COMEDK 2026 Morning Shift | COMEDK Year Wise Previous Years Questions

Chemistry

1. Ozone is formed by the reaction $$ \mathrm{O}_{2(g)}+\mathrm{O}_{(g)} \rightarrow \mathrm{O}_{3(g)}, \Delta \mathrm{H}=- 2. The number of structural isomers possible for a compound with molecular formula $\mathrm{C}_3 \mathrm{H}_9 \mathrm{~N}$ 3. $$ \text { Match the mixtures listed in Column I with the correct method used for their separation. } $$ .tg {border-co 4. An aqueous solution of an unknown solute " $X$ " is prepared by adding 4.0 g of it into 2.0 moles of water. What is the 5. The rate constants for two different reactions, $\mathrm{k}_1$ and $\mathrm{k}_2$ are $10^{16} \cdot \mathrm{e}^{-2000 / 6. The hybridisation of atomic orbitals of nitrogen in $\mathrm{NO}_2{ }^{+}, \mathrm{NO}_3{ }^{-}$and $\mathrm{NH}_4{ }^{+ 7. An aliphatic compound $[\mathrm{X}]$, Molecular formula $\left(\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}\right)$ can be pr 8. Rate law can be determined from a balanced chemical equation if 9. What is the percentage dissociation of 0.8 ml of Acetic acid (density is $1.04 \mathrm{~g} / \mathrm{ml}$ ) which is dis 10. A compound with molecular formula $\mathrm{C}_5 \mathrm{H}_{10}$ that gives acetone on ozonolysis is: 11. Consider the gaseous equilibrium $2 \mathrm{AB}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{AB}_{(\mathrm{g})}+\mathrm 12. Which one of the following statements is wrong? 13. $60 \%$ of a first order reaction was completed in 60 min , then $50 \%$ of the same reaction can be completed in: $[\lo 14. Consider a Galvanic cell in which the following reactions occurs: $\mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Ag}^{+}(\mathrm 15. Which among the following is NOT in accordance with the property stated against it? 16. $$ \text { Which one of the following is not the correct IUPAC name of the compound? } $$ 17. $$ \text { Identify the correct order of the type of reactions taking place in this sequence: } $$ 18. Which one of the following species will impart colour to an aqueous solution? 19. If the equilibrium constant for $\mathrm{N}_{2(g)}+\mathrm{O}_{2(g)} \rightleftharpoons 2 \mathrm{NO}_{(g)}$ is 49 The e 20. Which of the following options represent the correct bond order? 21. $$ \text { The decreasing order of reactivity towards electrophilic substitutions is: } $$ 22. Identify the correct values to be plotted in the graph, the slope of which can be used to determine the activation energ 23. The ion that has a spin only magnetic moment of 5.9 BM is: 24. In the reaction, $$ \mathrm{Cr}_2 \mathrm{O}_7^{2-}+4 \mathrm{H}_2 \mathrm{O}_2+2 \mathrm{H}^{+} \rightarrow 2 \mathrm{C 25. $$ \text { Match the Coordination compounds in Column I with the type of stereoisomerism given in Column II exhibited by 26. Identify the correct mathematical expression which represents the variation in molar conductivity of a weak acid having 27. Lassaigne's test for the detection of nitrogen fails in 28. $\Delta \mathrm{H}$ and $\Delta \mathrm{S}$ for a reaction are $35.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $83.6 \mathrm{ 29. When the initial concentration of a zero order reaction is doubled, the half-life of the reaction is: 30. The secondary structure of protein consists of: 31. What will be the change in the electrode potential of chromium electrode dipping into chromic sulphate solution, when th 32. Which of the following is a correct match? 33. $$ \text { Match reactions in Column I with the corresponding products formed as given in Column II. } $$ .tg {border-c 34. Identify the wrong statement from the following 35. Etard reaction is a method of preparation of benzaldehyde by oxidation of toluene. The oxidizing agent used in this reac 36. When 2-butyne is treated with dilute $\mathrm{H}_2 \mathrm{SO}_4 / \mathrm{HgSO}_4$, the product formed is: 37. Two statements, one Assertion and the other Reason are given. Choose the right option. Assertion: The Molar conductivity 38. The statements given below contains assertion and reason. Choose the correct option Assertion (A): Cr, Mo and W possess 39. $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ on heating with aqueous NaOH gives $\_\_\_\_$ 40. In the photoelectric emission, the energy of the emitted electron is: 41. Identify the name of the reaction involved in conversion of $A \rightarrow B$ and name the compound $B$. $$ \mathrm{CH}_ 42. The Crystal Field Stabilisation energy of (i) $\left[\mathrm{CoF}_6\right]^{3-}$ and (ii) $\left[\mathrm{Fe}\left(\mathr 43. Identify the correct statement 44. 0.02 M solution of sucrose is isotonic with 0.008 M solution of sodium sulphate. What is the percentage dissociation of 45. If the molar masses of two chemically non-reacting gases $\mathrm{A}_2$ and $\mathrm{B}_2$ are 28 amu and 32 amu respect 46. The basic character of transition metal monoxides follows the order: 47. Propanal on reaction with dilute NaOH , undergoes aldol condensation resulting in the formation of a compound A . identi 48. Select the reagents needed to convert Benzene to 4-Bromophenylpropene in the correct sequential order. (A). $\mathrm{Cl} 49. $$ \text { Identify the compounds } \mathrm{A} \text { and } \mathrm{B} \text { from the following reaction sequence: } 50. The reagent used in carbylamine reaction is $\_\_\_\_$ and the product of the reaction will be $\_\_\_\_$ 51. Two statements, Assertion and Reason are given. With reference to them, choose the correct option. Assertion: Hydrolysis 52. The heat of combustion of carbon to $\mathrm{CO}_2$ is $-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The heat released on th 53. Which among the following is an INCORRECT statement? 54. $3.482 \times 10^{-1} \mathrm{~g}$ of Fe gets deposited when an aqueous solution of Ferric sulphate is electrolysed for 55. The highest dipole moment is for: 56. The mass of precipitate formed when 50 mL of $16.9 \%$ aqueous solution of $\mathrm{AgNO}_3$ is mixed with 50 mL of $5.8 57. $$ \text { Identify X, Y and Z. } $$ 58. Which of the following is the correct reaction of Hinsberg's reagent with primary, secondary and tertiary amines? 59. The Bohr orbit of the hydrogen atom ( $n=1$ ) is $0.530 \mathop {\rm{A}}\limits^{\rm{o}} $. The radius of the first exci 60. Which of the following is NOT TRUE about nucleophilic addition reactions of aldehydes?

