Chemistry
1. Identify the starting compound from the following data:
$$\mathrm{C}_6 \mathrm{H}_{14} \mathrm{O}(\mathrm{X})$$ on react 2. $$5.8 \mathrm{~g}$$ of a gas maintained at $$95^{\circ} \mathrm{C}$$ occupies the same volume as $$0.368 \mathrm{~g}$$ o 3. A first order reaction proceeds to $$90 \%$$ completion. What will be the approximate time taken for $$90 \%$$ completio 4. What would be the volume of water required to dissolve $$0.2 \mathrm{~g}$$ of $$\mathrm{PbCl}_2$$ of molar mass $$278 \m 5. Which one of the following compounds would not undergo Aldol condensation? 6. Match the following characteristics of transition metals given in Column I with the examples listed in Column II
.tg { 7. Gaseous Nitrous oxide decomposes at $$298 \mathrm{~K}$$ to form Nitrogen gas and Oxygen gas. The $$\Delta \mathbf{H}$$ f 8. In neutral medium $$\mathrm{KMnO}_4$$ oxidises $$\mathrm{MnSO}_4$$ to _________ 9. What would be the van't Hoff factor for a solution prepared by dissolving $$3.42 \mathrm{~g}$$ of $$\mathrm{CaCl}_2$$ in 10. The Molar conductivity of $$0.05 \mathrm{M}$$ solution of $$\mathrm{MgCl}_2$$ is $$194.5 \mathrm{~ohm}^{-1} \mathrm{~cm} 11. The equilibrium constants for the reactions $$a, b$$, and $$c$$ are as given:
a) $$\mathrm{N}_2+3 \mathrm{H}_2=2 \mathrm 12. Identify the correct IUPAC name of $$[\mathrm{CoCl}_2(\mathrm{NO}_2)(\mathrm{NH}_3)_3]$$ 13. From among the following, identify the compound which forms two moles of a ketone on ozonolysis.
[A] 2,3-Dimethylbutane. 14. If electrolysis of water is carried out for a time duration of 2 hours, how much electric current in amperes would be re 15. For a reaction of the type, $$2 \mathrm{X}+\mathrm{Y} \rightarrow \mathrm{A}+\mathrm{B}$$, the following is the data col 16. Select the strongest base from the given compounds:
[A] p- $$\mathrm{NO}_2-\mathrm{C}_6 \mathrm{H}_4 \mathrm{NH}_2$$
[B] 17. The conversion of Propyne to Benzene can be brought out in 4 steps.
Choose the reagents to be used, in the proper sequen 18. Para and ortho hydrogen differ in: 19. What is the mole fraction of solute in a $$5 \mathrm{~m}$$ aqueous solution? 20. Identify the reagents $$\mathrm{X}, \mathrm{Y}$$ and $$\mathrm{Z}$$ used to bring out the following reactions.
21. A proton having mass equal to $$1.66 \times 10^{-27} \mathrm{~kg}$$ is accelerated to one tenth of the velocity of light 22. Match the details given in Column I with those given in Column II
.tg {border-collapse:collapse;border-spacing:0;}
.tg 23. Match the items in Column I with their description in Column II
.tg {border-collapse:collapse;border-spacing:0;}
.tg t 24. Choose the incorrect statement. 25. When Lead Storage battery is in the process of getting charged which one of the following reactions takes place? 26. The group number of the element in the periodic table with the electronic configuration $$(\mathrm{n}-1) \mathrm{d}^2 \m 27. Identify the final product formed during the course of the given reactions.
Pentan-2-one $$\xrightarrow{\mathrm{NaCN} / 28. Which one of the following will give a positive result when it is warmed with Chloroform and alcoholic solution of $$\ma 29. Choose the incorrect statement: 30. What would be the products obtained when a mixture of p-Methoxy benzaldehyde and Methanal are heated with $$50 \%$$ conc 31. Which of the following will show geometrical isomerism? 32. Identify the compounds A, B, C and D.
$$
\text { 1,2,2,2-tetrachloroethane } \xrightarrow[\Delta]{\mathrm{Zn}}[\mathrm{A 33. Match the Coordination compounds given in Column I with their characteristic features listed in Column II.
