subject stringclasses 3 values | problem stringlengths 116 1.32k | answer stringlengths 1 6 |
|---|---|---|
phy | A pendulum consists of a bob of mass $m=0.1 \mathrm{~kg}$ and a massless inextensible string of length $L=1.0 \mathrm{~m}$. It is suspended from a fixed point at height $H=0.9 \mathrm{~m}$ above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse $P=0.2 \mathrm{~kg}-\mathrm{m} / \mathrm{s}$ is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is $J \mathrm{~kg}-\mathrm{m}^2 / \mathrm{s}$. The kinetic energy of the pendulum just after the liftoff is $K$ Joules. What is the value of $K$? | 0.16 |
phy | In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance $\mathrm{C} \mu F$ across a $200 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. The power consumed by the lamp is $500 \mathrm{~W}$ while the voltage drop across it is $100 \mathrm{~V}$. Assume that there is no inductive load in the circuit. Take rms values of the voltages. The magnitude of the phase-angle (in degrees) between the current and the supply voltage is $\varphi$. Assume, $\pi \sqrt{3} \approx 5$. What is the value of $C$? | 100.00 |
phy | In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance $\mathrm{C} \mu F$ across a $200 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. The power consumed by the lamp is $500 \mathrm{~W}$ while the voltage drop across it is $100 \mathrm{~V}$. Assume that there is no inductive load in the circuit. Take rms values of the voltages. The magnitude of the phase-angle (in degrees) between the current and the supply voltage is $\varphi$. Assume, $\pi \sqrt{3} \approx 5$. What is the value of $\varphi$? | 60 |
chem | At $298 \mathrm{~K}$, the limiting molar conductivity of a weak monobasic acid is $4 \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. At $298 \mathrm{~K}$, for an aqueous solution of the acid the degree of dissociation is $\alpha$ and the molar conductivity is $\mathbf{y} \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. At $298 \mathrm{~K}$, upon 20 times dilution with water, the molar conductivity of the solution becomes $3 \mathbf{y} \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. What is the value of $\alpha$? | 0.22 |
chem | At $298 \mathrm{~K}$, the limiting molar conductivity of a weak monobasic acid is $4 \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. At $298 \mathrm{~K}$, for an aqueous solution of the acid the degree of dissociation is $\alpha$ and the molar conductivity is $\mathbf{y} \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. At $298 \mathrm{~K}$, upon 20 times dilution with water, the molar conductivity of the solution becomes $3 \mathbf{y} \times 10^2 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$. What is the value of $\mathbf{y}$? | 0.86 |
chem | Reaction of $\mathbf{x} \mathrm{g}$ of $\mathrm{Sn}$ with $\mathrm{HCl}$ quantitatively produced a salt. Entire amount of the salt reacted with $\mathbf{y} g$ of nitrobenzene in the presence of required amount of $\mathrm{HCl}$ to produce $1.29 \mathrm{~g}$ of an organic salt (quantitatively).
(Use Molar masses (in $\mathrm{g} \mathrm{mol}^{-1}$ ) of $\mathrm{H}, \mathrm{C}, \mathrm{N}, \mathrm{O}, \mathrm{Cl}$ and Sn as 1, 12, 14, 16, 35 and 119 , respectively). What is the value of $\mathbf{x}$? | 3.57 |
chem | Reaction of $\mathbf{x} \mathrm{g}$ of $\mathrm{Sn}$ with $\mathrm{HCl}$ quantitatively produced a salt. Entire amount of the salt reacted with $\mathbf{y} g$ of nitrobenzene in the presence of required amount of $\mathrm{HCl}$ to produce $1.29 \mathrm{~g}$ of an organic salt (quantitatively).
(Use Molar masses (in $\mathrm{g} \mathrm{mol}^{-1}$ ) of $\mathrm{H}, \mathrm{C}, \mathrm{N}, \mathrm{O}, \mathrm{Cl}$ and Sn as 1, 12, 14, 16, 35 and 119 , respectively). What is the value of $\mathbf{y}$? | 1.23 |
chem | A sample $(5.6 \mathrm{~g})$ containing iron is completely dissolved in cold dilute $\mathrm{HCl}$ to prepare a $250 \mathrm{~mL}$ of solution. Titration of $25.0 \mathrm{~mL}$ of this solution requires $12.5 \mathrm{~mL}$ of $0.03 \mathrm{M} \mathrm{KMnO}_4$ solution to reach the end point. Number of moles of $\mathrm{Fe}^{2+}$ present in $250 \mathrm{~mL}$ solution is $\mathbf{x} \times 10^{-2}$ (consider complete dissolution of $\mathrm{FeCl}_2$ ). The amount of iron present in the sample is $\mathbf{y} \%$ by weight.
