Show that
Question: Show that $\lim _{x \rightarrow 0} \sin \frac{1}{x}$ does not exist. Solution: Let $x=0+\mathrm{h}$, when $x$ is tends to $0^{+}$ Since $x$ tends to 0 , $h$ will also tend to 0 . Right Hand Limit(R.H.L.): $\lim _{x \rightarrow 0^{+}} f(x)$ $=\lim _{x \rightarrow 0^{+}} \sin \frac{1}{x}$ $=\lim _{h \rightarrow 0^{+}} \sin \frac{1}{0+h}$ $=\sin \frac{1}{0}$ $=\sin \infty$ $=\infty$ Let $x=0-h$, when $x$ is tends to $0^{-}$ Since $x$ tends to 0, h will also tend to 0 . Left Hand Limit(L.H...
Read More →The body of sponges does not possess
Question: The body of sponges does not possess tissue level of organisation though it is made of thousands of cells. Comment. Solution: Most of the multicellular organisms possess specialized or advanced tissue level but sponges have a cellular tissue level. They do not form tissues and their bodies perforated which allows water to pass through them easily....
Read More →Frogs are beneficial for mankind,
Question: Frogs are beneficial for mankind, justify the statement. Solution: They are an important part of the food chain. They help farmers by eating insects and pest and protect from insect infection. They are also used as a food source for humans in some regions of the world. For experiments and researches, they have been used....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1-\cos x}{1+\cos x} d x$ Solution: Let $I=\int \frac{1-\cos x}{1+\cos x} d x$ We have $\cos x=\cos \left(2 \times \frac{x}{2}\right)$ We know $\cos 2 \theta=1-2 \sin ^{2} \theta=2 \cos ^{2} \theta-1$ Hence, in the numerator, we can write $1-\cos x=2 \sin ^{2} \frac{x}{2}$ In the denominator, we can write $1+\cos x=2 \cos ^{2} \frac{x}{2}$ Therefore, we can write the integral as $I=\int \frac{2 \sin ^{2} \frac{x}{2}}{2 \cos ^{2} \frac{x}{2}}...
Read More →Give the location of hepatic caeca
Question: Give the location of hepatic caeca in a cockroach. What is their function? Solution: The hepatic caeca which are also known as gastric caeca is a 6-8 narrow and hollow ring-like blind tubules which are present in the junction of the foregut and midgut. They help in the digestion of food in cockroaches....
Read More →The special venous connection between
Question: The special venous connection between liver and intestine and between kidney and intestine is found in the frog, what are they called? Solution: The special venous connection between the liver and intestine is known as the hepatic portal system and between kidney and intestine is known as the renal portal system....
Read More →What is the difference between cutaneous
Question: What is the difference between cutaneous and pulmonary respiration? Solution: Cutaneous respiration refers to the exchange of gases which occurs through the from the skin while pulmonary respiration refers to the exchange of gases through the lungs....
Read More →Find the value
Question: Show that $\lim _{x \rightarrow 0} e^{-1 / x}$ does not exist. Solution: Left Hand Limit(L.H.L.): $\lim _{x \rightarrow 0^{-}} f(x)$ $=\lim _{x \rightarrow 0^{-}} e^{\frac{-1}{(-x)}}$ $=\lim _{x \rightarrow 0^{-}} e^{\frac{1}{x}}$ $=e^{\frac{1}{0}}$ $=e^{\infty}$ $\lim _{x \rightarrow 0^{+}} f(x)$ Right Hand Limit(R.H.L.): $=\lim _{x \rightarrow 0^{+}} e^{\frac{-1}{x}}$ $=e^{\frac{-1}{0}}$ $=e^{-\infty}$ $=\frac{1}{e^{\infty}}$ [ Formula $\frac{1}{\infty}=0$, anything to the power infi...
Read More →The digestive system of the frog is made
Question: The digestive system of the frog is made of the following parts. Arrange them in an order beginning from the mouth. Mouth, oesophagus, buccal cavity, stomach, intestine, cloaca, rectum, cloacal aperture Solution: Mouth Buccal cavity Oesophagus Stomach Intestine Rectum Cloaca Cloacal aperture is the order....
Read More →Which mouth part of cockroach
Question: Which mouth part of cockroach is comparable to our tongue? Solution: Hypopharynx is the mouth part of cockroach which is comparable to our tongue....
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 →Give two identifying features
Question: Give two identifying features of an adult male frog. Solution: (i) Presence of vocal sacs: The male frogs have saggy skinned vocal sacs in their necks (ii) Presence of Copulation pad: The male frogs have a copulatory pad on the forelimbs...
