Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{2 x^{4}+7 x^{3}+6 x^{2}}{x^{2}+2 x} d x$ Solution: Given: $\int \frac{2 x^{4}+7 x^{3}+6 x^{2}}{x^{2}+2 x} d x$ Take $\mathrm{x}$ is common on both numerator and denominator, $\Rightarrow \int \frac{x\left(2 x^{3}+7 x^{2}+6 x\right)}{x(x+2)} d x$ $\Rightarrow \int \frac{2 x^{3}+7 x^{2}+6 x}{x+2} d x$ Splitting $7 x^{2}$ into $4 x^{2}$ and $3 x^{2}$ $\Rightarrow \int \frac{2 x^{3}+4 x^{2}+3 x^{2}+6 x}{x+2} d x$ Common the $2 x^{2}$ from first...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int(3 x+4)^{2} d x$ Solution: Given: $\int(3 x+4)^{2} d x$ By applying, $(a+b)^{2}=a^{2}+b^{2}+2 a b$ $\Rightarrow \int\left((3 x)^{2}+4^{2}+2 \times 3 x \times 4\right) d x$ $\Rightarrow \int\left(9 x^{2}+16+24 x\right) d x$ By Splitting, we get, $\Rightarrow \int 9 x^{2} d x+\int 16 d x+\int 24 x d x$ $\Rightarrow 9 \int x^{2}+16 \int d x+24 \int x d x$ By applying, $\int \mathrm{x}^{\mathrm{n}} \mathrm{dx}=\frac{\mathrm{x}^{\mathrm{n}+1}}{\mathrm{...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{x^{5}+x^{-2}+2}{x^{2}} d x$ Solution: Given: $\int \frac{x^{5}+x^{-2}+2}{x^{2}} d x$ By Splitting, we get, $\Rightarrow \int\left(\frac{x^{5}}{x^{2}}+\frac{x^{-2}}{x^{2}}+\frac{2}{x^{2}}\right) d x$ $\Rightarrow \int\left(x^{5} \times x^{-2}+x^{-2} \times x^{-2}+2 \times x^{-2}\right) d x$ By applying, $\Rightarrow \int\left(x^{5-2}+x^{-2-2}+2 x^{-2}\right) d x$ $\Rightarrow \int\left(x^{3}+x^{-4}+2 x^{-2}\right) d x$ By Splitting, we get, ...
Read More →Mammals are most adapted among
Question: Mammals are most adapted among the vertebrates. Elaborate. Solution: Mammals are found in a variety of habitats like deserts, plains and mountains. They differ in the type of jaws and sexes are separate and fertilization is internal. They have pairs of limbs which are used for walking, burrowing, climbing etc. Their mammary glands produce milk to nourish their young ones. They are warm-blooded which helps them maintain their body temperature in different weather conditions. They have h...
Read More →Comment upon the habitats and external features
Question: Comment upon the habitats and external features of animals belonging to class, amphibia and reptilia. Solution: Amphibia They are thin and have smooth skin which can live on both land and water. Their eyes have eyelids and have a pair of limbs. A tympanum is representing the ears. Examples are Rana(frog) and cobra Reptiles They are covered with dry and confined skin and scales. They mostly live on land. Tympanum represents ear. They have a pair of limbs. They will creep and crawl. Thes...
Read More →What is the relationship between germinal layers
Question: What is the relationship between germinal layers and the formation of the body cavity in case of coelomate, acoelomates and pseudocoelomates? Solution: Germinal layers are those which formed during the process of gastrulation. The outer layer of germ is called ectoderm, the middle one is endoderm and the innermost is the endoderm. Coelomates are the organisms possessing coeloms. The coelom is the body cavity lined by the mesoderm. Examples of coelomates are phylum Annelida, Mollusca, a...
Read More →Give three major differences between chordates
Question: Give three major differences between chordates and non-chordates and draw a schematic sketch of a chordate showing those features. Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \sqrt{x}(3-5 x) d x$ Solution: Given: $\int \sqrt{x}(3-5 x) d x$ By multiplying $\sqrt{x}$ inside the bracket we get, $\Rightarrow \int(3 \sqrt{x}-5 x \sqrt{x}) d x$ $\Rightarrow \int\left(3 x^{\frac{1}{2}}-5 x^{1} \times x^{\frac{1}{2}}\right) d x$ $\Rightarrow \int\left(3 x^{\frac{1}{2}}-5 x^{1+\frac{1}{2}}\right) d x$ $\Rightarrow \int\left(3 x^{\frac{1}{2}}-5 x^{\frac{2}{2}}\right) d x$ $\Rightarrow 3 \int x^{\frac{1}{2}} d x-5 \int x^{\frac{...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{\cos a x-\cos b x}{\cos c x-1}$ Solution: $=\lim _{x \rightarrow 0} \frac{\cos a x-\cos b x}{\cos c x-1}$ $=\lim _{x \rightarrow 0} \frac{1-\cos b x-(1-\cos a x)}{\cos c x-1}$ $=\lim _{x \rightarrow 0} \frac{\frac{(1-\cos b x)}{(b x)^{2}} \times b^{2}-\frac{(1-\cos a x)}{(a x)^{2}} \times a^{2}}{\frac{-(1-\cos c x)}{(c x)^{2}} \times c^{2}}$ $=\frac{a^{2}-b^{2}}{c^{2}}$ $\therefore \lim _{x \rightarrow 0} \frac{\cos a x-\cos...
