Mathematics Class X

12 Topics | 4 Quizzes

What are Real Numbers?

Rational Numbers

Irrational Numbers

Natural Numbers

Euclid’s Division Lemma

Euclid’s Division Algorithm

Application of lemma

Fundamental theorem of Arithmetic

Concept Checkers-Real Numbers-Class X

Practice Questions-Real Numbers-Class X

Practice Questions 2-Real Numbers-Class X

Olympiad Questions-Real Numbers-Class X

13 Topics | 4 Quizzes

Degree of a Polynomial

Types of polynomials based on the number of terms

Types of Polynomials based on Degree

Value of Polynomial

Zero of a Polynomial

Graph of a Linear Polynomial

Graph of Quadratic Polynomial

Factorisation of Polynomials

Splitting the middle term:

Relationship between Zeroes and Coefficients of a Polynomial

Division Algorithm

Algebraic Identities

Practice Questions 2 – Polynomials – Class X

Olympiad Questions – Polynomials – Class X

Concept Checkers – Polynomials – Class X

Practice Questions – Polynomials – Class X

Pair of Linear Equations in Two Variables

4 Topics | 4 Quizzes

Linear Equations

Pair of Linear Equations

Graphical method of solution of a pair of Linear Equations

Algebraic Methods of Solving a Pair of Linear Equations

Practice Questions 2 – Pair of Linear Equations in Two Variables – Class X

Olympiad Questions – Pair of Linear Equations in Two Variables – Class X

Concept Checkers – Pair of Linear Equations in Two variables – Class X

Practice Questions – Pair of Linear Equations in Two Variables – Class X

Quadratic Equations

7 Topics | 4 Quizzes

Quadratic Polynomial

Quadratic Equation

Standard form of Quadratic Equation

Types of Quadratic Equations

Roots of a Quadratic Equation

Methods to solve the Quadratic Equations

Nature of Roots

Practice Questions 2 – Quadratic Equations – Class X

Olympiad Questions – Quadratic Equations – Class X

Concept Checkers – Quadratic Equations – Class X

Concept Checkers – Quadratic Equation – Class X

Arithmetic Progressions

5 Topics | 4 Quizzes

Arithmetic Progressions

Finite or Infinite Arithmetic Progressions

The general form of an AP

Arithmetic Series

Sum of first n terms of an Arithmetic series

Olympiad Questions-Arithmetic Progression-ClassX

Practice Questions 2-Arithmetic Progression-ClassX

Concept Checkers – Arithmetic Progressions – Class X

Practice Questions – Arithmetic Progressions – Class X

8 Topics | 4 Quizzes

Based on the length

Based on the angle

Centers of the Triangle

Similarity Criteria of Triangles

Basic Proportionality Theorem (Thales Theorem)

Converse of Basic Proportionality Theorem

Pythagoras Theorem (Baudhayan Theorem)

Practice Questions 2-Triangles-ClassX

Olympiad Questions-Triangles-ClassX

Concept Checkers – Triangles – Class X

Practice Questions – Triangles – Class X

Coordinate Geometry

9 Topics | 4 Quizzes

Cartesian coordinate system

Equation of a Straight Line

Distance formula

Section formula

Mid-point formula

Centroid of a Triangle

Area of a triangle given its vertices

Collinearity Condition

Using section formula

Concept Checkers – Coordinate Geometry – Class X

Practice Questions – Coordinate Geometry – Class X

Practice Questions 2-Coordinate Geometry-ClassX

Olympiad Questions-Coordinate Geometry-ClassX

Introduction to Trigonometry

7 Topics | 4 Quizzes

Trigonometric Ratios

Relation between Trigonometric Ratios

Trigonometric Ratios of Some Specific Angles

Trigonometric Ratios of Complementary Angles

Range of Trigonometric Ratios from 0 to 90 degrees

Trigonometric Identities

Practice Questions 2-Introduction to Trigonometry-Class X

Olympiad Questions-Introduction to Trigonometry-Class X

Concept Checkers -Trigonometry – Class X

Practice Questions -Trigonometry – Class X

Some Applications of Trigonometry

5 Topics | 2 Quizzes

APPLICATION OF TRIGONOMETRY

Horizontal Line

Angle of Elevation

Angle of Depression

Practice Questions-Some Applications of Trigonometry-Class X

Olympiad Questions-Some Applications of Trigonometry-Class X

5 Topics | 2 Quizzes

Introduction to Circles

Circle and line in a plane

Tangent to a Circle

Circle Theorems

Length of a tangent

Olympiad Questions-Circles-Class X

Practice Questions-Circles-Class X

3 Topics | 2 Quizzes

Division of a Line Segment

Construction of a Triangle similar to a given Triangle as per given Scale

Concept Checkers – Construction – Class X

Practice Questions-Construction-Class X

Areas Related to Circles

5 Topics | 3 Quizzes

Areas related to Circle

Area of a Sector of a Circle

Perimeter and Area of the Semi-circle

Areas of Segments of the Circle

Areas of Combinations of Plane Figures

Concept Checkers-Areas Related to Circles-Class X

Practice Questions-Areas Related to Circles-Class X

Olympiad Questions-Areas Related to Circles-Class X

Surface Areas and Volumes

4 Topics | 2 Quizzes

Volume of a combination of solids

Conversion of Solid from One Shape to Another

Frustum of a Cone

Olympiad Questions-Surface area and volume-Class X

Practice Questions-Surface area and volumes-Class X

8 Topics | 2 Quizzes

Mean of Grouped Data (Without Class-Interval)

Mean of Grouped Data (With Class-Interval)

