Reduce the equation 5x + 7y – 35 = 0 to slope-intercept
Question: Reduce the equation 5x + 7y 35 = 0 to slope-intercept form, and hence find the slope and the y-intercept of the line Solution: Given equation is $5 x+7 y-35=0$ We can rewrite it as $7 y=35-5 x$ $\Rightarrow 7 y=-5 x+35$ $\Rightarrow y=-\frac{5}{7} x+5$ This equation is in the slope-intercept form i.e. it is the form of $\mathrm{y}=\mathrm{m} \times \mathrm{x}+\mathrm{c}$, where $\mathrm{m}$ is the slope of the line and $\mathrm{c}$ is $\mathrm{y}$-intercept of the line Therefore, $\mat...
Read More →Find the intervals in which the following functions are increasing or decreasing.
Question: Find the intervals in which the following functions are increasing or decreasing. $f(x)=x^{4}-4 x^{3}+4 x^{2}+15$ Solution: Given:- Function $\mathrm{f}(\mathrm{x})=\mathrm{x}^{4}-4 \mathrm{x}^{3}+4 \mathrm{x}^{2}+15$ Theorem:- Let $f$ be a differentiable real function defined on an open interval $(a, b)$. (i) If $f^{\prime}(x)0$ for all $x \in(a, b)$, then $f(x)$ is increasing on $(a, b)$ (ii) If $f^{\prime}(x)0$ for all $x \in(a, b)$, then $f(x)$ is decreasing on $(a, b)$ Algorithm:-...
Read More →Match the hydrocarbons in Column
Question: Match the hydrocarbons in Column I with the boiling points given in Column II. Solution: (i) is b (ii) is c (iii) is a...
Read More →Match the reagent from Column I
Question: Match the reagent from Column I which on reaction with CH3 CH=CH2 gives some product given in Column II as per the codes given below : Solution: (i) is d (ii) is a (iii) is e (iv) is c (v) is b...
Read More →Reduce the equation
Question: Reduce the equation 2x 3y 5 = 0 to slope-intercept form, and find from it the slope and y-intercept. Solution: Given equation is $2 x-3 y-5=0$ We can rewrite it as 2x 5 = 3y $\Rightarrow 3 y=2 x-5$ $\Rightarrow y=\frac{2}{3} x-\frac{5}{3}$ This equation is in the slope-intercept form i.e. it is the form of $\mathrm{y}=\mathrm{m} \times \mathrm{X}+\mathrm{c}$, where $\mathrm{m}$ is the slope of the line and $\mathrm{c}$ is $\mathrm{y}$-intercept of the line Therefore, $\mathrm{m}=\frac{...
Read More →An alkane C8H18 is obtained as the only product
Question: An alkane C8H18 is obtained as the only product on subjecting a primary alkyl halide to Wurtz reaction. On monobromination, this alkane yields a single isomer of a tertiary bromide. Write the structure of alkane and the tertiary bromide. Solution:...
Read More →Write the structures and names of products
Question: Write the structures and names of products obtained in the reactions of sodium with a mixture of 1-iodo-2-methylpropane and 2-iodopropane. Solution: When the mixture of 1-iodo-2-methylpropane and 2-iodopropane is treated with sodium it gives a mixture of three products formed by intermolecular and intramolecular reaction as follows:...
Read More →The relative reactivity of 1°, 2°, 3°
Question: The relative reactivity of 1, 2, 3 hydrogens towards chlorination is 1: 3.8: 5. Calculate the percentages of all mono-chlorinated products obtained from 2-methyl butane. Solution: Amount of mono-chlorinated products = No. of hydrogen reactivity Mono-chlorinated products from 1 H = 9 1 = 9 Mono-chlorinated products from 2 H = 2 3.8 = 7.6 Mono-chlorinated products from 3 H = 1 5 = 5 Total mono-chlorinated products = 9+7.6+5 = 21.6 Yield % for 1 H chlorination = 9100/21.6 = 41.67% Yield %...
Read More →Find the intervals in which the following functions are increasing or decreasing.
