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: $\sqrt{a x+b}$ Solution: Let $\mathrm{f}(\mathrm{x})=\sqrt{\mathrm{ax}+\mathrm{b}}$ We need to find the derivative of $f(x)$ i.e. $f^{\prime}(x)$ 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) $f(x)=\sqrt{a x+b}$ $f(x+h)=\sqrt{a(x+h)+b}$ $=\sqrt{a x+a h+b}$ Putting values in (i), we get $f^{\prime}(x)=\li...
Read More →Evaluate:
Question: Evaluate: $\int \sin ^{2}(2 x+5) d x$ Solution: $\sin ^{2} x=\frac{1-\cos 2 x}{2}$ $\therefore$ The given equation becomes, $\Rightarrow \int \frac{1-\cos 2(2 x+5)}{2} \mathrm{dx}$ We know $\int \cos a x d x=\frac{1}{a} \sin a x+c$ $\Rightarrow \frac{1}{2} \int \mathrm{dx}-\frac{1}{2} \int \cos (4 \mathrm{x}+10) \mathrm{dx}$ $\Rightarrow \frac{\mathrm{x}}{2}-\frac{1}{8} \sin (4 \mathrm{x}+10)+\mathrm{c}$...
Read More →Nucleic acids exhibit secondary structure,
Question: Nucleic acids exhibit secondary structure, justify with example. Solution: DNA and RNA are known to exist in the form of a helix. DNA forms double helix and RNA forms a single-stranded helical form. As helix is considered to be a secondary structure, therefore, nucleic acids exist in secondary structure....
Read More →Is rubber a primary metabolite or a secondary
Question: Is rubber a primary metabolite or a secondary metabolite? Write four sentences about rubber. Solution: Rubber is secondary metabolite because the of its unknown function in plants physiology It is obtained from plant as exude which is sticky Rubber is used for synthesizing tyre, eraser etc....
Read More →Starch, Cellulose, Glycogen, Chitin are polysaccharides
Question: Starch, Cellulose, Glycogen, Chitin are polysaccharides found among the following. Choose the one appropriate and write against each. Cotton fibre __________________________ Exoskeleton of cockroach __________________________ Liver __________________________ Peeled potato __________________________ Solution: Cotton fibre- cellulose [more than 90%]. The exoskeleton of cockroach- chitin Liver- glycogen Peeled potato- starch...
Read More →Glycine and Alanine are different
Question: Glycine and Alanine are different with respect to one substituent on the -carbon. What are the other common substituent groups? Solution: -COOH, -NH2, and H are the common substituents....
Read More →How are prosthetic groups
Question: How are prosthetic groups different from co-factors? Solution: Cofactors are the no proteinous, may be organic or inorganic constituent of the enzyme. The prosthetic group belongs to organic cofactors, remains tightly bound with apoenzymes....
Read More →The reaction given below is catalysed
Question: The reaction given below is catalysed by oxidoreductase between two substrates A and A, complete the reaction. A reduced + A oxidized Solution: A[reduced] + A[Oxidized] A[oxidized] + A[reduced]...
Read More →Write the name of anyone amino acid,
Question: Write the name of anyone amino acid, sugar, nucleotide and fatty acid. Solution: Amino acid- Glycine Sugar- Glucose Nucleotide- Adenosine Fatty acid- Oleic acid...
Read More →Evaluate:
Question: Evaluate: $\int \frac{\mathrm{x}}{\sqrt{\mathrm{x}+\mathrm{a}}-\sqrt{\mathrm{x}+\mathrm{b}}} \mathrm{dx}$ Solution: Rationalise the given equation we get $\Rightarrow \int \frac{x}{\sqrt{x+a}-\sqrt{x-b}} \times \frac{\sqrt{x+a}+\sqrt{x-b}}{\sqrt{x+a}+\sqrt{x-b}} d x$ $\Rightarrow \int \frac{x(\sqrt{x+a}-\sqrt{x-b})}{x+a-x-b} d x$ $\Rightarrow \int \frac{x(\sqrt{x+a}-\sqrt{x-b})}{a-b} d x$ $\Rightarrow \frac{1}{a-b} \int x(\sqrt{x+a}-\sqrt{x-b}) d x$ Assume $x=\sqrt{t}$ $\Rightarrow \ma...
