When acidified K2Cr2O7 solution is added
Question: When acidified K2Cr2O7 solution is added to Sn2+ salts then Sn2+ changes to (i) Sn (ii) Sn3+ (iii) Sn4+ (iv) Sn Solution: Option (iii) is the answer....
Read More →Which of the following statements is not correct?
Question: Which of the following statements is not correct? (i) Copper liberates hydrogen from acids. (ii) In its higher oxidation states, manganese forms stable compounds with oxygen and fluorine. (iii) Mn3+ and Co3+ are oxidising agents in aqueous solution. (iv) Ti2+ and Cr2+ are reducing agents in aqueous solution. Solution: Option (i) Copper liberates hydrogen from acids is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{x}\left(\frac{\sin 4 x-4}{1-\cos 4 x}\right) d x$ Solution: Let I $=\int e^{x}\left(\frac{\sin 4 x-4}{1-\cos 4 x}\right) d x$ $=\int \mathrm{e}^{\mathrm{x}}\left\{\frac{2 \sin 2 \mathrm{x} \cos 2 \mathrm{x}}{2 \sin ^{2} \mathrm{x}}-\frac{4}{2 \sin ^{2} \mathrm{x}}\right\} \mathrm{dx}$ $=\int \mathrm{e}^{\mathrm{x}}\left\{\cot 2 \mathrm{x}-2 \operatorname{cosec}^{2} 2 \mathrm{x}\right\} \mathrm{dx}$ $\left.=\int \mathrm{e}^{\mathrm{x}} \cot 2 \...
Read More →KMnO4 acts as an oxidising agent in alkaline
Question: KMnO4 acts as an oxidising agent in alkaline medium. When alkaline KMnO4 is treated with KI, iodide ion is oxidised to ____________. (i) I2 (ii) IO (iii) IO3- (iv) IO4 Solution: Option (iii)IO3- is the answer....
Read More →The magnetic moment is associated with
Question: The magnetic moment is associated with its spin angular momentum and orbital angular momentum. Spin only magnetic moment value of Cr3+ ion is ___________. (i) 2.87 B.M. (ii) 3.87 B.M. (iii) 3.47 B.M. (iv) 3.57 B.M Solution: Option (ii)3.87 B.M. is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{x} \frac{x-1}{(x+1)^{3}} d x$ Solution: Let $I=\int e^{x} \frac{x+1-2}{(x+1)^{2}} d x$ $=\int e^{x}\left\{\frac{1}{(x+1)^{2}}+\frac{-2}{(x+1)^{2}}\right\} d x$ $=\int e^{x} \frac{1}{(x+1)^{2}} d x+\int e^{x} \frac{-2}{(x+1)^{2}} d x$' Integrating by parts $=e^{x} \frac{1}{(x+1)^{2}}-\int e^{x} \frac{-2}{(x+1)^{2}}+\int e^{x} \frac{-2}{(x+1)^{2}}$ $=e^{x} \frac{1}{(x+1)^{2}}+c$...
Read More →Interstitial compounds are formed
Question: Interstitial compounds are formed when small atoms are trapped inside the crystal lattice of metals. Which of the following is not the characteristic property of interstitial compounds? (i) They have high melting points in comparison to pure metals. (ii) They are very hard. (iii) They retain metallic conductivity. (iv) They are chemically very reactive. Solution: Option (iv)They are chemically very reactive is the answer...
Read More →Solve this
Question: Let $f: R \rightarrow R: f(x)(2 x-3)$ and $g: R \rightarrow R: g(x)=\frac{1}{2}(x+3)$ Show that $(f \circ g)=l_{R}=(g \circ f)$ Solution: To prove: (f o g) = IR = (g o f). Formula used: (i) f o g = f(g(x)) (ii) g o f = g(f(x)) Given: (i) $f: R \rightarrow R: f(x)=(2 x-3)$ (ii) $g: R \rightarrow R: g(x)=\frac{1}{2}(x+3)$ Solution: We have, f o g = f(g(x)) $=f\left(\frac{1}{2}(x+3)\right)$ $=\left[2\left(\frac{1}{2}(x+3)\right)-3\right]$ $=x+3-3$ $=x$ $=I_{R}$ g o f = g(f(x)) $=g(2 x-3)$...
