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Published on: 27/07/2018
Based on the current academic syllabus, some of the important questions are prepared from the chapter Number Systems.
Download CBSE Class 9th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 9th Standard CBSE Mathematics
Questions + Answers key
Take MCQ Mathematics Test
1.
Simplify: \({ \left[ { 5 }^{ 2 }{ \left( { 8 }^{ 1/3 }+{ 27 }^{ 1/3 } \right) }^{ 3 } \right] }^{ 1/5 }\)
2.
If \(p=\frac { 3-\sqrt { 2 } }{ 3+\sqrt { 2 } } \) and \(q=\frac { 3+\sqrt { 2 } }{ 3-\sqrt { 2 } } \) find \({ p }^{ 2 }+{ q }^{ 2 }\)
3.
Divide \(8\sqrt { 15 } \) by \(2\sqrt { 3 } \)
4.
Check whether \(7\sqrt { 5 } ,\frac { 7 }{ \sqrt { 5 } } .\sqrt { 2 } +21,\pi -5\) are irrational numbers or not.
5.
Express \(18.\overline{48} \) in the form of p/q, where p and q are integers, \(q\neq 0\) .
6.
Find five rational numbers between 1 and 2.
7.
Write three rational numbers between -2/5 and -1/5.
8.
Find two rational numbers between 0.1 and 0.2.
9.
Simplify: \(3\sqrt { 45 } -\sqrt { 125 } +\sqrt { 200 } -\sqrt { 50 } \)
10.
Write the following in decimal form and say what kind of decimal expansion each has:
\(\frac { 3 }{ 13 } \)
11.
If \({ 8 }^{ x }=\frac { 64 }{ { 2 }^{ x } } \) , then the value of x is
3
1
1/2
3/2
12.
(0.001)1/3 is equal to
0.1
0.001
0.01
0.0001
13.
The sum of \(0.\overline { 3 } \) and \(0.\overline { 2 } \)
\(\frac { 5 }{ 99 } \)
\(\frac { 5 }{ 9 } \)
\(\frac { 5 }{ 10 } \)
\(\frac { 5 }{ 100 } \)
14.
Which of the following numbers is an irrational number?
\(\sqrt { 23 } \)
\(\sqrt { 225 } \)
0.3796
\(7.\overline { 478 } \)
15.
The rational number between -1/5 and -2/5 is
0
-1/4
-3/10
-7/25
16.
A rational number lying between \(\sqrt { 2 } \) and \(\sqrt { 3 } \) is:
\(\frac { \sqrt { 2 } +\sqrt { 3 } }{ 2 } \)
\(\sqrt { 6 } \)
1.6
1.9
17.
Every rational number is:
a natural number
an integer
a real number
a whole number
18.
Which of the following is a rational number?
\(1+\sqrt { 3 } \)
\(\pi \)
\(2\sqrt { 3 } \)
0
19.
Prove that \(\frac { { 2 }^{ 30 }+{ 2 }^{ 29 }+{ 2 }^{ 28 } }{ { 2 }^{ 31 }+{ 2 }^{ 30 }+{ 2 }^{ 29 } } =\frac { 7 }{ 10 } \)
20.
(i) express 2.4 \(\overline { 248 } \) in the form of \(p\over q\) where \(p\over q\) is in its lowest form.
(ii) What is the value of p?
(iii) what is the value of q?
(iv) what name can be given to the number p?
(v) what name can be given to the number q?
(vi) Apala declares that p and q are co-prime. IS she correct? If so, which value of Apala is depicted by her declaration?
(vii) Which mathematical concept has been converted in this problem?
(viii) Write the formulae used in the solution.
21.
Are the following statements true or false? Justify your answers.
(i) Every real number is either irrational or rational.
(ii) \(\sqrt { 7 } \) is an irrational number but not a real number.
(iii) 4 is real but not irrational
22.
State whether the following statements are true or false.Give reason for your answer.
(i) Every whole number is a natural number.
(ii) Zero is neither a negative nor a positive integer.
(iii) There are finitely many rational numbers between any two given rational numbers.
1.
5
2.
98
3.
\(8 \sqrt{15} \div 2 \sqrt{3}=\frac{8 \sqrt{3} \times \sqrt{5}}{2 \sqrt{3}}=4 \sqrt{5}\)
4.
All are irrational numbers.
5.
610/33
6.
7/6,4/3,3/2,5/3 and 11/6
7.
-7/20,-3/10,-1/4
8.
0.125, 0.15
9.
\(4\sqrt { 5 } +5\sqrt { 2 } \)
10.
\(\frac { 3 }{ 13 } \)= 0.230769230769...=\(0.\overline { 230769 } \)
11.
(d)
3/2
12.
(a)
0.1
13.
(b)
\(\frac { 5 }{ 9 } \)
14.
(a)
\(\sqrt { 23 } \)
15.
(c)
-3/10
16.
(c)
1.6
17.
(c)
a real number
18.
(d)
0
19.
\(\frac { { 2 }^{ 30 }+{ 2 }^{ 29 }+{ 2 }^{ 28 } }{ { 2 }^{ 31 }+{ 2 }^{ 30 }+{ 2 }^{ 29 } } =\frac { { 2 }^{ 28 }\left( { 2 }^{ 2 }+{ 2 }^{ 1 }+1 \right) }{ { 2 }^{ 29 }\left( { 2 }^{ 2 }+{ 2 }^{ 1 }+1 \right) } \)
\(\\ =\frac { { 2 }^{ 2 }+{ 2 }^{ 1 }+1 }{ { 2 }^{ 29-28 }\left( { 2 }^{ 2 }+{ 2 }^{ 1 }+1 \right) }\)
\( \\ =\frac { 4+2+1 }{ { 2 }^{ 1 }(4+2+1) } =\frac { 7 }{ 2(5) } =\frac { 7 }{ 10 } \)
20.
(i) Let x =2.4 \(\overline { 178 } \)
Then x = 2.4178178178...
⇒ 10x = 24.178178178..... . ...(1)
⇒ 10000x = 24178.178178178 ....(2)
Subracting (1) from (2), we get
99990x = 24154
⇒ x = \(24154\over9990\)
⇒ x = \(12077\over4995\)
(ii) p = 12077
(iii) q = 4995
(iv) p is a natural number or a whole number or a positive integer.
(v) q is a natural number or a whole number or a positive integer.
(vi) Let us find out the HCF of p and q
p = 12077 = 13 x 929
q = 4995 = 3 x 3 x 3 x 5 x 37
\(\therefore\) HCF (p,q) = 1
\(\therefore\) p and q are co-prime.
\(\therefore\) Apala is correct.
So, the value 'deductive' is depicted by her declaration.
(vii) The mathematical concept 'Number system' has been converted in this problem.
(viii) The formulae used in the solution are as follows:
1. Method of expressing a recurring and non-terminating decimal in the form of a rational number.
2. Concept of natural numbers or whole numbers or positive integer.
3. reduction of a rational in its lowest terms.
4. Concept of co-prime numbers.
21.
( )
(i) True
(ii) False; because irrational number is a part of real number.
(iii) True
22.
( )
(i) False, because 0 is not a natural number.
(ii) True, because 0 is non-negative and non-positive integer.
(iii) False, because there are infinitely many rational number between two rational number.
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