Read More →Select an appropriate chemical bond among ester bond,
Question: Select an appropriate chemical bond among ester bond, glycosidic bond, peptide bond and hydrogen bond and write against each of the following. a. Polysaccharide ___________________________ b. Protein ___________________________ c. Fat ___________________________ d. Water ___________________________ Solution: a. Polysaccharides Glycosidic bond, formed by elimination of water molecule. b. Protein- peptide bond, it is the -CO-NH- BOND formed by elimination of water molecules. c. Fats- est...
Read More →Medicines are either man-made (i.e., synthetic)
Question: Medicines are either man-made (i.e., synthetic) or obtained from living organisms like plants, bacteria, animals etc. and hence the latter are called natural products. Sometimes natural products are chemically altered by man to reduce toxicity or side effects. Write against each of the following whether they were initially obtained as a natural product or as a synthetic chemical. a. Penicillin ___________________________ b. Sulfonamide ___________________________ c. Vitamin C _________...
Read More →Enzymes are biocatalysts.
Question: Enzymes are biocatalysts. They catalyse biochemical reactions. In general, they reduce the activation energy of reactions. Many Physico-chemical processes are enzyme-mediated. Which of the following reactions is not enzyme-mediated in the biological system? a. Dissolving CO2 in water b. Untwining the two strands of DNA c. Hydrolysis of sucrose d. Formation of peptide bond Solution: Option (a)Dissolving CO2 in wateris the answer....
Read More →Evaluate:
Question: Evaluate: $\int(5 x+3) \sqrt{2 x-1} d x$ Solution: Let $5 x+3=\lambda(2 x-1)+\mu$ $5 x+3=2 x \lambda-\lambda+\mu$ comparing coefficients we get $2 \lambda=5 ;-\lambda+\mu=3$ $\Rightarrow \lambda=\frac{5}{2} ; \mu=\frac{11}{2}$ Replacing $5 x+3$ by $\lambda(2 x-1)+\mu$ in the given equation we get $\Rightarrow \int \sqrt{2 \mathrm{x}-1} \lambda(2 \mathrm{x}-1)+\mu \mathrm{dx}$ $\Rightarrow \lambda \int(2 \mathrm{x}-1) \sqrt{2 \mathrm{x}-1} \mathrm{dx}+\int \sqrt{2 \mathrm{x}-1} \mu \mat...
Read More →Evaluate:
Question: Evaluate: $\int \frac{2-3 x}{\sqrt{1+3 x}} d x$ Solution: Let $2-3 x=\lambda(3 x+1)+\mu$ $2-3 x=3 x \lambda+\lambda+\mu$ comparing coefficients we get $3 \lambda=-3 ; \lambda+\mu=2$ $\Rightarrow \lambda=-1 ; \mu=3$ Replacing $2-3 x$ by $\lambda(3 x+1)+\mu$ in given equation we get $\Rightarrow \int \frac{\lambda(3 x+1)+\mu}{\sqrt{3 x+1}} d x$ $\Rightarrow \lambda \int \frac{3 x+1}{\sqrt{3 x+1}} d x+\mu \int \frac{1}{1} d x$ $\Rightarrow\left(\lambda \int \sqrt{3 x+1} d x+\mu \int(3 x+1...
Read More →Evaluate:
Question: Evaluate: $\int \frac{\mathrm{x}}{\sqrt{\mathrm{x}+4}} \mathrm{dx}$ Solution: In these questions, little manipulation makes the questions easier to solve Add and subtract 4 from the numerator $\Rightarrow \int \frac{x+4-4}{\sqrt{x+4}} d x$ $\Rightarrow \int \frac{x+4-4}{\sqrt{x+4}} d x$ $\Rightarrow \int \frac{x+4}{\sqrt{x+4}} d x-\int \frac{4}{\sqrt{x+4}} d x$ $\Rightarrow\left(\int \sqrt{\mathrm{x}+4} \mathrm{dx}-4 \int(\mathrm{x}+4)^{\frac{-1}{2}} \mathrm{dx}\right)$ $\Rightarrow \f...
Read More →Evaluate:
Question: Evaluate: $\int \frac{3 x+5}{\sqrt{7 x+9}} d x$ Solution: Let $3 x+5=\lambda(7 x+9)+\mu$ $3 x+5=7 x \lambda+9 \lambda+\mu$ comparing coefficients, we get $7 \lambda=3 ; 9 \lambda+\mu=1$ $\Rightarrow \lambda=\frac{3}{7} ; \mu=\frac{8}{7}$ Replacing $3 x+5$ by $\lambda(7 x+9)+\mu$ in the given equation we get $\Rightarrow \int \frac{\lambda(7 \mathrm{x}+9)+\mu}{\sqrt{7 \mathrm{x}+9}} \mathrm{dx}$ $\Rightarrow \lambda \int \frac{7 \mathrm{x}+9}{\sqrt{7 \mathrm{x}+9}} \mathrm{dx}+\mu \int ...
