Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{1-\cos m x}{1-\cos n x}$ Solution: $=\lim _{x \rightarrow 0} \frac{1-\cos m x}{1-\cos n x}$ $=\lim _{x \rightarrow 0} \frac{\frac{1-\cos m x}{m x \times m x}}{\frac{1-\cos n x}{n x \times n x}} \times \frac{m \times m}{n \times n}$ $=\frac{\mathrm{m}^{2}}{\mathrm{n}^{2}}$ $\therefore \lim _{x \rightarrow 0} \frac{1-\cos m x}{1-\cos n x}=\frac{m^{2}}{n^{2}}$...
Read More →Match the following list of animals
Question: Match the following list of animals with their level of organisation. Choose the correct match showing the division of labour with animal example. a. i-B, ii-C, iii-D, and iv-A b. i-B, ii-D, iii-C, and iv-A c. i-D, ii-A, iii-B, and iv-C d. i-A, ii-D, iii-C, and iv-B Solution: Option (c)i-D, ii-A, iii-B, and iv-C is the answer....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{1-\cos 2 m x}{1-\cos 2 n x}$ Solution: $=\lim _{x \rightarrow 0} \frac{1-\cos 2 m x}{1-\cos 2 n x}$ $=\lim _{x \rightarrow 0} \frac{\frac{1-\cos 2 m x}{(2 m x)^{2}} \times(2 m x)^{2}}{\frac{1-\cos 2 n x}{(2 n x)^{2}} \times(2 n x)^{2}}$ $=\frac{\frac{1}{2}}{\frac{1}{2}} \times \frac{\mathrm{m} \times \mathrm{m}}{\mathrm{n} \times \mathrm{n}}\left[\because \frac{1-\cos \theta}{\theta \times \theta}=\frac{1}{2}\right]$ $=\frac...
Read More →Which one of the following is a non-poisonous
Question: Which one of the following is a non-poisonous snake? a. Cobra b. Viper c. Python d. Krait Solution: Option (c)Python is the answer....
Read More →Which one of the following is oviparous?
Question: Which one of the following is oviparous? a. Platypus b. Flying fox (Bat) c. Elephant d. Whale Solution: Option (a)Platypusis the answer....
Read More →Which one of the following statements is incorrect?
Question: Which one of the following statements is incorrect? a. In cockroaches and prawns excretion of waste material occurs through malpighian tubules. b. In ctenophores, locomotion is mediated by comb plates. c. In Fasciola, flame cells help in excretion d. Earthworms are hermaphrodites and yet cross-fertilization takes place among them. Solution: Option (a)In cockroaches and prawns excretion of waste material occurs through malpighian tubules. is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \sqrt{x}\left(x^{3}-\frac{2}{x}\right) d x$ Solution: Given: $\int \sqrt{x}\left(x^{3}-\frac{2}{x}\right) d x$ Opening the bracket, we get, $\Rightarrow \int\left(x^{\frac{1}{2}} \times x^{3}-x^{\frac{1}{2}} \times \frac{2}{x}\right) d x$ $\Rightarrow \int\left(x^{\frac{1}{2}+3}-x^{\frac{1}{2}-1} \times 2\right) d x$ $\Rightarrow \int\left(x^{\frac{7}{2}}-2 x^{-\frac{1}{2}}\right) d x$ By multiplying, $\Rightarrow \int x^{\frac{7}{2}} d x-2 \int ...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0}(\operatorname{cosec} x-\cot x)$ Solution: $=\lim _{x \rightarrow 0}(\csc x-\cot x)$ $=\lim _{x \rightarrow 0}\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x}\right)$ $=\lim _{x \rightarrow 0}\left(\frac{1-\cos x}{\sin x}\right)$ $=\lim _{x \rightarrow 0}\left(\frac{2 \times \sin \frac{x}{2} \times \sin \frac{x}{2}}{2 \times \sin \frac{x}{2} \times \cos \frac{x}{2}}\right)[\because 1-\cos \theta=2 \sin \theta \times \sin \theta]$ $=\li...
Read More →Which one of the following statements is incorrect?
