Match the followings and choose
Question: Match the followings and choose the correct option Options: a. A-ii, B-iv, C-v, D-i E-iii b. A-iii, B-ii, C-iv, D-i E-v c. A-i, B-ii, C-iii, D-iv E-v d. A-v, B-iv, C-iii, D-ii E-i Solution: Option (a)A-ii, B-iv, C-v, D-i E-iiiis the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{\sqrt{1+\cos x}} d x$ Solution: In the given equation $\cos x=\cos ^{2} \frac{x}{2}-\sin ^{2} \frac{x}{2}$ Also, $\cos ^{2} \frac{x}{2}+\sin ^{2} \frac{x}{2}=1$ Substituting in the above equation we get, $\Rightarrow \int \frac{1}{\sqrt{\cos ^{2} \frac{x}{2}+\sin ^{2} \frac{x}{2}+\left(\cos ^{2} \frac{x}{2}-\sin ^{2} \frac{x}{2}\right)}} d x$ $\Rightarrow \int \frac{1}{\sqrt{\cos ^{2} \frac{x}{2}+\sin ^{2} \frac{x}{2}+\cos ^{2} \frac{x}{...
Read More →Find the derivation of each of the following from the first principle:
Question: Find the derivation of each of the following from the first principle:. $\frac{5-x}{5+x}$ Solution: Let $f(x)=\frac{5-x}{5+x}$ We need to find the derivative of f(x) i.e. f(x) We know that, $\mathrm{f}^{\prime}(\mathrm{x})=\lim _{\mathrm{h} \rightarrow 0} \frac{\mathrm{f}(\mathrm{x}+\mathrm{h})-\mathrm{f}(\mathrm{x})}{\mathrm{h}}$ (i) $f(x)=\frac{5-x}{5+x}$ $\mathrm{f}(\mathrm{x}+\mathrm{h})=\frac{5-(\mathrm{x}+\mathrm{h})}{5+(\mathrm{x}+\mathrm{h})}=\frac{5-\mathrm{x}-\mathrm{h}}{5+\m...
Read More →Mycorrhiza is a symbiotic association
Question: Mycorrhiza is a symbiotic association of a fungus with root system which helps in A. Absorption of water B. Mineral nutrition C. Translocation D. Gaseous exchange Options: a. Only A b. Only B c. both A and B d. both B and C Solution: Option (c) is the answer....
Read More →Water potential of pure water at standard
Question: Water potential of pure water at standard temperature is equal to a. 10 b. 20 c. Zero d. None of the above Solution: Option (c)Zerois the answer....
Read More →When a plant undergoes senescence,
Question: When a plant undergoes senescence, the nutrients may be a. accumulated b. withdrawn c. translocated d. None of the above Solution: Option (c) is the answer....
Read More →Which of the following is an example of imbibition
Question: Which of the following is an example of imbibition a? uptake of water by root hair b. exchange of gases in stomata c. swelling of seed when putting in soil d. opening of stomata Solution: Option (c)swelling of seed when putting in soilis the answer....
Read More →The process of guttation takes place
Question: The process of guttation takes place a. when the root pressure is high and the rate of transpiration is low. b. when the root pressure is low and the rate of transpiration is high c. when the root pressure equals the rate of transpiration d. when the root pressure, as well as rate of transpiration, are high. Solution: Option (a)when the root pressure is high and the rate of transpiration is lowis the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \frac{1}{\sqrt{1-\cos 2 x}} d x$ Solution: In the given equation $\cos 2 x=\cos ^{2} x-\sin ^{2} x$ Also we know $\cos ^{2} x+\sin ^{2} x=1$ $\therefore$ Substituting the values in the above equation we get $\Rightarrow \int \frac{1}{\sqrt{\sin ^{2} x+\cos ^{2} x-\left(-\sin ^{2} x+\cos ^{2} x\right)}} d x$ $\Rightarrow \int \frac{1}{\sqrt{\sin ^{2} x+\cos ^{2} x+\sin ^{2} x-\cos ^{2} x}} d x$ $\Rightarrow \int \frac{1}{\sqrt{2 \sin ^{2} x}} \mat...
Read More →The form of sugar transported through phloem is
Question: The form of sugar transported through phloem is a. glucose b. fructose c. sucrose d. ribose Solution: Option (c)sucroseis the answer....
