10th Class Mathematics Real Numbers Question Bank

Real Numbers Total Questions - 25

1)

Which of the following numbers have terminating decimal expansion?

A)
\[\frac{8}{225}\]

B)
\[\frac{5}{18}\]

C)
\[\frac{11}{21}\]

D)
       \[\frac{21}{150}\]
View Solution
2)

A positive integer n when divided by 9, gives 7 as remainder. What will be the remainder when \[(3n-1)\] is divided by 9?

A)
1

B)
       2

C)
3

D)
       4
View Solution
3)

The fraction \[\frac{2\left( \sqrt{2}+\sqrt{6} \right)}{3\left( \sqrt{2}+\sqrt{3} \right)}\] is equal to___ .

A)
\[\frac{2\sqrt{2}}{3}\]

B)
1

C)
\[\frac{2\sqrt{3}}{3}\]

D)
       \[\frac{4}{3}\]
View Solution
4)

\[1.22\overline{4}\]can be expressed as a fraction in simplest form as ____.

A)
\[\frac{450}{551}\]

B)
\[\frac{1224}{1000}\]

C)
       \[\frac{551}{450}\]

D)
       \[\frac{1000}{1224}\]
View Solution
5)

            Given that H.C.F. (306, 954, 1314) = 18, find L.C.M. (306, 954, 1314).

A)
1183234

B)
1123238

C)
       1183914

D)
       1123328
View Solution
6)

If 'a' and 'b' are rational numbers and \[\frac{2+\sqrt{3}}{2-\sqrt{3}}=a+b\sqrt{3},\]then \[{{(a+b)}^{2}}=\_\_\_\_\_\_\_.\]

A)
121

B)
171

C)
116

D)
       198
View Solution
7)

The descending order of the surds \[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4}\]is,__

A)
\[\sqrt[6]{4},\sqrt[6]{3},\sqrt[3]{2}\]

B)
\[\sqrt[9]{4},\sqrt[3]{2},\sqrt[6]{3}\]

C)
       \[\sqrt[3]{2},\sqrt[6]{3},\sqrt[9]{4}\]

D)
       \[\sqrt[6]{3},\sqrt[9]{4},\sqrt[3]{2}\]
View Solution
8)

The product of two consecutive natural numbers is always ____-

A)
An even number

B)
An odd number

C)
A prime number

D)
Divisible by 3
View Solution
9)

The value of \[\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}\] \[+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}\] is _____.

A)
0

B)
1

C)
       2

D)
       4
View Solution
10)

The 100th root of \[{{10}^{({{10}^{10}})}}\] is ___.

A)
\[{{10}^{{{8}^{10}}}}\]

B)
\[{{10}^{{{10}^{8}}}}\]

C)
       \[{{\left( \sqrt{10} \right)}^{{{\left( \sqrt{10} \right)}^{10}}}}\]

D)
       \[{{10}^{{{\left( \sqrt{10} \right)}^{\sqrt{10}}}}}\]
View Solution
11)

The value of \[\frac{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}+\frac{a-\sqrt{{{a}^{2}}-{{b}^{2}}}}{a+\sqrt{{{a}^{2}}-{{b}^{2}}}}\] is __.

A)
\[\frac{{{a}^{2}}}{{{b}^{2}}}\]

B)
\[\frac{{{b}^{2}}}{{{a}^{2}}}\]

C)
\[\frac{a}{b}\]

D)
       \[\frac{2(2{{a}^{2}}-{{b}^{2}})}{{{b}^{2}}}\]
View Solution
12)

The rationalizing factor of \[\sqrt[7]{{{x}^{3}}{{y}^{5}}{{z}^{2}}}\] is __.

A)
\[\sqrt[7]{{{z}^{5}}{{y}^{2}}{{x}^{4}}}\]

B)
\[\sqrt[47]{{{x}^{3}}{{y}^{2}}z}\]

C)
\[\sqrt{{{x}^{4}}{{y}^{2}}{{z}^{5}}}\]

D)
                               \[\sqrt[3]{{{y}^{2}}{{x}^{4}}{{z}^{3}}}\]
View Solution
13)

Which of the following is an irrational number?

A)
\[\pi \]

B)
\[\frac{22}{7}\]

C)
Both (a) and (b)

D)
Neither (a) nor (b)
View Solution
14)

A real number \[\frac{{{2}^{2}}\times {{3}^{2}}\times {{7}^{3}}}{{{2}^{2}}\times {{5}^{3}}\times {{3}^{5}}\times {{7}^{4}}}\]will have     _______.

A)
Terminating decimal expansion

B)
Non-terminating decimal expansion

C)
Repeating decimal expansion

D)
Both (b) and (c)
View Solution
15)

According to the Fundamental Theorem of Arithmetic, if p (a prime number) divides \[{{b}^{2}}\]and b is positive, then _____.

A)
b divides p

B)
\[{{b}^{2}}\]divides p

C)
p divides b

D)
       None of these
View Solution
16)

In a seminar the number of participants in Mathematics, Physics and Biology are 192 240 and 168. Find the minimum number of rooms required if in each room same number of participants is to be seated and all of them being in the same subject.

A)
20

B)
25

C)
       28

D)
       30
View Solution
17)

Sam, Advik and Trishu go for a morning walk. They step off together and their steps measure 35 cm, 32 cm and 40 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

A)
1109

B)
       1102

C)
                   1100

D)
       1120
View Solution
18)

A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9s are wrong and the other digits are correct, then the correct answer would be _____.

A)
553681

B)
       555181

C)
       555681

D)
       556581
View Solution
19)

A boy was asked to multiply a given number by (8/17). Instead, he divided the given number by (8/17) and got the result 225 more than what he should have got if he had multiplied the number by (8/17). The given number was _____.

A)
8

B)
17

C)
64

D)
       136
View Solution
20)

Four different electronic devices make a beep after every 30 minutes, 1 hour, \[1\frac{1}{2}\]hour and 1 hour 45 minutes respectively. All the devices beeped together at 12 noon. They will again beep together at _____.

A)
12 midnight

B)
3a.m.

C)
6a.m.

D)
       9a.m.
View Solution
21)

Which of the following statements is INCORRECT?

A)
For natural numbers a and b, if a divides \[{{b}^{2}}\]then a divides b.

B)
For any natural number \[n,\,\sqrt{n-1}+\sqrt{n+1}\]is irrational.

C)
Product of distinct prime numbers is always equal to their L.C.M.

D)
For any natural number n, \[{{6}^{n}}\] never ends with digit zero.
View Solution
22)

Fill in the blanks.

(i) Every point on the number line is a P number which may either Q or R.

(ii) S numbers have either terminating or non-terminating repeating decimal expansion.

A)

P Q R S

Real     Integer Natural Irrational



B)

P Q R S

Rational Integer Real   Irrational



C)

P Q R S

Irrational Rational Integers Natural



D)

P Q R S

Real    Rational irrational Rational


View Solution

Column-l	Column-II
(P) Rational form of \[0.\overline{32}\]is	(i) \[\frac{14}{55}\]
(Q) Rational form of \[0.\overline{254}\]is	(ii) \[\frac{11}{45}\]
(R) Rational form of \[0.\overline{12}\]is	(iii) \[\frac{32}{99}\]
(S) Rational form of \[0.\overline{24}\]is	(iv) \[\frac{11}{90}\]