The five-kingdom classification
Question: The five-kingdom classification was proposed by a. R.H. Whittaker b. C.Linnaeus c. A. Roxberg d. Virchow Solution: Option (a)R.H. Whittakeris the answer....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \pi} \frac{\sin 3 x-3 \sin x}{(\pi-x)^{3}}$ 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 $\frac{0}{0}$ By using $L$ hospital Rule, Differtiate both sides w.r.t $x$ So $\lim _{x \rightarrow \pi} \frac{\sin 3 x-3 \sin x}{(\pi-x)^{3}}=\lim _{x \rightarrow \pi} \frac{3 \cos 3 x-3 \cos x}{-3(\pi-x)^{2}}$ Agai...
Read More →All eukaryotic unicellular organisms
Question: All eukaryotic unicellular organisms belong to a. Monera b. Protista c. Fungi d. Bacteria Solution: Option (b) Protista is the answer....
Read More →If f(x) attains a local minimum at x=c,
Question: If $f(x)$ attains a local minimum at $x=c$, then write the values of $f^{\prime}(c)$ and $f^{\prime \prime}(c)$. Solution: Iff(x) attains a local minimum atx = c, then the first order derivative of the function at the given point must be equal to zero, i.e.f'(x) = 0 atx = c⇒⇒f'(c) = 0 The second order derivative of the function at the given point must be greater than zero, i.e. $f^{\prime \prime}(C)0$...
Read More →Write sufficient conditions for a point x=c to be a point of local maximum.
Question: Write sufficient conditions for a point x=c to be a point of local maximum. Solution: We know that at the extreme points of a functionf(x), the first order derivative of the function is equal to zero, i.e.f'(x) = 0 atx = c⇒⇒f'(c) = 0 Also, at the point of local maximum, the second order derivative of the function at the given point must be less than zero, i.e.f''(c) 0...
Read More →Write necessary condition for a point x = c to be an extreme point of the function f(x).
Question: Write necessary condition for a point x = c to be an extreme point of the function f(x). Solution: We know that at the extreme points of a functionf(x), the first order derivative of the function is equal to zero, i.e.f'(x) = 0 atx = c⇒⇒f'(c) = 0...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{4}} \frac{1-\tan x}{x-\frac{\pi}{4}}$ 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 Formis $\frac{0}{0}$ By using $L$ hospital Rule, Differtiate both sides w.r.t $x$ So $\lim _{x \rightarrow \frac{\pi}{4}} \frac{1-\tan x}{x-\frac{\pi}{4}}=\lim _{x \rightarrow \frac{\pi}{4}} \frac{0-\sec ^{2} x}{1-0}=\li...
Read More →Some of the properties of tissues are
Question: Some of the properties of tissues are not the constituents of their cells. Give three examples to support the statement. Solution: Blood is a connective tissue that is made up of RBCs, WBCs and Platelets. It functions as a nutrient transporter inside the body whereas the blood cells don not play this function. Bone is a specialized connective tissue which functions as mechanical support that is made up of osteocytes. These osteocytes do not provide mechanical support. Dry skin is made ...
Read More →The least value of the function
Question: The least value of the function $f(x)=a x+\frac{b}{x}(a0, b0, x0)$ is_____________ Solution: The given function is $f(x)=a x+\frac{b}{x}(a0, b0, x0)$. $f(x)=a x+\frac{b}{x}$ Differentiating both sides with respect tox, we get $f^{\prime}(x)=a-\frac{b}{x^{2}}$ For maxima or minima, $f^{\prime}(x)=0$ $\Rightarrow a-\frac{b}{x^{2}}=0$ $\Rightarrow x^{2}=\frac{b}{a}$ $\Rightarrow x=\sqrt{\frac{b}{a}} \quad(x0)$ Now, $f^{\prime \prime}(x)=\frac{2 b}{x^{3}}$ At $x=\sqrt{\frac{b}{a}}$, we hav...
Read More →What is the similarity and dissimilarity between
Question: What is the similarity and dissimilarity between whole moong daal and broken moong daal in terms of respiration and growth? Based on these parameters classify them into living or nonliving? Solution: Whole moong daal has an intact embryo whose respiration rate is slow during the phase of dormancy. When these are provided with growth condition, like providing it with water, growth is restored and the seed moong daal) germinates and forms a new plant and the broken moong daals embryo isn...
Read More →The least value of the function
Question: The least value of the function $f(x)=a x+\frac{b}{x}(a0, b0, x0)$ is_____________ Solution: The given function is $f(x)=a x+\frac{b}{x}(a0, b0, x0)$. $f(x)=a x+\frac{b}{x}$ Differentiating both sides with respect tox, we get $f^{\prime}(x)=a-\frac{b}{x^{2}}$ For maxima or minima, $f^{\prime}(x)=0$ $\Rightarrow a-\frac{b}{x^{2}}=0$ $\Rightarrow x^{2}=\frac{b}{a}$ $\Rightarrow x=\sqrt{\frac{b}{a}} \quad(x0)$ Now, $f^{\prime \prime}(x)=\frac{2 b}{x^{3}}$ At $x=\sqrt{\frac{b}{a}}$, we hav...
Read More →Do you consider a person in coma-living or dead?
Question: Do you consider a person in coma-living or dead? Solution: A coma is defined as a prolonged state of unconsciousness. The person who is suffering coma will be unaware of the surroundings. A state of mind which keep the person sleepy even though the person is alive. The working of the brain will be at its lower stage of alertness. The person will live with the help of machines which is linked to the organs. However, a lot many metabolic activities still take place and people often come ...
