If x is a positive real number and exponents are rational numbers, simplify

Ans.

Q.17. If = 1/27, prove that m – n = 1.
Ans.

Hence, m - n = 1

Q.18. Write the following in ascending order of magnitude.

Ans.

On Comparing (1), (2) and (3), we get

The document RS Aggarwal Solutions: Exercise 1G - Number System | Extra Documents & Tests for Class 9 is a part of the Class 9 Course Extra Documents & Tests for Class 9.
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FAQs on RS Aggarwal Solutions: Exercise 1G - Number System - Extra Documents & Tests for Class 9

 1. What is the purpose of R.S. Aggarwal Solutions for Class 9 Number System?
Ans. The purpose of R.S. Aggarwal Solutions for Class 9 Number System is to provide a comprehensive guide for students to understand and solve problems related to number systems. It helps students practice and master the concepts covered in the textbook.
 2. How can R.S. Aggarwal Solutions for Class 9 Number System help in exam preparation?
Ans. R.S. Aggarwal Solutions for Class 9 Number System can help in exam preparation by providing step-by-step solutions to the exercises and problems given in the textbook. It helps students understand the concepts and develop problem-solving skills, which are essential for scoring well in exams.
 3. Are the solutions in R.S. Aggarwal Solutions for Class 9 Number System easy to understand?
Ans. Yes, the solutions in R.S. Aggarwal Solutions for Class 9 Number System are designed to be easy to understand. They provide detailed explanations and step-by-step approaches to solving problems, making it easier for students to grasp the concepts and apply them in solving similar problems.
 4. Can R.S. Aggarwal Solutions for Class 9 Number System be used for self-study?
Ans. Yes, R.S. Aggarwal Solutions for Class 9 Number System can be used for self-study. The solutions are comprehensive and provide a thorough understanding of the topics covered. Students can refer to these solutions while practicing problems on their own, which will help them strengthen their concepts and improve their problem-solving skills.
 5. Are R.S. Aggarwal Solutions for Class 9 Number System available in the same language as the article title?
Ans. Yes, R.S. Aggarwal Solutions for Class 9 Number System are available in the same language as the article title. The solutions are written in a language that is easy to understand and comprehend for students studying in Class 9. This ensures that students can easily follow the solutions and clarify any doubts they may have.

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