Evaluate the following integrals:
Question: Evaluate the following integrals: $e^{2 x} \sin x d x$ Solution: Let $I=\int e^{2 x} \sin x d x$ Integrating by parts, $I=\sin x \int e^{2 x} d x-\int \frac{d}{d x} \sin x \int e^{2 x} d x$ $I=\sin x \frac{e^{2 x}}{2}-\int \cos x \frac{e^{2 x}}{2} d x$ $I=\sin x \frac{e^{2 x}}{2}-\frac{1}{2} \int e^{2 x} \cos x d x$ Again integrating by parts, $I=\sin x \frac{e^{2 x}}{2}-\frac{1}{2}\left\{\cos x \int e^{2 x} d x-\int \frac{d}{d x} \cos x \int e^{2 x} d x\right\}$ $I=\sin x \frac{e^{2 x...
Read More →An aqueous pink solution of cobalt(II) chloride
Question: An aqueous pink solution of cobalt(II) chloride changes to deep blue on the addition of an excess of HCl. This is because____________. (i) [Co(H2O)6]2+ is transformed into [CoCl6]4 (ii) [Co(H2O)6]2+ is transformed into [CoCl4]2 (iii) tetrahedral complexes have smaller crystal field splitting than octahedral complexes. (iv) tetrahedral complexes have larger crystal field splitting than octahedral complex. Solution: Option (ii)[Co(H2O)6]2+ is transformed into [CoCl4]2 and (iii) tetrahedr...
Read More →Which of the following options are correct
Question: Which of the following options are correct for [Fe(CN)6]3 complex? (i) d2sp3hybridisation (ii) sp3d2hybridisation (iii) paramagnetic (iv) diamagnetic Solution: Option (i) and (iii) are the answers....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{2 x} \sin x \cos x d x$ Solution: Let $I=\int e^{2 x} \sin x \cos x d x$ $=\frac{1}{2} \int \mathrm{e}^{2 \mathrm{x}} 2 \sin \mathrm{x} \cos \mathrm{x} \mathrm{dx}$ $=\frac{1}{2} \int \mathrm{e}^{2 \mathrm{x}} \sin 2 \mathrm{x} \mathrm{dx}$ We know that, $\int e^{a x} \sin b x d x=\frac{e^{a x}}{a^{2}+b^{2}}\{a \sin b x-b \cos b x\}+c$ $=\frac{e^{2 x}}{8}\{2 \sin 2 x-2 \cos 2 x\}+c$ $I=\frac{1}{2} \frac{e^{2 x}}{8}\{2 \sin 2 x-2 \cos 2 x\}+c$ ...
Read More →The atomic number of Mn, Fe,
Question: The atomic number of Mn, Fe, Co and Ni are 25, 26 27 and 28 respectively. Which of the following outer orbital octahedral complexes have the same number of unpaired electrons? (i) [MnCl6]3 (ii) [FeF6]3 (iii) [CoF6]3 (iv) [Ni(NH3)6]2+ Solution: Option (i) and (iii) is the answer....
Read More →The atomic number of Mn,
Question: The atomic number of Mn, Fe and Co are 25, 26 and 27 respectively. Which of the following inner orbital octahedral complexions are diamagnetic? (i) [Co(NH3)6]3+ (ii) [Mn(CN)6]3 (iii) [Fe(CN)6]4 (iv) [Fe(CN)6]3 Solution: Option (i)[Co(NH3)6]3+ and (iii) [Fe(CN)6]4are the answers....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: Solution: Let $I=\int e^{2 x} \cos (3 x+4) d x$ Integrating by parts $I=e^{2 x} \frac{\sin (3 x+4)}{3}-\int 2 e^{2 x} \frac{\sin (3 x+4)}{3} d x$ $=\frac{1}{3} e^{2 x} \sin (3 x+4)-\frac{2}{3} \int e^{2 x} \sin (3 x+4) d x$ $=\frac{1}{3} e^{2 x} \sin (3 x+4)-\frac{2}{3}\left\{-e^{2 x} \frac{\cos (3 x+4)}{3}+\int 2 e^{2 x} \frac{\cos (3 x+4)}{3} d x\right\}$ $I=\frac{e^{2 x}}{9}[2 \cos (3 x+4)+3 \sin (3 x+4)]+c$ Hence, $I=\frac{e^{2 x}}{9}[2 \cos (3 x+4...
