CBSE Class 9 Maths Number Systems MCQs Set 05

Question. Which of the following numbers has the terminating decimal representation?
(a) 1/7
(b) 1/3
(c) 3/5
(d) 17/3
Answer: c

Question. The greater between √17 - √12 and √11 - √6 is.
(a) √17 - √12
(b) √11 - √6
(c) Both are equal
(d) Cannot compare
Answer: b

Question. The rational number between 1/2 and 1/3 is
(a) 2/5
(b) 1/5
(c) 3/5
(d) 4/5
Answer: a

 Question. If 25^x-1 = 52^x-1- 100, then the value of x is.
(a) 3
(b) 2
(c) 4
(d) 1
Answer: b

Question. 0.123 can be expressed in rational form as
(a) 900 / 111 
(b) 111 / 900
(c) 123 / 10
(d) 121 / 900
Answer: b

Question. If 4⁴⁴ + 4⁴⁴ + 4⁴⁴ + 4⁴⁴ = 4^x , than x is
(a) 45
(b) 44
(c) 176
(d) 11
Answer: a 

Question. The value of (6√27 - √6 3/4)² equals 
(a) √3/2
(b) 3/2
(c) √3/4
(d) 3/4
Answer: d

Question. If m = cab / a - b, then b equals
(a) m(a - b) / ca
(b) cab - ma / ca
(c) 1 / 1 + c
(d) ma / m + ca
Answer: d

 Question. The fraction 2(√2 + √6) / 3(√2 + √3) is equal to
(a) 2√2 / 3
(b) 1
(c) 2√3 / 3
(d) 4 / 3
Answer: d

Question. If x = 2 - √3 , then the values of x² + 1/x² and x² - 1/x² respectively are.
(a) 14, 8√3
(b) -14,- 8√3
(c) 14,- 8√3
(d) -14, 8√3
Answer: c

Question. 2√6 / √2 + √3 + √5 equals
(a) √2 + √3 - √5
(b) 4 - √2 - √3
(c) √2 + 3√ + √6 - 5
(d) 1/2 (√2 + √5 - √3)
Answer: a

 Question. Rational number between √2 and √3 is
(a) √2 + √3 / 2
(b) √2 x √3 / 2
(c) 1.5
(d) 1.8
Answer: c

 Question. The ascending order of the surds ³√2, ⁶√3, ⁹√4 is
(a) ⁹√4, ⁶√3, ³√2
(b) ⁹√4, ³√2, ⁶√3
(c) ³√2, ⁶√3, ⁹√4
(d) ⁶√3, ⁹√4, ³√2
Answer: a

Question. If (a + 1/a)² = 9, then a³ + 1/a³ equals
(a) 10√3/3
(b) 3√3
(c) 18
(d) 7√7
Answer: c

Question. Assertion : Rational number lying between two rational numbers a and b is a + b/2.
Reason : There is one rational number lying between any two rational numbers.
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: c

Question. Assertion : √2 is an irrational number.
Reason : A number is called irrational, if it cannot be written in the form q/p , where p and q are integers and q ≠ 0.
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: a

Question. Assertion : 17² • 17⁵ = 17³
Reason : If a > 0 be a real number and p and q be rational numbers. Then a^p • a^q = a^p+q .
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: d

Question. Assertion : A rational number between 1/3 and 1/2 is 5/12.
Reason : Rational number between two numbers a and b is √ab .
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: c

Question. Assertion : If √2 = 1.414, √3 = 1.732, then √5 = √2 + √3 .
Reason : Square root of a positive real number alwaysexists. 
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: d

Question. Assertion : 5 - √2 = 5 - 1.414 = 3.586 is an irrational number.
Reason : The difference of a rational number and an irrational number is an irrational number.
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: a

Question. Assertion : √2, √3 are examples of irrational numbers.
Reason : An irrational number can be expressed in the form p/q .
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: c

Question. Assertion : 2 + √6 is an irrational number.
Reason : Sum of a rational number and an irrational number is always an irrational number.
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: a

Question. Assertion : 0.271 is a terminating decimal and we can express this number as 271/1000 which is of the form p/q , where p and q are integers and q ≠ 0.
Reason : A terminating or non-terminating decimal expansion can be expressed as rational number.
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: c

Question. Assertion : Every integer is a rational number.
Reason : Every integer ‘m’ can be expressed in the form m1
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.
Answer: a

 
FILL IN THE BLANK :

Question. ⁴√1008/63 is equal to ..........
Answer: (1008/63)^1/4 = (16)¹⁴ = (2⁴)^1/4 = 2

Question. The sum/difference of a rational and an irrational number is .......... .
Answer: irrational

Question. 0.72737475 is .......... number. (rational/irrational)
Answer: irrational

Question. Value of a is .......... of √3 - 1/√3 + 1 = a + b√3
Answer: 2

Question. Between two rational numbers, there exist ..........number of rational numbers. 
Answer: infinite

TRUE/FALSE:

Question. Every rational number is an integer.
Answer: False

Question. Every whole number is a natural number.
Answer: False

Question. Every natural number is a whole number.
Answer: True

Question. All rational numbers can be represented by some point on the number line.
Answer: True

Question. The sum or difference of a rational number and an irrational number is an irrational
Answer: True