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If there are n variables in a dimensionally homogeneous equation and if these variables contain m primary dimensions, then the variables can be grouped into how many non-dimensional parameters?

Correct Answer: n-m
The non-dimensional groups are called pi-terms. If there are n variables in a dimensionally homogenous equation and if these variables contain m primary dimensions, then the variables can be grouped into (n – m) non dimensional parameters.

What is the general form of the general solution of a non-homogeneous DE (uh(t)= general solution of the homogeneous equation, up(t)= any particular solution of the non-homogeneous equation)?

The principle of dimensional homogeneity serves the following useful concepts (i) It helps to check whether an equation of any physical phenomenon is dimensionally homogenous or not (ii) It helps to determine the dimensions of a physical quantity (iii) It helps to convert the units from one system to another Identify the correct statements

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult.
Why are ants called the 'Earth's' most successful species?

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult. Antennae are used by ants to

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult. What does the Western Harvester do in winter ?

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult. What kind of homes do the army of ants build ?

Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Ants have been living on the earth for more than 100 million years and can be found almost anywhere on the planet. It is estimated that there are about 20000 different species of ants. For this reason ants have been called Earth's most successful species. If you watch ants for any length of time you will see that they really do communicate with each other and very effectively too. Ants communicate by touching each other with their antennae. Ants also use chemicals called pheromones to leave scent trails for other ants to follow. Ants build many different types of homes. Many ants build simple little mounds out of dirt or sand. Other ants use small sticks mixed with dirt and sand to make a stronger mound that offers protection from rain. Western Harvester ants make a small mound on top, but then tunnels up to 15 feet straight down to hibernate during winter. Ant mounds consist of many chambers connected by tunnels. Different chambers are used for nurseries, food storage, and resting places for the worker ants. Some ants live in wood like termites. Army ants don't make a home at all but travel in a large groups searching for food. Ants are social insects which means they live in large colonies or groups. Some colonies consist of millions of ants. There are three types of ants in each species, the queen, the sterile female workers and males. The male ants only serve one purpose, to mate with future queen ants and do not live very long. The queen grows to adulthood, mates, and then spends rest of her life laying eggs. A colony may have only one queen, or there may be many queens depending on the species. Ants go through four stages of development: egg, larva, pupa and adult. What is the purpose of male ants ?

Read the passage carefully and select the best answer to each question out of the given four alternatives.
The Amazon basin has been continuously inhabited for at least 10, 000 years, possibly more. Its earliest inhabitants were stone-age peoples, living in hundreds of far-flung tribes, some tiny, others numbering in the tens of thousands. It was from the west that Europeans explorers first arrived. In 1541 a Spanish expedition from Quito, led by Gonzalo Pizarro, ran short of supplies while exploring east of the Andes in what is today Peru. Pizarros cousin Francisco de Orellana offered to take 60 men along with the boats from the expedition and forage for supplies. De Orellana floated down the Rio Napo to its confluence with the Amazon, near Iquitos (Peru), and then to the mouth of the Amazon. Along the way his expedition suffered numerous attacks by Indians; some of the Indian warriors, they reported, were female, like the Amazons of Greek mythology, and thus the worlds greatest river got its name. No one made a serious effort to claim this sweaty territory, however, until the Portuguese built a fort near the mouth of the river at Belém in 1616, and sent Pedro Teixeira up the river to Quito and back between 1637 and 1639. During the 17th and 18th centuries, Portuguese bandeirantes (groups of roaming adventurers) penetrated ever further into the rain forest in pursuit of gold and Indian slaves, exploring as far as present-day Rondônia, and the Guaporé and Madeira river valleys. Amazonian Indians had long used the sap from rubber trees to make waterproof bags and other items. European explorers recognized the potential value of natural latex, but were unable to market it because it tended to grow soft in the heat, or brittle in the cold, and thus had limited appeal outside the rain forest. However, in 1842 American Charles Goodyear developed vulcanization (made natural rubber durable) and in 1890 Irelands John Dunlop patented pneumatic rubber tires. Soon there was an unquenchable demand for rubber in the recently industrialized USA and Europe, and the price of rubber on international markets soared. As profits skyrocketed, so did exploitation of the seringueiros, or rubber tappers, who were lured into the Amazon, mostly from the drought-stricken northeast, by the promise of prosperity only to be locked into a cruel system of virtual slavery dominated by seringalistas (owners of rubber-bearing forests). Rigged scales, hired guns, widespread illiteracy among the rubber tappers, and monopoly of sales and purchases all combined to perpetuate the workers debt and misery. In addition, seringueiros had to contend with jungle fevers, Indian attacks and all manner of deprivation.
From where did the Europeans explorers first arrive?