Read More →Evaluate:
Question: Evaluate: $\int \frac{2 x+1}{\sqrt{3 x+2}} d x$ Solution: Let $2 x+1=\lambda(3 x+2)+\mu$ $2 x+1=3 x \lambda+2 \lambda+\mu$ comparing coefficients we get $3 \lambda=2 ; 2 \lambda+\mu=1$ $\Rightarrow \lambda=\frac{2}{3} ; \mu=\frac{-1}{3}$ Replacing $2 x+1$ by $\lambda(3 x+2)+\mu$ in the given equation we get $\Rightarrow \int \frac{\lambda(3 \mathrm{x}+2)+\mu}{\sqrt{3 \mathrm{x}+2}} \mathrm{dx}$ $\Rightarrow \lambda \int \frac{3 x+2}{\sqrt{3 x+2}} d x+\mu \int \frac{1}{\sqrt{3 x+2}} d 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: $\frac{1}{x^{5}}$ Solution: Let , $f(x)=\frac{1}{x^{5}}$ We need to find the derivative of $f(x)$ i.e. $f^{\prime}(x)$ We know that, $f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$ (i) $f(x)=\frac{1}{x^{5}}$ $f(x+h)=\frac{1}{(x+h)^{5}}$ Putting values in (i), we get $\mathrm{f}^{\prime}(\mathrm{x})=\lim _{\mathrm{h} \rightarrow 0} \frac{\frac{1}{(\mathrm{x}+\mathrm{h})^{5}}-\frac{1}{\mathrm{x}^{5}}}{\m...
Read More →The primary structure of a protein
Question: The primary structure of a protein molecule has a. Two ends b. One end c. Three ends d. No ends Solution: Option (a)Two endsis the answer....
Read More →The number of ‘ends’ in a glycogen molecule
Question: The number of ends in a glycogen molecule would be a. Equal to the number of branches plus one b. Equal to the number of branch points c. One d. Two, one on the left side and another on the right side Solution: Option (d)Two, one on the left side and another on the right side is the answer....
Read More →Evaluate:
Question: Evaluate: $\int(x+2) \sqrt{3 x+5} d x$ Solution: Here multiply and divide the question by 3 We get $\Rightarrow \frac{1}{3} \int 3(\mathrm{x}+2) \sqrt{3 \mathrm{x}+5} \mathrm{dx}$ $\Rightarrow \frac{1}{3} \int(3 \mathrm{x}+6) \sqrt{3 \mathrm{x}+5} \mathrm{dx}$ Add and subtract 1 from above equation $\Rightarrow \frac{1}{3} \int(3 x+6+1-1) \sqrt{3 x+5} d x$ $\Rightarrow \frac{1}{3} \int(3 x+5-1) \sqrt{3 x+5} d x$ $\Rightarrow \frac{1}{3} \int(3 x+5)^{\frac{3}{2}} d x-\int \frac{1}{3} \s...
Read More →Glycogen is a homopolymer
Question: Glycogen is a homopolymer made of a. Glucose units b. Galactose units c. Ribose units d. Aminoacids Solution: Option (a)Glucose units is the answer....
Read More →Proteins perform many physiological functions.
Question: Proteins perform many physiological functions. For example, some functions as enzymes. Which of the following represents an additional function that some proteins discharge? a. Antibiotics b. Pigment conferring colour to skin c. Pigments making colours of flowers d. Hormones Solution: Option (d)Hormones is the answer....
Read More →Evaluate:
Question: Evaluate: $\int \frac{\mathrm{x}-1}{\sqrt{\mathrm{x}+4}} \mathrm{dx}$ Solution: In these questions, little manipulation makes the questions easier to solve Add and subtract 5 from the numerator $\Rightarrow \int \frac{x+5-5-1}{\sqrt{x+4}} d x$ $\Rightarrow \int \frac{x+4-5}{\sqrt{x+4}} d x$ $\Rightarrow \int \frac{x+4}{\sqrt{x+4}} d x-\int \frac{5}{\sqrt{x+4}} d x$ $\Rightarrow\left(\int \sqrt{x+4} d x-5 \int(x+4)^{\frac{-1}{2}} d x\right)$ $\Rightarrow \frac{(x+4)^{\frac{3}{2}}}{\frac...
Read More →