Read More →Excretory organs of different animals are given below.
Question: Excretory organs of different animals are given below. Choose correctly and write in the space provided. a. ____________________, b. ____________________, c. ____________________ d. ____________________, e. ____________________, f. ____________________ Solution: a. Balanoglossus Proboscis gland b. Leech Nephridia c. Locust Malpighian tubule d. Liver fluke Flame cells e. Sea urchin Absent f. Pila Metanephrida LONG ANSWER TYPE QUESTIONS...
Read More →Give an example for each of the following
Question: Give an example for each of the following a. A viviparous animal b. A fish possessing a poison sting c. A fish possessing an electric organ d. An organ, which regulates buoyancy e. Animal, which exhibits alternation of generation f. An oviparous animal with mammary gland Solution: a. A viviparous animal Panthera leo b. A fish possessing a poison sting Trygon c. A fish possessing an electric organ Torpedo d. An organ, which regulates buoyancy Air bladder e. Animal, which exhibits altern...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{6}} \frac{2-\sqrt{3} \cos x-\sin x}{(6 x-\pi)^{2}}$ Solution: $=\lim _{x \rightarrow \frac{\pi}{6}} \frac{2-\sqrt{3} \cos x-\sin x}{(6 x-\pi)^{2}}$ $=\lim _{y \rightarrow 0} \frac{2-\sqrt{3} \cos \left(y+\frac{\pi}{6}\right)-\sin \left(y+\frac{\pi}{6}\right)}{y^{2} \times 36}$ $=\frac{1}{36} \times \lim _{y \rightarrow 0} \frac{2-\frac{3}{2} \cos y+\frac{\sqrt{3}}{2} \sin y-\frac{1}{2} \cos y-\frac{\sqrt{3}}{2} \sin y}{y^{...
Read More →Name a. A limbless animal
Question: Name a. A limbless animal b. A cold-blooded animal c. A warm-blooded animal d. An animal possessing dry and cornified skin e. An animal having a canal system and spicules f. An animal with cnidoblasts Solution: a. A limbless animal Icthyophis b. A cold-blooded animal Trygon c. A warm-blooded animal Macaca (monkey) d. An animal possessing dry and cornified skin Naja (Cobra) e. An animal having a canal system and spicules Euspongia f. An animal with cnidoblasts Hydra...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{(1+\sqrt{x})^{2}}{\sqrt{x}} d x$ Solution: Given: $\int \frac{(1+\sqrt{x})^{2}}{\sqrt{x}} d x$ By applying $(a+b)^{2}=a^{2}+b^{2}+2 a b$ $\Rightarrow \int \frac{(1)^{2}+(\sqrt{x})^{2}+2 \times 1 \times \sqrt{x}}{\sqrt{x}} \mathrm{dx}$ $\Rightarrow \int \frac{1+x+2 \sqrt{x}}{\sqrt{x}} d x$ By Splitting, we get, $\Rightarrow \int\left(\frac{1}{\sqrt{x}}+\frac{x}{\sqrt{x}}+\frac{2 \sqrt{x}}{\sqrt{x}}\right) d x$ $\Rightarrow \int x^{-\frac{1}{...
Read More →Mention two similarities between
Question: Mention two similarities between a. Aves and mammals b. A frog and crocodile c. A turtle and pila Solution: (a) Aves and mammals are warm-blooded and have 4 chambered heart (b) A frog and crocodile are cold-blooded and are oviparous (c) Turtle and pilla are cold-blooded and are oviparous animals...
Read More →Give the characteristic features of the following
Question: Give the characteristic features of the following citing one example of each a. Chondrichthyes and Osteichthyes b. Urochordata and cephalochordate Solution: Chondrichthyes Their habitat is mainly marine and their body is streamlined. They have a cartilaginous endoskeleton. Examples are scoliosis and Trygon Osteichthyes The habitat is both marines as well as freshwater and they have a streamlined body. The endoskeleton is bony. Examples are Marine: Hippocampus (Sea horse), Freshwater: L...