Read More →IUPAC name of [Pt (NH3)2Cl(NO2)] is :
Question: IUPAC name of [Pt (NH3)2Cl(NO2)] is : A. Platinum diaminechloronitrite B. Chloronitrito-N-ammineplatinum (II) C. Diamminechloridonitrito-N-platinum (II) D. Diamminechloronitrito-N-platinate (II) Solution: Option (iii) is the answer....
Read More →What kind of isomerism exists between
Question: What kind of isomerism exists between [Cr(H2O)6]Cl3 (violet) and [Cr(H2O)5Cl]Cl2.H2O (greyish-green)? (i) linkage isomerism (ii) solvate isomerism (iii) ionisation isomerism (iv) coordination isomerism Solution: Option (ii)solvate isomerism is the answer....
Read More →Which of the following species is not expected
Question: Which of the following species is not expected to be a ligand? (i) NO (ii) NH4+ (iii) NH2CH2CH2NH2 (iv) CO Solution: Option (ii) NH4+is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \cos (\log x) d x$ Solution: Let $\mathrm{I}=\int \cos (\log \mathrm{x}) \mathrm{dx}$ Let $\log x=t$ $\frac{1}{x} d x=d t$ $d x=x d t$ $=\int e^{t} \cos t d t$ We know that, $\int \cos (\log x) d x=\frac{e^{\operatorname{ax}}}{a^{2}+b^{2}}\{a \sin (b x+c)-b \cos (b x+c)\}$ Hence, $a=1, b=1$ So, $\mathrm{I}=\frac{\mathrm{e}^{\mathrm{t}}}{2}[\cos \mathrm{t}+\sin \mathrm{t}]+\mathrm{c}$ Hence, $\int \cos (\log x) d x=\frac{e^{\log x}}{2}\{\cos (\log...
Read More →A chelating agent has two or more than
Question: A chelating agent has two or more than two donor atoms to bind to a single metal ion. Which of the following is not a chelating agent? (i) thiosulphate (ii) oxalate (iii) glycinato (iv) ethane-1,2-diamine Solution: Option (i) thiosulphate is the answer....
Read More →The compounds [Co(SO4)(NH3)5]Br
Question: The compounds [Co(SO4)(NH3)5]Br and [Co(SO4)(NH3)5]Cl represent (i) linkage isomerism (ii) ionisation isomerism (iii) coordination isomerism (iv) no isomerism Solution: Option (iv) no isomerismis the answer....
Read More →Due to the presence of ambidentate ligands
Question: Due to the presence of ambidentate ligands coordination compounds show isomerism. Palladium complexes of the type [Pd(C6H5)2(SCN)2] and [Pd(C6H5)2(NCS)2] are (i) linkage isomers (ii) coordination isomers (iii) ionisation isomers (iv) geometrical isomers Solution: Option (i) linkage isomers is the answer....
Read More →The CFSE for octahedral [CoCl6]4– is 18,000 cm–1.
Question: The CFSE for octahedral [CoCl6]4 is 18,000 cm1. The CFSE for tetrahedral [CoCl4]2 will be (i) 18,000 cm1 (ii) 16,000 cm1 (iii) 8,000 cm1 (iv) 20,000 cm1 Solution: Option (iii)8,000 cm1 is the answer....
Read More →Indicate the complex ion
Question: Indicate the complex ion which shows geometrical isomerism. (i) [Cr(H2O)4Cl2]+ (ii) [Pt(NH3)3 Cl] (iii) [Co(NH3)6]3+ (iv) [Co(CN)5(NC)]3 Solution: Option (i)[Cr(H2O)4Cl2]+is the answer....
Read More →The stabilisation of coordination compounds
Question: The stabilisation of coordination compounds due to chelation is called the chelate effect. Which of the following is the most stable complex species? (i) [Fe(CO)5] (ii) [Fe(CN)6]3 (iii) [Fe(C2O4)3]3 (iv) [Fe(H2O)6]3+ Solution: Option (iii) is the answer....
Read More →Prove that the function
Question: Prove that the function $f: N \rightarrow N: f(x)=3 x$ is one-one and into. Solution: To prove: function is one-one and into Given: $f: N \rightarrow N: f(x)=3 x$ We have, $f(x)=3 x$ For, $f\left(x_{1}\right)=f\left(x_{2}\right)$ $\Rightarrow 3 x_{1}=3 x_{2}$ $\Rightarrow x_{1}=x_{2}$ When, $f\left(x_{1}\right)=f\left(x_{2}\right)$ then $x_{1}=x_{2}$ $\therefore f(x)$ is one-one $f(x)=3 x$ Let $f(x)=y$ such that $y \in N$ $\Rightarrow y=3 x$ $\Rightarrow x=\frac{y}{3}$ If $v=1$ $\Right...
