Number System Class 9 Worksheet Maths Chapter 1

Q.1. The value of  is
(a) 0.45
(b)
(c) 45/1000
(d)
Ans.

9900 x = 2300
x = 23/99
Similarly x = 22/99



Q.2. If n is a natural number, then √n is
(a) Always a natural number
(b) Always a rational number
(c) Always a irrational number
(d) Sometimes a natural number and sometimes a surd
Ans. (d)

Q.3. If  
 
prove m-n = 1
Ans. 






⇒ 3^{3n - 3m +3} = 3⁰
⇒ 3n - 3m +3 = 0
⇒ n - m +1 = 0
⇒ m- n = 1

Q.4. The value of  ((23 + 2²)^2/3 + (150 - 29)^1/2)² is
(a) 196
(b) 286
(c) 400
(d) 324
Ans. (c)
((23 + 2²)^2/3 + (150 - 29)^1/2)²
((23 + 4)^2/3 + (121)^1/2)²
((27)^2/3 + (121)^1/2)²
((3³)^2/3 + (11))²
(9+11)²  = 20²  = 400
Hence option (c) is correct.

Q.5. If 
 

find a² - b² , a+ b
Ans.




= -9 - 4√5
a+b = 4√5 - 9 - 9 - 4√5 = -18
a-b = 4√5 - 9 + 9  + 4√5 = 8√5
a² - b² = (a+b)(a-b)
= -18 x 8√5
= - 144√5

Q.6. Give any two rational number between the irrational numbers 0.515115111511115....  and 0.53533533353333.... 
Ans. 
Pick any two number between them;
0.521, 0.527

Q.7. Explain the difference between rational number and irrational number with example.
Ans.
Rational number are those numbers expressed in the form of p/q, where p and q are co-primes & q ≠0.
Example: √2, √3, √11 etc.
Irrational numbers can't be expressed in the form mentioned above.
Example: 2, 3/4, 4/3, 0, 1, -2

Rational and Irrational numbers

Q.8. Find a if 

Ans.
 
Squaring both side,
13 - a√10 = 8+5+ 2√40
-a√10  = 2√40

a = -4

Q.9. If x + √13 = 4, find the value of x -1/x
Ans.

Q.10. Find the value of 

Ans.



Q.11. Simplify (11+√11)(11-√11)
Ans. 
11² - 11 = 121 -11 = 110

Q.12. Find x and y if 

Ans.


x = 13, y = -3

Q.13. find the value of  

Ans. 


Q.14. Simplify  
if x = √7 + √6
Ans. 



= 13 + 2√42 + 13 - 2√42 - 2
= 24

Q.15. If xy = 1 and x = 7 + 4√3, what is the value of  

Ans. 
x = 7 + 4√3



1/x = y and y = 1/x,
so,

= (7 - 4√3)² + (7 + 4√3)² 
= 49-48 - 56√3 + 49 + 48 + 56√3
= 194

Q.16. Find x  if 4^x - 4^x-1 = 24.
Ans.

suppose 4^x = m
m - m/4 = 24
3m/4 = 24
m = (24 x 4)/3
m = 32
∴ 4^x = 32
= 2^2x = 2⁵
= 2x = 5
= x = 5/2

Q. 17. if x = 2 and y = 4, what is value of (x/y)^x-y + (y/x)^y-x
Ans. (2/4)^-2 + (4/2)^4-2 = 2² + 2² = 8

Q.18. Simplify 

Ans.