.tg {border 34. Choose the correct order of increasing acidic strength of the following compounds. 35. $$\mathrm{Mg}(\mathrm{OH})_2$$ is used as an antacid. If a person, suffering from acidity, produces $$2.5 \mathrm{~L}$$ 36. Given below are graphs showing the variation in velocity constant with temperature on Kelvin scale. Identify the graph w 37. Identify the correct statement describing the characteristics of $$\mathrm{C}_2$$ molecule. 38. One among the 4 Vitamins belonging to $$\mathrm{B}$$ Complex, can be stored in our body. Identify the Vitamin. 39. Which one of the following statements is correct?
40. In the given Redox equation, identify the stoichiometric coefficients $$\mathrm{w}, \mathrm{x}, \mathrm{y}$$ and $$\math 41. In the following question, Assertion (A) is given followed by a statement of Reason (R). Choose the correct answer.
Asse 42. Structures of 3 Monosaccharides are given below. Two of them are Anomers. Identify the two Anomers.
43. Which one of the following is an incorrect statement pertaining to the properties of Coordination compounds? 44. $$\mathrm{X}$$ is an electrolyte with a concentration of $$0.04 \mathrm{M}$$ whose formula is of the type $$\mathrm{X}_2 45. Identify the catalyst used in the reaction between Iodide and persulphate ions.
$$2 \mathrm{I}^{-}+\mathrm{S}_2 \mathrm{ 46. Find the correct matches of the substances, given in Column I, from their characteristic properties given in Column II.
47. A Gas taken in a closed vessel is heated from $$54^{\circ} \mathrm{C}$$ to $$1254^{\circ} \mathrm{C}$$. The pressure of 48. Which one of the following correctly represents the decreasing order of acidic nature of the given carboxylic acids:
[A] 49. If the depression in freezing point of an aqueous solution containing a solute, which is neither dissociated nor associa 50. The rate constant for a First order reaction at $$560 \mathrm{~K}$$ is $$1.5 \times 10^{-6}$$ per second. If the reactio 51. What would be the final product [$$\mathbf{X}$$] formed when p-Toluidine undergoes the following series of reactions?
$$ 52. The energy of an electron in the ground state of Hydrogen atom is $$-2.18 \times 10^{-18} \mathrm{~J}$$. What would be t 53. Identify the incorrect statement. 54. Choose the incorrect statement regarding Cellulose. 55. Which one of the following Coordination entities exhibits Facial and Meridional isomerism? 56. Arrange the following in the decreasing order of their Dipole moments.
a. Chlorobenzene
b. 1,2-Dichlorobenzene
c. 1,3-Di 57. The reactions taking place with $$\mathrm{2- Phenyl-2-bromopropane}$$ as the starting material is shown below. Identify 58. The reaction taking place in a galvanic cell is as given
$$\mathrm{A}(\mathrm{s})+\mathrm{B}^{2+}\left(\mathbf{1} \mathb 59. Which one of the following will undergo Nucleophilic substitution, by $$\mathrm{S}_{\mathrm{N}}{ }^1$$ mechanism, fastes
Mathematics
1. The particular solution of $$e^{\frac{d y}{d x}}=2 x+1$$ given that $$y=1$$ when $$x=0$$ is 2. $$
\text { If } A=\left(\begin{array}{ll}
1 & 2 \\
0 & 1
\end{array}\right) \quad P=\left(\begin{array}{cc}