(Assume: $\mathrm{KMnO}_4$ reacts only with $\mathrm{Fe}^{2+}$ in the solution
Use: Molar mass of iron as $56 \mathrm{~g} \mathrm{~mol}^{-1}$ ). What is the value of $\mathbf{x}$? | 1.87 |
chem | A sample $(5.6 \mathrm{~g})$ containing iron is completely dissolved in cold dilute $\mathrm{HCl}$ to prepare a $250 \mathrm{~mL}$ of solution. Titration of $25.0 \mathrm{~mL}$ of this solution requires $12.5 \mathrm{~mL}$ of $0.03 \mathrm{M} \mathrm{KMnO}_4$ solution to reach the end point. Number of moles of $\mathrm{Fe}^{2+}$ present in $250 \mathrm{~mL}$ solution is $\mathbf{x} \times 10^{-2}$ (consider complete dissolution of $\mathrm{FeCl}_2$ ). The amount of iron present in the sample is $\mathbf{y} \%$ by weight.
(Assume: $\mathrm{KMnO}_4$ reacts only with $\mathrm{Fe}^{2+}$ in the solution
Use: Molar mass of iron as $56 \mathrm{~g} \mathrm{~mol}^{-1}$ ). What is the value of $\mathbf{y}$? | 18.75 |
math | Consider the region $R=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0\right.$ and $\left.y^2 \leq 4-x\right\}$. Let $\mathcal{F}$ be the family of all circles that are contained in $R$ and have centers on the $x$-axis. Let $C$ be the circle that has largest radius among the circles in $\mathcal{F}$. Let $(\alpha, \beta)$ be a point where the circle $C$ meets the curve $y^2=4-x$. What is the radius of the circle $C$? | 1.5 |
math | Consider the region $R=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0\right.$ and $\left.y^2 \leq 4-x\right\}$. Let $\mathcal{F}$ be the family of all circles that are contained in $R$ and have centers on the $x$-axis. Let $C$ be the circle that has largest radius among the circles in $\mathcal{F}$. Let $(\alpha, \beta)$ be a point where the circle $C$ meets the curve $y^2=4-x$. What is the value of $\alpha$? | 2.00 |
math | Let $f_1:(0, \infty) \rightarrow \mathbb{R}$ and $f_2:(0, \infty) \rightarrow \mathbb{R}$ be defined by
\[f_1(x)=\int_0^x \prod_{j=1}^{21}(t-j)^j d t, x>0\]
and
\[f_2(x)=98(x-1)^{50}-600(x-1)^{49}+2450, x>0\]
where, for any positive integer $\mathrm{n}$ and real numbers $\mathrm{a}_1, \mathrm{a}_2, \ldots, \mathrm{a}_{\mathrm{n}}, \prod_{i=1}^{\mathrm{n}} \mathrm{a}_i$ denotes the product of $\mathrm{a}_1, \mathrm{a}_2, \ldots, \mathrm{a}_{\mathrm{n}}$. Let $\mathrm{m}_i$ and $\mathrm{n}_i$, respectively, denote the number of points of local minima and the number of points of local maxima of function $f_i, i=1,2$, in the interval $(0, \infty)$. What is the value of $2 m_{1}+3 n_{1}+m_{1} n_{1}$? | 57 |
math | Let $f_1:(0, \infty) \rightarrow \mathbb{R}$ and $f_2:(0, \infty) \rightarrow \mathbb{R}$ be defined by
\[f_1(x)=\int_0^x \prod_{j=1}^{21}(t-j)^j d t, x>0\]
and
\[f_2(x)=98(x-1)^{50}-600(x-1)^{49}+2450, x>0\]
where, for any positive integer $\mathrm{n}$ and real numbers $\mathrm{a}_1, \mathrm{a}_2, \ldots, \mathrm{a}_{\mathrm{n}}, \prod_{i=1}^{\mathrm{n}} \mathrm{a}_i$ denotes the product of $\mathrm{a}_1, \mathrm{a}_2, \ldots, \mathrm{a}_{\mathrm{n}}$. Let $\mathrm{m}_i$ and $\mathrm{n}_i$, respectively, denote the number of points of local minima and the number of points of local maxima of function $f_i, i=1,2$, in the interval $(0, \infty)$. What is the value of $6 m_{2}+4 n_{2}+8 m_{2} n_{2}$? | 6 |
math | Let $\mathrm{g}_i:\left[\frac{\pi}{8}, \frac{3 \pi}{8}\right] \rightarrow \mathbb{R}, \mathrm{i}=1,2$, and $f:\left[\frac{\pi}{8}, \frac{3 \pi}{8}\right] \rightarrow \mathbb{R}$ be functions such that $\mathrm{g}_1(\mathrm{x})=1, \mathrm{~g}_2(\mathrm{x})=|4 \mathrm{x}-\pi|$ and $f(\mathrm{x})=\sin ^2 \mathrm{x}$, for all $\mathrm{x} \in\left[\frac{\pi}{8}, \frac{3 \pi}{8}\right]$