Read More →Metabolism is a defining feature of all living
Question: Metabolism is a defining feature of all living organisms without exception. Isolated metabolic reactions in vitro are not living things but surely living reactions. Comment. Solution: Metabolism is defined as the total of all chemical reactions that take place inside the body. Metabolism is purely characteristic of living beings. No living organism can exhibit metabolism. In a cell-free system, these reactions can be replicated that is outside a living body. These reactions never lead ...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{4}} \frac{\operatorname{cosec}^{2} x-2}{\cot x-1}$ 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 $\frac{0}{0}$ By using $L$ hospital Rule, Differtiate both sides w.r.t $x$ So $\lim _{x \rightarrow \frac{\pi}{4}} \frac{\operatorname{cosec}^{2} x-2}{\cot x-1}=\lim _{x \rightarrow \frac{\pi}{4}} \...
Read More →A student of taxonomy was puzzled
Question: A student of taxonomy was puzzled when told by his professor to look for a key to identify a plant. He went to his friend to clarify what Key the professor was referring to? What would the friend explain to him? Solution: A key is used to identify plants and animals based on their similarities and dissimilarities. The keys made are based on the contrasting characters that are depicted by the organisms, these are known as couplets. Each statement in the key is called the lead....
Read More →Define a taxon. What is meant by taxonomic hierarchy?
Question: Define a taxon. What is meant by taxonomic hierarchy? Give a flow diagram from the lowest to the highest category for a plant and an animal. What happens to the number of individuals and number of shared characters as we go up the taxonomical hierarchy? Solution: The grouping of organisms at any level is known as Taxon. This can be ranked as Species-genus-family-order-class-phylum/division-kingdom As we go from species to kingdom there is a decrease in the number of common characterist...
Read More →What are taxonomical aids?
Question: What are taxonomical aids? Give the importance of herbaria and museums. How are Botanical gardens and Zoological parks useful in conserving biodiversity? Solution: Collection of information, techniques, procedures which helps to identify classify an individual is called taxonomic aids. Importance of herbarium (a) Collection of dried, pressed preserved plants in sheets is called herbarium. (b) These sheets are arranged systemically according to the accepted system of classification. (c)...
Read More →Brassica campestris Linn
Question: Brassica campestris Linn a. Give the common name of the plant. b. What do the first two parts of the name denote? c. Why are they written in italics? d. What is the meaning of Linn written at the end of the name? Solution: a. Mustard b. The first name represents genus and second denotes specific epithet c. To indicate their Latin origin d. It refers to Linnaeus, Linnaeus was the first to discover this plant. He identified classified the plant hence to give him credit and honour Linnaeu...
Read More →The function
Question: The function $f(x)=\frac{x}{2}+\frac{2}{x}$ has a local minimum at $x=$________________ Solution: The given function is $f(x)=\frac{x}{2}+\frac{2}{x}, x \neq 0$. $f(x)=\frac{x}{2}+\frac{2}{x}$ Differentiating both sides with respect tox, we get $f^{\prime}(x)=\frac{1}{2}-\frac{2}{x^{2}}$ For maxima or minima, $f^{\prime}(x)=0$ Atx =2, we have $f^{\prime \prime}(-2)=\frac{4}{(-2)^{3}}=-\frac{1}{2}0$ So, $x=-2$ is the point of local maximum of $f(x)$. Atx = 2, we have $f^{\prime \prime}(...
Read More →A scientist has come across a plant
Question: A scientist has come across a plant which he feels is a new species. How will he go about its identification, classification and nomenclature? Solution: A new identify species can be easily classified by taxonomic aids. The scientist has to do comparative studies of the morphological anatomical features with the features of existing plants present in the taxonomical aids and according to binomial nomenclature given by Carl Linnaeus, the species can be classified. Some of the taxonomica...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{4}} \frac{\sec ^{2} x-2}{\tan x-1}$ 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 $\frac{0}{0}$ By using L hospital Rule, Differtiate both sides w.r.t $x$ So $\lim _{x \rightarrow \frac{\pi}{4}} \frac{\sec ^{2} x-2}{\tan x-1}=$ So $\lim _{x \rightarrow \frac{\pi}{4}} \frac{2 \sec x(\sec x \tan x...
Read More →What is meant by living?
Question: What is meant by living? Give any four defining features of life forms. Solution: The ability of an object which can self-replicate and self regulate is known as Living. The 4 defining characteristics are- (i) Growth (ii) Reproduction (iii) Metabolism (iv) Consciousness Growth: There are two types. Extrinsic and intrinsic growth. Which is deposited on the outer surface and one is inside the cell Reproduction: Biological process in which an organism gives rise to individuals similar to ...
Read More →The number and kinds of the organism
Question: The number and kinds of the organism are not constant. How do you explain this statement? Solution: Some factors are there which plays an important role in this. Season, extinction and human activities. Many of the living organisms are present at a particular time and some species are wiped out and mainly the deforestation by the hands of human being causes depletion in population. LONG ANSWER TYPE QUESTIONS...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{\sin 2 x(1-\cos 2 x)}{x^{3}}$ 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{\sin 2 x(1-\cos 2 x)}{x^{3}}=\lim _{x \rightarrow 0} \frac{\sin 2 x}{x} \times \frac{(1-\cos 2 x)}{x^{2}}=\lim _{x \rightarrow 0} \frac{2 \sin 2 x}{2 x} \times \frac{4(1-\cos 2...
Read More →Properties of cell organelles are not always
Question: Properties of cell organelles are not always found in the molecular constituents of cell organelles. Justify. Solution: This phenomenon of all living organism is due to underlying interactions. The properties of cellular organelles are not present in the molecular constituents....
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