\cos \theta 3. $$A$$ and $$B$$ are invertible matrices of the same order such that $$\left|(A B)^{-1}\right|=8$$ if $$|A|=2$$ then $$|B 4. The centre of the circle passing through $$(0,0)$$ and $$(1,0)$$ and touching the circle $$x^2+y^2=9$$ is 5. If the direction ratios of two lines are given by $$3 l m-4 l n+m n=0$$ and $$l+2 m+3 n=0$$, then the angle between the 6. Which of the following is a singleton set? 7. If the conjugate of $$(x+i y)(1-2 i)$$ be $$1+i$$, then 8. If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is 9. A die is thrown twice and the sum of numbers appearing is observed to be 8 . What is the conditional probability that th 10. $$\int x^x(1+\log x) d x$$ is equal to 11. The minimum value of $$Z=3 x+5 y$$, given subject to the constraints $$x+y \geq 2, x+3 y \geq 3, x, y \geq 0$$ is 12. $$
\lim _\limits{x \rightarrow 0} \frac{a^x-b^x}{x} \text { is equal to }
$$ 13. The coordinates of the vertices of the triangle are $$A(-2,3,6), B(-4,4,9)$$ and $$C(0,5,8)$$. The direction cosines of 14. How many factors of $$2^5 \times 3^6 \times 5^2$$ are perfect squares? 15. The general solution of the differential equation $$\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y$$ 16. The function $$f(x)=\frac{x}{2}+\frac{2}{x}$$ has a local minimum at 17. The scalar components of a unit vector which is perpendicular to each of the vectors $$\hat{\imath}+2 \hat{\jmath}-\hat{ 18. A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 qu 19. $$
\int \sqrt{\operatorname{cosec} x-1} d x=
$$ 20. $$
\int_0^2\left|x^2+2 x-3\right| d x \text { is equal to }
$$ 21. Bag A contains 3 white and 2 red balls. Bag B contains only 1 white ball. A fair coin is tossed. If head appears then 1 22. Let $$X$$ and $$Y$$ be the set of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then 23. In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2 24. If three numbers $$a, b, c$$ constitute both an A.P and G.P, then 25. $$
\cos ^6 A-\sin ^6 A \text { is equal to }
$$ 26. The distance between the foci of a hyperbola is 16 and its eccentricity is $$\sqrt{2}$$. Then its equation is 27. The ratio in which the line $$3 x+4 y+2=0$$ divides the distance between the lines $$3 x+4 y+5=0$$ and $$3 x+4 y-5=0$$ i 28. If $$2 A+3 B=\left[\begin{array}{ccc}2 & -1 & 4 \\ 3 & 2 & 5\end{array}\right]$$ and $$A+2 B=\left[\begin{array}{lll}5 & 29. $$
\text { If } \operatorname{cosec}(90+A)+x \cos A \cot (90+A)=\sin (90+A) \text { then the value of } x \text { is }
$ 30. $$
\mathrm{P} \text { is a point on the line segment joining the points }(3,2,-1) \text { and }(6,2,-2) \text {. If the 31. The area of the upper half of the circle whose equation is $$(x-1)^2+y^2=1$$ is given by 32. In the set $$\mathrm{W}$$ of whole numbers an equivalence relation $$\mathrm{R}$$ is defined as follows $$\mathrm{aRb}$$ 33. $$
\text { If } P(B)=\frac{3}{5} \quad P(A / B)=\frac{1}{2} \text { and } P(A \cup B)=\frac{4}{5} \text { then } P(A \cu 34. $$
\text { The function defined by } f(x)=\left\{\begin{array}{cc}
\frac{\sin x}{x}+\cos x & x>0 \\
-5 k & x=0 \\
\frac{ 35. $$
f(x)=2 x-\tan ^{-1} x-\log (x+\sqrt{x^2+1}) \text { is monotonically increasing, when }
$$ 36. Consider the first 10 natural numbers. If we multiply each number by $$-$$1 and add 1 to each number, the variance of th 37. A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides havi 38. $$
\text { Let } f(x)=\cos ^{-1}(3 x-1) \text {, then domain of } f(x) \text { is equal to }