Read More →The correct IUPAC name of [Pt(NH3)2Cl2] is
Question: The correct IUPAC name of [Pt(NH3)2Cl2] is (i) Diamminedichloridoplatinum (II) (ii) Diamminedichloridoplatinum (IV) (iii) Diamminedichloridoplatinum (0) (iv) Dichloridodiammineplatinum (IV) Solution: Option (i)Diamminedichloridoplatinum (II) is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{a x} \sin (b x+c) d x$ Solution: Let $I=\int e^{a x} \sin (b x+c) d x$ $=-e^{a x} \frac{\cos (b x+c)}{b}+\int a e^{a x} \frac{\cos (b x+c)}{b} d x$ $=-\frac{1}{b} e^{a x} \cos (b x+c)+\frac{a}{b} \int e^{a x} \cos (b x+c)$ $I=\frac{e^{a x}}{b^{2}}\{a \sin (b x+c)-b \cos (b x+c)\}-\frac{a^{2}}{b^{2}} I+c_{1}$ $\mathrm{I}=\left\{\frac{\mathrm{a}^{2}+\mathrm{b}^{2}}{\mathrm{~b}^{2}}\right\}-\frac{\mathrm{e}^{\mathrm{ax}}}{\mathrm{b}^{2}}\{\mathrm...
Read More →When 1 mol CrCl3.6H2O is treated with an excess
Question: When 1 mol CrCl3.6H2O is treated with an excess of AgNO3, 3 mol of AgCl are obtained. The formula of the complex is : (i) [CrCl3 (H2O)3].3H2O (ii) [CrCl2(H2O)4]Cl.2H2O (iii) [CrCl(H2O)5]Cl2.H2O (iv) [Cr(H2O)6]Cl3 Solution: Option (iv)[Cr(H2O)6]Cl3 is the answer....
Read More →When 0.1 mol CoCl3(NH3)5 is treated
Question: When 0.1 mol CoCl3(NH3)5 is treated with an excess of AgNO3, 0.2 mol of AgCl are obtained. The conductivity of the solution will correspond to (i) 1:3 electrolyte (ii) 1:2 electrolyte (iii) 1:1 electrolyte (iv) 3:1 electrolyte Solution: Option (ii) 1:2 electrolyte is the answer....
Read More →The colour of the coordination compounds depends
Question: The colour of the coordination compounds depends on the crystal field splitting. What will be the correct order of absorption of wavelength of light in the visible region, for the complexes, [Co(NH3)6]3+, [Co(CN)6]3, [Co(H2O)6]3+ (i) [Co(CN)6]3 [Co(NH3)6]3+[Co(H2O)6]3+ (ii) [Co(NH3)6]3+ [Co(H2O)6]3+ [Co(CN)6]3 (iii) [Co(H2O)6]3+ [Co(NH3)6]3+ [Co(CN)6]3 (iv) [Co(CN)6]3 [Co(NH3)6]3+ [Co(H2O)6]3+ Solution: Option (iii) [Co(H2O)6]3+ [Co(NH3)6]3+ [Co(CN)6]3 is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{a x} \cos b x d x$ Solution: Let $I=e^{a x} \cos b x d x$ Integrating by parts, $I=e^{a x} \frac{\sin b x}{b}-a \int e^{a x} \frac{\sin b x}{b} d x$ $=\frac{1}{b} e^{a x} \sin b x-\frac{a}{b} \int e^{a x} \sin b x d x$ $=\frac{1}{b} e^{a x} \sin b x-\frac{a}{b}\left[-e^{a x} \frac{\cos b x}{b}-a \int e^{a x} \frac{\cos b x}{b} d x\right]$ $=\frac{1}{b} e^{a x} \sin b x-\frac{a}{b^{2}} e^{a x} \cos b x-\frac{a^{2}}{b^{2}} \int e^{a x} \cos b x ...
Read More →Which of the following complexes formed
Question: Which of the following complexes formed by Cu2+ ions is most stable? Solution: Option (ii) is the answer....
Read More →