Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\log x}{x} d x$ Solution: Assume $\log x=t$ $\Rightarrow \mathrm{d}(\log \mathrm{x})=\mathrm{dt}$ $\Rightarrow \frac{1}{\mathrm{x}} \mathrm{dx}=\mathrm{dt}$ Substituting $t$ and dt in above equation we get $\Rightarrow \int t . d t$ $\Rightarrow \frac{t^{2}}{2}+c$ But $t=\log (x)$ $\Rightarrow \frac{\log ^{2} x}{2}+C$...
Read More →Monocarpic plants are those which
Question: Monocarpic plants are those which a. Bear flowers with one ovary b. Flower once and die c. Bear only one flower d. All of the above Solution: Option (b)Flower once and dieis the answer....
Read More →Differentiate
Question: Differentiate $\frac{2 \cot x}{\sqrt{x}}$ Solution: To find: Differentiation of $\frac{2 \cot x}{\sqrt{x}}$ Formula used: (i) $\left(\frac{u}{v}\right)^{\prime}=\frac{u^{\prime} v-u v^{\prime}}{v^{2}}$ where $v \neq 0$ (Quotient rule) (ii) $\frac{d \cot x}{d x}=-\operatorname{cosec}^{2} x$ (iii) $\frac{d x^{n}}{d x}=n x^{n-1}$ Let us take $u=(2 \cot x)$ and $v=$ $(\sqrt{x})$ $u^{\prime}=\frac{d u}{d x}=\frac{d(2 \cot x)}{d x}=-2 \operatorname{cosec}^{2} x$ $v^{\prime}=\frac{d v}{d x}=\...
Read More →ABA acts antagonistically to
Question: ABA acts antagonistically to a. Ethylene b. Cytokinin c. Gibberellic acid d. IAA Solution: Option (c)Gibberellic acid is the answer....
Read More →To increase sugar production in sugarcanes,
Question: To increase sugar production in sugarcanes, they are sprayed with a. IAA b. Cytokinin c. Gibberellin d. Ethylene Solution: Option (c)Gibberellin is the answer....
Read More →Plasticity in plant growth means that
Question: Plasticity in plant growth means that a. Plant roots are extensible b. Plant development is dependent on the environment c. Stems can extend d. None of the above Solution: Option (b)Plant development is dependent on the environment is the answer....
Read More →Differentiate
Question: Differentiate $\frac{\cos x}{\log x}$ Solution: To find: Differentiation of $\frac{\cos x}{\log x}$ Formula used: (i) $\left(\frac{u}{v}\right)^{\prime}=\frac{u^{\prime} v-u v^{\prime}}{v^{2}}$ where $v \neq 0$ (Quotient rule) (ii) $\frac{d \cos x}{d x}=-\sin x$ (iii) $\frac{d \log x}{d x}=\frac{1}{x}$ Let us take $u=(\cos x)$ and $v=(\log x)$ $u^{\prime}=\frac{d u}{d x}=\frac{d(\cos x)}{d x}=-\sin x$ $v^{\prime}=\frac{d v}{d x}=\frac{d(\log x)}{d x}=\frac{1}{x}$ Putting the above obta...
Read More →The term synergistic action of hormones refers to
Question: The term synergistic action of hormones refers to a. When two hormones act together but bring about the opposite effects. b. When two hormones act together and contribute to the same function. c. When one hormone affects more than one function. d. When many hormones bring about anyone function. Solution: Option (b)When two hormones act together and contribute to the same function. is the answer....
Read More →Growth can be measured in various ways.
Question: Growth can be measured in various ways. Which of these can be used as parameters to measure growth a. Increase in cell number b. Increase in cell size c. Increase in length and weight d. All the above Solution: Option (d)All the above is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{\cos 3 x-\cos x} d x$ Solution: The denominator is of the form $\cos C-\cos D=-2 \sin \left(\frac{c+d}{2}\right) \cdot \sin \left(\frac{c-d}{2}\right)$ $\therefore \cos 3 x-\cos x=-2 \sin \left(\frac{3+1}{2} x\right) \sin \left(\frac{3-1}{2} x\right)$ $\therefore \cos 3 x-\cos x=-2 \sin 2 x \cdot \sin x$ $-2 \sin 2 x \cdot \sin x=-2 \cdot 2 \cdot \sin x \cdot \cos x \cdot \sin x$ $-2 \sin 2 x \cdot \sin x=-4 \sin ^{2} x \cdot \cos x$ Als...