Define $\mathrm{S}_i=\int_{\frac{\pi}{8}}^{\frac{3 \pi}{8}} f(\mathrm{x}) \cdot \mathrm{g}_i(\mathrm{x}) \mathrm{dx}, i=1,2$. What is the value of $\frac{16 S_{1}}{\pi}$? | 2 |
math | Considering only the principal values of the inverse trigonometric functions, what is the value of
\[
\frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^{2}}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^{2}}+\tan ^{-1} \frac{\sqrt{2}}{\pi}
\]? | 2.35 |
math | Let $\alpha$ be a positive real number. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g:(\alpha, \infty) \rightarrow \mathbb{R}$ be the functions defined by
\[
f(x)=\sin \left(\frac{\pi x}{12}\right) \quad \text { and } \quad g(x)=\frac{2 \log _{\mathrm{e}}(\sqrt{x}-\sqrt{\alpha})}{\log _{\mathrm{e}}\left(e^{\sqrt{x}}-e^{\sqrt{\alpha}}\right)}
\]
Then what is the value of $\lim _{x \rightarrow \alpha^{+}} f(g(x))$? | 0.5 |
math | In a study about a pandemic, data of 900 persons was collected. It was found that
190 persons had symptom of fever,
220 persons had symptom of cough,
220 persons had symptom of breathing problem,
330 persons had symptom of fever or cough or both,
350 persons had symptom of cough or breathing problem or both,
340 persons had symptom of fever or breathing problem or both,
30 persons had all three symptoms (fever, cough and breathing problem).
If a person is chosen randomly from these 900 persons, then what the probability that the person has at most one symptom? | 0.8 |
math | Let $z$ be a complex number with non-zero imaginary part. If
\[
\frac{2+3 z+4 z^{2}}{2-3 z+4 z^{2}}
\]
is a real number, then the value of $|z|^{2}$ is | 0.5 |
math | Let $\bar{z}$ denote the complex conjugate of a complex number $z$ and let $i=\sqrt{-1}$. In the set of complex numbers,what is the number of distinct roots of the equation
\[
\bar{z}-z^{2}=i\left(\bar{z}+z^{2}\right)
\]? | 4 |
math | Let $l_{1}, l_{2}, \ldots, l_{100}$ be consecutive terms of an arithmetic progression with common difference $d_{1}$, and let $w_{1}, w_{2}, \ldots, w_{100}$ be consecutive terms of another arithmetic progression with common difference $d_{2}$, where $d_{1} d_{2}=10$. For each $i=1,2, \ldots, 100$, let $R_{i}$ be a rectangle with length $l_{i}$, width $w_{i}$ and area $A_{i}$. If $A_{51}-A_{50}=1000$, then what is the value of $A_{100}-A_{90}$? | 18900 |
math | What is the number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits $0,2,3,4,6,7$? | 569 |
math | Let $A B C$ be the triangle with $A B=1, A C=3$ and $\angle B A C=\frac{\pi}{2}$. If a circle of radius $r>0$ touches the sides $A B, A C$ and also touches internally the circumcircle of the triangle $A B C$, then what is the value of $r$? | 0.83 |
phy | Two spherical stars $A$ and $B$ have densities $\rho_{A}$ and $\rho_{B}$, respectively. $A$ and $B$ have the same radius, and their masses $M_{A}$ and $M_{B}$ are related by $M_{B}=2 M_{A}$. Due to an interaction process, star $A$ loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains $\rho_{A}$. The entire mass lost by $A$ is deposited as a thick spherical shell on $B$ with the density of the shell being $\rho_{A}$. If $v_{A}$ and $v_{B}$ are the escape velocities from $A$ and $B$ after the interaction process, the ratio $\frac{v_{B}}{v_{A}}=\sqrt{\frac{10 n}{15^{1 / 3}}}$. What is the value of $n$? | 2.3 |
