Correct IUPAC name for is ___________.
Question: Correct IUPAC name for is ___________. (i) 2- ethyl-3-methylpentane (ii) 3,4- dimethylhexane (iii) 2-sec-butylbutane (iv) 2, 3-dimethylbutane Solution: Option (ii) 3,4- dimethylhexaneis the answer....
Read More →Find the equation of the line passing through the point (2, 3) and
Question: Find the equation of the line passing through the point (2, 3) and perpendicular to the line 4x + 3y = 10 Solution: Given: The given line is $4 x+3 y=10$. The line perpendicular to this line passes through $(2,3)$. Formula to be used: The product of slopes of two perpendicular lines = - 1 Slope of this line is $-4 / 3$. $\therefore$ the slope of the perpendicular line $=\frac{-1}{-4 / 3}=3 / 4$. The equation of the line can be written in the form $y=\left(\frac{3}{4}\right) x+c$ (c is ...
Read More →Without using the derivative,
Question: Without using the derivative, show that the function $f(x)=|x|$ is A. strictly increasing in $(0, \infty)$ B. strictly decreasing in $(-\infty, 0)$. Solution: We have, $f(x)=|x|=\{x, x0$ (a)Let $\mathrm{x}_{1}, \mathrm{x}_{2} \in(0, \infty)$ and $\mathrm{x}_{1}\mathrm{x}_{2}$ $\Rightarrow \mathrm{f}\left(\mathrm{x}_{1}\right)\mathrm{f}\left(\mathrm{x}_{2}\right)$ So, $f(x)$ is increasing in $(0, \infty)$ (b) Let $x_{1}, x_{2} \in(-\infty, 0)$ and $x_{1}x_{2}$ $\Rightarrow-\mathrm{x}_{1...
Read More →What is the correct order of decreasing
Question: What is the correct order of decreasing stability of the following cations? (i) II I III (ii) II III I (iii) III I II (iv) I II III Solution: Option (i)II I III is the answer....
Read More →The principle involved in paper chromatography is
Question: The principle involved in paper chromatography is (i) Adsorption (ii) Partition (iii) Solubility (iv) Volatility Solution: Option (ii)Partition is the answer....
Read More →During the hearing of a court case,
Question: During the hearing of a court case, the judge suspected that some changes in the documents had been carried out. He asked the forensic department to check the ink used at two different places. According to you which technique can give the best results? (i) Column chromatography (ii) Solvent extraction (iii) Distillation (iv) Thin-layer chromatography Solution: Option (iv)Thin-layer chromatography is the answer....
Read More →The fragrance of flowers is due to the presence
Question: The fragrance of flowers is due to the presence of some steam volatile organic compounds called essential oils. These are generally insoluble in water at room temperature but are miscible with water vapour in the vapour phase. A a suitable method for the extraction of these oils from the flowers is: (i) Distillation (ii) Crystallisation (iii) Distillation under reduced pressure (iv) Steam distillation Solution: Option (iv) Steam distillationis the answer....
Read More →In which of the following,
Question: In which of the following, functional group isomerism is not possible? (i) Alcohols (ii) Aldehydes (iii) Alkyl halides (iv) Cyanides Solution: Option (iii)Alkyl halides is the answer....
Read More →Electronegativity of carbon atoms depends
Question: Electronegativity of carbon atoms depends upon their state of hybridisation. In which of the following compounds, the carbon marked with an asterisk is most electronegative? (i) CH3 CH2 *CH2 CH3 (ii) CH3 *CH = CH CH3 (iii) CH3 CH2 C *CH (iv) CH3 CH2 CH = *CH2 Solution: Option (iii)CH3 CH2 C *CHis the answer....
Read More →Show that
Question: Show that $f(x)=\frac{1}{1+x^{2}}$ is neither increasing nor decreasing on $R$. Solution: We have, $\mathrm{f}(\mathrm{x})=\frac{1}{1+\mathrm{x}^{2}}$ Case 1 When $x \in[0, \infty)$ Let $\mathrm{x}_{1}\mathrm{x}_{2}$ $\Rightarrow \mathrm{x}_{1}^{2}\mathrm{x}_{2}^{2}$ $\Rightarrow 1+\mathrm{x}_{1}^{2}1+\mathrm{x}_{2}^{2}$ $\Rightarrow \frac{1}{1+x_{1}^{2}}\frac{1}{1+x_{2}^{2}}$ $\Rightarrow f\left(x_{1}\right)f\left(x_{2}\right)$ $\Rightarrow \therefore f(x)$ is decreasing on $[0, \inft...