Read More →Apples are generally wrapped in waxed paper to
Question: Apples are generally wrapped in waxed paper to a. Prevent sunlight from changing its colour b. Prevent aerobic respiration by checking the entry of O2. c. Prevent ethylene formation due to injury d. Make the apples look attractive Solution: Option (b)Prevent aerobic respiration by checking the entry of O2 is the answer....
Read More →Match the following:
Question: Match the following: Options: a A iv, B iii, C v, D ii, E i b A v, B iii, C iv, D ii, E i c A iv, B i, C iv, D iii, E ii d A v, B iii, C ii, D i, E iv Solution: Option (a)A iv, B iii, C v, D ii, E i is the answer....
Read More →Differentiate
Question: Differentiate $\frac{\sqrt{a}+\sqrt{x}}{\sqrt{a}-\sqrt{x}}$ Solution: To find: Differentiation of $\frac{\sqrt{a}+\sqrt{x}}{\sqrt{a}-\sqrt{x}}$ Formula used: (i) $\left(\frac{u}{v}\right)^{\prime}=\frac{u^{\prime} v-u v^{\prime}}{v^{2}}$ where $v \neq 0$ (Quotient rule) (ii) $\frac{d x^{n}}{d x}=n x^{n-1}$ Let us take $u=(\sqrt{a}+\sqrt{x})$ and $v=(\sqrt{a}-\sqrt{x})$ $u^{\prime}=\frac{d u}{d x}=\frac{d(\sqrt{a}+\sqrt{x})}{d x}=\frac{1}{2 \sqrt{x}}$ $v^{\prime}=\frac{d v}{d x}=\frac{d...
Read More →The effect of apical dominance can be overcome
Question: The effect of apical dominance can be overcome by which of the following hormone: a. IAA b. Ethylene c. Gibberellin d. Cytokinin Solution: Option (d)Cytokininis the answer....
Read More →Coconut water contains
Question: Coconut water contains a. ABA b. Auxin c. Cytokinin d. Gibberellin Solution: Option (c)Cytokinin is the answer....
Read More →Ethylene is used for
Question: Ethylene is used for a. Retarding ripening of tomatoes b. Hastening of ripening of fruits c. Slowing down the ripening of apples d. Both b and c Solution: Option (b)Hastening of ripening of fruits is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{\sin x \cos ^{2} x} d x$ Solution: We know $\sin ^{2} x+\cos ^{2} x=1$ $\Rightarrow \int \frac{\sin ^{2} x+\cos ^{2} x}{\sin x \cos ^{2} x}$ $\Rightarrow \int \frac{\sin ^{2} x}{\sin x \cos ^{2} x} d x+\int \frac{\cos ^{2} x}{\sin x \cos ^{2} x} d x$ $\Rightarrow \int \frac{\sin x}{\cos ^{2} x} d x+\int \frac{1}{\sin x} d x$ $\Rightarrow \int \tan x \sec x d x+\int \csc x d x$ $d(\sec x)=\tan x \cdot \sec x$ $\therefore \int \tan x \sec ...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{e^{x-1}+x^{e-1}}{e^{x}+x^{e}} d x$ Solution: Multiplying and dividing the numerator by e we get the given as $\Rightarrow \frac{1}{e} \int \frac{e^{x}+e x^{e-1}}{e^{x}+x^{e}} d x \ldots$ (1) Assume $e^{x}+x^{e}=t$ $\Rightarrow d\left(e^{x}+x^{e}\right)=d t$ $\Rightarrow e^{x}+e x^{e-1}=d t$ Substituting $\mathrm{t}$ and dt in equation 1 we get $\Rightarrow \frac{1}{\mathrm{e}} \int \frac{\mathrm{d} t}{t}$ $=\ln |t|+c$ But $t=e^{x}+x^{e}$ $\...
