Maths Case Studies February 14 is celebrated as International Book Giving Day and many countries in the world celebrate this day. Read More » BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. Read More » A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile is increased by 1 unit, it would take only 128 tiles to cover the floor. (i) Assuming the original length of each side of a tile be x units, make a quadratic equation from the above information. 1 1 (iii (ii) Write the corresponding quadratic equation in standard form, ) (a) Find the value of x, the length of side of a tile by factorisation. Read More » In a school examination hall, the teacher makes students sit in such a way that no students can cheat from other student. So, the teacher decides to mark the numbers on each chair from 1. 2. 3……. Read More » A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm. Read More » A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area Read More » In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD Read More » A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. Read More » On a Sunday, your Parents took you to a fair. You could see lot of toys displayed, and you wanted them to buy a RUBIK’s cube and strawberry ice-cream for you. Observe the figures and answer the question Read More » The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important monument of Indian Architecture. Read More » Adventure camps are the perfect place for the children to practice decision making for themselves without parents and teachers guiding their every move. Some students of a school reached for adventure at Sakleshpur. Read More » Pookalam is the flower bed or flower pattern designed during Onam in Kerala. Read More » Scale drawing of an object is the same shape at the object but a different size. Read More » Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure Read More » In figure 1, a right triangle ABC in which ∠B = 90 is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC. Read More » Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh Read More » In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression: (a) Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP. (b) Which figure has 61 matchsticks? Read More » Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles.The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground. Read More » Your friend Veer wants to participate in a 200m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. He wants to do in 31 seconds. Read More » Raj and Ajay are very close friends. Both the families decide to go to Read More » In an AP, the sum of the first n terms is given by Sn = 6n – n2. Find its 30th term. Read More » Mr. Vinod is a pilot in Air India. During the Covid-19 pandemic, many Indian passengers were stuck at Dubai Airport. The government of India sent special aircraft to take them. Mr. Vinod was leading this operation. Read More » Shanta runs an industry in a shed which was in the shape of a cuboid surmounted by half cylinder. The dimensions of the base were 15 m x 7m x 8 m. The diameter of the half cylinder was 7 m and length was 15 m. Read More » A hot air balloon is rising vertically from a point A on the ground which is at distance of 100m from a car parked at a point P on the ground. Amar, who is riding the balloon, observes that it took him 15 seconds to reach a point B which he estimated to be equal to the horizontal distance of his starting point from the car parked at P. Read More » Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is. The left-right (horizontal) direction is commonly called X-axis. The up-down (vertical) direction is commonly called Y-axis. In Green Park, New Delhi Suresh is having a rectangular plot ABCD as shown in the following figure. Read More » Deepa has to buy a scooty. She can buy scooty either making cashdown payment of ₹ 25,000 or by making 15 monthly instalments as below. Ist month – ₹ 3425, IInd month – ₹ 3225, Read More » A boy is standing on the top of light house. He observed that boat P and boat Q are approaching the light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. Read More » Alia and Shagun are friends living on the same street in Patel Nagar. Shagun’s house is at the intersection of one street with another street on which there is a library. Read More » India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. Read More » One evening, Kaushik was in a park. Children were playing cricket. Birds were singing on a nearby tree of height 80m. He observed a bird on the tree at an angle of elevation of 45°. When a sixer was hit, a ball flew through the tree frightening the bird to fly away. Read More » Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane. Read More » Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86m at the Asian Grand Prix in 2017 is the maximum distance for an Indian female athlete. Keeping her as a role model, Read More » In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water Read More » A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple: Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you ‘win’. One such outcome is written as ‘RB’. Read More » A golf ball is spherical with about 300 – 500 dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter 4.2 cm and the surface has 315 dimples (hemi-spherical) of radius 2 mm. Read More » Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will have adequate space for parking. Read More » Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables Read More » Two schools ‘P’ and ‘Q’ decided to award prizes to their students for two games of Hockey x per student and Cricket y per student. Read More » Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. Read More » In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm. Read More » In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure Read More » India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. Read More » The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise Read More » While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased Read More »

February 14 is celebrated as International Book Giving Day and many countries in the world celebrate this day. Read More »

BINGO is game of chance. The host has 75 balls numbered 1 through 75. Each player has a BINGO card with some numbers written on it. Read More »

