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
1
COMEDK 2026 Morning Shift
MCQ (Single Correct Answer)
+1
-0
An object is placed 25 cm in front of a fully silvered concave mirror of focal length 15 cm . A plane mirror is placed 35 cm behind the concave mirror on the side opposite to the object. The final image after reflection first from the concave mirror and then from the plane mirror is formed at:
A
37.5 cm in front of the plane mirror
B
72.5 cm behind the concave mirror
C
107.5 cm behind the concave mirror
D
37.5 cm in front of the concave mirror
2
COMEDK 2026 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A bar magnet of length 12 cm is placed such that its north pole points towards the geographic north. Two neutral points which are separated by 16 cm are obtained on the equatorial axis of the bar magnet. What is the pole strength of the bar magnet if the horizontal component of the earth's field is $1.25 \times 10^{-5} \mathrm{~T}$ ?
A
3.024 Am
B
1.042 Am
C
10.24 Am
D
2.032 Am
3
COMEDK 2026 Morning Shift
MCQ (Single Correct Answer)
+1
-0
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 resultant is at $90^{\circ}$ with the smaller force, the magnitudes of A and B , in N are
A
$28 \mathrm{~N}, 20 \mathrm{~N}$
B
$40 \mathrm{~N}, 8 \mathrm{~N}$
C
$29 \mathrm{~N}, 21 \mathrm{~N}$
D
$35 \mathrm{~N}, 13 \mathrm{~N}$
4
COMEDK 2026 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A nucleus of uranium -235 absorbs a slow neutron and undergoes nuclear fission according to the reaction: ${ }_{92}^{235} U+{ }_0^1 n \rightarrow{ }_{56}^{141} B a+{ }_{36}^{92} K r+3{ }_0^1 n+Q$
If the average energy released per fission is 202 MeV , the energy released when 2.35 g of $U^{235}$ undergoes complete fission is approximately;
[Given $1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}$, Avogadro number $=6.02 \times 10^{23}$ ]
A
$1.945 \times 10^{10} J$
B
$19.45 \times 10^{11} J$
C
$1.945 \times 10^{11} J$
D
$19.45 \times 10^{10} \mathrm{~J}$
Paper Analysis
Total Questions
Chemistry 60
Mathematics 60
Physics 60
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