In aquatic plants like Pistia and Eichhornia,
Question: In aquatic plants like Pistia and Eichhornia, leaves and roots are found near _____________. Solution: In aquatic plants like Pistia and Eichhornia, leaves and roots are found near Node....
Read More →In swampy areas like the Sunderbans in
Question: In swampy areas like the Sunderbans in West Bengal, plants bear special kind of roots called _____________. Solution: In swampy areas like the Sunderbans in West Bengal, plants bear special kind of roots called pneumatophores....
Read More →In Opuntia, the stem is modified into a flattened
Question: In Opuntia, the stem is modified into a flattened green structure to perform the function of leaves (i.e., photosynthesis). Cite two other examples of modifications of plant parts for photosynthesis. Solution: In Australian Acasia the petiole takes the shape of the leaf and turns green to perform the function of photosynthesis. The stem, i.e., about one internode long modifies into a leaf-like structure to carry out photosynthesis, as in Asparagus....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{5 \cos ^{3} x+6 \sin ^{3} x}{2 \sin ^{2} x \cos ^{2} x} d x$ Solution: Given: $\int \frac{5 \cos ^{3} x+6 \sin ^{3} x}{2 \sin ^{2} x \cos ^{2} x} d x$ By Splitting we get, $\Rightarrow \int \frac{5 \cos ^{3} x}{2 \sin ^{2} x \cos ^{2} x} d x+\int \frac{6 \sin ^{3} x}{2 \sin ^{2} x \cos ^{2} x} d x$ $\Rightarrow \frac{5}{2} \int \frac{\cos x \cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x+3 \int \frac{\sin ^{2} x \sin ^{1} x}{\sin ^{2} x \cos ^{2}...
Read More →Roots obtain oxygen from the air in the soil for respiration.
Question: Roots obtain oxygen from the air in the soil for respiration. In the absence or deficiency of O2, root growth is restricted or completely stopped. How do the plants growing in marshlands or swamps obtain their O2 required for root respiration? Solution: In some plants such as Rhizophora growing in swampy areas, many roots come out of the ground and grow vertically upwards. Such roots, called pneumatophores, help to get oxygen for respiration....
Read More →Match the following and choose
Question: Match the following and choose the correct option Options: a. A-i, B-ii, C-iii, D-iv b. A-ii, B-i, C-iv, D-iii c. A-iv, B-ii, C-i, D-iii d. A-ii, B-iv, C-i, D-iii Solution: Option (b)A-ii, B-i, C-iv, D-iiiis the answer....
Read More →Which of the following plants is used
Question: Which of the following plants is used to extract the blue dye? a. Trifolium b. Indigofera c. Lupin d. Cassia Solution: Option (b)Indigofera is the answer....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{4}} \frac{1-\tan x}{1-\sqrt{2} \sin x}$ Solution: $=\lim _{x \rightarrow \frac{\pi}{4}} \frac{1-\tan x}{1-\sqrt{2} \sin x}$ Let, $y=x-\frac{\pi}{4}$ $=\lim _{y \rightarrow 0} \frac{2 \tan x}{1-\cos x+\sin x}$ $=\lim _{y \rightarrow 0} \frac{\frac{2 \cos \frac{x}{2}}{\cos x}}{\sin \frac{x}{2}+\cos \frac{x}{2}}$ $=2$ $\therefore \lim _{x \rightarrow \frac{\pi}{4}} \frac{1-\tan x}{1-\sqrt{2} \sin x}=2$...
Read More →The placenta is attached to the developing
Question: The placenta is attached to the developing seed near the a. Testa b. Hilum c. Micropyle d. Chalaza Solution: Option (b) Hilum is the answer....
Read More →Many pulses of daily use belong to one of
Question: Many pulses of daily use belong to one of the families below (tick the correct answer) a. Solanaceae b. Fabaceae c. Liliaceae d. Poaceae Solution: Option (b)Fabaceae is the answer....
