Mathematics Class IX

8 Topics | 8 Quizzes

Irrational Numbers

Real Numbers and their Decimal Expressions

Representating Real Numbers on the Number Line

Operations on Real Numbers

Identities Related to Square Roots

Rationalizing the Denominator

Laws of Exponents for Real Numbers

Concept Checkers 1-Number Systems-Class IX

Concept Checkers 2-Number Systems-Class IX

Practice Questions 1-Number Systems-Class IX

Practice Questions 2-Number Systems-Class IX

Practice Questions 3-Number Systems-Class IX

Practice Questions 4 – Number Systems – Class IX

Olympiad Questions 1-Number Systems-Class IX

Olympiad Questions 2-Number systems-Class IX

6 Topics | 8 Quizzes

Polynomials in One Variable

Zeros of a Polynomial

Remainder Theorem

Factorization of Polynomials

Algebraic Identities

Practice Questions 5 – Polynomials – Class IX

Concept Checkers – Polynomials – Class IX

Practice Questions 1 – Polynomials – Class IX

Practice Questions 2 – Polynomials – Class IX

Practice Questions 3 – Polynomials – Class IX

Practice Questions 4 – Polynomials – Class IX

Olympiad Questions – Polynomials – Class IX

Olympiad Questions 2 – Polynomials – Class IX

Coordinate Geometry

3 Topics | 4 Quizzes

Quadrants of the Cartesian Plane

Coordinates of a Point

Concept Checkers – Coordinate Geometry – Class IX

Practice Questions – Coordinate geometry – Class IX

Olympiad Questions – Coordinate Geometry – Class IX

Olympiad Questions 2 – Coordinate Geometry – Class IX

Linear Equations in Two Variables

5 Topics | 7 Quizzes

Linear Equations

Solutions of a Linear Equation

Graph of a Linear Equation in Two Variables

Equations of Lines Parallel to x-axis and y-axis

Practice Questions 3 – Linear equation in two variables – Class IX

Practice Questions 4 – Linear equation in two variables – Class IX

Concept Checkers – Linear Equations in two variables – Class IX

Practice Questions 1 – Linear Equations in two variables – Class IX

Practice Questions 2 – Linear Equations in two variables – Class IX

Olympiad Questions – Linear Equations in two varaibles – Class IX

Olympiad Questions 2 – Linear Equation in two variables – Class IX

Introduction to Euclid’s Geometry

3 Topics | 4 Quizzes

Euclid’s Definitions, Axioms and Postulates

Equivalent Versions of Euclid’s Fifth Postulate

Concept Checkers – Introduction to Euclid’s Geometry – Class IX

Practice Questions – Introduction to Euclid’s geometry – Class IX

Olympiad Questions – Introduction to Euclid’s Geometry – Class IX

Olympiad Questions 2 – Introduction to Euclid’s geometry – Class IX

Lines and Angles

7 Topics | 6 Quizzes

Basic Terms and Definitions

Intersecting Lines and Non-Intersecting Lines

Parallel Lines and a Transversal

Lines Parallel to the same Line

Angle Sum Property of a Triangle

Concept Checkers – Lines and Angles – Class IX

Practice Questions 1 – Lines and Angles – Class IX

Practice Questions 2 – Lines and Angles – Class IX

Practice Questions 3 – Lines and angles – Class IX

Olympiad Questions – Lines and Angles – Class IX

Olympiad Questions 2 – Lines and angles – Class IX

5 Topics | 4 Quizzes

Congruence of Triangles

Criteria for Congruence of Triangles

Some Properties of a Triangle

Inequalities in a Triangle

Concept Checkers – Triangles – Class IX