Mathematics

1. $$ \text { The solution of } \boldsymbol{d} \boldsymbol{y}=\boldsymbol{\operatorname { c o s }} \boldsymbol{x}(\mathbf{2 2. $$ \text { The conjugate of } z=\frac{(\mathbf{4}+\boldsymbol{i})(\mathbf{1}-\boldsymbol{i})}{(\mathbf{1}+\boldsymbol{i} 3. If A and B are two square matrices of the same order such that $\mathrm{AB}=\mathrm{A}$ and $\mathrm{BA}=\mathrm{B}$, th 4. If $f(x)=\left\{\begin{array}{l}\frac{\sqrt{1+x}-\sqrt{1-x}}{\sin x} \\ \boldsymbol{k}, x=0\end{array}, x \neq 0\right.$ 5. The area of the region bounded by the line $y=x+2$ and the curve $x=-y^2$ is 6. If $x=4$ is a root of $\left|\begin{array}{cc}x & 3 \\ 1 & x-2\end{array}\right|=5$, then the other root is: 7. The difference between the distance of any point on the hyperbola from the two foci is $\mathbf{1 6}$ and the eccentrici 8. $$ \text { If } x=a(\theta-\sin \theta) \text { and } y=a(1-\cos \theta) \text {, then } \frac{\left(\mathbf{1}+\boldsym 9. The area of the region in the first quadrant enclosed by the $x$-axis, the line $x=\sqrt{3} y$ and the circle $x^2+y^2=4 10. Which of the following is the simplest form of the expression $\boldsymbol{\operatorname { t a n }}^{-\mathbf{1}}\left(\ 11. $$ \mathop {\lim }\limits_{x \to 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x} \text { is equal to: } $$ 12. A square plate is contracting at a uniform rate of $2 \mathrm{~cm}^2 / \mathrm{min}$. The rate at which the perimeter is 13. If $A=\{x: x$ is the first three odd numbers $\}$ $B=\{2 x+3: 0 \leq x 14. Samhita faces a three-headed dragon. She wins a "Tactical medal" if she manages to defeat exactly one of the three heads 15. $$ \int e^{2 x} \cos (5 x+3) d x= $$ 16. Given $A=\left(\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right)$ and $f(x)=x^2-2 x-3$ then $f(A)$ is: 17. The value of $\mathop {\lim }\limits_{x \to 3}\left[\frac{1}{x-3}+\frac{9 x}{27-x^3}\right]$ is: 18. $$ \int \sqrt{2 a x-x^2} d x= $$ 19. Consider the following list of ordered pairs: $(1,0),(-2,-1),(7,-6),(-3,4)$ and $(0,2)$ Which of the following options c 20. Given $P=\left[\begin{array}{lll}2 & \boldsymbol{\alpha} & 1 \\ 1 & 2 & 2 \\ 1 & 3 & 3\end{array}\right]$ is the adjoint 21. The radius of a circle is $\mathbf{5 ~ c m}$. A chord of this circle is equal to the radius. Then the length of the arc 22. If for a distribution of 20 items, $\sum(x-4)=10$ and $\sum(x-4)^2=85$ then the standard deviation is: 23. The odds against Arjun solving a problem are $\mathbf{5 : 2}$ and the odds in favour of Bhavana solving the same problem 24. If $\mathbf{3 ~ c m} / \mathbf{s}$ is the rate at which the side of an equilateral triangle increases, then the rate of 25. If $\sin A+\sin 2 A=x$ and $\cos A+\cos 2 A=y$ then the value of the expression $\left(x^2+y^2\right)\left(x^2+y^2-3\rig 26. Given the matrices $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 2\end{array}\right]$ and $B=\left[\begin 27. The order and degree of the differential equation $\left(\frac{d y}{d x}\right)^2+\frac{d x}{d y}=x$ is: 28. A teacher has two jars of candy on her desk: Jar 1: Contains 3 Strawberry candies and 2 Orange candies. Jar 2: Contains 29. $$ \text { The direction ratios of the vector }(\hat{\imath}+\hat{\jmath}) \times(\hat{\jmath}+\hat{k}) \text { are } $$ 30. The product of three numbers in geometric progression is 8 and the sum of the product of the numbers taken