Read More →Name the different cell junctions found in tissues.
Question: Name the different cell junctions found in tissues. Solution: Adhering junction, Gap junction and Tight junction are the cell junctions found in tissues....
Read More →A muscle fibre tapers at both ends and
Question: A muscle fibre tapers at both ends and does not show striations. Name the muscle fibre. Solution: Smooth muscle fibres can taper at both ends and does not show any striations. Smooth muscles functioning cannot be controlled directly....
Read More →What is the scientific term given
Question: What is the scientific term given to earthworms body segments? Solution: The earthworms body segmentation is known as metamerism. It is important for its locomotion....
Read More →Name the process by which a tadpole
Question: Name the process by which a tadpole develops into an adult frog. Solution: The process by which a tadpole develops into an adult frog is known as metamorphosis....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{x^{3}-3 x^{2}+5 x-7+x^{2} a^{x}}{2 x^{2}} d x$ Solution: Let $I=\int \frac{x^{2}-3 x^{2}+5 x-7+x^{2} a^{x}}{2 x^{2}} d x$ $\Rightarrow I=\frac{1}{2} \int \frac{x^{3}-3 x^{2}+5 x-7+x^{2} a^{x}}{x^{2}} d x$ $\Rightarrow I=\frac{1}{2} \int\left(\frac{x^{3}}{x^{2}}-\frac{3 x^{2}}{x^{2}}+\frac{5 x}{x^{2}}-\frac{7}{x^{2}}+\frac{x^{2} a^{x}}{x^{2}}\right) d x$ $\Rightarrow I=\frac{1}{2} \int\left(x-3+\frac{5}{x}-\frac{7}{x^{2}}+a^{x}\right) d x$ $...
Read More →Identify the sex of a frog in
Question: Identify the sex of a frog in which sound-producing vocal sacs are present. Solution: Sound producing vocal sacs are present in Male frogs only. They are used for amplifying their mating calls to attract female frogs. They are absent in female frogs....
Read More →How many times do nymphs moult
Question: How many times do nymphs moult to reach the adult form of a cockroach? Solution: A nymph requires to moult 13 times to reach the adult cockroach form....
Read More →Where are sclerites present
Question: Where are sclerites present in cockroach? Solution: Sclerites are present in all the body segments of cockroaches. The sclerites are hard chitinous plates present in an insect....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int(a \tan x+b \cot x)^{2} d x$ Solution: Let $\mathrm{I}=\int(\mathrm{a} \tan \mathrm{x}+\mathrm{b} \cot \mathrm{x})^{2} \mathrm{dx}$ We know $(a+b)^{2}=a^{2}+2 a b+b^{2}$ Therefore, we can write the integral as $\mathrm{I}=\int\left[(\mathrm{a} \tan \mathrm{x})^{2}+2(\mathrm{a} \tan \mathrm{x})(\mathrm{b} \cot \mathrm{x})+(\mathrm{b} \cot \mathrm{x})^{2}\right] \mathrm{dx}$ $\Rightarrow \mathrm{I}=\int\left(\mathrm{a}^{2} \tan ^{2} \mathrm{x}+2 \ma...
Read More →State the number of segments in earthworm
Question: State the number of segments in earthworm which are covered by a prominent dark band or clitellum. Solution: he 14th, 15th and 16th number of the segment in earthworms are covered by prominent dark band or clitellum as it has a tissue known as clitellum....
Read More →Match the following and choose the correct option
Question: Match the following and choose the correct option Options: a. A-iii, B-i, C-ii, D-iv b. A-ii, B-i, C-iv, D-iii c. A-iii, B-iv, C-ii, D-i d. A-iii, B-i, C-iv, D-ii Solution: Option (d)A-iii, B-i, C-iv, D-ii is the answer....
Read More →Match the following with reference to cockroach
Question: Match the following with reference to cockroach and choose the correctOption Options: a. A-iii, B-iv, C-ii, D-i b. A-iv, B-iii, C-ii, D-i c. A-iv, B-ii, C-iii, D-i d. A-ii, B-iv, C-iii, D-i Solution: Option (b)A-iv, B-iii, C-ii, D-iis the answer....
Read More →Match the following and choose the correct option
Question: Match the following and choose the correct option Options: a. A-ii, B-iii, C-iv, D-i b. A-iii, B-ii, C-iv, D-i c. A-i, B-iii, C-ii, D-i d. A-ii, B-iv, C-iii, D-i Solution: Option (a)A-ii, B-iii, C-iv, D-iis the answer....
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