Practice Questions – Triangles – Class IX

Olympiad Questions – Triangle – Class IX

Olympiad Questions 2-Triangles-Class IX

5 Topics | 5 Quizzes

Angle Sum Property of a Quadrilateral

Types of Quadrilateral

Properties of a Parallelogram

The Mid-Point Theorem

Concept Checkers – Quadrilaterals – Class IX

Concept Checkers2-Quadrilaterals-ClassIX

Practice Questions-Quadrilaterals-ClassIX

Olympiad Questions – Quadrilaterals – Class IX

Olympiad Questions 2-Quadrilaterals-Class IX

Areas of Parallelogram and Triangles

5 Topics | 4 Quizzes

Figure on the same Base and Between the same Parallels

Parallelograms on the same Base and Between the same Parallels

Triangles on the same Base and Between the same Parallels

Concept Checkers-Areas of Parallelograms and Triangles-ClassIX

Practice Questions- Areas of Parallelograms and Triangles-Class IX

Olympiad Questions – Areas of Parallelograms and Triangles – Class IX

Olympiad Questions 2-Areas of Parallelogram and Triangles-Class IX

5 Topics | 4 Quizzes

Terms related to circle

Angles Subtended by a Chord at a Point

Angle Subtended by an Arc of a Circle

Cyclic Quadrilaterals

Concept Checkers 2-Circles-Class IX

Olympiad Questions 2-Circles-Class IX

Practice Questions-Circle-Class IX

Olympiad Questions-Circles-Class IX

4 Topics | 3 Quizzes

Basic Constructions

Some Constructions of Triangles

Practice Questions-Constructions-Class IX

Essay Type Questions-Constructions-Class IX

Concept Checkers-Construction-Class IX

Heron’s Formula

4 Topics | 4 Quizzes

Area of a Triangle – by Heron’s Formula

Application of Heron’s Formula in Finding Areas of Quadrilaterals

Concept Checkers 2- Heron’s Formula-Class IX

Olympiad Questions 2-Herons Formula-Class IX

Concept Checkers-Heron’s formula-Class IX

Olympiad Questions-Heron’s formula-Class IX

Surface Areas and Volumes

5 Topics | 2 Quizzes

Surface Area and Volume of a Cube

Surface Area and Volume of a Right Circular Cylinder

Surface Area and Volume of a Right Circular Cone

Surface Area and Volume of a Sphere

Practice Questions-Surface Areas and Volume-Class IX

Olympiad Questions – Surface Areas and Volume – Class IX

5 Topics | 2 Quizzes

Collection of Data

Geographical Representation of Data

Measures of Central Tendency

Practice Questions-Statistics-Class IX

Olympiad Questions-Statistics-Class IX

3 Topics | 4 Quizzes

Probability – An Experimental Approach

Concept Checkers 2-Probability-Class IX

Olympiad Questions 2-Probability-Class IX

Olympiad Questions-Probability-Class IX

Practice Questions-Probability-Class IX

Mock Test 1-Class IX

Mock Test 2-Class IX

Mock Test 3-Class IX

Practice Questions 4 – Number Systems – Class IX

Mathematics Class IX Number Systems Practice Questions 4 – Number Systems – Class IX

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Question 1 of 15

1. Question
1 point(s)
If \(x=2.\overline3-0.\overline9,\ y=2.\overline5-0.\overline5 \) then \(x^2+y^2-2xy \) is
- \(\dfrac{1}{4} \)
- \(\dfrac{1}{3} \)
- \(\dfrac{1}{2} \)
- \(\dfrac{1}{5} \)
Correct

Incorrect

Hint

$x=2+\dfrac{3}{9}-1=\dfrac{3}{2}\\ \\ y=2+\dfrac{5}{9}-\dfrac{5}{9}=2\\ \\ x^2+y^2-2xy=\dfrac{9}{4}+4-\dfrac{2\times3\times2}{2}\\ \\ =\dfrac{9}{4}+4-6\\ \\ =\dfrac{9+16}{4}-24=\dfrac{1}{4}$
Question 2 of 15