in pairs is 1 31. $$ \int \frac{x+1}{x\left(1+x e^x\right)} d x= $$ 32. Let $\vec{p}$ and $\vec{q}$ be the position vectors of P and Q with respect to the origin. If points R and S divide PQ i 33. The length of the latus rectum of the curve represented by $x=3(\cos t+\sin t)$ and $y=4(\cos t-\sin t)$ is: 34. If the function $f(x)=x^4-31 x^2+\boldsymbol{a} x+5$ has a turning point at $x=1$, then the value of ' $\boldsymbol{a}$ 35. Advika chooses one of three scarves every morning: Red, Blue, or Green. The probability she chooses Red is $20 \%$. T 36. $$ \int \frac{e^{\log \left(1+\frac{1}{x^2}\right)}}{x^2+\frac{1}{x^2}} d x= $$ 37. Which of the following is NOT a comer point of the feasible region determined by the constraints: $$ \begin{aligned} & x 38. The angle between the two lines whose direction cosines satisfy the relations $\boldsymbol{l}+\boldsymbol{m}+\boldsymbol 39. In how many ways can the squares of a $\mathbf{4} \times \mathbf{2}$ grid ( 4 rows and 2 columns) be filled with the let 40. The value of the expression $\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)+\sin ^{-1}\left(\sin \frac{22 \pi}{3}\right)+\t 41. A straight line passes through the point $P\left(\log _2 16, \log _3 27\right)$ such that the portion of the line interc 42. Let L be the foot of the perpendicular drawn from the point $P(5,3 k-7,-4)$ to the YZ - plane. If the distance of point 43. Distance between $8 x+15 y-20=0$ and $8 x+15 y+14=0$ is: 44. In a bank the principal increases continuously at the rate of $4 \%$ per annum. In how many years will ₹ 1000 triple its 45. $$ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin ^5 x \cos ^7 x d x= $$ 46. A batch of $\mathbf{1 0}$ cupcakes consists of $\mathbf{5}$ chocolate, $\mathbf{3}$ vanilla, and $\mathbf{2}$ strawberry 47. If a straight line passing through a fixed point $(a, b)$, where $\boldsymbol{a}, \boldsymbol{b}>\mathbf{0}$, makes posi 48. Let $\mathbf{P}$ be a point on the line $L_1: \frac{x-2}{2}=y+1=\frac{z-1}{2}$ such that its distance from the point $A( 49. The range of the function $f(x)={ }^{(7-x)} P_{(x-3)}$ is 50. The set expression $A \cup\left(B \cap\left(A^{\prime} \cup B^{\prime}\right)\right)$ is equivalent to 51. \text { The remainder when } \mathbf{7}^{\mathbf{1 0 3}} \text { is divided by } \mathbf{2 5} \text { is } 52. The function $y=||x|-1|$ is differentiable for all values of ' $x$ ' except 53. "A storage room must be kept at a temperature (T) such that triple the temperature is at least $\mathbf{1 5}^{\circ} \ma 54. The derivative of $y=\sin ^2\left[\cot ^{-1}\left(\sqrt{\frac{\mathbf{1}-\boldsymbol{x}}{\mathbf{1}+\boldsymbol{x}}}\rig 55. An engineering team is testing a new prototype drone. The drone has constant success rate of $\frac{\mathbf{2}}{\mathbf{ 56. Let ' $\boldsymbol{a}$ ' and ' $\mathbf{b}$ ' be two numbers where $\boldsymbol{a} 57. $$ \text { The expression } \frac{1-\tan ^2\left(\frac{\pi}{4}-A\right)}{1+\tan ^2\left(\frac{\pi}{4}-A\right)} \text { 58. The behaviour of the function $f(x)=\sin \left(2 x+\frac{\pi}{4}\right)$ on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\righ 59. $$ \text { The particular solution of the equation } \sin \left(\frac{d y}{d x}\right)=a \text {, where } a \in \mathbb{ 60. $$ \begin{aligned} &\text { Find the co-ordinates of the orthocentre of the triangle formed by the lines }\\ &\begin{ali