$$ 39. The solution of the differential equation $$\frac{d y}{d x}+y \cos x=\frac{1}{2} \sin 2 x$$ 40. The area bounded by the curve $$y^2=4 a^2(x-1)$$ and the lines $$x=1, y=4 a$$ is 41. $$
\text { If } f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to }
$$ 42. If $$\left[\begin{array}{ccc}2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5\end{array}\right]$$ is a singular matrix, then $$x$ 43. The sum of the degree and order of the following differential equation $$\left[1-\left(\frac{d y}{d x}\right)^2\right]^{ 44. If $$f(x)=\frac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}$$ then the value of $$f^{\prime}(0)$$ is equal to 45. Solution of $$x-y+z=4 ; x-2 y+2 z=9$$ and $$2 x+y+3 z=1$$ is 46. If $$\cos \alpha=k \cos \beta$$ then $$\cot \left(\frac{\alpha+\beta}{2}\right)$$ is equal to 47. $$
\int e^x\left(1+\tan x+\tan ^2 x\right) d x \text { is equal to }
$$ 48. In a $$\triangle A B C$$, if coordinates of point $$A$$ is $$(1,2)$$ and equation of the medians through $$B$$ and $$C$$ 49. The distance of the point $$(2,3,4)$$ from the line $$1-x=\frac{y}{2}=\frac{1}{3}(1+z)$$ is 50. The altitude of a cone is $$20 \mathrm{~cm}$$ and its semi vertical angle is $$30^{\circ}$$. If the semi vertical angle 51. If the position vector of a point $$A$$ is $$\vec{a}+2 \vec{b}$$ and $$\vec{a}$$ divides $$A B$$ in the ratio $$2: 3$$, 52. $$
\text { The value of } \sin ^{-1}\left[\cos \left(39 \frac{\pi}{5}\right)\right] \text { is }
$$ 53. The probability distribution of a discrete random variable X is given as
.tg {border-collapse:collapse;border-spacing: 54. 18 Points are indicated on the perimeter of a triangle $$\mathrm{ABC}$$ as shown below. If three points are chosen then 55. $$
\text { If } \vec{a} \text { and } \vec{b} \text { are unit vectors, then the angle between } \vec{a} \text { and } \ 56. If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is 57. What can be said regarding a line if its slope is negative? 58. The range of $$x$$ which satisfy the inequation : $$-5 \leq \frac{2-3 x}{4} \leq 9$$ is 59. $$
\int \frac{\cos 4 x+1}{\cot x-\tan x} d x=
$$ 60. Le $$x$$ be the arithmetic mean and $$y, z$$ be the two geometric means between any two positive numbers, then $$\frac{y
Physics
1. A man grows into a giant such that his height increases to 8 times his original height. Assuming that his density remain 2. The mass number of two nuclei $$\mathrm{P}$$ and $$\mathrm{Q}$$ are 27 and 125 respectively. The ratio of their radii $$ 3. The current sensitivity of a galvanometer having 20 divisions is $$10 \mu \mathrm{A} /$$ div. If the resistance of the g 4. In a nuclear reaction 2 deuteron nuclei combine to form a helium nucleus. The energy released in $$\mathrm{MeV}$$ will b 5. Two point charges $$20 \mu \mathrm{C}$$ and $$-10 \mu \mathrm{C}$$ are separated by a distance of $$1 \mathrm{~m}$$ in a 6. The critical angle of a medium having the refractive index $$\sqrt2$$ is : 7. A spherical metal ball of density '$$\rho$$' and radius '$$r$$' is immersed in a liquid of density '$$\sigma$$'. When an 8. In an adiabatic expansion of air, the volume is increased by $$6.2 \%$$. The percentage change in pressure is $$(\gamma= 9. Water from a tap of cross-sectional area $$1 \mathrm{~cm}^2$$, falls vertically downwards at $$2 \mathrm{~m} / \mathrm{s 10.