Read More →Find the derivation of each of the following from the first principle:
Question: Find the derivation of each of the following from the first principle: $\frac{2 x+3}{3 x+2}$ Solution: Let, $f(x)=\frac{2 x+3}{3 x+2}$ We need to find the derivative of f(x) i.e. f(x) We know that $f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$ (i) $f(x)=\frac{2 x+3}{3 x+2}$ $\mathrm{f}(\mathrm{x}+\mathrm{h})=\frac{2(\mathrm{x}+\mathrm{h})+3}{3(\mathrm{x}+\mathrm{h})+2}=\frac{2 \mathrm{x}+2 \mathrm{~h}+3}{3 \mathrm{x}+3 \mathrm{~h}+2}$ Putting values in (i), we get $f^{\p...
Read More →The lower surface of leaf will have more
Question: The lower surface of leaf will have more number of stomata in a a. dorsiventral leaf b. isobilateral leaf c. both a and b d. none of the above Solution: Option (a)dorsiventral leaf is the answer....
Read More →Which one of the following will not directly
Question: Which one of the following will not directly affect transpiration? a. temperature b. light c. wind speed d. chlorophyll content of leaves Solution: Option (d) is the answer....
Read More →If the solve the problem
Question: $\int \sin x \cos 2 x \sin 3 x d x$ Solution: We know $2 \sin A \cos B=\sin (A+B)+\sin (A-B)$ $\therefore \sin 3 x \cos 2 x=\frac{\sin 5 x+\sin x}{2}$ $\therefore$ The given equation becomes $\Rightarrow \int \frac{1}{2}(\sin 5 x-\sin x) \sin x d x$ $\Rightarrow \int \frac{1}{2}\left(\sin 5 x \sin x d x-\sin ^{2} x d x\right)$ We know $2 \sin A \sin B=\cos (A-B)-\cos (A+B)$ $\therefore \sin 5 x \sin x=\frac{\cos 4 x-\cos 6 x}{2}$ Also $\sin ^{2} x=\frac{1-\cos 2 x}{2}$ $\therefore$ Abo...
Read More →Which of the following statements does
Question: Which of the following statements does not apply to reverse osmosis? a. it is used for water purification. b. In this technique, a pressure greater than the osmotic pressure is applied to the system c. It is a passive process d. It is an active process Solution: Option (c)It is a passive process is the answer....
Read More →Find the derivation of each of the following from the first principle:
Question: Find the derivation of each of the following from the first principle: $\frac{1}{\sqrt{2-3 x}}$ Solution: Let $f(x)=\frac{1}{\sqrt{2-3 x}}$ We need to find the derivative of f(x) i.e. f(x) We know that $f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$ (i) $f(x)=\frac{1}{\sqrt{2-3 x}}$ $\mathrm{f}(\mathrm{x}+\mathrm{h})=\frac{1}{\sqrt{2-3(\mathrm{x}+\mathrm{h})}}=\frac{1}{\sqrt{2-3 \mathrm{x}-3 \mathrm{~h}}}$ Putting values in (i), we get $\mathrm{f}^{\prime}(\mathrm{x})=\li...
Read More →If the solve the problem
Question: $\int \sin 2 x \sin 4 x \sin 6 x d x$ Solution: We need to simplify the given equation to make it easier to solve We know $2 \sin A \sin B=\cos (A-B)-\cos (A+B)$ $\therefore \sin 4 x \sin 2 x=\frac{\cos 2 x-\cos 6 x}{2}$ $\therefore$ The above equation becomes $\Rightarrow \int \frac{1}{2}(\cos 2 x-\cos 6 x) \sin 6 x d x$ $\Rightarrow \frac{1}{2} \int((\cos 2 x \sin 6 x)-(\cos 6 x \sin 6 x)) d x$ We know $2 \sin A \cos B=\sin (A+B)+\sin (A-B)$ $\therefore \sin 6 x \cos 2 x=\frac{\sin 8...
Read More →Write briefly the significance of mitosis
Question: Write briefly the significance of mitosis and meiosis in a multicellular organism. Solution: Mitosis creates the cells necessary to add more mass to the body, as well as more cells to cope with the growth, such as new blood cells. In case of injury, mitosis is involved in the healing of the tissues. Meiosis also produces genetic variation by way of the process of recombination. It helps to conserve the no. of chromosomes in a species....