Mode of Grouped Data

Median of Grouped Data

Graphical Representation of Cumulative Frequency Distribution

Practice Questions-Statistics-Class X

Olympiad Questions-Statistics-Class X

4 Topics | 1 Quiz

Sum of Probabilities

Sure or Certain Event

Complementary Events

Olympiad Questions-Probability-Class X

Mock Test 1-Class X

Mock Test 2 – Class X

Mock Test 3 – Class X

Concept Checkers-Areas Related to Circles-Class X

Mathematics Class X Areas Related to Circles Concept Checkers-Areas Related to Circles-Class X

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Question 1 of 10

1. Question
1 point(s)
If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm. The diameter of the larger circle is
- 13 cm
- 26 cm
- 15 cm
- 10 cm
Correct

Incorrect

Hint

$\pi r^2=\pi r^2_1+\pi r^2_2\\ \\ \pi r^2=\pi(r^2_1+r^2_2)\\ \\ r^2=5^2+12^2\\ \\ =169\Rightarrow r=13\ cm\\ \\ D=2\times13=26\ cm$
Question 2 of 10

2. Question
1 point(s)
The circumference of a circle is 22 cm. The area of its quadrant is
- \(\dfrac{77}{8}\ cm^2 \)
- \(\dfrac{77}{4}\ cm^2 \)
- \(\dfrac{22}{3}\ cm \)
- \(77\ cm^2 \)
Correct

Incorrect

Hint

$2\times\dfrac{22}{7}\times r=22\\ \\ \Rightarrow r=\dfrac{22\times7}{2\times22}=\dfrac{7}{2}\ cm$
Area of quadrant $=\dfrac{1}{4}\pi\ r^2$
$=\dfrac{1}{4}\times\dfrac{22}{7}\times\dfrac{7}{2}\times\dfrac{7}{2}=\dfrac{77}{8}\ cm^2$
Question 3 of 10

3. Question
1 point(s)
The distance covered by a wheel of diameter 35 cm in one revolution is
- 100 cm
- 110 cm
- 120 cm
- 75 cm
Correct

Incorrect

Hint

Required distance $=2\pi r$
$=2\times\dfrac{22}{7}\times\dfrac{35}{2}=110\ cm$
Question 4 of 10

4. Question
1 point(s)
The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes
- \(\dfrac{154}{3}\ cm^2 \)
- \(56\ cm^2 \)
- \(154\ cm^2 \)
- \(155\ cm^2 \)
Correct

Incorrect

Hint

$\theta=\dfrac{360}{60}\times5=30^o$
Area $=\dfrac{\theta}{360}\times\pi r^2=\dfrac{30}{360}\times\dfrac{22}{7}\times14\times14=\dfrac{154}{3}\ cm^2$
Question 5 of 10

5. Question
1 point(s)
Find the area of the circle inscribed in a square of side ‘a’ cm
- \(\dfrac{\pi a^2}{4} \)
- \(\dfrac{\pi}{4} \)
- \(a^2 \)
- \(\dfrac{\pi a^2}{2} \)
Correct

Incorrect

Hint

Radius $=\dfrac{a}{2}$
Area $=\pi\left(\dfrac{a}{2}\right)^2$
$=\dfrac{\pi a^2}{4}\ cm^2$
Question 6 of 10

6. Question
1 point(s)
The ratio of the areas of a circle and an equilateral triangle whose diameter and side are respectively equal
- \(\dfrac{\pi}{2} \)
- \(\dfrac{\pi}{3} \)
- \(\dfrac{\pi}{\sqrt3} \)
- \(\dfrac{\pi}{4} \)
Correct

Incorrect

Hint

$2r=a\Rightarrow \dfrac{r}{a}=\dfrac{1}{2}$
Ratio $=\dfrac{\pi r^2}{\dfrac{\sqrt3}{4}a^2}$
$=\dfrac{4\pi}{\sqrt3}\left(\dfrac{r}{a}\right)^2=\dfrac{4\pi}{\sqrt3}\times\dfrac{1}{4}=\dfrac{\pi}{\sqrt3}$
Question 7 of 10

7. Question
1 point(s)
If the circumference and the area of a circle are numberically equal, the diameter of the circle is
- 2 units
- 4 units
- 6 units
- 3 units
Correct

Incorrect

Hint

$2\pi r=\pi r^2\\ \\ \Rightarrow 2r=r^2\\ \\ \Rightarrow r=2\\ \\ d=4\ units$
Question 8 of 10

8. Question
1 point(s)
The radius of a wheel is 0.25 m. The number of revolutions it will make to trauel a distance of 11 km
- 7002
- 7000
- 6000
- 6500
Correct

Incorrect

Hint

Number of revolutions $=\dfrac{11\times1000}{2\times\frac{22}{7}\times0.25}=7000$
Question 9 of 10

9. Question
1 point(s)
The area of the largest triangle that is inscribed in a semicircle of radius r unit?
- \(\dfrac{r^2}{2} \)
- \(r^3 \)
- \(\sqrt r \)
- \(r^2 \)
Correct

Incorrect

Hint

Area of $\triangle ABC=\dfrac{1}{2}\times2r\times r$
$=r^2\ \text{sq unit}$
Question 10 of 10

10. Question
1 point(s)
The angle subtended at the centre of a circle of radius 10 cm by an arc of length \( 5\pi\ cm\)
- \(60^o \)
- \(90^o \)
- \(45^o \)
- \(180^o \)
Correct

Incorrect

Hint

Length of arc of a circle $=\dfrac{\theta}{360}\times2\pi r$
$5\pi=\dfrac{\theta}{360}2\times\pi\times 10\\ \\ \theta=\dfrac{5\times360}{20}=90^o$

Concept Checkers-Areas Related to Circles-Class X

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