Question: Find the intervals in which the following functions are increasing or decreasing. $f(x)=\frac{1}{4} x^{4}+\frac{2}{3} x^{3}-\frac{5}{2} x^{2}-6 x+7$ Solution: Given:- Function $\mathrm{f}(\mathrm{x})=\frac{1}{4} \mathrm{x}^{4}+\frac{2}{3} \mathrm{x}^{3}-\frac{5}{2} \mathrm{x}^{2}-6 \mathrm{x}+7$ Theorem:- Let $f$ be a differentiable real function defined on an open interval $(a, b)$. (i) If $f^{\prime}(x)0$ for all $x \in(a, b)$, then $f(x)$ is increasing on $(a, b)$ (ii) If $f^{\prime...
Read More →Suggest a route for the preparation
Question: Suggest a route for the preparation of nitrobenzene starting from acetylene? Solution: (i) By intermolecular condensation method, we can cycle acetylene and then treated at high temperature in a red hot iron tube. (ii) The aliphatic compound thus converted into benzene is treated with con.HNO3 and Conc.H2SO4 which undergoes nitration to give nitrobenzene....
Read More →Why does the presence of a nitro group
Question: Why does the presence of a nitro group make the benzene ring less reactive in comparison to the unsubstituted benzene ring? Explain. Solution: Nitro group has a nitrogen atom bonded to two highly electronegative oxygen atoms. This results in a net decrease of electron density around nitrogen atom and imparts a positive + charge on nitrogen....
Read More →Find the equation of the line which is at a distance of 3 units from the origin
Question: Find the equation of the line which is at a distance of 3 units from the origin such that tan $\propto=\frac{5}{12}$ here is the acute angle which this perpendicular makes with the positive direction of the x-axis. Solution: To Find:The equation of the line. Given : $\propto=\frac{5}{12}$ and $p=3$ units. Since $\tan \alpha=\frac{\text { opp }}{\text { adj }}=\frac{5}{12}$ Using Pythagoras theorem : hyp $=\sqrt{25+144}=\sqrt{169}=13$ units. From the figure: $\cos \propto=\frac{\text { ...
Read More →Despite their – I effect,
Question: Despite their I effect, halogens are o- and p-directing in halo-arenes. Explain. Solution: Halogens have an outer configuration of ns2p5 which shows it can accept one electron and are close to completing its octate; halogens show a strong affinity to attract one electron and thus having a higher electronegativity and show negative inductive effect....
Read More →How will you convert benzene into
Question: How will you convert benzene into (i) p nitrobromobenzene (ii) m nitrobromobenzene Solution: (i) when bromine is treated with Br2 in presence anhydrous FeBr3 it undergoes electrophilic substitution to give bromobenzene. Again treated with conc. HNO3 and Conc. H2SO4 at 323K we get a p-nitrobromobenzene (ii) We need to deactivate the benzene by the introduction of a nitro group using conc. HNO3 and H2SO4 and then treat with Br2 in presence of FeBr3 we will get m-nitrobromobenzene....
Read More →The intermediate carbocation formed in the reactions of HI,
Question: The intermediate carbocation formed in the reactions of HI, HBr and HCl with propane is the same and the bond energy of HCl, HBr and HI is 430.5 kJ mol-1, 363.7 kJ mol-1 and 296.8 kJ mol-1 respectively. What will be the order of reactivity of these halogen acids? Solution: HI HBrHCl is the increasing order of reactivity. The increasing order of reactivity of halogen is same as their increase in bond energies....
Read More →Rotation around carbon-carbon
Question: Rotation around carbon-carbon single bond of ethane is not completely free. Justify the statement. Solution: The single bond in ethane is a bond, which is a coaxial overlap of orbitals, so the C ─ C bond can be rotated on its axis. But this rotation is not completely free due to the torsional strain that the bond undergoes due to rotation....
Read More →Alkynes on reduction with sodium
Question: Alkynes on reduction with sodium in liquid ammonia form trans alkenes. Will the butene thus formed on the reduction of the 2-butyne show the geometrical isomerism? Solution: The negative charged developed on one carbon attacks the proton from NH3 and another sodium atom lose its electron to develop a second negative charge on the atom. This negative charge is finally neutralised by the attack of the second proton to give a trans-but-2-ene. This but-2-ene produced shows geometrical isom...