Read More →If the solve the problem
Question: $\int \sin m x \cos n x d x, m \neq n$ Solution: We know $2 \sin A \cos B=\sin (A+B)+\sin (A-B)$ $\therefore \sin m x \cos n x=\frac{\sin (m+n) x+\sin (m-n) x}{2}$ $\therefore$ The above equation becomes $\Rightarrow \int \frac{1}{2}(\sin (\mathrm{m}+\mathrm{n}) \mathrm{x}+\sin (\mathrm{m}-\mathrm{n}) \mathrm{x}) \mathrm{dx}$ We know $\int \sin \mathrm{ax} \mathrm{dx}=\frac{-1}{\mathrm{a}} \cos \mathrm{ax}+c$ $\Rightarrow \frac{1}{2}\left(\frac{-1}{m+n} \cos (m+n) x-\frac{1}{(m-n)} \co...
Read More →Write a brief note on the following
Question: Write a brief note on the following a. Synaptonemal complex b. Metaphase plate Solution: a. Synaptonemal complex It is made up of protein formed between two homologous chromosomes. The complex formed during zygotene which is the substage of Prophase I. It contains a recombination nodule which consists of enzyme recombinase involved in crossing over. b. Metaphase plate The metaphase plate is the imaginary line which is formed in the centre of the cell during metaphase. The chromosomes w...
Read More →Find the derivation of each of the following from the first principle:
Question: Find the derivation of each of the following from the first principle: $\frac{1}{\sqrt{6 x-5}}$ Solution: Let $f(x)=\frac{1}{\sqrt{6 x-5}}$ We need to find the derivative of f(x) i.e. f(x) We know that, $f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$ (i) $f(x)=\frac{1}{\sqrt{6 x-5}}$ $\mathrm{f}(\mathrm{x}+\mathrm{h})=\frac{1}{\sqrt{6 \mathrm{x}+6 \mathrm{~h}-5}}$ Putting values in (i), we get $f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{\frac{1}{\sqrt{6 x+6 h-5}}-\frac{1...
Read More →Differentiate between the events
Question: Differentiate between the events of mitosis and meiosis. Solution: MITOSIS 1. Prophase will be short duration 2. Only a single metaphasis plate is formed during metaphase. 3. Sister chromatids tend to move opposite pole during anaphase 4. Cytokinesis occurs after mitosis MEIOSIS 1. Prophase I is a long duration and prophase II is a short duration 2. MetaphaseI- two metaphasic plates and Metaphase II is a single metaphasic. 3. Two homologous chromatids separate during anaphase I. 4. It ...
Read More →If the solve the problem
Question: $\int \cos m x \cos n x d x, m \neq n$ Solution: We know $2 \cos A \cos B=\cos (A-B)+\cos (A+B)$ $\therefore \cos m x \cos n x=\frac{\cos (m-n) x+\cos (m+n) x}{2}$ $\therefore$ The above equation becomes $\Rightarrow \int \frac{1}{2}(\cos (\mathrm{m}-\mathrm{n}) \mathrm{x}+\cos (\mathrm{m}+\mathrm{n}) \mathrm{x}) \mathrm{d} \mathrm{x}$ We know $\int \cos a x d x=\frac{1}{a} \sin a x+c$ $\Rightarrow \frac{1}{2}\left(\frac{1}{m-n} \sin (m-n) x+\frac{1}{m+n} \sin (m+n) x\right)$ $\Rightar...
Read More →What are the various stages of meiotic prophase-I?
Question: What are the various stages of meiotic prophase-I? Enumerate the chromosomal events during each stage? Solution: Prophase I- a. Leptotene stage: Nuclear membrane starts to disappear. Chromatin material starts condensing. Centriole reaches opposite poles. In some members of Liliaceae chromosomes remain attached to the nuclear membrane bouquet stage. b. Zygotene: Pairing of homologous chromosomes start. To hold these homologous chromosomes a protein called synaptonemal complex develops. ...
Read More →Comment on the statement – Telophase
Question: Comment on the statement Telophase is reverse of prophase. Solution: In Prophase- Chromosome condenses. Nuclear membrane disintegrates. Organelles like mitochondria, endoplasmic reticulum, Golgi apparatus disappears. Cells at the end of prophase do not show Golgi complexes, endoplasmic reticulum and nucleolus. The chromosome clusters will be surrounded by the nuclear envelope at the telophase stage....
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