Describe various stem modifications
Question: Describe various stem modifications associated with food storage, climbing and protection. Solution: (i) Food storage Underground stems of potato, ginger, turmeric, Samarkand, Colocasia are modified to store food in them. (ii) Climbing Stem tendrils which develop from axillary buds, are slender and spirally coiled and help plants to climb such as in gourds (cucumber, pumpkins, watermelon) and grapevines. (iii) Protection Axillary buds of stems may also get modified into woody, straight...
Read More →Differentiate between
Question: Differentiate between a. Bract and Bracteole b. Pulvinus and petiole c. Pedicel and peduncle d. Spike and spadix e. Stamen and staminoid f. Pollen and pollenium Solution: a. A bract is present at the base of the pedicle whereas bracteolate is present between bract and flower. b. Pulvinus is swollen leaf base present in the leguminous plants whereas petiole is a subcylindrical stalk which connects the leaf base with the lamina. c. The pedicle is a stalk of flower and peduncle is a stalk...
Read More →Find the value
Question: Let $f(x)=\left\{\begin{array}{l}\frac{|x-3|}{(x-3)^{\prime}} x \neq 3 \\ 0, \quad x=3\end{array}\right.$ Show that $\lim _{x \rightarrow 3} f(x)$ does not exist. Solution: Left Hand Limit(L.H.L.): $\lim _{x \rightarrow 3^{-}} f(x)=\lim _{x \rightarrow 3^{-}} \frac{|x-3|}{x-3}$ $=\lim _{x \rightarrow 3^{-}} \frac{-(x-3)}{x-3}$ $=\lim _{x \rightarrow 3^{-}}-1$ $=-1$ Right Hand Limit(R.H.L.): $\lim _{x \rightarrow 3^{+}} f(x)=\lim _{x \rightarrow 3^{+}} \frac{|x-3|}{x-3}$ $=\lim _{x \rig...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\cos ^{2} x-\sin ^{2} x}{\sqrt{1+\cos 4 x}} d x$ Solution: Let $I=\int \frac{\cos ^{2} x-\sin ^{2} x}{\sqrt{1+\cos 4 x}} d x$ We know $\cos 2 \theta=2 \cos ^{2} \theta-1=\cos ^{2} \theta-\sin ^{2} \theta$ Hence, in the numerator, we can write $\cos ^{2} x-\sin ^{2} x=\cos 2 x$ In the denominator, we can write $4 x=2 \times 2 x$ $\Rightarrow 1+\cos 4 x=1+\cos (2 \times 2 x)$ $\Rightarrow 1+\cos 4 x=2 \cos ^{2} 2 x$ Therefore, we can write th...
Read More →The rhizome of ginger is like the roots of other plants
Question: The rhizome of ginger is like the roots of other plants that grow underground. Despite this fact, ginger is a stem and not a root. Justify. Solution: Ginger is a stem, not a root because it posses nodes and internodes which are not possessed by the roots....
Read More →Tendrils of grapevines are homologous
Question: Tendrils of grapevines are homologous to the tendril of pumpkins but are analogous to that of a pea. Justify the above statement. Solution: The tendrils of grapevines are homologous to the tendril of pumpkins as both are originated from the same part of the plant i.e. stem but have different functions. In grapevines, the function of tendrils is to climb while in pumpkin is creeping....
Read More →Why is maize grain usually called
Question: Why is maize grain usually called as a fruit and not a seed? Solution: The maize grain is usually called fruit because it is a ripened ovary which contains a ripened ovule....
Read More →Solve this
Question: Let $f(x)=\left\{\begin{array}{l}\frac{x}{|x|^{\prime}} x \neq 0 \\ 0, x=0\end{array}\right.$ Show that $\lim _{x \rightarrow 0} f(x)$ does not exist. Solution: Left Hand Limit(L.H.L.): $\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{-}} \frac{x}{|x|}$ $=\lim _{x \rightarrow 0^{-}} \frac{x}{(-x)}$ $=\lim _{x \rightarrow 0^{-}}-1$ $=-1$ Right Hand Limit(R.H.L.): $\lim _{x \rightarrow 0^{+}} f(x)=\lim _{x \rightarrow 0^{+}} \frac{x}{|x|}$ $=\lim _{x \rightarrow 0^{+}} \frac{x}{...
