Practice Worksheet (Part - 1) - Number System Notes | EduRev

Q.1. Which of the following is an irrational number?
(a) 

(b) √3
(c) 1/2
(d) 

Ans. (b)

Q.2. The numberin p/q form is
(a) 267/1000
(b) 26/10
(c) 241/900
(d) 241/999
Ans. (c)
Solution:
let x be the p/q form, x =
multiply both side by 100, 100 x =     ...(i)
multiply both side by 10
1000 x =    ....(ii)
1000 x - 100 x =  = 241
900 x = 241
⇒ x = 241/900
Hence, option (c) is correct

Q.3. Every point on the number line represent, which of the following numbers ?
(a) Natural numbers
(b) Irrational number
(c) Rational number
(d) Real number
Ans. (d)

Q.4. Which of the following is not a surd ?
(a) √6
(b) √7
(c) ∛343
(d) √11
Ans. (c)

Q.5. Show that 3√5 is an irrational number.
Ans. 
Let us assume 3√5 is a rational number,
3√5 = p/q, where p and q are co-primes,
√5 = p/3q
Clearly √5 is irrational, while number on right q ≠ 0 are rational
∴ Irrational = Rational
But above deduced can't be right. Therefore our supposition is wrong making 3√5 an irrational number.

Q.6. What is the decimal form of the following no's.
(a) 18/11
(b) 3/26
(c) 1/17
(d) 2/13
Ans.
(a) 18/11 = 1.63636363...
(b) 3/26 = 0.11538461538
(c) 1/17 = 0.05882352941
(d) 2/13 = 0.15384615384

Q.7. The conjugate pair of 2 + √3 is
(a) 2 - √3
(b) 2 + √3
(c) 2√3
(d) 4 - √3
Ans. (a)

Q.8. Simplify: 

Ans.




Q.9. Rationalise: 

Ans.



Q.10. Find the value of 

Ans.



= 5+4 - 4√5 - 5 - 4 -  4√5  = -8√5

Q.11. If , 
find the value of a & b.
Ans.

Rationalising LHS
 




∴ a = 11/7 and b = 6/7

Q.12. Evaluate: 

Ans.
 


Q.13.  If  , 
find the value of x³ - 2x² - 7x+5
Ans.


x = 2 + √3
x³ - 2x² - 7x + 5
= x(x² - 2x - 7) + 5
= (2 + √3) [(2 + √3)² - 2(2 + √3) - 7 ]+5
= (2 + √3) [4 + 3+4√3 - 4 + 2√3 - 7]+5
= (2 + √3)(-4 + 2√3) + 5
= (2 + √3) x 2(-2+√3)+5
= 2[(√3 + 2)(√3 - 2)] + 5
= 2[(√3)² - 2² ]+5
= 2[3-4]+5
= 2(-1) + 5
= -2+5
= 3

Q.14. Express  in p/q form.
Ans.
let x be the p/q form,
so, x =  
10x =
1000x =
1000x - 10x = -  
990x = 15555
x= 15555/990
= 1037/66

Q.15. Insert five rational no's between 3/5 and 4/5.
Ans.
3/5 and 4/5

30/50 and 40/50
∴ pick any five number between 30 and 40
31/50,  32/50,  36/50,  37/50,  39/50

Q.16. Insert 3 irrational number between 2.6 and 3.8
Ans.
2.6 and 3.8
irrational numbers are non repeating non - terminating
2.61010010001.....
2.802002000200002......
3.604004000400004.......

Q.17. If 27^x = 9/3^x , find x
Ans.
27^x = 9/3^x
⇒ 3^3x = (3)²/(3)^x
⇒ 3^3x = 3^2-x
⇒ 3x = 2-x
⇒ 4x = 2
⇒ x = 4/2
⇒ x = 0.5

Q.18. Write the value of 

Ans.


= 15