Read More →Gadolinium belongs to 4f series.
Question: Gadolinium belongs to 4f series. Its atomic number is 64. Which of the following is the correct electronic configuration of gadolinium? (i) [Xe] 4f 75d16s2 (ii) [Xe] 4f 65d26s2 (iii) [Xe] 4f 86d2 (iv) [Xe] 4f 95s1 Solution: Option (i)[Xe] 4f 75d16s2is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{x}(\cot x+\log \sin x) d x$ Solution: Let $I=\int e^{x}(\cot x+\log \sin x) d x$ $=\int e^{x} \cot x d x+\int e^{x} \log \sin x d x$ Integrating by parts $=\int e^{x} \log \sin x d x+\int e^{x} \cot x d x$ $=(\log \sin x) e^{x}-\int e^{x} \frac{d}{d x} \log \sin x d x+\int e^{x} \cot x d x+c$ $=(\log \sin x) e^{x}-\int e^{x} \cot x d x+\int e^{x} \cot x d x+c$ $=(\log \sin x) e^{x}+c$...
Read More →Which of the following is amphoteric oxide?
Question: Which of the following is amphoteric oxide? Mn2O7, CrO3, Cr2O3, CrO, V2O5, V2O4 (i) V2O5, Cr2O3 (ii) Mn2O7, CrO3 (iii) CrO, V2O5 (iv) V2O5, V2O4 Solution: Option (i)V2O5, Cr2O3 is the answer...
Read More →KMnO4 acts as an oxidising agent in acidic medium.
Question: KMnO4 acts as an oxidising agent in acidic medium. The number of moles of KMnO4 that will be needed to react with one mole of sulphide ions in acidic solution is (i) 2/5 (ii) 3/5 (iii) 4/5 (iv) 1/5 Solution: Option (i)2/5 is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{x}[\sec x+\log (\sec x+\tan x)] d x$ Solution: Let $I=\int e^{x}[\sec x+\log (\sec x+\tan x)] d x$ $I=\int e^{x} \sec x d x+\int \log (\sec x+\tan x) d x$ Integrating by parts $=\int e^{x} \sec x d x+e^{x} \log (\sec x+\tan x)-\int e^{x} \sec x d x$ $=e^{x} \log (\sec x+\tan x)+c$...
Read More →There are 14 elements in the actinoid series.
Question: There are 14 elements in the actinoid series. Which of the following elements does not belong to this series? (i) U (ii) Np (iii) Tm (iv) Fm Solution: Option (iii)Tmis the answer....
Read More →When KMnO4 solution is added to the oxalic acid solution,
Question: When KMnO4 solution is added to the oxalic acid solution, the decolourisation is slow in the beginning but becomes instantaneous after some time because (i) CO2 is formed as the product. (ii) The reaction is exothermic. (iii) MnO4 catalyses the reaction. (iv) Mn2+ acts as an autocatalyst. Solution: Option (iv)Mn2+ acts as an autocatalyst is the answer....