Question: Which one of the following statements is incorrect? a. Mesoglea is present in between ectoderm and endoderm in Obelia. b. Exhibits radial symmetry Asterias c. Fasciola is a pseudocoelomate animal d. Taenia is a triploblastic animal Solution: Option (c)Fasciola is a pseudocoelomate animalis the answer....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{\cos 2 x-1}{\cos x-1}$ Solution: $=\lim _{x \rightarrow 0} \frac{\cos 2 x-1}{\cos x-1}$ $=\lim _{x \rightarrow 0} \frac{\cos 2 x-1}{\cos x-1} \times \frac{4 \times x \times x}{2 x \times 2 x}$ $=4 \times \lim _{x \rightarrow 0} \frac{\frac{\cos 2 x-1}{2 x \times 2 x}}{\frac{\cos x-1}{x \times x}}$ $=4 \times \frac{\lim _{x \rightarrow 0} \frac{\cos 2 x-1}{(2 x)^{2}}}{\lim _{x \rightarrow 0} \frac{\cos x-1}{x^{2}}}$ $=4 \time...
Read More →Which one of the following sets of animals
Question: Which one of the following sets of animals belongs to a single taxonomic group? a. Cuttlefish, Jellyfish, Silverfish, Dogfish, Starfish b. Bat, Pigeon, Butterfly c. Monkey, Chimpanzee, Man d. Silkworm, Tapeworm, Earthworm Solution: Option (c)Monkey, Chimpanzee, Man is the answer....
Read More →Birds and mammals share one of the following
Question: Birds and mammals share one of the following characteristics as a common feature. a. Pigmented skin b. Pneumatic bones c. Viviparity d. Warm-blooded Solution: Option (d)Warm-bloodedis the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals:] $\int\left(x^{e}+e^{x}+e^{e}\right) d x$ Solution: Given: $\int\left(x^{e}+e^{x}+e^{e}\right) d x$ By Splitting, we get, $\Rightarrow \int x^{e} d x+\int e^{x} d x+\int e^{e} d x$ By using the formula, $\int x^{n} d x=\frac{x^{n+1}}{n+1}$ $\Rightarrow \frac{x^{e+1}}{e+1}+\int e^{x} d x+\int e^{e} d x$ By applying the formula, $\int a^{x} d x=\frac{a^{x}}{\log a}$ $\Rightarrow \frac{x^{e+1}}{e+1}+\frac{e^{x}}{\log _{e} e}+\int e^{e} d x$ We know that, ...
Read More →Which of the following pairs of animals
Question: Which of the following pairs of animals has non-glandular skin a. Snake and Frog b. Chameleon and Turtle c. Frog and Pigeon d. Crocodile and Tiger Solution: Option (b)Chameleon and Turtle is the answer....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{2}} \frac{\tan 2 x}{x-\frac{\pi}{2}}$ Solution: $=\lim _{x \rightarrow \frac{\pi}{2}} \frac{\tan 2 x}{x-\frac{\pi}{2}}$ As $x$ tends to $\pi / 2, x-\pi / 2$ tends to zero. Let, $\mathrm{y}=\mathrm{x}-\frac{\pi}{2}$ $=\lim _{y \rightarrow 0} \frac{\tan \left(2 y+\frac{\pi}{2} \times 2\right)}{y}$ $=\lim _{y \rightarrow 0} \frac{\tan (\pi+2 y)}{y}$ $=\lim _{y \rightarrow 0} \frac{\tan 2 y}{2 y} \times 2$ $=2$ $\therefore \li...
Read More →Which one of the following sets of animals
Question: Which one of the following sets of animals shares a four-chambered heart? a. Amphibian, Reptiles, Birds b. Crocodiles, Birds, Mammals c. Crocodiles, Lizards, Turtles d. Lizards, Mammals, Birds Solution: Option (b)Crocodiles, Birds, Mammals is the answer....
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{\sin (\pi-x)}{\pi(\pi-x)}$ Solution: $=\lim _{x \rightarrow 0} \frac{\sin (\pi-x)}{\pi(\pi-x)}$ $=\lim _{x \rightarrow 0} \frac{\sin x}{\pi(\pi-x)} \times \frac{x}{x}$ $=\lim _{x \rightarrow 0} \frac{\sin x}{x} \times \lim _{x \rightarrow 0} \frac{\pi-(\pi-x)}{\pi(\pi-x)}$ $=1 \times \lim _{x \rightarrow 0}\left(\frac{1}{\pi-x}-\frac{1}{\pi}\right)$ $=\frac{1}{\pi}-\frac{1}{\pi}$ $=0$ $\therefore \lim _{x \rightarrow 0} \fra...
Read More →Given below are types of cells present in some animals.