In the figure, first the capacitors are fully charged by closing the key $$\mathrm{K}$$. Then after opening the Key a d 11. The energy gap between valance band and the conduction band for a given material is $$6 \mathrm{~eV}$$, then the materia 12. PQRS is square of side $$1 \mathrm{~m}$$. A charge of $$100 \mu \mathrm{C}$$ is placed at the centre of the square. Then 13. When angle of incidence on one face of the equilateral glass prism is $$3 / 4^{\text {th }}$$ of the angle of prism, the 14. If the ratio of specific heat of a gas at constant pressure to that at constant volume is $$\gamma$$, the change in inte 15. A magnetic field does not interact with: 16. A person has a normal near point $$25 \mathrm{~cm}$$. What is the magnifying power of the simple microscope he used, if 17. If reaction is $$\mathrm{R}$$ and coefficient of friction is $$\mu$$, what is work done against friction in moving a bod 18. The electric flux from cube of side $$1 \mathrm{~m}$$ is '$$\Phi$$' When the side of the cube is made $$3 \mathrm{~m}$$ 19. An uniform sphere of mass $$M$$ and radius $$R$$ exerts a force of $$F$$ on a small mass $$m$$ placed at a distance of 3 20. The magnetic permeability '$$\mu$$' a of a paramagnetic substance is : 21. A lens of power $$+1 \mathrm{D}$$ is made in contact with another lens of power $$-2 \mathrm{D}$$ the combination will t 22. A particle at rest decays in to two particles of mass $$m_1$$ and $$m_2$$ and move with velocities $$v_1$$ and $$v_2$$. 23. An electron and a proton having mass $$m_e$$ and $$m_p$$ respectively, initially at rest, move through the same distance 24. $$220 \mathrm{~V}$$ ac is more dangerous than $$220 \mathrm{~V}$$ dc Why? 25. The ground state energy of hydrogen atom is $$-13.6 \mathrm{~eV}$$. If the electron jumps from the $$3^{\text {rd }}$$ e 26. In the young's double slit experiment the fringe width of the interference pattern is found to be $$3.2 \times 10^{-4} \ 27. What will be change in wave length, if a light of wave length $$600 \mathrm{~nm}$$ travels from air enters a medium of r 28. A resistor of wire $$24 \mathrm{~cm}$$ length and resistance $$8 \Omega$$ is stretched in to a uniform wire of $$48 \mat 29. A metallic rod of $$10 \mathrm{~cm}$$ is rotated with a frequency 100 revolution per second about an axis perpendicular 30. Two open organ pipes A and B of length $$22 \mathrm{~cm}$$ and $$22.5 \mathrm{~cm}$$ respectively produce 2 beats per se 31. The time dependence of a physical quantity P is give by $$\mathrm{P=P}_0 \exp \left(-\alpha t^2\right)$$ where $$\alpha$ 32. The molecules of a given mass of a gas have root mean square speed of $$120 \mathrm{~m} / \mathrm{s}$$ at $$88^{\circ} \ 33. The acceleration due to gravity at a height of $$7 \mathrm{~km}$$ above the earth is the same as at a depth d below the 34. A tentative explanation of observations without assuming that it is true is called 35. Find the pole strength of a magnet of length $$2 \mathrm{~cm}$$, if the magnetic field strength $B$ at distance $$10 \ma 36. In the head-on collision of two alpha particles $$\alpha_1$$ and $$\alpha_2$$ with the gold nucleus, the closest approac 37. Two black bodies $$\mathrm{P}$$ and $$\mathrm{Q}$$ have equal surface areas and are kept at temperatures $$127^{\circ} \ 38. The SI unit of electrical conductivity is : 39. What should be the inductance of an inductor connected to $$200 \mathrm{~V}, 50 \mathrm{~Hz}$$ source so that the maximu 40. The nucleus of a helium atom travels along the inside of a straight hollow tube $$4 \mathrm{~m}$$ long which forms part 41. In the given circuit the diode $$D_1$$ and $$D_2$$ have the forward resistance $$25 \Omega$$ and infinite backward resis 42. The radius of the current carrying circular coil is doubled keeping the current passing through it the same. Then the ra 43. If the resultant of all external forces acting on a system of