Prove the following
Question: (i) (a) (b) (c) (ii) (c) (b) (a) (iii) (a) (c) (b) (iv) (c) (a) (b) Solution: Option (iii) is the answer....
Read More →Evaluate the integral:
Question: Evaluate the integral: $\int \sqrt{2 x-x^{2}} d x$ Solution: Key points to solve the problem: - Such problems require the use of method of substitution along with method of integration by parts. By method of integration by parts if we have $\int f(x) g(x) d x=f(x) \int g(x) d x-\int f^{\prime}(x)\left(\int g(x) d x\right) d x$ - To solve the integrals of the form: $\int \sqrt{a x^{2}+b x+c} d x$ after applying substitution and integration by parts we have direct formulae as described b...
Read More →Which of the following compounds
Question: Which of the following compounds will give racemic mixture on nucleophilic substitution by OH ion? (i) (a) (ii) (a), (b), (c) (iii) (b), (c) (iv) (a), (c) Solution: Option (i)(a) is the answer....
Read More →Evaluate the integral:
Question: Evaluate the integral: $\int \sqrt{x^{2}-2 x} d x$ Solution: Key points to solve the problem: - Such problems require the use of method of substitution along with method of integration by parts. By method of integration by parts if we have $\int f(x) g(x) d x=f(x) \int g(x) d x-\int f^{\prime}(x)\left(\int g(x) d x\right) d x$ - To solve the integrals of the form: $\int \sqrt{a x^{2}+b x+c} d x$ after applying substitution and integration by parts we have direct formulae as described b...
Read More →Which of the carbon atoms prese
Question: Which of the carbon atoms present in the molecule given below are asymmetric? (i) a, b, c, d (ii) b, c (iii) a, d (iv) a b, c Solution: Option (ii) is the answer....
Read More →Reaction of C6H5CH2Br with aqueous
Question: Reaction of C6H5CH2Br with aqueous sodium hydroxide follows ____________. (i) SN1 mechanism (ii) SN2 mechanism (iii) Any of the above two depending upon the temperature of the reaction (iv) Saytzeff rule Solution: Option (i)SN1 mechanismis the answer....
Read More →Molecules whose mirror image is non-superimposable
Question: Molecules whose mirror image is non-superimposable over them are known as chiral. Which of the following molecules is chiral? (i) 2-Bromobutane (ii) 1-Bromobutane (iii) 2-Bromopropane (iv) 2-Bromopropan-2-ol Solution: Option (i)2-Bromobutaneis the answer....
Read More →Prove that
Question: Let $f: R \rightarrow R: f(x)=\frac{1}{2}(3 x+1) .$ Show that $f$ is invertible and find $f^{-1}$. Solution: To Show: that $\mathrm{f}$ is invertible To Find: Inverse of $f$ [NOTE: Any functions is invertible if and only if it is bijective functions (i.e. one-one and onto)] one-one function: A function $f: A \rightarrow B$ is said to be a one-one function or injective mapping if different elements of A have different images in B. Thus for $x_{1}, x_{2} \in A \ f\left(x_{1}\right), f\le...
Read More →Evaluate the integral:
Question: Evaluate the integral: $\int \sqrt{3-x^{2}} d x$ Solution: Key points to solve the problem: - Such problems require the use of method of substitution along with method of integration by parts. By method of integration by parts if we have $\int f(x) g(x) d x=f(x) \int g(x) d x-\int f^{\prime}(x)\left(\int g(x) d x\right) d x$ - To solve the integrals of the form: $\int \sqrt{a x^{2}+b x+c} d x$ after applying substitution and integration by parts we have direct formulae as described bel...
Read More →Chloromethane on treatment with
Question: Chloromethane on treatment with an excess of ammonia yields mainly Solution: Option (iii) is the answer....
Read More →The reaction of toluene with chlorine
Question: The reaction of toluene with chlorine in the presence of iron and the absence of light yields ____________. Solution: Option (d) is the answer....
Read More →Solve this
Question: Let $f: Q \rightarrow Q: f(x)=3 x-4$. Show that $f$ is invertible and find $f^{-1}$. Solution: To Show: that $\mathrm{f}$ is invertible To Find: Inverse of $f$ [NOTE: Any functions is invertible if and only if it is bijective functions (i.e. one-one and onto)] one-one function: A function $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is said to be a one-one function or injective mapping if different elements of $A$ have different images in $B$. Thus for $x_{1}, x_{2} \in A \ f\left(x...
Read More →What should be the correct IUPAC
Question: What should be the correct IUPAC name for diethylbromomethane? (i) 1-Bromo-1,1-diethylmethane (ii) 3-Bromopentane (iii) 1-Bromo-1-ethylpropane (iv) 1-Bromopentane Solution: Option (ii)3-Bromopentane is the answer....
