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Chap 1 : Number Systems www.rava.org.in

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CHAPTER CHAPTER 11

1. OBJECTIVE QUESTIONS

1. The value of x, when () ()2 3 288

xx41 is (a) 1 (b) 1 (c) 0 (d) None

Ans : (a) 1

23
xx41 23
52
x 1

2. The rational number between 1/2 and 1/3 is

(a) 2/5 (b) 1/5 (c) 3/5 (d) 4/5

Ans : (a) 2/5

Since,

21
.05, 31
.03

Rational number lies between .03 and 0.5 is

.04 104
52

3. Set of natural numbers is a subset of

(a) Set of even numbers (b) Set of odd numbers (c) Set of composite numbers (d) Set of real numbers

Ans : (d) Set of real numbers

Since, set of real numbers contains all natural numbers, integers, rational and irrational numbers. 4. .0 123 can be expressed in rational form as (a)

111900

(b)

900111

(c) 10123
(d)

900121

Ans : (b)

900111

Let, x . ......0 12333 ...(1)

Multiply (1) by 10 on both sides, we get

x10 . .......1 2333 ...(2)

Subtracting (1) from (2), we get

x9 .111 x /111 900

5. The fraction

32 322 6

j h is equal to(a) 322
(b) 1 (c) 323
(d) 34

Ans : (d)

34

Let, y

32 32
26`
j h

Squaring (1) both sides, we get

y 2

32 322 6

2 _ f i h p 94
2326
2 f h p 94

2326212

f h p 94

23824 3

f h p 916
2323
eo 916

Taking square root, we get

y /43

6. If x0$, then xxx

(a) xx (b) xx 4 (c) x 8 (d) x 78

Ans : (d) x

78
xxx xx //3212 ^h .xx /34 ^h x /74 x /78 x 78

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7.

10 373

6525

15 3 232

^^^hh h (a) 1 (b) 2 (c) 1/2 (d) 3

Ans : (a) 1

10 373

6525

15 3 232

^^^hh h

10 373

10 310 3

6525#
6565

15 3 232

15 3 215 3 2##

773

10 32565

^^hh 332

15 3 2

^h

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Chap 1 : Number Systems www.cbse.online

30 3 2 30 10 30 6 1

8. The rationalising factor of abc

2345
is (a) abc 325
(b) abc 324
(c) abc 323
(d) abc 32

Ans : (a) abc

325

Since, multiplication of abc

2345
by abc 325
gives rational number.

R.F. of

abc 2345
abc 325

9. Four rational numbers between 3 and 4 are:

(a) ,,,5354156 (b) ,,,513514516517 (c) 3.1, 3.2, 4.1, 4.2 (d) 3.1, 3.2, 3.8, 3.9

Ans : (d) 3.1, 3.2, 3.8, 3.9

To find four rational numbers between 3 and 4.

5 35#
and 545# 515
and 520

Between 515 and 520 lies ,,,516517518519

Now, from the given options (a) and (b) does not

contain rational number between 3 and 5. (c) has 4.1 and 4.2 that does not lie between 3 and 4.

10. Value of x satisfying xx325

, is (a) 6 (b) 7 (c) 8 (d) 9

Ans : (a) 6

x 6 satisfies the given equation

11. If both ''a and ''b are rational numbers, then ''a and ''b

from ab325355 , respectively are (a) ,1191119 (b) ,1119119 (c) ,112118 (d) ,11101121 (a) ,1191119

We have, 32535

ab5 32535

325325#

ab5 ab5 () ( )()( )

32535325

22
or 1135325 ^^hh

119653510

1119 9 5

11951119

On comparing, we get a 119, b 1119.12. Simplify : 2222 2 nn n 34
h h (a) 281 n1 (b) 2 n1 (c) 12 n (d) 7/8

Ans : (d) 7/8

22222
nnn 34
hh 222
nnn 441
122
nn 41
12 nn14 12 3

181 87

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13. A rational number equivalent to a rational number

19 7 is (a) 11917
(b) 5714 (c) 3821 (d) 5721

Ans : (d) 5721

Simplest form of 11917 11917

Simplest form of 5714 5714

Simplest form of 3821 3821

Simplest form of 5721 197

14. The numerator of aabaab

aabaab 2222
2222
is (a) a 2 (b) b 2 (c) ab 22
(d) ab42 22

Ans : (d) ab42

22
aab aab aabaab 2222
2222
aaab aab2

2222 22

abaab aab2

22222 22

^h bab42 222

15. The ascending order of the surds ,,234

369
is (a) ,,432 963
(b) ,,423 936
(c) ,,234 369
(d) ,,342 693

Ans : (a) ,,432

963

Surds are ,,23431

61
91
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