2. Question
1 point(s)
If \(x=\dfrac{\sqrt2+\sqrt1}{\sqrt2-\sqrt1},y=\dfrac{\sqrt2-\sqrt1}{\sqrt2+\sqrt1} \). The value of \(x^2-y^2 \) is
- \(96 \)
- \(34 \)
- \(10 \)
- \(2\sqrt2 \)
Correct

Incorrect

Hint

$x=\dfrac{\sqrt2+\sqrt1}{\sqrt2-\sqrt1}\times\dfrac{\sqrt2+\sqrt1}{\sqrt2+\sqrt1}\\ \\ =\dfrac{(\sqrt2+\sqrt1)^2}{2-1}=2+1+2\sqrt2=3+2\sqrt2\\ \\ y=3-2\sqrt2\\ \\ x^2+y^2=(x+y)^2-2xy\\ \\ =6^2-2(9-8)\\ \\ 36-2=34$
Question 3 of 15

3. Question
1 point(s)
If \(a=3+2\sqrt2 \) and \(b=\dfrac{1}{a} \) then \(a^2+b^2= \)
- 49
- 34
- 100
- 102
Correct

Incorrect

Hint

$b=\dfrac{1}{a}=\dfrac{1}{3+2\sqrt2}\times\dfrac{3-2\sqrt2}{3-2\sqrt2}=3-2\sqrt2\\ \\ a^2+b^2=(3+2\sqrt2)^2+(3-2\sqrt2)^2\\ \\ =9+8+9+8=34$
Question 4 of 15

4. Question
1 point(s)
\(\dfrac{4^{-3}\times a^{-5}\times b^{-9}}{4^{-5}\times a^{-8}\times b^3}= \)
- \(\dfrac{16a^3}{b^7} \)
- \(1 \)
- \( \dfrac{a^8}{b^{-1}}\)
- \(\dfrac{2a^2}{b^2} \)
Correct

Incorrect

Hint

$4^{-3+5}\times a^{-5+8}\times b^{-4-3}=\dfrac{16a^3}{b^7}$
Question 5 of 15

5. Question
1 point(s)
\(2\sqrt[3]{189}+3\sqrt[3]{448}-7\sqrt[3]{56}= \)
- \(8\sqrt[3]{7} \)
- \(6\sqrt[3]{7} \)
- \(4\sqrt[3]{7} \)
- \(9\sqrt[3]{7} \)
Correct

Incorrect

Hint

$2(27\times7)^{\frac{1}{3}}+3(64\times7)^{\frac{1}{3}}-7(8\times7)^{\frac{1}{3}}\\ \\ =6(7)^{\frac{1}{3}}+12(7)^{\frac{1}{3}}-14(7)^{\frac{1}{3}}=4\sqrt[3]{7}$
Question 6 of 15

6. Question
1 point(s)
\(7\sqrt[4]{162}-5\sqrt[4]{32}+\sqrt[4]{1250}= \)
- \(6\sqrt[3]{2} \)
- \(6\sqrt[4]{2} \)
- \(6\sqrt[5]{2} \)
- \(16\sqrt[4]{2} \)
Correct

Incorrect

Hint

$7(81\times2)^{\frac{1}{4}}-5(16\times2)^{\frac{1}{4}}+(625\times2)^{\frac{1}{4}}\\ \\ =21(2)^{\frac{1}{4}}-10(2)^{\frac{1}{4}}+5(2)^{\frac{1}{4}}\\ \\ =2^{\frac{1}{4}}(21-10+5)=16\sqrt[4]{2}$
Question 7 of 15

7. Question
1 point(s)
If \(x=2-\sqrt3 \), the value of \(x^2+4x+4= \)
- \(12+2\sqrt3 \)
- \(19+8\sqrt3 \)
- \(1 \)
- \(19-8\sqrt3 \)
Correct

Incorrect

Hint

$(2-\sqrt3)^2+4(2-\sqrt3)+4\\ \\ =4+3-4\sqrt3+8-4\sqrt3+4\\ \\ =19-8\sqrt3$
Question 8 of 15

