Which of the following is rational?
- A$\sqrt{3}$
- B$\pi$
- C$\frac{4}{0}$
- ✓$\frac{0}{4}$
Answer: D.
View full solution →Question types
Number System question types
186 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
186
Questions
9
Question groups
5
Question types
01
M.C.Q
72 Q→02Assertion (A) & Reason (B) MCQ
12 Q→03True False[1 Marks ]
9 Q→04Fill In The Blanks[1 Marks ]
15 Q→051 Marks Question
33 Q→062 Marks Questions
21 Q→073 Marks Question
13 Q→08Case study (4 Marks)
2 Q→094 Marks Questions
9 Q→Sample Questions
Number System questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
An irrational number between $2$ and $2.5$ is:
- A$\sqrt{11}$
- ✓$\sqrt{5}$
- C$\sqrt{22.5}$
- D$\sqrt{12.5}$
Answer: B.
View full solution →The number $0.\overline{32}$ when expressed in the form $\frac{\text{p}}{\text{q}}$ $\big($p, q are integers and $\text{q}\neq0\big),$ is:
- A$\frac{8}{25}$
- ✓$\frac{29}{90}$
- C$\frac{32}{99}$
- D$\frac{32}{199}$
Answer: B.
View full solution →Which one of the following statements is true?
- AThe sum of two irrational numbers is always an irrational number.
- BThe sum of two irrational numbers is always a rational number.
- ✓The sum of two irrational numbers may be a rational number or an irrational number.
- DThe sum of two irrational numbers is always an integer.
Answer: C.
View full solution →The number $1.\overline{27}$ in the form $\frac{\text{p}}{\text{q}},$ where $p$ and $q$ are integers and $\text{q}\neq0,$ is:
- A$\frac{14}{9}$
- ✓$\frac{14}{11}$
- C$\frac{14}{13}$
- D$\frac{14}{15}$
Answer: B.
View full solution →Statement-1 (A): There are infinitely many rational numbers between any two integers.
Statement-2 (R):The square of an irrational number is always a rational number.
Statement-2 (R):The square of an irrational number is always a rational number.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-5
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- ✓Statement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: C.
View full solution →Statement-1 (A): If x and y are rational and irrational numbers respectively, then x + y is an irrational number.
Statement-2 (R): If x and y are two irrational numbers, then x + y is an irrational number
Statement-2 (R): If x and y are two irrational numbers, then x + y is an irrational number
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-4
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- ✓Statement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: C.
View full solution →Statement-1 (A): $\frac{13}{20}$ $\frac{14}{20}$ and $\frac{15}{20}$ are three rational numbers between $\frac{1}{2}$ and $\frac{4}{5}$
Statement-2 (R): A rational number between two rational numbers $p$ and $q$ is $\frac{1}{2}(p+q)$.
Statement-2 (R): A rational number between two rational numbers $p$ and $q$ is $\frac{1}{2}(p+q)$.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): $\pi$ is an irrational number.
Statement-2 (R): Euler's constant e is an irrational number.
Statement-2 (R): Euler's constant e is an irrational number.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-2
- ✓Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: B.
View full solution →Statement-1 (A): 0.7 and 0.00323232... are rational numbers.
Statement-2 (R): If the decimal expansion of a real number is either terminating or non-terminating recurring it is a rational number.
Statement-2 (R): If the decimal expansion of a real number is either terminating or non-terminating recurring it is a rational number.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Answer whether the following statements are true or false? Give reasons in support of your answer. Every rational number is a whole number.
Answer whether the following statements are true or false? Give reasons in support of your answer. Every integer is a whole number.
Answer whether the following statements are true or false? Give reasons in support of your answer. Every rational number is an integer.
Find whether the following statement are true or false: Every real number is either rational or irrational.
Answer whether the following statements are true or false? Give reasons in support of your answer. Every whole number is a natural number.
The decimal representation of a rational number is either _______ or ________.
The decimal form of an irrational number is neither ______ nor ______.
Every point on the number line corresponds to a ______ number which many be either ______ or ______.
Every real number is either ________ number or ________ number.
Every real number is either _______________ or _______________ number.
Express the following decimals in the form $\frac{\text{p}}{\text{q}}: 7.010$
View full solution →Express the following decimals in the form $\frac{\text{p}}{\text{q}}: 9.90$
View full solution →Give an example of two irrational numbers whose: Quotient is an irrational number.
Examine, whether the following numbers are rational or irrational: $\big(\sqrt{2}-2\big)^2$
View full solution →In the following equations, find which variables $x, y$ and $z$ etc. represent rational or irrational numbers:
$y^2=9$
View full solution →$y^2=9$
Express the following rational numbers as decimals: $\frac{327}{500}$
View full solution →Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers: $\sqrt{1.44}$
View full solution →Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers: $\sqrt{4}$
View full solution →Express the following rational numbers as decimals: $\frac{33}{26}$
View full solution →Express the following rational numbers as decimals: $\frac{2}{3}$
View full solution →Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$ $0.\bar{4}$
View full solution →Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$ $0.\overline{54}$
View full solution →Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$ $125.\bar{3}$
View full solution →Explain how irrational number is differ from rational numbers?
Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$
$0.\overline{47}$
View full solution →$0.\overline{47}$
Aarushi and Amin are playing with match-sticks by making different geometrical and other figures. Avni kept one match-stick horizontally and then two match-sticks vertically as shown in Figure and then asks Aarushi to join the open ends of horizontally and vertically placed strings by a thread. Avni's eleder sister Mira comes and ask them to find the length of the thread if each matchstick is of unit length.
Aarushi replies that the length of the thread can be found by using Pythagoras Theorem and it is equal to $\sqrt{1^2+2^2}=\sqrt{4+1}=\sqrt{5}$ units using your knowledge about numbers, answer the following questions.
(i) $\sqrt{5}$ is
(a) a rational number
(b) an irrational number
(c) non-terminating non-recurring
(d) not possible
(ii) The decimal representation of an irrational number is
(a) terminating $\quad$(b) non-terminating recurring $\quad$(c) an integer $\quad$(d) a whole number $\quad$
(iii) The decimal representation of a rational number cannot be
(a) terminating
(b) non-terminating
(c) non-terminating repeating
(d) non-terminating non-repeating
(iv) the sum 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
View full solution →Aarushi replies that the length of the thread can be found by using Pythagoras Theorem and it is equal to $\sqrt{1^2+2^2}=\sqrt{4+1}=\sqrt{5}$ units using your knowledge about numbers, answer the following questions.
(i) $\sqrt{5}$ is
(a) a rational number
(b) an irrational number
(c) non-terminating non-recurring
(d) not possible
(ii) The decimal representation of an irrational number is
(a) terminating $\quad$(b) non-terminating recurring $\quad$(c) an integer $\quad$(d) a whole number $\quad$
(iii) The decimal representation of a rational number cannot be
(a) terminating
(b) non-terminating
(c) non-terminating repeating
(d) non-terminating non-repeating
(iv) the sum 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
Ravish and Aarushi dedcided to visit world book fair which is organised every year. During their visit Aarushi was fascinated by the cover page of a book with $\pi / e$ written on it. $\pi$ and e are mathematical constants. In Euclidean geometry $\pi$ is defined as the ratio of a circle's circumference to its diameter. It is also referred to as Archimede's constant. The constant e is known as Euler's number and it is the limiting value of $\left(1+\frac{1}{n}\right)^n$ as $n$ approches infinity. Using the knowledge of rational and irrational numbers answer the following questions.
(i) $\pi$ represents
(a) an integer
(b) a rational number
(c) an irrational number
(d) a natural number
(ii) e represents
(a) a natural number
(b) an integer
(c) a rational number
(d) an irrational number
(iii) The product of any two irrational numbers is
(a) always an irrational number $\quad$(b) not necessarily an irrational number $\quad$
(c) never an irrational number $\quad$ (d) always an integer $\quad$
(iv) A rational number between $\sqrt{2}$ and $\sqrt{3}$ is
(a) $\frac{\sqrt{3}-\sqrt{2}}{2}$$\quad$(b) $\frac{\sqrt{3}+\sqrt{2}}{2}$$\quad$(c) $1 . \overline{6}$ $\quad$(d) $0 . \overline{2}+0 . \overline{3}$$\quad$
View full solution →(i) $\pi$ represents
(a) an integer
(b) a rational number
(c) an irrational number
(d) a natural number
(ii) e represents
(a) a natural number
(b) an integer
(c) a rational number
(d) an irrational number
(iii) The product of any two irrational numbers is
(a) always an irrational number $\quad$(b) not necessarily an irrational number $\quad$
(c) never an irrational number $\quad$ (d) always an integer $\quad$
(iv) A rational number between $\sqrt{2}$ and $\sqrt{3}$ is
(a) $\frac{\sqrt{3}-\sqrt{2}}{2}$$\quad$(b) $\frac{\sqrt{3}+\sqrt{2}}{2}$$\quad$(c) $1 . \overline{6}$ $\quad$(d) $0 . \overline{2}+0 . \overline{3}$$\quad$
Visualise the representation of $5.3\bar{7}$ on the number line upto 5 decimal places, that is upto $5.37777.$
View full solution →Represent $\sqrt{3.4},\sqrt{9.4},\sqrt{10.5}$ on the real number line.
View full solution →Represent $\sqrt{6},\sqrt{7},\sqrt{8}$ on the number line.
View full solution →Find a rational number and also an irrational number lying between the numbers $0.3030030003...$ and $0.3010010001...$
View full solution →Visualise $2.665$ on the number line, using successive magnification.
View full solution →Generate a Number System paper free
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