Read More →Evaluate the integral:
Question: Evaluate the integral: $\int \sqrt{2 a x-x^{2}} d x$ Solution: Key points to solve the problem: - Such problems require the use of method of substitution along with method of integration by parts. By method of integration by parts if we have $\int f(x) g(x) d x=f(x) \int g(x) d x-\int f^{\prime}(x)\left(\int g(x) d x\right) d x$ - To solve the integrals of the form: $\int \sqrt{a x^{2}+b x+c} d x$ after applying substitution and integration by parts we have direct formulae as described...
Read More →Which is the correct IUPAC name for?
Question: Which is the correct IUPAC name for? (i) 1-Bromo-2-ethylpropane (ii) 1-Bromo-2-ethyl-2-methylethane (iii) 1-Bromo-2-methylbutane (iv) 2-Methyl-1-bromobutane Solution: Option (iii)1-Bromo-2-methylbutane is the answer....
Read More →Which of the following alkyl halides
Question: Which of the following alkyl halides will undergo SN1 reaction most readily? (i) (CH3)3CF (ii) (CH3)3CCl (iii) (CH3)3CBr (iv) (CH3)3CI Solution: Option (iv) is the answer....
Read More →A primary alkyl halide would prefer
Question: A primary alkyl halide would prefer to undergo _____________. (i) SN1 reaction (ii) SN2 reaction (iii) Elimination (iv) Racemisation Solution: Option (ii)SN2 reaction is the answer....
Read More →Show that the function
Question: Show that the function $f: R \rightarrow R: f(x)=2 x+3$ is invertible and find $f^{-1}$. Solution: To Show: that $\mathrm{f}$ is invertible To Find: Inverse of $f$ [NOTE: Any functions is invertible if and only if it is bijective functions (i.e. one-one and onto)] one-one function: A function $f: A \rightarrow B$ is said to be a one-one function or injective mapping if different elements of $A$ have different images in $B$. Thus for $x_{1}, x_{2} \in A \ f\left(x_{1}\right), f\left(x_{...
Read More →What is ‘A’ in the following reaction?
Question: What is A in the following reaction? Solution: Option (iii) is the answer. In the above reaction, the addition of HCl across the double bond takes place as per the Markovnikov rule. According to Markovnikov rule, the negative part of the adding molecule gets attached to that carbon atom which possesses a lesser number of hydrogen atoms....
Read More →Evaluate the integral:
Question: Evaluate the integral: $\int \frac{\sqrt{16+(\log x)^{2}}}{x} d x$ Solution: Key points to solve the problem: - Such problems require the use of method of substitution along with method of integration by parts. By method of integration by parts if we have $\int f(x) g(x) d x=f(x) \int g(x) d x-\int f^{\prime}(x)\left(\int g(x) d x\right) d x$ - To solve the integrals of the form: $\int \sqrt{a x^{2}+b x+c} d x$ after applying substitution and integration by parts we have direct formula...
Read More →Ethylidene chloride is a/an ______________.
Question: Ethylidene chloride is a/an ______________. (i) vic-dihalide (ii) gem-dihalide (iii) allylic halide (iv) vinylic halide Solution: Option (ii)gem-dihalideis the answer....
Read More →Chlorobenzene is formed by the reaction
Question: Chlorobenzene is formed by the reaction of chlorine with benzene in the presence of AlCl3. Which of the following species attacks the benzene ring in this reaction? (i) Cl (ii) Cl+ (iii) AlCl3 (iv) [AlCl4] Solution: Option (ii)Cl+is the answer....
Read More →Solve this
Question: Let $A=\{2,3,4,5\}$ and $B=\{7,9,11,13\}$, and let $f=\{(2,7),(3,9),(4,11),(5,13)\} .$ Show that $f$ is invertible and find $f^{-1}$. Solution: To Show: that $\mathrm{f}$ is invertible To Find: Inverse of $f$ [NOTE: Any functions is invertible if and only if it is bijective functions (i.e. one-one and onto)] one-one function: A function $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is said to be a one-one function or injective mapping if different elements of $A$ have different image...
Read More →The position of –Br in the compound
Question: The position of Br in the compound in CH3CH==CHC(Br)(CH3)2 can be classified as ____________. (i) Allyl (ii) Aryl (iii) Vinyl (iv) Secondary Solution: Optuion (i)Allyl is the answer....
Read More →Which of the following is an example
Question: Which of the following is an example of vic-dihalide? (i) Dichloromethane (ii) 1,2-dichloroethane (iii) Ethylidene chloride (iv) Allyl chloride Solution: Option (ii)1,2-dichloroethane is the answer....
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