COMEDK 2026 Afternoon Shift | COMEDK Year Wise Previous Years Questions

Chemistry

1. The system that forms maximum boiling azeotrope is: 2. A Nitrogen containing organic compound with molecular formula $\mathrm{C}_3 \mathrm{H}_5 \mathrm{~N}$ undergoes the foll 3. Choose the incorrect statement. 4. The quantity of Ca that can be produced from molten $\mathrm{CaCl}_2$, with the same quantity of electricity (in coulomb 5. Choose the correct reason: o-hydroxybenzaldehyde is a liquid at room temperature while $p$-hydroxy-benzaldehyde is a hig 6. The number of bond pairs and lone pairs of electrons in the molecule $I F_5$ is: 7. For an ideal gas undergoing an isothermal change, there is $\_\_\_\_$ 8. Which one of the following is the correct statement? 9. The initial pressure of the system before decomposition for a first order gas phase reaction $A_{(g)} \rightarrow B_{(g) 10. Which of the following is an INCORRECT match? 11. Two statements $[A]$ and $[B]$ are given below. Choose the correct option. A) Protonated $\mathrm{R}-\mathrm{C} \mathrm{ 12. The frequency of photon which is emitted during a transition of electron of $\mathrm{He}^{+}$ion from fifth energy level 13. $$ \text { Match the reactions in List I with the final products formed as given in List II. } $$ .tg {border-collapse: 14. $$ \text { The product formed in the following reaction is: } $$ 15. How many molecules of $\mathrm{CO}_2(\mathrm{~g})$ are obtained on reaction of 24 grams of methane with 4 moles of oxyge 16. A small segment of a polypeptide gave on complete hydrolysis 3 molecules of alanine, 2 molecules of glycine and 3 molecu 17. The product and its colour when $\mathrm{MnO}_2$ is fused with KOH in presence of $\mathrm{O}_2$ : 18. $$ \text { Identify the aromatic compounds among the given set based on Huckel's rule: } $$ 19. In the redox reaction, taking place in acidic medium: $\mathrm{X} \mathrm{MnO}_4^{-}(\mathrm{aq})+\mathrm{YSO}_2(\mathrm 20. At $30^{\circ} \mathrm{C}$ the solubility of $\mathrm{PbI}_2$ salt in 0.2 M KI solution will be $X$, if the solubility p 21. An unsaturated organic compound $\left(\mathrm{C}_3 \mathrm{H}_6\right)$, undergoes the following series of reactions: I 22. An equilibrium mixture taken in 2 litre vessel of the reaction: $2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) 23. A first order reaction is $50 \%$ complete in 30 minutes at 300 K and in 10 minutes at 320 K . The activation energy of 24. Which of the following factors is altered by the addition of a catalyst during a chemical reaction? 25. The standard enthalpies of formation of $\mathrm{CH}_4(\mathrm{~g}), \mathrm{CO}_2(\mathrm{~g})$ and $\mathrm{H}_2 \math 26. With reference to the two statements Assertion and Reason, choose the correct option. Assertion: The order of reactivity 27. Which one of the following complex-isomerism pair matches correctly? 28. Identify the correct statement. 29. $x$ moles of $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ oxidises 1 mole of ferrous oxalate, in acidic medium. Hence ' $x$ 30. In the synthesis of $\mathrm{NH}_3$ from $\mathrm{H}_2$ and $\mathrm{N}_2$, if $6 \times 10^{-2}$ mole of hydrogen disap 31. The element with the highest third ionisation enthalpy is: 32. $$ \text { When the concentration of the reactant in a given reaction is halved and if the rate of reaction is halved, t 33. Arrange the given alkanes in increasing order of their boiling points. (A) 2, 2-dimethylpropane (B) 2-methylbutane (C) n 34. Which of the following does not correctly represent the order of the property indicated against it? 35. According to Molecular orbital theory, which of the following is correct with respect to bond order? 36. $$ \text { Match the characteristic from Col. I with the Vitamins given in Col. II. } $$ .tg {border-collapse:collapse; 37. A $5 \%$ solution (by mass) of cane sugar in water has a freezing point of 271 K . The freezing point of a $5 \%$ soluti 38. $$ \text { Among the given resonating structures of molecules negative mesomeric effect is represented by: } $$ 39. Identify the INCORRECT statement 40. $$ \text { What is the major product }[Z] \text { formed when compound }[C] \text { undergoes the following reactions: } 41. 500 mL of an aqueous solution of glucose $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6$ (Molar mass $180 \mathrm{gmol}^{-1} 42. Identify the complex which exhibits all 3 characteristics; paramagnetic; high spin configuration; octahedral geometry 43. Identify the final product formed when benzenamine reacts with the given reagents in the sequential order as: i. $\quad\ 44. Identify the law which is stated as "For any solutions, the partial vapour pressure of each volatile component in the so 45. Which of the following statement is correct? 46. Which of the following is always true about a spontaneous cell reaction in a galvanic cell? 47. Resistance of 0.2 M solution of an electrolyte is $50 \Omega$. The conductivity of the solution is $1.3 \mathrm{Sm}^{-1} 48. $$ \begin{aligned} &\text { Identify products }\left[\mathbf{P}_{\mathbf{1}}\right] \text { and }\left[\mathbf{P}_{\ 49. Choose the incorrect statement. 50. When 1 mole of benzene is mixed with 1 mole of toluene, the vapours will contain 51. $$ \begin{aligned} &\text { What is the major product }\left[\mathrm{P}_3\right] \text { formed when } n \text { - Hexan 52. Pick out the correct option Assertion(A): Mercury is not considered as a transition element Reason (R): Mercury is a liq 53. $$ \text { Consider the series of reactions given and identify the final product [Z]. } $$ $$ [X] \xrightarrow{\mathrm{C 54. The statements given below contains assertion and reason. Choose the correct option Assertion (A): Propene reacts with H 55. $$ \text { A compound }[X] \text { undergoes reactions as given. Identify compounds }[C] \text { and }[D] \text { formed 56. The $\Delta \mathrm{G}^{\circ}$ for the reaction, $C d^{2+}(a q)+Z n(s) \rightarrow Z n^{2+}(a q)+C d(s)$ is: $\left[E_{ 57. $$ \text { Identify the correct structure of o-ethyl anisole. } $$ 58. $$ \text { Identify the reagents, }[A] \text { and }[B] \text { used up when Salicylic acid undergoes the following reac 59. Which of the following is an INCORRECT statement? 60. $$ \begin{aligned} &\text { Using the data given below, the strongest reducing agent is: }\\ &\begin{array}{ll} \mathrm{

