Brinjal and potato belong to the same genus Solanum,
Question: Brinjal and potato belong to the same genus Solanum, but two different species. What defines them as separate species? Solution: In terms of reproduction, these two species varies. They share the same genus but they remain different species....
Read More →The maximum slope of the curve
Question: The maximum slope of the curve $y=-x^{3}+3 x^{2}+9 x-27$ is ___________ Solution: The given curve is $y=-x^{3}+3 x^{2}+9 x-27$. Slope of the curve, $m=\frac{d y}{d x}$ $\therefore m=\frac{d y}{d x}=-3 x^{2}+6 x+9$ Differentiating both sides with respect tox, we get $\frac{d m}{d x}=-6 x+6$ For maxima or minima, $\frac{d m}{d x}=0$ $\Rightarrow-6 x+6=0$ $\Rightarrow x=1$ Now, $\frac{d^{2} m}{d x^{2}}=-60$ So,x= 1 is the point of local maximum. Thus, the slope of the given curve is maxim...
Read More →A plant may have different names in different
Question: A plant may have different names in different regions of the country or world. How do botanists solve this problem? Solution: They have given a scientific name for each plant and animals. It became the common name throughout the world. Example: Mango is scientifically termed as Mangifera indica. Mango is called as Aam in India. But the scientific term is common....
Read More →The maximum slope of the curve
Question: The maximum slope of the curve $y=-x^{3}+3 x^{2}+9 x-27$ is ___________ Solution: The given curve is $y=-x^{3}+3 x^{2}+9 x-27$. Slope of the curve, $m=\frac{d y}{d x}$ $\therefore m=\frac{d y}{d x}=-3 x^{2}+6 x+9$ Differentiating both sides with respect tox, we get $\frac{d m}{d x}=-6 x+6$ For maxima or minima, $\frac{d m}{d x}=0$ $\Rightarrow-6 x+6=0$ $\Rightarrow x=1$ Now, $\frac{d^{2} m}{d x^{2}}=-60$ So,x= 1 is the point of local maximum. Thus, the slope of the given curve is maxim...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{\cot 2 x-\operatorname{cosec} 2 x}{x}$ Solution: To Find: Limits NOTE: First Check the form of imit. Used this method if the limit is satisfying any one from 7 indeterminate form. In this Case, indeterminate Form are $\infty \times \infty$ $\operatorname{cosec} 2 x-\cot 2 x=(1-\cos 2 x) / \sin 2 x$ $\lim _{x \rightarrow 0} \frac{\cot 2 x-\operatorname{cosec} 2 x}{x}=\lim _{x \rightarrow 0} \frac{\cos 2 x-1}{x \sin 2 x}=\lim ...
Read More →What is the difference between flora,
Question: What is the difference between flora, fauna and vegetation? Eichhornia crassipes is called as an exotic species while Rauwolfia serpentina is an endemic species in India. What do these terms exotic and endemic refer to? Solution: Flora is a plant life occurs in a particular region or time. Fauna is the total number of animals found in a particular region or time Vegetation is a term used for plant forms which do not include particular taxa or botanical characteristics Exotic species is...
Read More →How do you prepare your herbarium sheets?
Question: How do you prepare your herbarium sheets? What are the different tools you carry with you while collecting plants for the preparation of a herbarium? What information should a preserved plant material on the herbarium sheet provide for taxonomical studies? Solution: For preparing a herbarium sheet, the paper is cut in the desired length say, 29 x 41 cm.) The dried specimen is taken and mounted on the sheers with the help of glue. You may use sellotape if desired. Labels are out underne...
Read More →A plant species shows several morphological variations
Question: A plant species shows several morphological variations in response to an altitudinal gradient. When grown under similar conditions of growth, the morphological variations disappear and all the variants have common morphology. What are these variants called? Solution: These variants are called the ecotypes. Plants show changes in morphological features in response to the altitudinal gradient....
Read More →International Code of Botanical Nomenclature →ICBN)
Question: International Code of Botanical Nomenclature ICBN) has provided a code for classification of plants. Give hierarchy of units of classification botanists follow while classifying plants and mention different Suffixes used for the units. Solution: The hierarchy followed in plants: Species Genus Family Order Class Division Kingdom Suffixes used by botanists are as follows: Taxon Suffix (a) Division -phyta (b) Class -ae (c) Order -ales (d) Family aceae...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{\operatorname{cosec} x-\cot x}{x}$ Solution: To Find: Limits NOTE: First Check the form of imit. Used this method if the limit is satisfying any one from 7 indeterminate form. In this Case, indeterminate Form is $\infty \times \infty$ $\operatorname{cosec} x-\cot x=(1-\cos x) / \sin x$ $\lim _{x \rightarrow 0} \frac{\operatorname{cosec} x-\cot x}{x}=\lim _{x \rightarrow 0} \frac{1-\cos x}{x \sin x}=\lim _{x \rightarrow 0} \f...
Read More →In a given habitat we have 20 plant species
Question: In a given habitat we have 20 plant species and 20 animal species. Should we call this diversity or biodiversity? Justify your answer. Solution: Biodiversity is nothing but the total of organism present in a particular area whereas diversity is termed for a large area which may be used for living or non-living things....
Read More →A ball of snow when rolled over snow increases
Question: A ball of snow when rolled over snow increases in mass, volume and size. Is this comparable to growth as seen in living organisms? Why? Solution: The growth in case of ice ball is completely indifferent from growth. This happens due to the extrinsic growth by the deposition of the same material....