Question: Given below are types of cells present in some animals. Which of the following cells can differentiate to perform different functions? a. Choanocytes b. Interstitial cells c. Gastrodermal cells d. Nematocytes Solution: Option (b)Interstitial cells is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int\left\{x^{2}+e^{\log x}+\left(\frac{e}{2}\right)^{x}\right\} d x$ Solution: Given: $\int\left\{x^{2}+e^{\log x}+\left(\frac{e}{2}\right)^{x}\right\} d x$ By Splitting, we get, $\Rightarrow \int x^{2} d x+\int e^{\log x} d x+\int\left(\frac{e}{2}\right)^{x} d x$ By applying formula, $\int \mathrm{x}^{\mathrm{n}} \mathrm{dx}=\frac{\mathrm{x}^{\mathrm{n}+1}}{\mathrm{n}+1}$ $\Rightarrow \frac{x^{2+1}}{2+1}+\int e^{\log _{e} x} d x+\int\left(\frac{e}{2...
Read More →In some animal groups,
Question: In some animal groups, the body is found divided into compartments with a serial repetition of at least some organs. This characteristic feature is called a. Segmentation b. Metamerism c. Metagenesis d. Metamorphosis Solution: Option (b)Metamerism is the answer....
Read More →Evaluate the following limits
Question: Evaluate the following limits $\lim _{x \rightarrow 0} \frac{\sin a x+b x}{a x+\sin b x}$, where $a, b, a+b \neq 0$ Solution: $=\lim _{x \rightarrow 0} \frac{\sin (a x)+b x}{a x+\sin (b x)}$ $=\lim _{x \rightarrow 0} \frac{\sin (a x)+b x}{a x+\sin (b x)} \times \frac{b x}{a x} \times \frac{a}{b}$ $=\lim _{x \rightarrow 0} \frac{\frac{\sin a x+b x}{a x}}{\frac{a x+\sin b x}{b x}} \times \frac{a}{b}$ $=\frac{a}{b} \times \frac{\lim _{x \rightarrow 0} \frac{\sin a x+b x}{a x}}{\lim _{x \r...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{(1+x)^{3}}{\sqrt{x}} d x$ Solution: Given: Applying: $(a+b)^{3}=a^{3}+b^{3}+3 a b^{2}+3 a^{2} b$ $\Rightarrow \int \frac{1+x^{2}+3 x^{2} \times 1+3 \times 1^{2} \times x}{\sqrt{x}} d x$ $\Rightarrow \int \frac{1+x^{2}+3 x^{2}+3 x}{\sqrt{x}} d x$ By Splitting, we get, $\int x^{n} d x=\frac{x^{n+1}}{n+1}$ $\Rightarrow \frac{x^{\frac{1}{2}+1}}{-\frac{1}{2}+1}+\frac{x^{\frac{5}{2}+1}}{\frac{5}{2}+1}+3 \frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1}+\fr...
Read More →Evaluate the following limits:
Question: Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{a x+x \cos x}{b \sin x}$ Solution: $=\lim _{x \rightarrow 0} \frac{a x+x \cos x}{b \sin x}$ $=\lim _{x \rightarrow 0} \frac{a x}{b \sin x}+\frac{x \cos x}{b \sin x}$ $=\lim _{x \rightarrow 0} \frac{a x}{b \sin x}+\lim _{x \rightarrow 0} \frac{x \cos x}{b \sin x}$ $\left.=\frac{a}{b}+\frac{1}{b}\left[\because \lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1\right]_{x \rightarrow 0} \cos \theta=1\right]$ $=\frac{a+1}{...
Read More →Lichen is usually cited as an example of ‘symbiosis’
Question: Lichen is usually cited as an example of symbiosis in plants where an algal and a fungal species live together for their mutual benefit. Which of the following will happen if algal and fungal partners are separated from each other? a. Both will survive and grow normally and independent of each other. b. Both will die c. The algal component will survive while the fungal component will die. d. The fungal component will survive while the algal partner will die. Based on your answer how do...
Read More →The gametophyte is a dominant phase
Question: The gametophyte is a dominant phase in the life cycle of a bryophyte. Explain. Solution: Due to the alteration in the gametophytic and sporophytic life Bryophyte shows haplodiplonic life cycle. The major part is dominated by the haploid gametophytic phase. They are independent, photosynthetic and haploid phase. Inside gametophyte, the antheridium and archegonia are formed. Later fertilization will occur and zygote will be formed. Zygote developed into sporophytes which is small is depe...
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