Read More →Differentiate between:
Question: Differentiate between: a. Open and closed circulatory system b. Oviparity and viviparity c. Direct and indirect development d. Acoelomate and pseudocoelomate e. Notochord and nerve cord f. Polyp and medusa Solution: (a) Blood is pumped out the heart and the cells and tissues are directly bathed in the open circulatory system whereas the closed circulatory system is circulated throughout the body with the help of series of vessels (b) Laying of fertilized and unfertilized eggs are known...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{x^{-1 / 3}+\sqrt{x}+2}{\sqrt[3]{x}} d x$ Solution: Given: $\int \frac{x^{\frac{1}{a}}+\sqrt{x}+2}{\sqrt[3]{x}} d x$ By Splitting them, $\Rightarrow \int \frac{x^{-\frac{1}{3}}}{\sqrt[2]{x}} d x+\int \frac{\sqrt{x}}{\sqrt[3]{x}} d x+\int \frac{2}{\sqrt[3]{x}} d x$ $\Rightarrow \int x^{-\frac{1}{3}} \times x^{-\frac{1}{3}} d x+\int x^{\frac{1}{2}} \times x^{-\frac{1}{3}} d x+2 \int x^{-\frac{1}{3}} d x$ $\Rightarrow \int x^{-\frac{1}{2}-\frac...
Read More →Match the following and write correct
Question: Match the following and write correct choice in space provided a. _____, b. ______, c. _____, d. ___, e. _____, f. ____, Solution: a. Pila Presence of shell b. Cockroach Jointed appendages c. Asterias Water vascular system d. Torpedo Electric organ e. Parrot Perching f. Dogfish Placoid scales...
Read More →Endoparasites are found inside the host body.
Question: Endoparasites are found inside the host body. Mention the special structure, possessed by these and which enables them to survive in those conditions. Solution: For the survival of that condition they have to adapt: High reproductive capacity Presence of adhesive organs or suckers to cling on to the host. Loss of digestive system. Loss of unnecessary sense organs....
Read More →Match the following
Question: Match the following Solution: a. Amphibia Dual habitat b. Mammals Mammary glands c. Chondrichthyes Cartilaginous notochord d. Osteichthyes Air bladder e. Cyclostomata Sucking and circular mouth without jaws f. Aves Pneumatic bones...
Read More →Fill up the blank spaces appropriately
Question: Fill up the blank spaces appropriately Solution: A = Malpighian tubules B = Open C = Annelida D = Mollusca E = Feather-like gills F = Amphibians have kidneys as their excretory organs...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{\sqrt{1+\sin x}-\sqrt{1-\cos x}}{x}$ Solution: $=\lim _{x \rightarrow 0} \frac{\sqrt{1+\sin x}-\sqrt{1-\sin x}}{x}$ $=\lim _{x \rightarrow 0} \frac{\sqrt{1+\sin x}-\sqrt{1-\sin x}}{x} \times \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}+\sqrt{1-\sin x}}$ $=\lim _{x \rightarrow 0} \frac{1+\sin x-(1-\sin x)}{x(\sqrt{1+\sin x}+\sqrt{1-\sin x})}$ $=\lim _{x \rightarrow 0} \frac{2 \times \sin x}{(\sqrt{1+\sin x}+\sqrt{1-...
Read More →There has been an increase in the number of chambers
Question: There has been an increase in the number of chambers in the heart during the evolution of vertebrates. Give the names of the class of vertebrates having two, three or four-chambered heart. Solution: Two-chambered hearts: Chrondrichytes and osteocytes Three- chambered heart: Amphibia and Reptile Four-chambered heart: Aves and mammalian...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{x^{-1 / 3}+\sqrt{x}+2}{\sqrt[3]{x}} d x$ Solution: Given: $\int \frac{x^{\frac{1}{a}}+\sqrt{x}+2}{\sqrt[3]{x}} d x$ By Splitting them, $\Rightarrow \int \frac{x^{-\frac{1}{3}}}{\sqrt[2]{x}} d x+\int \frac{\sqrt{x}}{\sqrt[3]{x}} d x+\int \frac{2}{\sqrt[3]{x}} d x$ $\Rightarrow \int x^{-\frac{1}{3}} \times x^{-\frac{1}{3}} d x+\int x^{\frac{1}{2}} \times x^{-\frac{1}{3}} d x+2 \int x^{-\frac{1}{3}} d x$ $\Rightarrow \int x^{-\frac{1}{2}-\frac...
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