Mathematics

1. $$ \text { The degree of the differential equation } \sqrt{1+\left(\frac{d y}{d x}\right)^{1 / 3}}=\frac{d^2 y}{d x^2} \ 2. If $f(x)=x^3+\frac{3}{2} x^2+3 x+3$, then $f(x)$ is 3. Let point Q be the image of point $P(2,-1)$ in the line $3 x+5=4 y$. Find the area of the circle that has the segment PQ 4. The foci of a hyperbola are the same as those of the ellipse with equation $9 x^2+16 y^2=144$. If the length of the tran 5. Suppose 'a' and 'b' are non-zero constants satisfying the following system of equations $\boldsymbol{a} \sin ^3 x+\bolds 6. The variance of a set of 20 observations is 16 . If 7 is added to each observation, and then $\mathbf{5}$ is subtracted 7. $$ \text { If }(\vec{a}+\vec{b}) \perp \vec{b} \text { and }(\vec{a}+2 \vec{b}) \perp \vec{a} \text {, then } $$ 8. Let the population of a species of birds surviving at a time ' $\boldsymbol{t}$ ' be governed by the differential equati 9. A coffee roaster has $\mathbf{1 2}$ rare coffee beans with intensity scores ranked from $\mathbf{1}$ (mildest) to $\math 10. A coach needs to select a $\mathbf{4}$-player starting lineup from a pool of $\mathbf{1 0}$ players: 5 guards 3 forward 11. $$ \text { The domain of the function } f(x)=\sin ^{-1}(\sqrt{x-1}) $$ 12. If the matrix $M=\left[\begin{array}{ccc}x+5 & a & -4 \\ -2 & 0 & b \\ c & 6 & y+1\end{array}\right]$ is a skew symmetri 13. If $\boldsymbol{k}$ is the arithmetic mean of two given quantities and $\boldsymbol{p}, \boldsymbol{q}$ are the geometri 14. The feasible region represented by the constraints: $$ \begin{aligned} & x+2 y \leq 120 \\ & x+y \geq 60 \\ &amp 15. $$ \text { The range of the relation } R=\left\{(x, y): y=x+\frac{6}{x} \text {; where } x, y \in \mathbb{N} \text { and 16. Let A be a square matrix of order $3 \times 3$. If $|A|=-4$, then the value of $\left|\frac{A^{-1}}{-2}\right|$ is: 17. An open hemispherical storage tank has radius 13 m . Oil flows into the tank such that the depth ' $\boldsymbol{h}$ ' of 18. $$ \text { The second derivative of } \sin 3 \boldsymbol{x} \boldsymbol{\operatorname { c o s }} \mathbf{5 x} \text { is 19. If $\mathop {\lim }\limits_{x \to 0}\left(\frac{p \sin 2 x+1-\cos 2 x}{x+\tan x}\right)=1$ then the value of ' $p$ ' is 20. Let the line $L_1$ be a line passing through the point $(\mathbf{0},-\mathbf{6})$ and making an angle of $\mathbf{1 5 0} 21. $$ \mathop {\lim }\limits_{x \to {\pi \over 2}}\left(\frac{1-\sin x}{\cos x}\right) \text { is equal to } $$ 22. If $X=\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]+\cos ^{-1}\left[\cos \left(\frac{7 \pi}{6}\rig 23. If the coefficients of $x^2$ and $x^3$ in the expansion of $(3+k x)^9$ are equal, then the value of ' $\boldsymbol{k}$ ' 24. Matrix $A=\left[\begin{array}{ccc}1 & 1 & 2 \\ 1 & -2 & 2 \\ 1 & 0 & -1\end{array}\right]$, Given $\boldsymbol{M}_{\math 25. $$ \int_0^{\frac{\pi}{2}} \frac{3 \sin x+4 \cos x}{\sin x+\cos x} d x= $$ 26. The function $f(x)=e^{a x}+e^{-a x}, x \in \mathbb{R}$ and $a 27. $$ \text { If the projection of } \vec{a}=5 \hat{\imath}+\hat{\jmath}+\lambda \hat{k} \text { on } \vec{b}=2 \hat{\imath 28. The equation of the perpendicular drawn from the point $A(6,1,3)$ to the line $\frac{x-1}{2}=\frac{2-y}{-1}=\frac{z-3}{2 29. A line L passes through the point of intersection of the lines $3 x+y-10=0$ and $x-y-2=0$. If the perpendicular distance 30. $$ \text { The particular