Read More →Give an account of Glycolysis.
Question: Give an account of Glycolysis. Where does it occur? What is the end product? Trace the fate of these products in both aerobic and anaerobic respiration. Solution: Glycolysis is the process which involves the splitting of glucose (a 6C compound) into two molecules of pyruvic acid (a 3C compound). It occurs in the cytoplasm of the cell. The end products of glycolysis are two pyruvates (pyruvic acid) molecules, a total of four ATP molecules, and two molecules of NADH. Glycolysis occurs in...
Read More →Enumerate the assumptions that we undertake in making the respiratory balance sheet.
Question: Enumerate the assumptions that we undertake in making the respiratory balance sheet. Are these assumptions valid for a living system? Compare fermentation and aerobic respiration in this context. Solution: The metabolic pathway for respiration is sequential as Glycolysis Krebs Cycle Electron transport system. Each of them occurs one after the other in sequential order. (i) The NADH which is synthesized during the glycolysis process is taken from the cytoplasm to the mitochondria of the...
Read More →Oxygen is critical for aerobic respiration.
Question: Oxygen is critical for aerobic respiration. Explain its role concerning ETS. Solution: Oxygen plays a crucial role at the end of ETC because it removes the hydrogen from the electron transport system. It acts as a hydrogen acceptor in the electron transport chain. If oxygen is absent then the transportation of electron will not happen through the coenzymes and there will be no formation of proton pump and ATP will not be produced by oxidative phosphorylation....
Read More →Differentiate
Question: Differentiate $\frac{x^{4}}{\sin x}$ Solution: To find: Differentiation of $\frac{x^{4}}{\sin x}$ Formula used: (i) $\left(\frac{u}{v}\right)^{\prime}=\frac{u^{\prime} v-u v^{\prime}}{v^{2}}$ where $v \neq 0$ (Quotient rule) (ii) $\frac{d x^{n}}{d x}=n x^{n-1}$ (iii) $\frac{d \sin x}{d x}=\cos x$ Let us take $u=\left(x^{4}\right)$ and $v=(\sin x)$ $u^{\prime}=\frac{d u}{d x}=\frac{d\left(x^{4}\right)}{d x}=4 x^{3}$ $v^{\prime}=\frac{d v}{d x}=\frac{d(\sin x)}{d x}=\cos x$ Putting the a...
Read More →In the following flow chart,
Question: In the following flow chart, replace the symbols a,b,c and d with appropriate terms. Briefly explain the process and give any two application of it. Solution: a = Glyceraldehyde 3 phosphate b = PEP (Phosphoenol pyruvic acid) c = C2H5OH d = Lactic acid The process is fermentation. Aerobic conditions are present in the cell. When there are anaerobic conditions the pyruvic acid gets converted to either lactic acid and it is known as homolactic fermentation. In some micro-organisms which a...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{\sin 2 x}{\sin \left(x-\frac{\pi}{6}\right) \sin \left(x+\frac{\pi}{6}\right)} d x$ Solution: $\sin (A-B)=\sin A \cos B-\cos A \sin B$ $\therefore$ We can write $\sin \left(x-\frac{\pi}{6}\right)=\sin x \cos \frac{\pi}{6}-\cos x \sin \frac{\pi}{6}$ $\sin (A+B)=\sin A \cos B+\cos A \sin B$ $\therefore$ We can write $\sin \left(x+\frac{\pi}{6}\right)=\sin x \cos \frac{\pi}{6}+\cos x \sin \frac{\pi}{6}$ $\therefore$ The given equation becomes ...
Read More →The respiratory pathway is believed to be a catabolic pathway.
Question: The respiratory pathway is believed to be a catabolic pathway. However, the nature of the TCA cycle is amphibolic. Explain. Solution: The respiratory pathway is believed to be a catabolic pathway because it breakdown the substrate. In the TCA cycle, the pyruvate is further broken down to Acetyl CoA, and this Acetyl CoA can also be synthesized to fatty acid whenever it is required for fatty acid metabolism or synthesis. In this cycle both breakdown and synthesis take place....
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