Read the passage carefully and select the best answer to each question out of the given four alternatives.
The Amazon basin has been continuously inhabited for at least 10, 000 years, possibly more. Its earliest inhabitants were stone-age peoples, living in hundreds of far-flung tribes, some tiny, others numbering in the tens of thousands. It was from the west that Europeans explorers first arrived. In 1541 a Spanish expedition from Quito, led by Gonzalo Pizarro, ran short of supplies while exploring east of the Andes in what is today Peru. Pizarros cousin Francisco de Orellana offered to take 60 men along with the boats from the expedition and forage for supplies. De Orellana floated down the Rio Napo to its confluence with the Amazon, near Iquitos (Peru), and then to the mouth of the Amazon. Along the way his expedition suffered numerous attacks by Indians; some of the Indian warriors, they reported, were female, like the Amazons of Greek mythology, and thus the worlds greatest river got its name. No one made a serious effort to claim this sweaty territory, however, until the Portuguese built a fort near the mouth of the river at Belém in 1616, and sent Pedro Teixeira up the river to Quito and back between 1637 and 1639. During the 17th and 18th centuries, Portuguese bandeirantes (groups of roaming adventurers) penetrated ever further into the rain forest in pursuit of gold and Indian slaves, exploring as far as present-day Rondônia, and the Guaporé and Madeira river valleys. Amazonian Indians had long used the sap from rubber trees to make waterproof bags and other items. European explorers recognized the potential value of natural latex, but were unable to market it because it tended to grow soft in the heat, or brittle in the cold, and thus had limited appeal outside the rain forest. However, in 1842 American Charles Goodyear developed vulcanization (made natural rubber durable) and in 1890 Irelands John Dunlop patented pneumatic rubber tires. Soon there was an unquenchable demand for rubber in the recently industrialized USA and Europe, and the price of rubber on international markets soared. As profits skyrocketed, so did exploitation of the seringueiros, or rubber tappers, who were lured into the Amazon, mostly from the drought-stricken northeast, by the promise of prosperity only to be locked into a cruel system of virtual slavery dominated by seringalistas (owners of rubber-bearing forests). Rigged scales, hired guns, widespread illiteracy among the rubber tappers, and monopoly of sales and purchases all combined to perpetuate the workers debt and misery. In addition, seringueiros had to contend with jungle fevers, Indian attacks and all manner of deprivation.
Where did De Orellano float down to for its confluence with the Amazon?

Read the passage carefully and select the best answer to each question out of the given four alternatives.
The Amazon basin has been continuously inhabited for at least 10, 000 years, possibly more. Its earliest inhabitants were stone-age peoples, living in hundreds of far-flung tribes, some tiny, others numbering in the tens of thousands. It was from the west that Europeans explorers first arrived. In 1541 a Spanish expedition from Quito, led by Gonzalo Pizarro, ran short of supplies while exploring east of the Andes in what is today Peru. Pizarros cousin Francisco de Orellana offered to take 60 men along with the boats from the expedition and forage for supplies. De Orellana floated down the Rio Napo to its confluence with the Amazon, near Iquitos (Peru), and then to the mouth of the Amazon. Along the way his expedition suffered numerous attacks by Indians; some of the Indian warriors, they reported, were female, like the Amazons of Greek mythology, and thus the worlds greatest river got its name. No one made a serious effort to claim this sweaty territory, however, until the Portuguese built a fort near the mouth of the river at Belém in 1616, and sent Pedro Teixeira up the river to Quito and back between 1637 and 1639. During the 17th and 18th centuries, Portuguese bandeirantes (groups of roaming adventurers) penetrated ever further into the rain forest in pursuit of gold and Indian slaves, exploring as far as present-day Rondônia, and the Guaporé and Madeira river valleys. Amazonian Indians had long used the sap from rubber trees to make waterproof bags and other items. European explorers recognized the potential value of natural latex, but were unable to market it because it tended to grow soft in the heat, or brittle in the cold, and thus had limited appeal outside the rain forest. However, in 1842 American Charles Goodyear developed vulcanization (made natural rubber durable) and in 1890 Irelands John Dunlop patented pneumatic rubber tires. Soon there was an unquenchable demand for rubber in the recently industrialized USA and Europe, and the price of rubber on international markets soared. As profits skyrocketed, so did exploitation of the seringueiros, or rubber tappers, who were lured into the Amazon, mostly from the drought-stricken northeast, by the promise of prosperity only to be locked into a cruel system of virtual slavery dominated by seringalistas (owners of rubber-bearing forests). Rigged scales, hired guns, widespread illiteracy among the rubber tappers, and monopoly of sales and purchases all combined to perpetuate the workers debt and misery. In addition, seringueiros had to contend with jungle fevers, Indian attacks and all manner of deprivation.
In which year did the fort was built by Portuguese near the river Belem?