Read More →Tendrils are found in the following plants.
Question: Tendrils are found in the following plants. Identify whether they are stem tendrils or leaf tendrils. a.Cucumber a. Peas c. Pumpkins d. Grapevine e. Watermelons Solution: a. Cucumber Stem tendrils b. Peas Leaf tendrils c. Pumpkins stem tendrils d. Grapevines stem tendrils e. Watermelons stem tendrils...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\cos x}{1-\cos x} d x$ Solution: Let $I=\int \frac{\cos x}{1-\cos x} d x$ On multiplying and dividing $(1+\cos x)$, we can write the integral as $I=\int \frac{\cos x}{1-\cos x}\left(\frac{1+\cos x}{1+\cos x}\right) d x$ $\Rightarrow I=\int \frac{\cos x(1+\cos x)}{(1-\cos x)(1+\cos x)} d x$ $\Rightarrow I=\int \frac{\cos x+\cos ^{2} x}{1-\cos ^{2} x} d x$ $\Rightarrow I=\int \frac{\cos x+\cos ^{2} x}{\sin ^{2} x} d x\left[\because \sin ^{2} ...
Read More →How can you differentiate between
Question: How can you differentiate between free central and axile placentation? Solution: When the placenta is axial and the ovules are attached to it in a multilocular ovary, the placentation is said to be axile. Examples china rose, tomato and lemon. When the ovules are borne on the central axis and septa are absent, the placentation is called free central. Examples Dianthus and Primrose....
Read More →Mango and coconut are ‘drupe’ type of fruits.
Question: Mango and coconut are drupe type of fruits. In mango fleshy mesocarp is edible. What is the edible part of coconut? What does milk of tender coconut represent? Solution: The edible part of the coconut is the endosperm. The milk of tender coconut represents the oily endosperm in liquid form. Later it gets deposited along the walls of endocarp and forms edible flesh....
Read More →You have heard about several insectivorous plants that feed on insects.
Question: You have heard about several insectivorous plants that feed on insects. Nepenthes or the pitcher plant is one such example, which usually grows in shallow water or marshlands. What part of the plant is modified into a pitcher? How does this modification help the plant for food even though it can photosynthesize like any other green plant? Solution: The pitcher plant cant photosynthesize like other green plants so it gets its food from the insects as these insects are a good source of N...
Read More →Find the value
Question: If $f(x)=|x|-3$, find $\lim _{x \rightarrow 3} f(x)$ Solution: Left Hand Limit(L.H.L.): $\lim _{x \rightarrow 3^{-}} f(x)$ $=\lim _{x \rightarrow 3^{-}}|x|-3$ $=\lim _{x \rightarrow 3^{-}}-(x-3)$ $=-(3-3)$ $=0$ Right Hand Limit(R.H.L.): $\lim _{x \rightarrow 3^{+}} f(x)$ $=\lim _{x \rightarrow 3^{+}}|x|-3$ $=\lim _{x \rightarrow 3^{+}}(x-3)$ $=3-3$ $=0$ Since, $\lim _{x \rightarrow 3^{-}} f(x)=\lim _{x \rightarrow 3^{+}} f(x)$ We can say that the limit exists and $\lim _{x \rightarrow ...
Read More →Reticulate venation is found in dicot leaves
Question: Reticulate venation is found in dicot leaves while in monocot leaves venation is of parallel type. Mention one exception to this generalization. Solution: Similar and Dioscorea are monocots having reticulate venation. Calophyllum and Eryngium are dicots parallel venation....
Read More →A typical angiosperm flower consists of four floral parts.