Read More →The endosperm, a product of double fertilization
Question: The endosperm, a product of double fertilization in angiosperms is absent in the seeds of a. Coconut b. Orchids c. Maize d. Castor Solution: Option (b) Orchids is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\sin ^{3} x-\cos ^{3} x}{\sin ^{2} x \cos ^{2} x} d x$ Solution: Given: $\int \frac{\sin ^{3} x-\cos ^{3} x}{\sin ^{2} x \cos ^{2} x} d x$ By Splitting, we get, $\Rightarrow \int\left(\frac{\sin ^{3} x}{\sin ^{2} x \cos ^{2} x}-\frac{\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}\right) d x$ By cancelling the $\sin ^{2} x$ on first and $\cos ^{2} x$ on second, $\Rightarrow \int\left(\frac{\sin x}{\cos ^{2} x}-\frac{\cos x}{\sin ^{2} x}\right) d x$ W...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \pi} \frac{\sqrt{2+\cos x}-1}{(\pi-x)^{2}}$ Solution: $=\lim _{x \rightarrow \pi} \frac{\sqrt{2+\cos x}-1}{(\pi-x)^{2}}$ $=\lim _{x \rightarrow \pi} \frac{\sqrt{2+\cos x}-1}{(\pi-x)^{2}} \times \frac{\sqrt{2+\cos x}+1}{\sqrt{2+\cos x}+1}$ $=\lim _{x \rightarrow \pi} \frac{1+\cos x}{(\pi-x)^{2}} \times \frac{1}{\sqrt{2+\cos x}+1}$ Let, $y=x-\pi$ $=\lim _{y \rightarrow 0} \frac{1-\cos y}{x^{2} \times \sqrt{2-\cos y}+1}$ $=\frac{1}{4}$ ...
Read More →Venation is a term used to describe the pattern
Question: Venation is a term used to describe the pattern of arrangement of a. Floral organs b. Flower in inflorescence c. Veins and veinlets in a lamina d. All of them Solution: Option (c)Veins and veinlets in a lamina is the answer....
Read More →Roots developed from parts of the plant
Question: Roots developed from parts of the plant other than radicle are called a. Taproots b. Fibrous roots c. Adventitious roots d. Nodular roots Solution: Option (c)Adventitious roots is the answer....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{6}} \frac{\cot ^{2} x-3}{\operatorname{cosec} x-2}$ Solution: $=\lim _{x \rightarrow \frac{\pi}{6}} \frac{\cot x \times \cot x-3}{\csc x-2}$ $=\lim _{x \rightarrow \frac{\pi}{6}} \frac{(\cos x \times \cos x)-3 \times \sin x \times \sin x}{\sin x(1-2 \sin x)}$ $=\lim _{x \rightarrow \frac{\pi}{6}} \frac{1-4 \times \sin x \times \sin x}{\sin x(1-2 \sin x)}$ $=\lim _{x \rightarrow \frac{\pi}{6}} \frac{(1-2 \sin x) \times(1+2 ...
Read More →The mature seeds of plants such as gram and peas possess no
Question: The mature seeds of plants such as gram and peas possess no endosperm, because of a. These plants are not angiosperms b. There is no double fertilization in them c. The endosperm is not formed in the d. Endosperm gets used up by the developing embryo during seed development Solution: Option (d)Endosperm gets used up by the developing embryo during seed development is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int\left(\operatorname{se}^{2} x+\operatorname{cosec}^{2} x\right) d x$ Solution: Given: By Splitting, we get, $\Rightarrow \int \sec ^{2} x d x+\int \operatorname{cosec}^{2} x d x$ By applying the formula, $\int \sec ^{2} x d x=\tan x$ $\int \operatorname{codec}^{2} x d x=-\operatorname{cotx}$ $\Rightarrow \tan x-\cot x+c$...