Read More →Which of the following reactions are disproportionation
Question: Which of the following reactions are disproportionation reactions? (a) Cu+ Cu2+ + Cu (b) 3MnO4 + 4H+ 2MnO4 + MnO2 + 2H2O (c) 2KMnO4 K2MnO4 + MnO2 + O2 (d) 2MnO4 + 3Mn2+ + 2H2O 5MnO2 + 4H+ (i) a, b (ii) a, b, c (iii) b, c, d (iv) a, d Solution: Option (i)(i) a, bis the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{x}(\tan x-\log \cos x) d x$ Solution: Let $I=\int e^{x}(\tan x-\log \cos x) d x$ $I=\int e^{x} \tan x d x-\int e^{x} \log \cos x d x$ Integrating by parts, $=\int e^{x} \tan x d x-\left\{e^{x} \log \cos x-\int e^{x}\left(\frac{d}{d x} \log \cos x\right) d x\right.$ $=\int e^{x} \tan x d x-e^{x} \log \cos x d x-\int e^{x} \tan x d x$ $=-e^{x} \log \cos x d x+c$ $=e^{x} \log \sec x+c$...
Read More →Prove that
Question: Let $f: R \rightarrow R: f(x)=x^{2}, g: R \rightarrow R: g(x)=\tan x$ and $h: R \rightarrow R: h(x)=\log x .$ Find a formula for h o (g o f). Show that [h o (g of)] $\sqrt{\frac{\pi}{4}}=0$ Solution: To find: formula for h o (g o f) To prove: Formula used: $f$ o $f=f(f(x))$ Given: (i) $f: R \rightarrow R: f(x)=x^{2}$ (ii) $g: R \rightarrow R: g(x)=\tan x$ (iii) $h: R \rightarrow R: h(x)=\log x$ Solution: We have, ho $(g \circ f)=h \circ g(f(x))=h \circ g\left(x^{2}\right)$ $=h\left(g\l...
Read More →Which of the following oxidation state
Question: Which of the following oxidation state is common for all lanthanoids? (i) +2 (ii) +3 (iii) +4 (iv) +5 Solution: Option (ii)+3 is the answer....
Read More →The magnetic nature of elements depends
Question: The magnetic nature of elements depends on the presence of unpaired electrons. Identify the configuration of transition element, which shows the highest magnetic moment. (i) 3d7 (ii) 3d5 (iii) 3d8 (iv) 3d2 Solution: Option (ii)3d5 is the answer....
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int e^{x} \sec x(1+\tan x) d x$ Solution: Let $I=\int e^{x} \sec x(1+\tan x) d x$ $=\int e^{x} \operatorname{secx} d x+\int e^{x} \operatorname{secxtan} x d x$ Integrating by parts, $=e^{x} \operatorname{secxdx}-\int e^{x} \frac{d}{d x} \operatorname{secxdx}+\int e^{x} \operatorname{secxtan} x d x$ $=e^{x} \operatorname{secxdx}-\int e^{x} \operatorname{secxtan} x d x+\int e^{x} \operatorname{secxtan} x d x$ $=e^{x} \operatorname{secx} d x+c$...
Read More →On addition of a small amount of KMnO4
Question: On addition of a small amount of KMnO4 to concentrated H2SO4, a green oily compound is obtained which is highly explosive. Identify the compound from the following. (i) Mn2O7 (ii) MnO2 (iii) MnSO4 (iv) Mn2O3 Solution: Option (i)Mn2O7 is the answer....
Read More →Generally, transition elements form coloured salts
Question: Generally, transition elements form coloured salts due to the presence of unpaired electrons. Which of the following compounds will be coloured in solid-state? (i) Ag2SO4 (ii) CuF2 (iii) ZnF2 (iv) Cu2Cl2 Solution: Option (ii)CuF2 is the answer...
Read More →Metallic radii of some transition elements
Question: Metallic radii of some transition elements are given below. Which of these elements will have the highest density? (i) Fe (ii) Ni (iii) Co (iv) Cu Solution: Option (iv)Cu is the answer....
Read More →Prove that
Question: Let $f: R \rightarrow R: f(x)=|x|$, prove that $f$ o $f=f$. Solution: To prove: f o f = f Formula used: f o f = f(f(x)) Given: (i) f : R R : f(x) = |x| Solution: We have, $f \circ f=f(f(x))=f(|x|)=|| x||=|x|=f(x)$ Clearly $f$ o $f=f$ Hence Proved....
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