Read More →The minimum value
Question: The minimum value of $f(x)=x^{2}+\frac{250}{x}$ is _______________ Solution: The given function is $f(x)=x^{2}+\frac{250}{x}, x \neq 0$. $f(x)=x^{2}+\frac{250}{x}$ Differentiating both sides with respect tox, we get $f^{\prime}(x)=2 x-\frac{250}{x^{2}}$ For maxima or minima, $f^{\prime}(x)=0$ $\Rightarrow 2 x-\frac{250}{x^{2}}=0$ $\Rightarrow x^{3}=\frac{250}{2}=125$ $\Rightarrow x=5$ Now, $f^{\prime \prime}(x)=2+\frac{500}{x^{3}}$ Atx= 5, we have $f^{\prime \prime}(5)=2+\frac{500}{(5)...
Read More →The minimum value
Question: The minimum value of $f(x)=x^{2}+\frac{250}{x}$ is _______________ Solution: The given function is $f(x)=x^{2}+\frac{250}{x}, x \neq 0$. $f(x)=x^{2}+\frac{250}{x}$ Differentiating both sides with respect tox, we get $f^{\prime}(x)=2 x-\frac{250}{x^{2}}$ For maxima or minima, $f^{\prime}(x)=0$ $\Rightarrow 2 x-\frac{250}{x^{2}}=0$ $\Rightarrow x^{3}=\frac{250}{2}=125$ $\Rightarrow x=5$ Now, $f^{\prime \prime}(x)=2+\frac{500}{x^{3}}$ Atx= 5, we have $f^{\prime \prime}(5)=2+\frac{500}{(5)...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{\tan 2 x-\sin 2 x}{x^{3}}$ Solution: To Find: Limits NOTE: First Check the form of imit. Used this method if the limit is satisfying any one from 7 indeterminate form. In this Case, indeterminate Form is $\frac{0}{0}$ $\lim _{x \rightarrow 0} \frac{\tan 2 x-\sin 2 x}{x^{3}}=\lim _{x \rightarrow 0} \frac{\sin 2 x+\sin 2 x \cos 2 x}{x^{3}}=\lim _{x \rightarrow 0} \frac{\sin 2 x(1-\cos 2 x)}{x^{3}}=\lim _{x \rightarrow 0} \frac...
Read More →Which is the largest botanical garden
Question: Which is the largest botanical garden in the world? Name a few well known botanical gardens in India. Solution: The worlds largest botanical garden is situated in London which is known as Kew Royal Gardens. Other known botanical gardens are: 1. Sanjay Gandhi Jaivik Udyan in Patna 2. Hyderabad Botanical Garden 3. NTR Garden, Hyderabad 4. Botanical Garden Sarangpur 5. Cubbon Park, Bangalore...
Read More →Define metabolism.
Question: Define metabolism. Solution: Metabolism is defined as the total of all biochemical reactions taking place within any living organism to sustain and maintain life....
Read More →Amoeba multiplies by mitotic cell division.
Question: Amoeba multiplies by mitotic cell division. Is this phenomena growth or reproduction? Explain. Solution: Amoeba is a single cell organism; its growth through mitosis is the same as reproduction since it divides to give rise to the new individual. Mitosis is responsible for growth....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{(\tan x-\sin x)}{x^{3}}$ Solution: To Find: Limits NOTE: First Check the form of imit. Used this method if the limit is satisfying any one from 7 indeterminate form. In this Case, indeterminate Form is $\frac{0}{0}$ NOTE : $\tan x-\sin x=\frac{\sin x}{\cos x}-\sin x=\frac{\sin x-\sin x \cos x}{\cos x}=\sin x\left(\frac{1-\cos x}{\cos x}\right)$ $\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{x^{3}}=\lim _{x \rightarrow 0} \fra...
Read More →What is Monograph?
Question: What is Monograph? Solution: A description of a single ting or a group of things is known as a monograph. It will have the information regarding anyone taxon....
Read More →Couplet in taxonomic key means ________________ .
Question: Couplet in taxonomic key means ________________ . Solution: The taxonomic key provides a certain structure on the basis of which the user can sort out the taxonomic position of the unknown species. Couplet means a pair which is of contrasting characters of an organism....
Read More →What does ICZN stand for?
Question: What does ICZN stand for? Solution: ICZN stands for International Code of Zoological Nomenclature. It regulates a uniform system of zoological nomenclature....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{2 \sin x-\sin 2 x}{x^{3}}$ Solution: To Find: Limits NOTE: First Check the form of imit. Used this method if the limit is satisfying any one from 7 indeterminate form. In this Case, indeterminate Form is $\frac{0}{0}$ We know that $\sin 2 x=2 \sin x \cos x$ Formula used: $\lim _{x \rightarrow 0} \frac{1-\cos x}{x^{2}}=\frac{1}{2}$ and $\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$ So, by using the above formula, we have $\lim ...
Read More →Linnaeus is considered as Father of Taxonomy.
Question: Linnaeus is considered as Father of Taxonomy. Name two other botanists known for their contribution to the field of plant taxonomy? Solution: George Bentham and Joseph Dalton Hooker are known botanists who gave the natural system of classification of flowering plants....
Read More →If m and M respectively denote the minimum and maximum values
Question: If $m$ and $M$ respectively denote the minimum and maximum values of $f(x)=(x+1)^{2}+3$ in the interval $[-3,1]$, then the ordered pair $(m, M)=$_____________ Solution: The given function is $f(x)=(x+1)^{2}+3, x \in[-3,1]$. $f(x)=(x+1)^{2}+3$ Differentiating both sides with respect tox, we get $f^{\prime}(x)=2(x+1)$ For maxima or minima, $f^{\prime}(x)=0$ $f^{\prime}(x)=0$ $\Rightarrow 2(x+1)=0$ $\Rightarrow x+1=0$ $\Rightarrow x=-1$ Now, $f^{\prime \prime}(x)=20$ So,x=1 is the point o...
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