particles is zero, then from an inertial frame one can sur 44. The reverse current in the semiconductor diode changes from $$20 \mu \mathrm{A}$$ to $$40 \mu \mathrm{A}$$ when the reve 45. A drone is flying due west, a little above the train, with a speed of $$10 \mathrm{~m} / \mathrm{s}$$. A 270 meter long 46. $$\mathrm{F}_{\mathrm{A}}, \mathrm{F}_{\mathrm{B}}$$ and $$\mathrm{F}_{\mathrm{C}}$$ are three forces acting at point $$ 47. A wheel is free to rotate about a horizontal axis through O. A force of $$200 \mathrm{~N}$$ is applied at a point $$\mat 48. A hockey player hits the ball at an angle of $$37^{\circ}$$ from the horizontal with an initial speed of $$40 \mathrm{~m 49. What feature of the infrared waves make it useful for the haze photography? 50. A spring of force constant $$k$$ is cut into lengths of ratio $$1:3:4$$. They are connected in series and the new force 51. A light having wavelength $$6400^{\circ} \mathrm{A}$$ is incident normally on a slit of width $$2 \mathrm{~mm}$$. Then t 52. Which of the following statement is true when a gamma decay occurs from the nucleus of an atom? 53. The current passing through the 100$$\Omega$$ resistor in the given electrical circuit is :
54. The force between two electric point charges at rest in air is $$F_1$$ When the same arrangement is kept inside water, t 55. A neutron makes a head on elastic collision with a lead nucleus. The ratio of nuclear mass to neutron mass is 206 . The 56. A battery is made of 12 cells having emf $$5 \mathrm{~V}$$ each. If three cells are unknowingly connected wrong, the res 57. A circular loop of area $$0.04 \mathrm{~m}^2$$ carrying a current of $$10 \mathrm{~A}$$ is held with its plane perpendic 58. In the photoelectric experiment, the frequency of the incident radiation is doubled. What will be its effect on the phot 59. One volt induced emf is produced in the secondary coil when the current through the primary coil is changed from $$3 \ma 60. The current drawn by the primary coil of an ideal transformer, which steps up $$22 \mathrm{~V}$$ into $$220 \mathrm{~V}$
1
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0
The reaction taking place in a galvanic cell is as given
$$\mathrm{A}(\mathrm{s})+\mathrm{B}^{2+}\left(\mathbf{1} \mathbf{1} \mathbf{1 0} \mathbf{0}^{-\mathrm{M}} \mathbf{M}\right) \rightarrow \mathrm{B}_{(\mathrm{s})}+\mathrm{A}^{2+}(0.1 \mathrm{M}).$$
The emf of the cell is $$+2.651 \mathrm{~V}$$. If the standard emf of the cell is $$+2.71 \mathrm{~V}$$, what is the value of $$\mathrm{X}$$ ?
A
X = 6
B
X = 2
C
X = 3
D
X = 4
2
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0
Which one of the following will undergo Nucleophilic substitution, by $$\mathrm{S}_{\mathrm{N}}{ }^1$$ mechanism, fastest?
A
$$
\mathrm{Br}-\mathrm{CH}_2-\mathrm{CH}=\mathrm{CH}_2
$$
B
$$
\mathrm{C}_6 \mathrm{H}_5 \mathrm{Br}
$$
C
$$
\mathrm{CH}_3-\mathrm{CH}=\mathrm{CHBr}
$$
D
$$
\mathrm{C}_6 \mathrm{H}_{11} \mathrm{Br}
$$
3
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0
The particular solution of $$e^{\frac{d y}{d x}}=2 x+1$$ given that $$y=1$$ when $$x=0$$ is
A
$$
y=\left(x+\frac{1}{2}\right) \log |2 x+1|-x+1
$$
B
$$
y=(x+1) \log |2 x+1|-x+1
$$
C
$$
y=\left(x+\frac{1}{2}\right) \log |2 x+1|-\frac{1}{2} x+1
$$
D
$$
y=\left(x-\frac{1}{2}\right) \log |2 x+1|-x-1
$$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \text { If } A=\left(\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right) \quad P=\left(\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right) \quad Q=P^T A P, \quad \text { then } P Q^{2014} P^T \text { is equal to } $$
A
$$
\left(\begin{array}{cc}
1 & 2^{2014} \\
0 & 1
\end{array}\right)
$$
B
$$
\left(\begin{array}{cc}
1 & 4028 \\
0 & 1
\end{array}\right)
$$
C
$$
\left(P^T\right)^{2013} A^{2014} P^{2013}
$$
D
$$
P^T A^{2014} P
$$
Paper analysis
Total Questions
Chemistry
59
Mathematics
60
Physics
60
COMEDK
Papers