Read More →The length of the perpendicular segment from the origin
Question: The length of the perpendicular segment from the origin to a line is 2 units and the inclination of this perpendicular is such that sin $\propto=\frac{1}{3}$ and is acute Find the equation of the line. Solution: To Find: The equation of the line . Given : $\mathrm{p}=2$ units and $\sin \propto=\frac{1}{3}$. Since $\sin \propto=\frac{\text { opp }}{\text { hyp }}=\frac{1}{3}$ Using Pythagoras theorem: $\operatorname{adj}=\sqrt{9-1}=\sqrt{8}=2 \sqrt{2}$ units. i.e; $\cos \alpha=\frac{\te...
Read More →Why do alkenes prefer to undergo electrophilic
Question: Why do alkenes prefer to undergo electrophilic addition reaction while arenes prefer electrophilic substitution reactions? Explain. Solution: Alkenes undergo addition reaction to give a more stable saturated product. In this reaction hybridization changes from sp2to sp3. The resonance stability of arene is maintained by a substitution reaction....
Read More →The molecules having dipole moment are
Question: The molecules having dipole moment are __________. (i) 2,2-Dimethylpropane (ii) trans-Pent-2-ene (iii) cis-Hex-3-ene (iv) 2, 2, 3, 3 Tetramethylbutane. Solution: Option (ii)trans-Pent-2-ene and (iii)cis-Hex-3-ene are the answers....
Read More →Find the intervals in which the following functions are increasing or decreasing.
Question: Find the intervals in which the following functions are increasing or decreasing. $f(x)=x^{4}-4 x$ Solution: Given:- Function $f(x)=x^{4}-4 x$ Theorem:- Let $f$ be a differentiable real function defined on an open interval $(a, b)$. (i) If $f^{\prime}(x)0$ for all $x \in(a, b)$, then $f(x)$ is increasing on $(a, b)$ (ii) If $f^{\prime}(x)0$ for all $x \in(a, b)$, then $f(x)$ is decreasing on $(a, b)$ Algorithm:- (i) Obtain the function and put it equal to $f(x)$ (ii) Find $f^{\prime}(x...
Read More →Which of the following is correct?
Question: Which of the following is correct? Solution: Option (i) and (iii) are the answers....
Read More →In an electrophilic substitution reaction of nitrobenzene,
Question: In an electrophilic substitution reaction of nitrobenzene, the presence of nitro group ________. (i) deactivates the ring by an inductive effect. (ii) activates the ring by an inductive effect. (iii) decreases the charge density at ortho and para position of the ring relative to meta position by resonance. (iv) increases the charge density at meta position relative to the ortho and para positions of the ring by resonance Solution: Option (i) and (iii) are the answers....
Read More →Find the intervals in which the following functions are increasing or decreasing.
Question: Find the intervals in which the following functions are increasing or decreasing. $f(x)=x^{4}-4 x$ Solution: Given:- Function $f(x)=x^{4}-4 x$ Theorem:- Let $f$ be a differentiable real function defined on an open interval $(a, b)$. (i) If $f^{\prime}(x)0$ for all $x \in(a, b)$, then $f(x)$ is increasing on $(a, b)$ (ii) If $f^{\prime}(x)0$ for all $x \in(a, b)$, then $f(x)$ is decreasing on $(a, b)$ Algorithm:- (i) Obtain the function and put it equal to $f(x)$ (ii) Find $f^{\prime}(x...
Read More →Find the equation of the line for which
Question: Find the equation of the line for which $p=4$ and $\propto=1800$ Solution: Given: $p=4$ and $\alpha=1800$ Here $p$ is the perpendicular that makes an angle $\propto$ with positive direction of $x$-axis, hence the equation of the straight line is given by: Formula used: $x \cos \propto+y \sin \propto=p$ $x \cos 1800+y \sin 1800=4$ i.e; $\cos 1800=\cos (5 \times 360)=\cos (5 \times 2 \pi)=\cos 360=1$ similarly, $\sin 1800=\sin (5 \times 360)=\sin (5 \times 2 \pi)=\sin 360=0$ hence, $x \t...
Read More →