8. Question
1 point(s)
The value of \(x \) when \(2^{x+4}.3^{x+1}=288 \) is
- 1
- -1
- 0
- 2
Correct

Incorrect

Hint

$2^{x+4}\ 3^{x+1}=2^5\times3^2\\ \\ x+4=5\\ \\ \text{and}\ x+1=2\\ \\ x=1$
Question 9 of 15

9. Question
1 point(s)
The value of a in \(\dfrac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3}=a+b\sqrt{15} \)
- 2
- -1
- -3
- 4
Correct

Incorrect

Hint

$\dfrac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3}\times\dfrac{\sqrt5-\sqrt3}{\sqrt5-\sqrt3}=\dfrac{(\sqrt5-\sqrt3)^2}{2}\\ \\ \dfrac{8-2\sqrt{15}}{2}=4-\sqrt{15}\\ \\ a=4$
Question 10 of 15

10. Question
1 point(s)
Express \(0.87\overline{591} \) in the form of \(\dfrac{p}{q} \)
- \(\dfrac{87591}{10000} \)
- \(\dfrac{591}{999} \)
- \(\dfrac{87591}{99999} \)
- \(\dfrac{7292}{8325} \)
Correct

Incorrect

Hint

Let $x=0.87591591$
$100x=87.591591\\ \\ 100000x=87591.591\\ \\ 100000x-100x=87591-87\\ \\ 99900x=87504\\ \\ x=\dfrac{87504}{99900}=\dfrac{7292}{8325}$
Question 11 of 15

11. Question
1 point(s)
The square root of \(0.\overline4 \) is
- \(0.\overline6 \)
- \(0.\overline7 \)
- \(0.\overline8 \)
- \(0.\overline9 \)
Correct

Incorrect

Hint

$0.\overline4=\dfrac{4}{9}=\dfrac{2}{3}=0.666=0.\overline6$
Question 12 of 15

12. Question
1 point(s)
If \(\sqrt{18225}=135 \) the value of \(\sqrt{182.25}+\sqrt{1.8225}+\sqrt{0.018225}+\sqrt{0.00018225} \) is
- 1.49985
- 14.9985
- 149.985
- 1499.85
Correct

Incorrect

Hint

$13.5+1.35+0.135+0.0135=14.9985$
Question 13 of 15

13. Question
1 point(s)
If \(2^{x-1}+2^{x+1}=640 \), the value of \(x= \)
- 7
- 8
- 9
- 6
Correct

Incorrect

Hint

$2^{x-1}\bigg\{1+2^2\bigg\}=640\\ \\ 2^{x-1}=128=2^7\\ \\ \Rightarrow x-1=7\Rightarrow x=8$
Question 14 of 15

14. Question
1 point(s)
The product of \((0.\overline{09}\times7.\overline3)= \)
- \(1 \)
- \(0 \)
- \(\dfrac{2}{3} \)
- \(\dfrac{1}{2} \)
Correct

Incorrect

Hint

$\dfrac{9}{99}\times7\dfrac{3}{9}\\ \\ =\dfrac{1}{11}\times\dfrac{66}{9}=\dfrac{2}{3}$
Question 15 of 15

15. Question
1 point(s)
\(\dfrac{1}{1+2^{x-y}}+\dfrac{1}{1+2^{y-x}}=? \)
- \(x \)
- \(x-y \)
- \(1 \)
- \( 0\)
Correct

Incorrect

Hint

$\dfrac{1}{1+\frac{2^x}{2^y}}+\dfrac{1}{1+\frac{2^y}{2^x}}\\ \\ \Rightarrow\dfrac{2^y}{2^y+2^x}+\dfrac{2^x}{2^y+2^x}\\ \\ =\dfrac{2^y+2^x}{2^y+2^x}=1$

Practice Questions 4 - Number Systems - Class IX

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