solution of the differential equation }(x-y)(d x+d y)=(d x-d y) \text { when } y=-1 \text { an 31. $$ \int \tan ^{-1}\left(\sqrt{\frac{1-\sin x}{1+\sin x}}\right) d x= $$ 32. The area enclosed by the curve $y=-x^2$ and the line $x+y+2=0$ is 33. Let $A=\left[a_{i j}\right]$ be a square matrix of order $3 \times 3$, where the elements are defined as $a_{i j}=\left\ 34. Find the area bounded by the curve $y=|2-x|$, the $x$-axis, and the lines $x=0$ and $x=5$ 35. $$ \int \frac{\log x}{(1+x)^2} d x $$ 36. The conjugate of the multiplicative inverse of the complex number $\boldsymbol{z}=\frac{\mathbf{1}+\mathbf{7} \boldsymbo 37. The absolute maximum and minimum values of the function $f(x)=\sin x+\sqrt{3} \cos x$ in $[0, \pi]$ are 38. Every term of a geometric progression is positive, and every term is the sum of the two preceding terms. Then the common 39. $$ \text { If } y=\tan ^{-1}\left(\frac{\sqrt{1+x^3}+\sqrt{1-x^3}}{\sqrt{1+x^3}-\sqrt{1-x^3}}\right) \text { then } \fra 40. Vishnu has two jars of marbles, Jar A and Jar B. Jar A contains 3 yellow marbles and 2 green marbles. Jar B contains 4 41. Cards are numbered from 12 to 51 . Two cards are drawn one after the other without replacement. Find the probability tha 42. A movie screen on a wall is $\mathbf{2 0}$ feet high and $\mathbf{1 0}$ feet above the floor. What is the maximum viewin 43. $$ \text { The expression } \frac{\tan \left(x-\frac{\pi}{2}\right) \cos \left(\frac{3 \pi}{2}+x\right)-\sin ^3\left(\fr 44. The function $\boldsymbol{x}+\boldsymbol{y}=\boldsymbol{\operatorname { t a n }}^{-\mathbf{1}} \boldsymbol{y}$ is the so 45. The function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=\frac{x}{x^2+1} \quad \forall x \in \mathbb{R}$ is 46. $$ \begin{aligned} &\text { Consider two skew lines in 3D space. }\\ &M_1: \frac{x-1}{1}=\frac{2-y}{1}=\frac{z-5}{1} \te 47. $$ \int \frac{d x}{x \sqrt{x^2+4}}= $$ 48. Let $A$ and $B$ be two subsets of $\xi=\{\mathbf{1}, \mathbf{2}, \mathbf{3},-------, \mathbf{4 4}, \mathbf{4 5}\}$ such 49. If $P(A \cup B)=0.85, P(B)=0.50$ and $P(A \cap B)=0.30$. Then $P\left(A \cap B^{\prime}\right)=$ 50. If $\log y=\log (\sin x)-x^2$, then $\frac{d^2 y}{d x^2}+\mathbf{4} x \frac{d y}{d x}+\mathbf{4} x^2 y=$ 51. Given $A=\left[\begin{array}{lll}x & 1 & -2\end{array}\right]$ and $B=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 52. Consider the lines $L_1$ and $L_2$ given by the following vector equations: $$ L_1: \vec{r}=(\hat{i}+\hat{j}-\hat{k})+\l 53. A student needs to buy notebooks $(n)$ for a semester. Double the number of notebooks plus 5 must strictly exceed 15 , b 54. $$ \text { If }{ }^{\mathrm{n}} C_{13},{ }^{\mathrm{n}} C_{14} \text { and }{ }^{\mathrm{n}} C_{15} \text { are in arith 55. If $2 \sin \theta=\left(x+\frac{1}{x}\right)$, then $\sin 3 \theta+\frac{1}{2}\left(x^3+\frac{1}{x^3}\right)=$ 56. If the two ends of the major axis of an ellipse are $(5,0)$ and $(-5,0)$ and one focus lies on the line $3 x-5 y-9=0$, t 57. The function $\boldsymbol{f}(\boldsymbol{x})=|\boldsymbol{x}|+|\boldsymbol{x}-\mathbf{1}|$ is: 58. A company is migrating its database, and two software engineers, Ishaan and Kavya, take turns running a data-sync script 59. Given the sets $A=\{1,2,3\} ; B=\{2,3,5\}$ and $C=\{4,5,6\}$ identify which of the following statement is incorrect. 60. $$ \int\left(\sin ^6 x+\cos ^6 x+3 \sin ^2 x \cos ^2 x\right) d x= $$