Read More →The IUPAC name for
Question: The IUPAC name for (i) 1-Chloro-2-nitro-4-methylbenzene (ii) 1-Chloro-4-methyl-2-nitrobenzene (iii) 2-Chloro-1-nitro-5-methylbenzene (iv) m-Nitro-p-chlorotoluene Solution: Option (ii)1-Chloro-4-methyl-2-nitrobenzene is the answer....
Read More →The IUPAC name for is ________.
Question: The IUPAC name for is ________. (i) 1-hydroxypentane-1,4-dione (ii) 1,4-dioxopentanol (iii) 1-carboxybutan-3-one (iv) 4-oxopentanoic acid Solution: Option (iv) 4-oxopentanoic acidis the answer....
Read More →Which of the following is the correct IUPAC name?
Question: Which of the following is the correct IUPAC name? (i) 3-Ethyl-4, 4-dimethylheptane (ii) 4,4-Dimethyl-3-ethylheptane (iii) 5-Ethyl-4, 4-dimethylheptane (iv) 4,4-Bis(methyl)-3-ethylheptane Solution: Option (i)3-Ethyl-4, 4-dimethylheptane the answer....
Read More →Find the equation of the line passing through the point (0, 3) and
Question: Find the equation of the line passing through the point (0, 3) and perpendicular to the line x 2y + 5 = 0 Solution: Given: The given line is $x-2 y+5=0$. The line perpendicular to this given line passes through $(0,3)$ Formula to be used: The product of slopes of two perpendicular lines = - 1. The slope of this line is 1/2 . $\therefore$ the slope of the perpendicular line $=\frac{-1}{1 / 2}=-2$. The equation of the line can be written in the form $y=(-2) x+c$ (c is the y - intercept) ...
Read More →Show that
Question: Show that $f(x)=\frac{1}{1+x^{2}}$ decreases in the interval $[0, \infty)$ and increases in the interval $(-\infty, 0]$. Solution: We have, $f(x)=\frac{1}{1+x^{2}}$ Case 1 When $x \in[0, \infty)$ Let $\mathrm{x}_{1}, \mathrm{x}_{2} \in(0, \infty]$ and $\mathrm{x}_{1}\mathrm{x}_{2}$ $\Rightarrow \mathrm{x}_{1}^{2}\mathrm{x}_{2}^{2}$ $\Rightarrow 1+\mathrm{x}_{1}^{2}1+\mathrm{x}_{2}^{2}$ $\Rightarrow \frac{1}{1+x_{1}^{2}}\frac{1}{1+x_{2}^{2}}$ $\Rightarrow f\left(x_{1}\right)f\left(x_{2}...
Read More →Find the equation of the line which is parallel to the line
Question: Find the equation of the line which is parallel to the line 2x 3y = 8 and whose y - intercept is 5 units. Solution: Given: The given line is $2 x-3 y=8$. The line parallel to this line has a $y$-intercept of 5 units. Formula to be used: If $a x+b y=c$ is a straight line then the line parallel to the given line is of the form $a x+b y=d$, where $a, b, c, d$ are arbitrary real constants. A line parallel to the given line has a slope of $\frac{2}{3}$ and is of the form $2 x-3 y=k$, where ...
Read More →Assertion (A): Silicons are water-repelling in nature.
Question: Assertion (A): Silicons are water-repelling in nature. Reason (R): Silicons are organosilicon polymers, which have (R2SiO) as repeating unit. (i) A and R both are correct and R is the correct explanation of A. (ii) Both A and R are correct but R is not the correct explanation of A. (iii) A and R both are not true. (iv) A is not true but R is true. Solution: Option (ii) is correct....
