89.Let the largest number that divides 491, 332 and 862
and leaves the same remainder r in each case be x. Find
the L.C.M of x and r?
1)742 2)864 3)784 4)708 5)None
Answers
Answer:
Very early on, scientists began grouping the living organisms under different categories. Some biologists classified organisms into plants and animals. Ernst Haeckel, Robert Whittaker, and Carl Woese are some biologists who attempted a broader system of classification. Amongst these, the Five Kingdom Classification proposed by Robert Whittaker stood out and is widely used.
Whitaker proposed that organisms should be broadly divided into kingdoms, based on certain characters like the structure of the cell, mode of nutrition, the source of nutrition, interrelationship, body organization, and reproduction. According to this system, there are five main kingdoms. They are:
Kingdom Monera
Kingdom Protista
Kingdom Fungi
Kingdom Animalia
Kingdom Plantae
Kingdoms are divided into subgroups at various levels. The following flowchart shows the hierarchy of classification.
Kingdom → Phylum → Class → Order → Family → Genus → Species
Five Kingdom Classification
(Source: Wikipedia)
Distinguishing Features of the Five Kingdoms
Kingdom Monera
These organisms are prokaryotic and unicellular. They do not have a well-defined nucleus and also lack cell organelles. Some organisms show the presence of cell wall while there are others without a cell wall. Consequently, some organisms are autotrophic and others are heterotrophic. Examples include Bacteria, Cyanobacteria, and Mycoplasma.
Kingdom Protista
Organisms grouped under Kingdom Protista are all unicellular, but eukaryotic organisms. These are the simplest forms of eukaryotes that exhibit either autotrophic or heterotrophic mode of nutrition. Some organisms have appendages such as cilia or flagella or pseudopodia to move around. Some examples are Diatoms, Protozoans like Amoeba, Paramoecium
Five Kingdom Classification
(Source: Wikipedia)
Kingdom Fungi
Heterotrophic, Multicellular and Eukaryotic organisms are grouped under Kingdom Fungi. Their mode of nutrition is saprophytic as they use decaying organic matter as food. They have cell walls, which are made up of a substance called Chitin. Fungi also form a symbiotic association with some blue-green algae. Yeast, Mushroom, Aspergillus are examples of Fungi.
Kingdom Plantae
These are Eukaryotic, Multicellular organisms with a cell wall that is made up of cellulose. They are autotrophs and synthesize their own food through the process of photosynthesis. This kingdom includes all plants.
Based on the body differentiation and presence or absence of specialized vascular tissue, Kingdom Plantae is divided into different divisions, namely Thallophyta, Bryophyta, Pteridophyta, Gymnosperms, and Angiosperms. Examples are Spirogyra, Ferns, Pines, and Mango Plant etc.
Kingdom Animalia
This Kingdom includes organisms that are Multicellular, Eukaryotic, without the presence of cell wall. They have a heterotrophic mode of nutrition. They also exhibit great diversity. Some organisms are simple while others have a complex body with specialized tissue differentiation and body organs.
The Animal Kingdom is divided into many phyla and classes. Some of the phyla are Porifera, Coelenterata, Arthropoda, Echinodermata, Chordata etc. Examples – Hydra, Starfish, Earthworms, Monkeys, Birds etc.
Step-by-step explanation:
If the largest number that divides 491, 332 and 862 and leaves the same remainder r in each case is x, then the L.C.M of x and r is the option (1): 742.
Step-by-step explanation:
It is given that,
“x” is the largest number that gives out "r" as the reminder when divided with 491, 332 and 862.
1. When the reminder is the same in any case, then we need to calculate the difference between the given numbers i.e.,
862 – 332 = 530
862 – 491 = 371
491 – 332 = 159
2. We will find the H.C.F of the numbers that we got after the subtraction i.e., the H.C.F of 530, 371 & 159
530 = 2 * 5 * 53
371 = 7 * 53
159 = 3 * 53
∴ H.C.F = 53 ← this is the value of x, the largest number
3. To find the value of r (remainder) we will now divide 862, 491 & 332 by 53.
53 ) 491 ( 9
477
--------------
14
-------------
53) 332 ( 6
318
---------------
14
----------------
53 ) 862 ( 16
53
------------------
332
318
-------------------
14
----------------------
In each case, we receive the remainder the value of r = 14.
4. Now, we will find the L.C.M of x = 53 and r = 14 as asked in the question
L.C.M of 53 and 14 = 53 * 14 = 742 ← option (1)
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