A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile is increased by 1 unit, it would take only 128 tiles to cover the floor. (i) Assuming the original length of each side of a tile be x units, make a quadratic equation from the above information. 1 1 (iii (ii) Write the corresponding quadratic equation in standard form, ) (a) Find the value of x, the length of side of a tile by factorisation. Read More »

In a school examination hall, the teacher makes students sit in such a way that no students can cheat from other student. So, the teacher decides to mark the numbers on each chair from 1. 2. 3……. Read More »

A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm. Read More »

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area Read More »

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD Read More »

A group of students of class X visited India Gate on an education trip. The teacher and students had interest in history as well. Read More »

On a Sunday, your Parents took you to a fair. You could see lot of toys displayed, and you wanted them to buy a RUBIK’s cube and strawberry ice-cream for you. Observe the figures and answer the question Read More »

The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important monument of Indian Architecture. Read More »

Adventure camps are the perfect place for the children to practice decision making for themselves without parents and teachers guiding their every move. Some students of a school reached for adventure at Sakleshpur. Read More »

Rohan wants to measure the distance of a pond during the visit to his native. He marks points A and B on the opposite edges of a pond as shown in the figure Read More »

In figure 1, a right triangle ABC in which ∠B = 90 is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC. Read More »

Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh Read More »

In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures. One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression: (a) Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP. (b) Which figure has 61 matchsticks? Read More »

Vijay is trying to find the average height of a tower near his house. He is using the properties of similar triangles.The height of Vijay’s house if 20m when Vijay’s house casts a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long on the ground and the house of Ajay casts 20m shadow on the ground. Read More »

Your friend Veer wants to participate in a 200m race. He can currently run that distance in 51 seconds and with each day of practice it takes him 2 seconds less. He wants to do in 31 seconds. Read More »

Mr. Vinod is a pilot in Air India. During the Covid-19 pandemic, many Indian passengers were stuck at Dubai Airport. The government of India sent special aircraft to take them. Mr. Vinod was leading this operation. Read More »

Shanta runs an industry in a shed which was in the shape of a cuboid surmounted by half cylinder. The dimensions of the base were 15 m x 7m x 8 m. The diameter of the half cylinder was 7 m and length was 15 m. Read More »

A hot air balloon is rising vertically from a point A on the ground which is at distance of 100m from a car parked at a point P on the ground. Amar, who is riding the balloon, observes that it took him 15 seconds to reach a point B which he estimated to be equal to the horizontal distance of his starting point from the car parked at P. Read More »

Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is. The left-right (horizontal) direction is commonly called X-axis. The up-down (vertical) direction is commonly called Y-axis. In Green Park, New Delhi Suresh is having a rectangular plot ABCD as shown in the following figure. Read More »

Deepa has to buy a scooty. She can buy scooty either making cashdown payment of ₹ 25,000 or by making 15 monthly instalments as below. Ist month – ₹ 3425, IInd month – ₹ 3225, Read More »

A boy is standing on the top of light house. He observed that boat P and boat Q are approaching the light house from opposite directions. He finds that angle of depression of boat P is 45° and angle of depression of boat Q is 30°. Read More »

Alia and Shagun are friends living on the same street in Patel Nagar. Shagun’s house is at the intersection of one street with another street on which there is a library. Read More »

India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. Read More »

One evening, Kaushik was in a park. Children were playing cricket. Birds were singing on a nearby tree of height 80m. He observed a bird on the tree at an angle of elevation of 45°. When a sixer was hit, a ball flew through the tree frightening the bird to fly away. Read More »

Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane. Read More »

Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86m at the Asian Grand Prix in 2017 is the maximum distance for an Indian female athlete. Keeping her as a role model, Read More »

In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water Read More »

A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival. Making Purple: Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you ‘win’. One such outcome is written as ‘RB’. Read More »

A golf ball is spherical with about 300 – 500 dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter 4.2 cm and the surface has 315 dimples (hemi-spherical) of radius 2 mm. Read More »

Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will have adequate space for parking. Read More »

Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables Read More »

Two schools ‘P’ and ‘Q’ decided to award prizes to their students for two games of Hockey x per student and Cricket y per student. Read More »

Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. Read More »

In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm. Read More »

In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure Read More »

India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country. Read More »

The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise Read More »

While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased Read More »