1. Number Systems Class 9 Mathematics NCERT Exemplar Solutions (CBSE)
Chapter 1: Number Systems – Class 9 Mathematics NCERT Exemplar Solutions (CBSE Board)
Chapter 1: Number Systems
Exercise 1.1
Write the correct answer in each of the following:
1. Every rational number is
(A) a natural number (B) an integer
(C) a real number (D) a whole number
2. Between two rational numbers
(A) there is no rational number
(B) there is exactly one rational number
(C) there are infinitely many rational numbers
(D) there are only rational numbers and no irrational numbers
3. Decimal representation of a rational number cannot be
(A) terminating
(B) non-terminating
(C) non-terminating repeating
(D) non-terminating non-repeating
4. The product of any two irrational numbers is
(A) always an irrational number
(B) always a rational number
(C) always an integer
(D) sometimes rational, sometimes irrational
5. The decimal expansion of the number 2 is
(A) a finite decimal
(B) 1.41421
(C) non-terminating recurring
(D) non-terminating non-recurring
6. Which of the following is irrational ?
(A) 49 
(B) 123
(C) 7
(D) 81
7. Which of the following is irrational?
(A) 0.14 (B) 0.1416 (C) 0.1416 (D) 0.4014001400014...
8. A rational number between 2 and 3 is
(A) 2+32
(B) 2×32
(C) 1.5 (D) 1.8
9. The value of 1.999... in the form pq
, where p and q are integers and q≠0
, is
(A) 1910
(B) 19991000
(C) 2 (D) 19
10. 23+3
is equal to
(A) 26
(B) 6 (C) 33
(D) 46
11. 10×15
is equal to
(A) 65
(B) 56
(C) 25
(D) 105
12. The number obtained on rationalising the denominator of 17-2
is
(A) 7+23
(B) 7-23
(C) 7+25
(D) 7+245
13. 19-8 
is equal to
(A) 123-22
(B) 13+22
(C) 3-22
(D) 3+22
14. After rationalising the denominator of 733-22
, we get the denominator as
(A) 13 (B) 19 (C) 5 (D) 35
15. The value of 32+488+12
is equal to
(A) 2 (B) 2 (C) 4 (D) 8
16. If 2=1.4142
, then 2-12+1
is equal to
(A) 2.4142 (B) 5.8282 (C) 0.4142 (D) 0.1718
17. 432²
equals
(A) 2-16
(B) 2-6
(C) 216
(D) 26
18. The product 32 .42 .1232
equals
(A) 2
(B) 2 (C) 122
(D) 1232
19. Value of 4(81)-2
is
(A) 19 (B) 13
(C) 9 (D) 181
20. Value of (256)0.16×(256)0.09
is
(A) 4 (B) 16 (C) 64 (D) 256.25
21. Which of the following is equal to x
?
(A) x127-x57
(B) 12x413 
(C) x323
(D) x127×x57
Exercise :1.4
1. Express 0.6+0.7+0.47
in the form pq
, where p
and q
are integers and q≠0 .
2. Simplify : 7310+3-256+5-3215+32
3. If a=3+52 
, then find the value of a²+1a²
.
4. If x=3+23-2
and =3-23+2
, then find the value of x²+y²
.
Solution: We have,
x=3+23-2=3+23-2×3+23+2
x=3+6+6+232-22=5+263-2=5+26
And
y=3-23+2×3-23-2
y=3-6-6+232-22=5-263-2=5-26
x+y=5+26+5-26=10
x×y=3+23-2×3-23+2=1 
Now ,
x2+y2=x+y2-2xy
=102-2×1
=100-2=98
5.
Posted 4 months ago