Physics

1. An atom has a single electron. Its ground state energy is -30 eV and its first excited state energy is -8 eV . The atom 2. Paramagnetic substances A. Move from a region of strong magnetic field to weak magnetic field B. Has susceptibility less 3. A wire of length 1 m has a resistance of $20 \Omega$ at $0^{\circ} \mathrm{C}$. It is uniformly stretched so that its le 4. An object is placed 25 cm in front of a fully silvered concave mirror of focal length 15 cm . A plane mirror is placed 3 5. A bar magnet of length 12 cm is placed such that its north pole points towards the geographic north. Two neutral points 6. Forces A and B act at a point. The sum of their magnitudes is 50 N and the magnitude of their resultant is 20 N . If the 7. A nucleus of uranium -235 absorbs a slow neutron and undergoes nuclear fission according to the reaction: ${ }_{92}^{235 8. Two bodies of specific heats $C_1$ and $C_2$, having the same heat capacities are combined to form a single composite bo 9. In a PN junction diode, the forward bias is increased gradually from 0 Volt to 1 Volt. Which of the following statements 10. Two charges 1 C and 2 C are placed at coordinates $(0,3)$ and $(4,3)$ respectively in an XY plane. What is the work done 11. Two long parallel conductors $X$ and $Y$ are placed vertically at a distance $d$ apart. Conductor X carries a current I 12. A $50 \Omega$ galvanometer is shunted by a resistance of $S \Omega$. If $8 \%$ of total current passes through the galva 13. A current of 3 A enters one vertex P of an equilateral triangle PQR having three resistors of $1 \Omega$ each forming th 14. Current in a conductor is expressed as $I=8 t^3+3 t^2+2$, where current I is measured in amperes and time t is measured 15. A diffraction pattern due to a single slit of width 0.12 mm is obtained with a blue green light of wavelength 500 nm . T 16. A square loop of wire 2.2 cm on each side contains 2 turns and has a total resistance of $0.0002 \Omega$. It is located 17. What is the charge on $15 \mu F$ in the circuit given? 18. The speed of transverse wave in aluminium wire is $\frac{1}{10}$ times the speed of longitudinal wave in the wire. The s 19. Two spheres of masses $M_1$ and $M_2$ are in air separated by a distance of d m . The gravitational force of attraction 20. Which of the following is incorrect for displacement current A. Displacement current exists only when electric field cha 21. In a Young's double slit experiment, the slit separation is 1.5 mm . The setup is illuminated simultaneously by light of 22. A small hollow vessel which has a small circular hole of radius $r$ in its base, is immersed in a tank of oil of density 23. Two-point charges of equal magnitude 0.01 C and opposite in sign are separated by 0.2 mm , forming an electric dipole. T 24. 1 kg of water at $100^{\circ} \mathrm{C}$ is converted to steam at the same temperature. Volume of 1 cc of water changes 25. A mercury-198 nucleus is bombarded by a neutron, which causes a nuclear reaction $$ n_0^1+\mathrm{Hg}_{80}^{198} \longri 26. A ball falls under gravity from a height of 10 m with an initial downward velocity u . It loses one third of its energy 27. In the given circuit, an ideal voltmeter connected across $6 \Omega$ reads 5 V . The internal resistance $r$ of each cel 28. A machine gun fires a bullet of mass m with a velocity of $1000 \mathrm{~m} / \mathrm{min}$. The man holding the gun can 29. Four masses each 2 kg are placed at the corners A, B, C, D of a mass less square frame. 40 kg mass is at the centre O of 30. Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $45^{\circ}$ with 31. A car, starting from rest, accelerates at a rate of $\beta$ through a distance S , then continues at constant speed for 32. A glass slab of 16 cm thickness has its bottom surface silvered. An air bubble is located inside the glass slab at a dis 33. A body is projected vertically upwards from the surface of earth with a velocity ' $v$ ' to reach a height of $10 R$, wh 34. An AC generator having 400 turns and an area of cross section of $2 \times 10^{-3} \mathrm{~m}^2$ rotates with an angula 35. An object of mass 10 g executes SHM along the $x$-axis with frequency of $\left(\frac{10}{\pi}\right) \mathrm{Hz}$. At t 36. A circular coil of radius 7 cm and 40 turns is rotated about its vertical diameter with an angular speed of 40 radians p 37. A light rod of length 1 m is suspended from ceiling horizontally by means of two vertical wires of equal length tied to 38. An ideal gas has molar specific heat $\frac{5 R}{2}$ at constant pressure. If 1662 J of heat brings about 50 K temperatu 39. A silicon sample is doped simultaneously with donor impurity phosphorus at a concentration of $N_D=3 \times 10^{22} \mat 40. The velocity of a body moving in a viscous medium is given by $v=\frac{A}{B+C}\left[1-e^{\frac{-t}{B}}\right]$ where $t$ 41. A proton is moving along negative $X$ axis. If a uniform magnetic field is applied parallel to the positive $Z$ axis, th 42. The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $r_1=3.14 \mathrm{~m}$ and $r_ 43. Two vessels A and B contain same mass of Oxygen and Hydrogen respectively at the same temperature. The volume of $B$ is 44. Two conducting spherical shells $A$ and $B$ of radii 4 cm and 6 cm respectively are placed with their centres 17 cm apar 45. A uniform electric field $E=3 \hat{i}+6 \hat{j}+\hat{k}$ passes through a closed cuboidal surface. One face of the cuboi 46. A particle starts rotating from rest. The instantaneous angular displacement is $\theta=3 t^3-t^2$, where $\theta$ is in 47. Point charge $\sqrt{2} C, \sqrt{2} C$, and $-2 C$ are placed at the three vertices of a right-angled triangle in air. [a 48. A solenoid having resistance $R=60 \Omega$ and inductance $L=0.4 \mathrm{H}$ is connected to an AC source $V=100 \sqrt{2 49. A motor cyclist starts from the top of an inclined plane of height $h$ to go around a globe of death trap of radius $r$. 50. An object is placed at an unknown distance from a convex objective lens of focal length 5 cm . The objective lens forms 51. From the same point, two stones A and B are thrown simultaneously, A is thrown up vertically with a velocity of $10 \mat 52. If a clear liquid has a refractive index of 1.45 and a transparent solid has a refractive index of 2.9 , then for total 53. Two deuterons are fused to form one alpha particle. If binding energy per nucleon of deuterium is 1.05 MeV and that of a 54. If wattless current flows in an AC circuit, then the circuit is: A. LR circuit B. Purely capacitive circuit C. Purely re 55. In the circuit given, the reverse breakdown voltage of the Zener diode is 4.8 V . The current through the Zener and the 56. In a Young's double slit experiment, the slits are separated by 0.5 mm . Fringes are obtained on a screen which is place 57. What is the ratio of de Broglie wavelength of an electron to that of proton if the velocity of proton is $\frac{1}{6}$ t 58. An atom with one electron has ionization energy of 24 eV . An electron in this atom makes a transition from an excited e 59. Genetic Engineering is related to the principle of 60. A monochromatic beam of photons of intensity to $1.5 \mathrm{Wm}^{-2}$ and energy 11.2 eV is incident on a material of w