Read More →Find the equation of the line through the point
Question: Find the equation of the line through the point ( - 1, 5) and making an intercept of - 2 on the y - axis. Solution: Given: The $y$ - intercept $=-2$. The line passes through $(-1,5)$. Formula to be used: y = mx + c where m is the slope of the line and c is the y - intercept. The equation of the line is $y=m x+(-2)=m x-2$. Now, this line passes through $(-1,5)$. $\therefore 5=m(-1)-2=-m-2$ i.e. $m=-(5+2)=-7$ $\therefore y=(-7) x+(-2)=-7 x-2$ i.e. $7 x+y+2=0$...
Read More →Show that
Question: Show that $f(x)=\frac{1}{x}$ is a decreasing function on $(0, \infty)$. Solution: we have $\mathrm{f}(\mathrm{x})=\frac{1}{\mathrm{x}}$ let $x_{1}, x_{2} \in(0, \infty)$ We have, $x_{1}x_{2}$ $\Rightarrow \frac{1}{x_{1}}\frac{1}{x_{2}}$ $\Rightarrow f\left(x_{1}\right)f\left(x_{2}\right)$ Hence, $x_{1}x_{2} \Rightarrow f\left(x_{1}\right)f\left(x_{2}\right)$ So, $f(x)$ is decreasing function...
Read More →Assertion (A): If aluminium atoms replace
Question: Assertion (A): If aluminium atoms replace a few silicon atoms in three the dimensional network of silicon dioxide, the overall structure acquires a negative charge. Reason (R): Aluminium is trivalent while silicon is tetravalent. (i) Both A and R are correct and R is the correct explanation of A. (ii) Both A and R are correct but R is not the correct explanation of A. (iii) Both A and R are not correct (iv) A is not correct but R is correct. Solution: Option (i)Both A and R are correct...
Read More →Match the species given in Column I
Question: Match the species given in Column I with the hybridisation given in Column II. Solution: (i) is b (ii) is c (iii) is b (iv) is a (v) is b (vi) is c...
Read More →Find the equation of the bisectors of the angles between the coordinate axes.
Question: Find the equation of the bisectors of the angles between the coordinate axes. Solution: Given: The straight lines are x = 0 and y = 0. Formula to be used: If $\theta$ is the angle between two straight lines $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ then the equation of their angle bisector is $\therefore$ the equation of the angle bisectors is $\left|\frac{x}{\sqrt{1^{2}}}\right|=\left|\frac{y}{\sqrt{1^{2}}}\right|$ i.e. $x=\pm y$...
Read More →Prove that f(x)=a x+b, where a, b are constants
Question: Prove that $f(x)=a x+b$, where $a$, $b$ are constants and $a0$ is a decreasing function on $R$. Solution: we have, $f(x)=a x+b, a0$ let $\mathrm{x}_{1}, \mathrm{x}_{2} \in \mathrm{R}$ and $\mathrm{x}_{1}\mathrm{x}_{2}$ $\Rightarrow \mathrm{ax}_{1}\mathrm{ax}_{2}$ for some $\mathrm{a}0$ $\Rightarrow \mathrm{ax}_{1}+\mathrm{b}\mathrm{ax}_{2}+\mathrm{b}$ for some $\mathrm{b}$ $\Rightarrow f\left(x_{1}\right)f\left(x_{2}\right)$ Hence, $x_{1}x_{2} \Rightarrow f\left(x_{1}\right)f\left(x_{2...
Read More →Match the species given in Column
Question: Match the species given in Column I with properties given in Column II. Solution: (i) is c (ii) is d (iii) is a (iv) is e (v) is b...
Read More →Find the equation of the line cutting off an intercept - 2 from the
Question: Find the equation of the line cutting off an intercept - 2 from the y - axis and equally inclined to the axes. Solution: Given: The line is equally inclined to both the axes. The angle between the coordinate axes $=90^{\circ}$ If the inclination to both the axes is $\theta$ then $\theta+\theta=90^{\circ}$ i.e. $\theta=45 \theta^{\circ}$ $\therefore$ slope of the line, $m=\tan \theta=\tan 45^{\circ}=1$ The y - intercept = - 2 units Formula to be used: $y=m x+c$ where $m$ is the slope of...
Read More →