The decimal expansion of the number $\sqrt{2}$ is
- Aa finite decimal
- B1.41421
- Cnon-terminating recurring
- ✓non-terminating non-recurring
Answer: D.
View full solution →Question types
Number System [NEW] question types
173 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
173
Questions
9
Question groups
5
Question types
01
M.C.Q
63 Q→02Assertion (A) & Reason (B) MCQ
12 Q→03Fill In The Blanks[1 Marks ]
11 Q→04True False[1 Marks ]
9 Q→051 Marks Question
33 Q→062 Marks Questions
21 Q→073 Marks Question
13 Q→084 Marks Questions
9 Q→09Case study (4 Marks)
2 Q→Sample Questions
Number System [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Every rational number is
- Aa natural number
- Ban integer
- ✓a real number
- Da whole number
Answer: C.
View full solution →Between two rational numbers
- Athere is no rational number
- Bthere is exactly one rational number
- ✓there are infinitely many rational numbers
- Dthere are only rational numbers and no irrational numbers.
Answer: C.
View full solution →A rational number between $\sqrt{2}$ and $\sqrt{3}$ is
- A$\frac{\sqrt{2}+\sqrt{3}}{2}$
- B$\frac{\sqrt{2} \cdot \sqrt{3}}{2}$
- ✓1.5
- D1.8
Answer: C.
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 →Statement-1 (A): The sum of any two irrational numbers is an irrational number.
Statement-2 (R): There are two irrational numbers whose sum is a rational number.
Statement-2 (R): There are two irrational numbers whose sum is a rational number.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- ✓Statement-1 is true, Statement-2 is false.
Answer: D.
View full solution →Statement-1 (A): There are two rational numbers whose sum and product both are rationals.
Statement-2 (R): There are numbers which cannot be written in the form $\frac{p}{q}, q \neq 0, p, q$ both are integers.
Statement-2 (R): There are numbers which cannot be written in the form $\frac{p}{q}, q \neq 0, p, q$ both are integers.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is true, Statement-2 is false.
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): The product of any two irrational numbers is an irrational number.
Statement-2 (R): There are two irrational numbers whose product is not an irrational number.
Statement-2 (R): There are two irrational numbers whose product is not an irrational number.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- ✓Statement-1 is true, Statement-2 is false.
Answer: D.
View full solution →Statement-1 (A): The decimal representation of $\frac{3}{8}$ is terminating.
Statement-2 (R): If the denominator of a rational number is of the form $2^m \times 5^n$, where m, n are non-negative integers, then its decimal representation is terminating.
Statement-2 (R): If the denominator of a rational number is of the form $2^m \times 5^n$, where m, n are non-negative integers, then its decimal representation is terminating.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is true, Statement-2 is false.
Answer: A.
View full solution →The value of $1.999 \ldots$ in the form of $\frac{m}{n}$, where $m$ and $n$ are integers and $n \neq 0$, is _______________ .
View full solution →The sum of a rational number and an irrational number is _______________ number.
The simplest form of $1 . \overline{6}$ is _______________ .
View full solution →The product of a non-zero rational number with an irrational number is always an _______________ number.
The decimal expansion of $\sqrt{2}$ is _______________ and _______________ .
View full solution →Find whether the following statement are true or false:
$\pi$ is an irrational number.
View full solution →$\pi$ is an irrational number.
Find whether the following statement are true or false:
Irrational numbers cannot be represented by points on the number line.
Irrational numbers cannot be represented by points on the number line.
Find whether the following statement are true or false:
Every real number is either rational or irrational.
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.
Every whole number is a natural number.
Answer whether the following statements are true or false? Give reasons in support of your answer.
Every rational number is a whole number.
Every rational number is a whole number.
In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
y2 = 9
y2 = 9
In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
$\text{w}^2=27$
View full solution →$\text{w}^2=27$
In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
$\text{t}^2=0.4$
View full solution →$\text{t}^2=0.4$
Give an example of two irrational numbers whose:
Sum is a rational number.
Sum is a rational number.
Give an example of two irrational numbers whose:
Sum is an irrational number.
Sum is an irrational number.
Look at several examples of rational numbers in the form $\frac{\text{p}}{\text{q}}(\text{q}\neq0),$ where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?
View full solution →Is zero is rational number? Can you write it in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0?$
View full solution →In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
z2 = 0.04
z2 = 0.04
In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
x2 = 5
x2 = 5
In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
$\text{v}^2=3$
View full solution →$\text{v}^2=3$
Give two rational numbers lying between 0.515115111511115 and 0. 5353353335...
Give two rational numbers lying between 0.232332333233332 and 0.212112111211112.
Find two irrational numbers between 0.5 and 0.55.
Find one irrational number between $0.2101$ and $0.2222\ ...=0.\bar{2}$
View full solution →Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}.$
View full solution →Visualise the representation of $5.3\bar{7}$ on the number line upto 5 decimal places, that is upto 5.37777.
View full solution →Visualise 2.665 on the number line, using successive magnification.
Represent $\sqrt{6},\sqrt{7},\sqrt{8}$ on the number line.
View full solution →Represent $\sqrt{3.4},\sqrt{9.4},\sqrt{10.5}$ on the real number line.
View full solution →Prove that $\sqrt{3}+\sqrt{5}$ is an irrational number.
View full solution →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$
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
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