Physics

1. Uniform electric field of $5 \times 10^3 \mathrm{NC}^{-1}$ is maintained in the positive Y direction. Now a point charge 2. Pick out the correct statement from the following; 3. Two neutral bodies of masses $m_1$ and $m_2$ are kept at a distance of $r \mathrm{~cm}$ from one another in a vacuum med 4. An electric coil is rated $400 \mathrm{~W}, 200 \mathrm{~V}$. It is cut into two equal parts and connected in parallel t 5. Resonance is produced between a turning fork and a resonance column tube with upper end open and lower end closed by wat 6. A boy, standing at a certain height, kicks a football horizontally with a velocity of $19.6 \mathrm{~ms}^{-1}$. What wil 7. A capacitor of capacitance $8 \mu \mathrm{~F}$ is fully charged by connecting it to a source of 200 V . It is then disco 8. A hydrogen atom absorbs energy and rises to $n=3$ state from its ground state $n=1$. If the potential energy of the atom 9. On both sides of a magnetic needle, two short magnets A and B are placed on the same horizontal line which is perpendicu 10. A parallel combination of ' $n$ ' cells of emf ' $E$ ' and internal resistance ' $r$ ' each, are connected across the ex 11. A particle moves along a parabolic path $y=9 x^2$ in such a way that the x component of velocity remains constant. If, t 12. A source of alternating emf $\varepsilon=\varepsilon_0 \sin (\omega t)$ is connected to a capacitor. Then the instantane 13. If the intensity of the central maximum in the Young's double slit experiment is $\mathrm{I}_0$, what will be the intens 14. The dimensional formula for specific resistance is: 15. A charge of $5 \mu \mathrm{C}$ is placed at the centre of a spherical shell $S_1$ of radius 10 cm . Now this system is e 16. The main function of cadmium used in the nuclear reactor is: 17. What is the frequency of the electron in the first orbit of hydrogen atom of orbital radius $0.5 \times 10^{-10} \mathrm 18. An object is dropped from a certain point A at a height ' h ' from the ground. During it's journey straight downwards, t 19. In a single slit diffraction experiment, the diffraction pattern is observed on a screen placed at a distance of 2 m fro 20. A wire, made of a certain material of length-l and area of cross section-a can withstand a maximum load $=\mathrm{W}$ wi 21. A bullet, fired into a door gets embedded exactly at it's centre, causing the door to rotate about it's vertical axis, p 22. In the equation $X=G^{-1 / 2} h^{1 / 2} c^{5 / 2}$, where G- universal gravitation constant, $h$ - Planck's constant and 23. Force constant of interatomic bond, in a certain element, is $7.1 \mathrm{Nm}^{-1}$. If the atom oscillates in SHM in a 24. A circular coil of radius $r=10 c m$ having 300 turns carries a current of 2 A . The coil is suspended vertically in a u 25. The width of the fringes obtained with a light of wave length $6.2 \times 10^{-8} \mathrm{~m}$ is 1.82 mm . If the whole 26. If $\mu_0$ is the permeability of free space and $\varepsilon_0$ permittivity of free space then the dimension for $\lef 27. An electric field and magnetic field $1.8 \times 10^4 \mathrm{Vm}^{-1}$ and $6 \times 10^{-3} \mathrm{~T}$ respectively 28. Two point charges $P=+25 \mu C$ and $Q=-16 \mu C$ are placed 5 cm apart. Find the position of the point at which the res 29. The basic principle used behind the working of electron microscope is: 30. When a current of 2.5 A passes through the primary coil of a transformer of 200 number turns, the magnetic flux linked w 31. A block of a certain material is heated to a temperature of $500^{\circ} \mathrm{C}$ and then placed on a large ice bloc 32. The critical angle for a typical glass air interface is $42^{\circ}$. If a ray of light falls normally on one of the fac 33. Which of the following statements is/are true? (A) Three vectors not lying in a plane give zero resultant (B) Three vect 34. Bodies $P, Q, R, S$ are labelled as having charges $Q_P=0.5 \times 10^{-19} C, Q_Q=0.7 \times 10^{-19} C$, $Q_R=2.1 \tim 35. When metal of work function 1.4 eV is exposed to a radiation, the maximum kinetic energy of the electron emitted is 0.4 36. Following graph shows four different processes, adiabatic, isothermal, isobaric and isochoric for an ideal gas, from the 37. The distance between the objective and eye piece of astronomical telescope in normal adjustment is 27 cm and its magnify 38. A block of metal, of 25 g mass moves down without acceleration when the plane is inclined at an angle of $30^{\circ}$. W 39. The current through the circular coil is halved and the radius of the coil is doubled. If $B_1$ and $B_2$ are respective 40. In a given circuit, the instantaneous values of the alternating voltage and current are $V=0.5 \sin \left(80 \pi t+\frac 41. If the ratio of the nuclear radii of two atoms is $2: 3$ then the ratio of their mass numbers is: 42. The ratio of the angle of deviation produced by a thin prism, when it is placed in air to the angle of deviation produce 43. A vessel of volume $27 \times 10^4 \mathrm{cc}$, contains a mixture of Hydrogen (molar mass $=2 \mathrm{~g} \mathrm{~mol 44. In a uniform electric field $10^6 N C^{-1}$ an electric dipole of length 4 cm is placed with its axis making an angle $6 45. The variation of the stopping potential ( $\mathrm{V}_{\mathrm{o}}$ ) with the frequency of incident radiation( $n$ ) is 46. An object placed 40 cm in front of a thin convex lens is moved to 60 cm from the lens. If the focal length of the lens i 47. The voltage - current graph for a metal wire of uniform area of cross section at two different temp $T$ and $T^{\prime}$ 48. An electronic device operates at 2 MHz . The oscillating circuit has an inductance $20 \times 10^{-5} \mathrm{H}$. What 49. A singer, during his performance, stands on the edge of a circular turntable, and begins to walk along its edge with a s 50. A pith ball of mass ' $m$ ' gram and charge ' $Q$ ' is suspended using a mass less silk thread near a large charged cond 51. The material selected for making a permanent magnet should have: 52. Calculate the vapour pressure that can help the formation of a spherical droplet of water of radius $6.25 \times 10^{-5} 53. The atomic mass of an element $10 X^{20}$ is 19.98170 amu. The binding energy per nucleon of that element is: [given mas 54. Find the mass of oxygen gas with which $1.882 \times 10^{23}$ degrees of freedom are associated at N.T.P. Given: Molar m 55. A metallic circular loop is placed with its plane perpendicular to a uniform magnetic field of 0.3 T . If the radius of 56. What is the minimum wavelength of radiation required to detect a p-n junction diode made of a semiconductor having band 57. A galvanometer of resistance $50 \Omega$ is having 30 divisions and a current sensitivity $10 \mathrm{~mA} /$ div. What 58. A block of mass 1.5 kg moves along the floor of a hall with a speed of $5 \mathrm{~ms}^{-1}$. It strikes an uncompressed 59. Find the current through the $40 \Omega$ resistor in the given circuit having a diode, three resistors and two cells. 60. Two particles, one heavy and the other light, placed at 50 cm from each other, are under the influence of gravitational