Read More →In an inflorescence where flowers are borne laterally
Question: In an inflorescence where flowers are borne laterally in acropetal succession, the position of the youngest floral bud in the floral axis shall be a. Proximal b. Distal c. Intercalary d. Anywhere Solution: Option (b)Distal is the answer....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sqrt{2}-\sqrt{1+\sin x}}{\sqrt{2} \cos ^{2} x}$ Solution: $=\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sqrt{2}-\sqrt{1+\sin x}}{\sqrt{2} \cos x \cos x}$ $=\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sqrt{2}-\sqrt{1+\sin x}}{\sqrt{2} \cos x \cos x} \times \frac{\sqrt{2}+\sqrt{1+\sin x}}{\sqrt{2}+\sqrt{1+\sin x}}$ $=\lim _{x \rightarrow \frac{\pi}{2}} \frac{1-\sin x}{\sqrt{2}+\sqrt{1+\sin x}(\sqrt{2} \cos x \cos x)...
Read More →Rearrange the following zones as seen
Question: Rearrange the following zones as seen in the root in vertical section and choose the correct option. A. Root hair zone B. Zone of meristems C. Rootcap zone D. Zone of maturation E. Zone of elongation Options: a. C, B, E, A, D b. A, B, C, D, E c. D, E, A, C, B d. E, D, C, B, A Solution: Option (a)C, B, E, A, D is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\sin ^{2} x}{1+\cos } d x$ Solution: Given: $\int \frac{\sin ^{2} x}{1+\cos x} d x$ We know that, $\sin ^{2} x=1-\cos ^{2} x$ $\Rightarrow \int \frac{1-\cos ^{2} x}{1+\cos x} d x$ We treat $1-\cos ^{2} x a s a^{2}-b^{2}=(a+b)(a-b)$ $\Rightarrow \int \frac{(1)^{2}-(\cos x)^{2}}{1+\cos x} d x$ $\Rightarrow \int \frac{(1+\cos x)(1-\cos x)}{1+\cos x} d x$ $\Rightarrow \int(1-\cos x) d x$ By Splitting, we get, $\Rightarrow \int \mathrm{dx}-\int ...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{4}} \frac{\tan ^{3} x-\tan x}{\cos \left(x+\frac{\pi}{4}\right)}$ Solution: $=\lim _{x \rightarrow \frac{\pi}{4}} \frac{\left(\frac{-\sin x(\cos 2 x)}{\cos x \cos x \cos x}\right)}{\left(\frac{\cos x-\sin x}{\sqrt{2}}\right)}$ $=-\sqrt{2} \times \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x(\cos x+\sin x)}{\cos x \times \cos x \times \cos x}$ $=-\sqrt{2} \times \frac{\frac{1}{\sqrt{2}} \times \sqrt{2}}{\frac{1}{\sqrt{2}...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow a} \frac{\cos x-\cos a}{\cot x-\cot a}$ Solution: $=\lim _{x \rightarrow a} \frac{\cos x-\cos a}{\cot x-\cot a}$ $=\lim _{x \rightarrow a} \frac{(\cos x-\cos a)}{\frac{\sin (a-x)}{\sin x \sin a}}$ $=\sin a \times \lim _{x \rightarrow a} \frac{\sin \left(\frac{x+a}{2}\right) \times \sin x}{\cos \left(\frac{x-a}{2}\right)}$ $=\sin ^{3} a$ $\therefore \lim _{x \rightarrow a} \frac{\cos x-\cos a}{\cot x-\cot a}=\sin a \times \sin a \time...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{5 x^{4}+12 x^{3}+7 x^{2}}{x^{2}+x} d x$ Solution: Given: $\int \frac{5 x^{4}+12 x^{3}+7 x^{2}}{x^{2}+x} d x$ Now spilt $12 x^{3}$ into $7 x^{3}$ and $5 x^{3}$ $\Rightarrow \int \frac{5 x^{4}+7 x^{3}+5 x^{3}+7 x^{2}}{x^{2}+x} d x$ Now common $5 x^{3}$ from two elements $7 x$ from other two elements, $\Rightarrow \int \frac{5 x^{2}(x+1)+7 x(x+1)}{x^{2}+x} d x$ $\Rightarrow \frac{\int\left(5 x^{2}+7 x\right)(x+1)}{x(x+1)} d x$ $\Rightarrow \in...
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