COMEDK 2026 Morning Shift

MCQ (Single Correct Answer)

-0

The ion that has a spin only magnetic moment of 5.9 BM is:

$\mathrm{Fe}^{3+}$

$\mathrm{Mn}^{3+}$

$\mathrm{Ni}^{2+}$

$\mathrm{Co}^{3+}$

COMEDK 2026 Morning Shift

MCQ (Single Correct Answer)

-0

In the reaction,

$$ \mathrm{Cr}_2 \mathrm{O}_7^{2-}+4 \mathrm{H}_2 \mathrm{O}_2+2 \mathrm{H}^{+} \rightarrow 2 \mathrm{CrO}_5+\mathrm{H}_2 \mathrm{O} $$

The change in oxidation state of Cr is:

+6 to +3

+6 to +10

No change in oxidation state

+3 to +6

COMEDK 2026 Morning Shift

MCQ (Single Correct Answer)

-0

$$ \text { Match the Coordination compounds in Column I with the type of stereoisomerism given in Column II exhibited by them. } $$

$$ \text { Column I } $$		$$ \text { Column I } $$
A	$$ \left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}_2\right] $$	P	fac-mer
B	$$ \mathrm{Ni}\left[\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}_2\right] $$	Q	cis -trans
C	$$ \left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3\left(\mathrm{NO}_2\right)_3\right] $$	R	only cis isomer shows optical isomerism
D	$$ \left[\mathrm{Pt} \mathrm{Cl}_2(\mathrm{en})_2\right]^{2+} $$	S	does not exhibit isomerism.

$$ A-S \quad B-R \quad C-Q \quad D-P $$

$$ A-S \quad B-P \quad C-Q \quad D-R $$

$$ A-Q \quad B-S \quad C-O \quad D-R $$

$$ A-R \quad B-P \quad C-S \quad D-Q $$

COMEDK 2026 Morning Shift

MCQ (Single Correct Answer)

-0

Identify the correct mathematical expression which represents the variation in molar conductivity of a weak acid having concentration C and ionisation constant $\mathrm{K}_{\mathrm{a}}$

( $\lambda_m^{\infty}=$ molar conductivity at infinite dilution, $\lambda_{\mathrm{m}}=$ molar conductivity at concentration C )

$K_a=\lambda_m^2 C / \lambda_m^{\infty}\left(\lambda_m^{\infty}-\lambda_m\right)$

$K_a=\lambda_m \lambda_m^{\infty}-\left(\lambda_m^{\infty}\right)^2+\lambda_m^2 C$

$\lambda_m+\lambda_m^{\infty}+K_a C^{\frac{1}{2}}=0$

$K_a=\lambda_m^2 C / \lambda_m^{\infty}\left(\lambda_m^{\infty}+\lambda_m\right)$

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