COMEDK 2026 Afternoon Shift

MCQ (Single Correct Answer)

-0

The number of bond pairs and lone pairs of electrons in the molecule $I F_5$ is:

5,1

6,0

4,2

4,1

COMEDK 2026 Afternoon Shift

MCQ (Single Correct Answer)

-0

For an ideal gas undergoing an isothermal change, there is $\_\_\_\_$

no change in Internal energy of the system and heat released by the system is equal to the work done by the system

an increase in Internal energy of the system and heat absorbed by the system is greater than the work done on the system

a decrease in Internal energy of the system and heat released by the system is equal to the work done by the system

no change in Internal energy of the system and heat absorbed by the system is equal to the work done by the system

COMEDK 2026 Afternoon Shift

MCQ (Single Correct Answer)

-0

Which one of the following is the correct statement?

Acetone reacts with $\mathrm{NH}_2-\mathrm{NH}_2 / \mathrm{KOH}$ in Glycol on heating to form the saturated hydrocarbon, Butane

Acetone undergoes reaction in presence of $\mathrm{Ba}(\mathrm{OH})_2$ on heating to form 4-Methylpent-3-en-2-one

Acetophenone on reaction with $\mathrm{I}_2 / \mathrm{Na}_2 \mathrm{CO}_3(\mathrm{aq})$ does not undergo any reaction due to the presence of deactivating $-\mathrm{COCH}_3$ group

Acetophenone cannot be prepared on reacting Benzoyl chloride with Dimethyl cadmium in ether solvent

COMEDK 2026 Afternoon Shift

MCQ (Single Correct Answer)

-0

The initial pressure of the system before decomposition for a first order gas phase reaction $A_{(g)} \rightarrow B_{(g)}+C_{(g)}$ was $\mathrm{P}_{\mathrm{i}}$. After lapse of time ' t ', total pressure of the system increased by ' x ' units and became $\mathrm{P}_{\mathrm{t}}$. The rate constant ' k ' for the reaction is given as:

$k=\frac{2.303}{t} \log \frac{P_i}{P_i+x}$

$k=\frac{2.303}{t} \log \frac{P_i}{2 P_i-P_t}$

$k=\frac{2.303}{t} \log \frac{P_i}{2 P_i+P_t}$

$k=\frac{2.303}{t} \log \frac{P_i}{P_i-P_t}$

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