# A student observed $31$ Quisqualis plants each with $36$ nodes, $15$ Hibiscus plants each with $21$nodes and $77$ Calotropis plants each with $11$ nodes. All these plants contain leaves at every node. What is the total number of leaves of these three plants put together?

A. $2593$

B. $1585$

C. $237$

D. $4241$

Answer

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**Hint:**Flowers are arranged in the plant in a particular manner, this is called an inflorescence. The same way leaves are also arranged in a plant stem or branch. This arrangement is called phyllotaxy. The position of the leaves is never random; each leaf has a definite place in the stem or branch. This arrangement varies from one plant species to another.

**Complete answer:**

The leaves arise from the nodes on the stem; the distance between the nodes may be short or long depending on the plant species. These leaves are called cauline leaves because they arise from a stem. Depending on the number of leaves, cauline leaves can be arranged into three main types:

Alternate type arrangement only one leaf will arise from a single node. If one leaf arises from one side of the stem, the next one will grow on the opposite side from another node. This way all leaves will get sufficient sunlight to perform photosynthesis. The examples of plants that show this arrangement are- sunflower, Hibiscus, etc.

Plants with opposite type arrangement have two leaves at each node. Opposite type arrangement can be further classified into two types- superimposed opposite arrangement and decussate opposite. In the superimposed arrangement, the two leaves grow from the same node on both sides of the stem. Each set of leaves superimpose their predecessor. This arrangement is seen in quisqualis, guava, etc.

Decussate arrangement is exhibited when one set of leaves arise from the nodes and the next set arises from another node at right angles from the first set. This arrangement is repeated. This arrangement is seen in Calotropis, gardenia, etc.

The last type of arrangement seen in cauline leaves is whorled. In this case, more than three leaves arise from the same node. This is seen in the Alstonia plant, Nerium plant, etc. Because the arrangement of leaves is regular, it is possible to calculate the total number of leaves in each plant.

According to the question, $31$ Quisqualis have $36$ nodes. Quisqualis shows the opposite superimposed arrangement. Therefore, there are two leaves at each node.

The total number of leaves for Quiqualis ($31 \times 36 \times 2$) is $2232$. Hibiscus shows alternate phyllotaxy, therefore, the total number of leaves for Hibiscus plants ($15 \times 21$) is $315$. Calotropis shows decussate phyllotaxy, the total number of leaves for Calotropis plants ($77 \times 11 \times 2$) is $1694$. The leaves from all three plants ($2232 + 315 + 1694$), gives a sum total of $4241$.

**Hence, the correct answer is option (D).**

**Note:**Branches also give rise to leaves; such leaves are called Ramal leaves. When leaves arise from a very short stem, they are called radical leaves. It seems as though the leaves arise from the root, hence, the name radical. An example of these leaves is the ones that grow in radish.

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