phy | The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction ${ }_{7}{ }_{7} \mathrm{~N}+$ ${ }_{2}^{4} \mathrm{He} \rightarrow{ }_{1}^{1} \mathrm{H}+{ }_{8}^{19} \mathrm{O}$ in a laboratory frame is $n$ (in $M e V$ ). Assume that ${ }_{7}^{16} \mathrm{~N}$ is at rest in the laboratory frame. The masses of ${ }_{7}^{16} \mathrm{~N},{ }_{2}^{4} \mathrm{He},{ }_{1}^{1} \mathrm{H}$ and ${ }_{8}^{19} \mathrm{O}$ can be taken to be $16.006 u, 4.003 u, 1.008 u$ and 19.003 $u$, respectively, where $1 u=930 \mathrm{MeV}^{-2}$. What is the value of $n$? | 2.32 |
phy | At time $t=0$, a disk of radius $1 \mathrm{~m}$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha=\frac{2}{3} \mathrm{rads}^{-2}$. A small stone is stuck to the disk. At $t=0$, it is at the contact point of the disk and the plane. Later, at time $t=\sqrt{\pi} s$, the stone detaches itself and flies off tangentially from the disk. The maximum height (in $m$ ) reached by the stone measured from the plane is $\frac{1}{2}+\frac{x}{10}$. What is the value of $x$? $\left[\right.$ Take $\left.g=10 m s^{-2}.\right]$ | 0.52 |
phy | Consider an LC circuit, with inductance $L=0.1 \mathrm{H}$ and capacitance $C=10^{-3} \mathrm{~F}$, kept on a plane. The area of the circuit is $1 \mathrm{~m}^{2}$. It is placed in a constant magnetic field of strength $B_{0}$ which is perpendicular to the plane of the circuit. At time $t=0$, the magnetic field strength starts increasing linearly as $B=B_{0}+\beta t$ with $\beta=0.04 \mathrm{Ts}^{-1}$. What is the maximum magnitude of the current in the circuit in $m A$? | 4 |
phy | A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. When the acceleration due to gravity is $g$, the range of the projectile is $d$. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is $g^{\prime}=\frac{g}{0.81}$, then the new range is $d^{\prime}=n d$. What is the value of $n$? | 0.95 |
chem | 2 mol of $\mathrm{Hg}(g)$ is combusted in a fixed volume bomb calorimeter with excess of $\mathrm{O}_{2}$ at $298 \mathrm{~K}$ and 1 atm into $\mathrm{HgO}(s)$. During the reaction, temperature increases from $298.0 \mathrm{~K}$ to $312.8 \mathrm{~K}$. If heat capacity of the bomb calorimeter and enthalpy of formation of $\mathrm{Hg}(g)$ are $20.00 \mathrm{~kJ} \mathrm{~K}^{-1}$ and $61.32 \mathrm{~kJ}$ $\mathrm{mol}^{-1}$ at $298 \mathrm{~K}$, respectively, the calculated standard molar enthalpy of formation of $\mathrm{HgO}(s)$ at 298 $\mathrm{K}$ is $\mathrm{X} \mathrm{kJ} \mathrm{mol} \mathrm{m}^{-1}$. What is the value of $|\mathrm{X}|$?
[Given: Gas constant $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ ] | 90.39 |
chem | What is the reduction potential $\left(E^{0}\right.$, in $\left.\mathrm{V}\right)$ of $\mathrm{MnO}_{4}^{-}(\mathrm{aq}) / \mathrm{Mn}(\mathrm{s})$?
[Given: $\left.E_{\left(\mathrm{MnO}_{4}^{-}(\mathrm{aq}) / \mathrm{MnO}_{2}(\mathrm{~s})\right)}^{0}=1.68 \mathrm{~V} ; E_{\left(\mathrm{MnO}_{2}(\mathrm{~s}) / \mathrm{Mn}^{2+}(\mathrm{aq})\right)}^{0}=1.21 \mathrm{~V} ; E_{\left(\mathrm{Mn}^{2+}(\mathrm{aq}) / \mathrm{Mn}(\mathrm{s})\right)}^{0}=-1.03 \mathrm{~V}\right]$ | 0.77 |
chem | A solution is prepared by mixing $0.01 \mathrm{~mol}$ each of $\mathrm{H}_{2} \mathrm{CO}_{3}, \mathrm{NaHCO}_{3}, \mathrm{Na}_{2} \mathrm{CO}_{3}$, and $\mathrm{NaOH}$ in $100 \mathrm{~mL}$ of water. What is the $p \mathrm{H}$ of the resulting solution?
