Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $x^{1 / x}$ Solution: Let $y=x^{\frac{1}{x}}$ Taking log both the sides: $\Rightarrow \log y=\log x^{\frac{1}{x}}$ $\Rightarrow \log y=\frac{1}{x} \log x$ $\left\{\log x^{a}=\operatorname{alog} x\right\}$ Differentiating with respect to $\mathrm{x}$ : $\Rightarrow \frac{\mathrm{d}(\log \mathrm{y})}{\mathrm{dx}}=\frac{\mathrm{d}\left(\frac{1}{\mathrm{x}} \log \mathrm{x}\right)}{\mathrm{dx}}$ $\Rightarrow \frac{\mathrm{d}(\log y...
Read More →Explain the role of mouth cavity
Question: Explain the role of mouth cavity in digestion of food. Solution: Moistening of food with saliva, Tongue helps in thorough mixing of food with saliva. Crushing of food into smaller pieces by teeth, Partial digestion of starch by enzyme amylase contained in saliva, Rolling of crushed, moistened and partially digested food into small ball or bolus by the tongue....
Read More →What is common amongst Cuscuta,
Question: What is common amongst Cuscuta, Ticks and Leeches ? Solution: All are parasites which obtain their nutrition from their hosts direcdy without killing them....
Read More →In each of the following situations,
Question: In each of the following situations, what happens to the rate of photosynthesis ? (a) Cloudy days (b) No rainfall in the area (c) Good manuring (d) Stomata get blocked due to dirt. Solution: (a) Cloudy Days: Photosynthesis is reduced due to low light intensity. (b) No Rainfall: Rate of photosynthesis decreases due to wilting of leaves, closure of stomata and reduced availability of hydration. (c) Good Manuring: Rate of photosynthesis increases as good manuring increases soil fertility ...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $x^{1 / x}$ Solution: Let $y=x^{\frac{1}{x}}$ Taking log both the sides: $\Rightarrow \log y=\log x^{\frac{1}{x}}$ $\Rightarrow \log y=\frac{1}{x} \log x$ $\left\{\log x^{a}=\operatorname{alog} x\right\}$ Differentiating with respect to $\mathrm{x}$ : $\Rightarrow \frac{\mathrm{d}(\log \mathrm{y})}{\mathrm{dx}}=\frac{\mathrm{d}\left(\frac{1}{\mathrm{x}} \log \mathrm{x}\right)}{\mathrm{dx}}$ $\Rightarrow \frac{\mathrm{d}(\log y...
Read More →Mention the major events during
Question: Mention the major events during photosynthesis. (CCE 2011, 2012) Solution: 1. Photolysis: With the help of light energy, oxygen evolving Z-complex splits up water into its components - protons $\left(\mathrm{H}^{+}\right)$, electrons $\left(\mathrm{e}^{-}\right)$and oxygen. 2. Absorption of Light Energy: Chlorophyll absorbs light energy. 3. Primary Reaction: Chlorophyll converts the absorbed light energy into chemical energy. It is called primary reaction of photosynthesis. It builds u...
Read More →Why is blood circulation in human
Question: Why is blood circulation in human heart called double circulation ? (CCE 2011) Solution: Blood circulation in human heart is called double circulation as blood passes twice through the heart in order to complete one cycleonce through right side as deoxygenated blood and once through left side as oxygenated blood. Deoxygenated blood passes to lungs. It returns to left side as oxygenated blood. Oxygenated blood is supplied to different parts of the body. It returns to right side of the h...
Read More →Solve this
Question: If $\sqrt{y+x}+\sqrt{y-x}=c$, show that $\frac{d y}{d x}=\frac{y}{x}-\sqrt{\frac{y^{2}}{x^{2}}-1}$ Solution: We are given with an equation $\sqrt{y+x}+\sqrt{y-x}=c$, we have to prove that $\frac{d y}{d x}=\frac{y}{x}-\sqrt{\frac{y^{2}}{x^{2}}-1}$ by using the given equation we will first find the value of $\frac{d y}{d x}$ and we will put this in the equation we have to prove, so by differentiating the equation on both sides with respect to $x$, we get, $\frac{\left(1+\frac{d y}{d x}\r...
Read More →Why is the rate of breathing in aquatic
Question: Why is the rate of breathing in aquatic organisms much faster than in terrestrial organisms ? (CCE 2011, 2012) Solution: Most of the aquatic organisms obtain oxygen from water. The amount of dissolved oxygen is quite small as compared to the amount of oxygen in air. Therefore, in order to obtain required oxygen from water, the aquatic animals like fishes have to breathe much faster as compared to the terrestrial organisms....
Read More →Match the articles of columns A and B :
Question: Match the articles of columns A and B : Solution: a iv, b iii, ci, d ii....
Read More →Why does absorption of digested
Question: Why does absorption of digested food occur mainly in the small intestine ? Solution: Digestion of food is completed only in small intestine. Wall of the intestine bears a number of finger-like projections called villi. Villi provide a large surface area to the lining layer for absorption. The epithelium, lining the villi, is made of cells having a number of very fine projections known as microvilli. Microvilli are specialised for absorption. Wall of the intestine, especially the interi...
Read More →What causes movement of food inside
Question: What causes movement of food inside the alimentary canal ? Solution: Involuntary movement consisting of rhythmic contraction and expansion of the alimentary canal called peristalsis....
Read More →What is the significance of emulsification
Question: What is the significance of emulsification of fats ? Solution: Emulsification of fat is the conversion of large fat pieces into very fine fat globules which can be efficiently acted upon by lipase....