Question: A typical angiosperm flower consists of four floral parts. Give the names of the floral parts and their arrangements sequentially. Solution: Calyx It is the outermost whorl of the flower and the members are called sepals which are green, leaf-like and protects the flower in the bud stage. Corolla It is composed of petals. Petals are usually brightly coloured to attract insects for pollination. Androecium It is composed of stamens. Each stamen which represents the male reproductive orga...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1-\cos 2 x}{1+\cos 2 x} d x$ Solution: $\operatorname{Let} I=\int \frac{1-\cos 2 x}{1+\cos 2 x} d x$ We know $\cos 2 \theta=1-2 \sin ^{2} \theta=2 \cos ^{2} \theta-1$ Hence, in the numerator, we can write $1-\cos 2 x=2 \sin ^{2} x$ In the denominator, we can write $1+\cos 2 x=2 \cos ^{2} x$ Therefore, we can write the integral as $I=\int \frac{2 \sin ^{2} x}{2 \cos ^{2} x} d x$ $\Rightarrow I=\int \frac{\sin ^{2} x}{\cos ^{2} x} d x$ $\Righ...
Read More →The essential functions of roots are anchorage
Question: The essential functions of roots are anchorage and absorption of water and minerals in the terrestrial plant. What functions are associated with the roots of aquatic plants? How are the roots of aquatic plants and terrestrial plants different? Solution: The aquatic plants dont have to face problem in obtaining the water. Therefore the main function of the roots of the aquatic plants is anchorage....
Read More →Give two examples of roots that develop
Question: Give two examples of roots that develop from different parts of the angiosperms plant other than the radicle. Solution: Banyan tree roots develop from the lower nodes of the stem. They are prop roots which grow downwards and touch the soil. They meant for support. Sugarcane roots arise from the lower nodes of stem and enter the soil. They are stilt roots which are meant to provide strength to the plant....
Read More →Name the body part modified for food storage in the following
Question: Name the body part modified for food storage in the following a. Carrot __________________________ b. Colocasia __________________________ c. Sweet potato __________________________ d. Asparagus __________________________ e. Radish __________________________ f. Potato __________________________ g. Dahlia __________________________ h. Turmeric __________________________ i. Gladiolus __________________________ j. Ginger __________________________ k. Portulaca __________________________ S...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{6}} \frac{2 \sin ^{2} x+\sin x-1}{2 \sin ^{2} x-3 \sin x+1}$ Solution: $=\lim _{x \rightarrow \frac{\pi}{6}} \frac{2 \times \sin x \times \sin x+\sin x-1}{2 \times \sin x \times \sin x-3 \sin x+1}$ $=\lim _{x \rightarrow \frac{\pi}{6}} \frac{(2 \sin x-1) \times(\sin x+1)}{(2 \sin x-1)(\sin x-1)}$ $=-3$ $\therefore \lim _{x \rightarrow \frac{\pi}{6}} \frac{2 \times \sin x \times \sin x+\sin x-1}{2 \times \sin x \times \sin ...
Read More →In epigynous flower,
Question: In epigynous flower, ovary is situated below the _____________. Solution: In epigynous flower, the ovary is situated below the sepals, petals and androecium....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int(\tan x+\cot x)^{2} d x$ Solution: Given: $I=\int(\tan x+\cot x)^{2} d x$ $\Rightarrow \int\left(\tan ^{2} x+\cot ^{2} x+2 \tan x \cot x\right)^{1} d x$ We know that, $\tan ^{2} x=\sec ^{2} x-1$ $\cot ^{2} x=\operatorname{cosec}^{2} x-1$ $\tan x=\frac{1}{\cot x}$ $\Rightarrow \int\left(\sec ^{2} x-1+\operatorname{cosec}^{2}-1+\frac{2}{\cot x} \operatorname{cotx}\right) d x$ $\Rightarrow \int\left(\sec ^{2} x+\operatorname{cosec}^{2} x-2+2\right) d...
Read More →Which parts in ginger
Question: Which parts in ginger and onion are edible? Solution: In ginger, the edible part is a rhizome which is modified shoot that stores food materials. The edible part of the onion is fleshy scale leaves....
Read More →Reticulate and parallel venation
Question: Reticulate and parallel venation are characteristic of _____________ and _____________ respectively. Solution: Reticulate and parallel venation is characteristic of dicotyledons and monocotyledons respectively....
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