[Given: $p \mathrm{~K}_{\mathrm{a} 1}$ and $p \mathrm{~K}_{\mathrm{a} 2}$ of $\mathrm{H}_{2} \mathrm{CO}_{3}$ are 6.37 and 10.32, respectively; $\log 2=0.30$ ] | 10.02 |
chem | The treatment of an aqueous solution of $3.74 \mathrm{~g}$ of $\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}$ with excess KI results in a brown solution along with the formation of a precipitate. Passing $\mathrm{H}_{2} \mathrm{~S}$ through this brown solution gives another precipitate $\mathbf{X}$. What is the amount of $\mathbf{X}$ (in $\mathrm{g}$ )?
[Given: Atomic mass of $\mathrm{H}=1, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{~S}=32, \mathrm{~K}=39, \mathrm{Cu}=63, \mathrm{I}=127$ ] | 0.32 |
chem | Dissolving $1.24 \mathrm{~g}$ of white phosphorous in boiling NaOH solution in an inert atmosphere gives a gas $\mathbf{Q}$. What is the amount of $\mathrm{CuSO}_{4}$ (in g) required to completely consume the gas $\mathbf{Q}$?
[Given: Atomic mass of $\mathrm{H}=1, \mathrm{O}=16, \mathrm{Na}=23, \mathrm{P}=31, \mathrm{~S}=32, \mathrm{Cu}=63$ ] | 2.38 |
math | What is the greatest integer less than or equal to
\[
\int_{1}^{2} \log _{2}\left(x^{3}+1\right) d x+\int_{1}^{\log _{2} 9}\left(2^{x}-1\right)^{\frac{1}{3}} d x
\]? | 5 |
math | Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1. Let $a$ be the area of the triangle $A B C$. Then what is the value of $(64 a)^{2}$? | 1008 |
math | Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1. Then what is the inradius of the triangle ABC? | 0.25 |
chem | A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of $\mathrm{Sn} / \mathrm{HCl}$ gives a major product, which on treatment with an excess of $\mathrm{NaNO}_{2} / \mathrm{HCl}$ at $0{ }^{\circ} \mathrm{C}$ provides $\mathbf{P}$ as the product. $\mathbf{P}$, upon treatment with excess of $\mathrm{H}_{2} \mathrm{O}$ at room temperature, gives the product $\mathbf{Q}$. Bromination of $\mathbf{Q}$ in aqueous medium furnishes the product $\mathbf{R}$. The compound $\mathbf{P}$ upon treatment with an excess of phenol under basic conditions gives the product $\mathbf{S}$.
The molar mass difference between compounds $\mathbf{Q}$ and $\mathbf{R}$ is $474 \mathrm{~g} \mathrm{~mol}^{-1}$ and between compounds $\mathbf{P}$ and $\mathbf{S}$ is $172.5 \mathrm{~g} \mathrm{~mol}^{-1}$. What is the number of heteroatoms present in one molecule of $\mathbf{R}$?
[Use: Molar mass (in g mol${ }^{-1}$ ): $\mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{Br}=80, \mathrm{Cl}=35.5$
Atoms other than $\mathrm{C}$ and $\mathrm{H}$ are considered as heteroatoms] | 9 |
chem | A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of $\mathrm{Sn} / \mathrm{HCl}$ gives a major product, which on treatment with an excess of $\mathrm{NaNO}_{2} / \mathrm{HCl}$ at $0{ }^{\circ} \mathrm{C}$ provides $\mathbf{P}$ as the product. $\mathbf{P}$, upon treatment with excess of $\mathrm{H}_{2} \mathrm{O}$ at room temperature, gives the product $\mathbf{Q}$. Bromination of $\mathbf{Q}$ in aqueous medium furnishes the product $\mathbf{R}$. The compound $\mathbf{P}$ upon treatment with an excess of phenol under basic conditions gives the product $\mathbf{S}$.
The molar mass difference between compounds $\mathbf{Q}$ and $\mathbf{R}$ is $474 \mathrm{~g} \mathrm{~mol}^{-1}$ and between compounds $\mathbf{P}$ and $\mathbf{S}$ is $172.5 \mathrm{~g} \mathrm{~mol}^{-1}$. What is the total number of carbon atoms and heteroatoms present in one molecule of $\mathbf{S}$?
[Use: Molar mass (in $\mathrm{g} \mathrm{mol}^{-1}$ ): $\mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{Br}=80, \mathrm{Cl}=35.5$
Atoms other than $\mathrm{C}$ and $\mathrm{H}$ are considered as heteroatoms] | 51 |
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