Read More →Find the domain and the range of the cube root function,
Question: Find the domain and the range of the cube root function, f: $R \rightarrow R: f(x)=x^{1 / 3}$ for all $x \in R$. Also, draw its graph. Solution: Given: $f(x)=x^{1 / 3} \forall x \in R$ To Find: Domain and range of the given function. Here, $f(x)=x^{1 / 3}$ The domain of the above function would be, Domain $(f)=(-\infty, \infty)\{x \mid x \in R\}$ Because all real numbers have a cube root. There is no value of x which makes the function undefined. Now, to find the range Consider $f(x)=y...
Read More →What will happen if mucus is not
Question: What will happen if mucus is not secreted by gastric glands ? Solution: Mucus protects the stomach from corrosion by HCl and pepsin of gastric juice. In the absence of mucus, the lining layer of stomach wall will be corroded forming gastric ulcers. There will be excessive acidity and extreme discomfort....
Read More →Why is small intestine in herbivore
Question: Why is small intestine in herbivore longer than in carnivores ? (CCE 2013) Solution: Herbivorous diet has a large bulk. It is rich in cellulose. However, cellulose digesting enzymes are absent in them. For digestion of cellulose, herbivores depend upon bacteria. The food has to be kept for longer period in the intestine for complete digestion of cellulose. Therefore, small intestine where bacterial digestion of cellulose occurs has to be long. There is no such requirement in carnivores...
Read More →What are the adaptations of leaf
Question: What are the adaptations of leaf for photosynthesis ? Solution: Large Surface Area : Leaf has a large surface area to absorb maximum amount of lift. Leaf Orientation: It is such as to absorb the optimum amount of light. Veins: A number of veins occur in a leaf. They provide mechanical strength to the otherwise soft leaf. Veins also take part in quick transport of substances to and from the mesophyll cells. Transpiration: Leaf is the seat of transpiration. Transpiration cools the surfac...
Read More →A grocer bought sugar worth Rs 4500. He sold one-third of it at a gain of 10%.
Question: A grocer bought sugar worth Rs 4500. He sold one-third of it at a gain of 10%. At what gain per cent must the remaining sugar be sold to have a gain of 12% on the whole? Solution: CP of sugar = Rs 4500 Profit on one-third of the sugar $=10 \%$ CP of one-third of the sugar $=$ Rs $\frac{4500}{3}=$ Rs. 1500 SP of one $-$ third of the sugar $=\frac{100+\text { gain } \%}{100} \times \mathrm{CP}$ $=\mathrm{Rs} \frac{110}{100} \times 1500$ $=\mathrm{Rs} 1650$ Now, profit= Rs (1650 1500) = R...
Read More →Differentiate between an artery
Question: Differentiate between an artery and a vein. (CCE 2013) Solution:...
Read More →Match the words of column A with those of column B
Question: Match the words of column A with those of column B Solution: a ii,b i,c iv,d iii....
Read More →Solve this
Question: If $\mathrm{y}=\left\{\log _{\cos \mathrm{x}} \sin \mathrm{x}\right\}\left\{\log _{\sin \mathrm{x}} \cos \mathrm{x}\right\}^{-1}+\sin ^{-1}\left(\frac{2 \mathrm{x}}{1+\mathrm{x}^{2}}\right)$, find $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\mathrm{x}=\frac{\pi}{4}$ Solution: We are given with an equation $y=\left\{\log _{\cos x} \sin x\right\}\left\{\log _{\sin x} \cos x\right\}^{-1}+\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)$, we have to find $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$ by using...
Read More →Ahmed buys a plot of land for ₹ 480000. He sells of it at a loss of 6%.
Question: Ahmed buys a plot of land for ₹ 480000. He sells of it at a loss of 6%. At what gain per cent should he sell the remaining part of the plot to gain 10% on the whole? Solution: CP of the plot of land $=₹ 4,80,000$ CP of $\frac{2}{5}$ th of the land $=\frac{2}{5} \times 480000=₹ 1,92,000$ Loss on $\frac{2}{5}$ th of the land $=6 \%$ SP of $\frac{2}{5}$ th of the land $=$ CP $-$ Loss $=192000-\frac{6}{100} \times 192000$ $=₹ 1,80,480$ CP of $\frac{3}{5}$ th of the land $=480000-192000=₹ 2...
Read More →Find the domain and the range of the square root function,
Question: Find the domain and the range of the square root function, f: $\mathbf{R}^{+} U\{0\} \rightarrow \mathbf{R} \mathbf{f}(\mathbf{x})=\sqrt{x}$ for all non-negative real numbers. Also, draw its graph. Solution: Given $f(x)=\sqrt{x}$ To Find: Domain and Range of $\mathrm{f}(\mathrm{x})$. The domain of the given function is set of all positive real Numbers including 0 . In this case, if the value of $x$ is a negative The number then it makes the expression undefined. Therefore, Domain(f) $=...
Read More →How does aerobic respiration differ
Question: How does aerobic respiration differ from anaerobic respiration ? Solution:...
Read More →Leaves of a healthy plant were coated with vaseline.
Question: Leaves of a healthy plant were coated with vaseline. Will this plant remain healthy for long ? Give reasons for your answer. Solution: The plant will not remain healthy for long. Vaseline covers the cuticle and blocks the stomata. As a result It is unable to obtain oxygen from air for respiration, It is unable to perform photosynthesis as no carbon dioxide diffuses from air. In the absence of transpiration, the leaves get heated up and injured....
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