Chemistry
1. What would be the EMF of the cell in which the following reaction occurs:
$$\begin{aligned}
& \mathrm{Cd}(\mathrm{S})+2 2. $$\text { Identify }[\mathrm{B}] \text { and }[\mathrm{C}] \text { formed in the reactions given below. }$$
3. Identify the 2 chemical tests which is not answered by Glucose having an open chain structure
[A] Reaction with Schiff's 4. A d - block metal $$\mathrm{X}(\mathrm{Z}=26)$$ forms a compound $$[\mathrm{X}(\mathrm{CN})_2(\mathrm{CO})_4]^{+}$$. Cal 5. Which one of the following compounds shows Geometrical isomerism? 6. A sweet smelling organic compound $$[\mathrm{A}]\left(\mathrm{C}_9 \mathrm{H}_{10} \mathrm{O}_2\right)$$ undergoes acid 7. Arrange the following ions in the increasing order of their $$\Delta H_{(\text {hydration})}$$ values.
$$\mathrm{Cr}^{2+ 8. What is the final product formed when Toluene undergoes the following series of reactions?
9. The time required for $$80 \%$$ of a first order reaction is "$$y$$" times the half-life period of the same reaction. Wh 10. The standard enthalpy of formation of $$\mathrm{CH}_4$$, the standard enthalpy of sublimation of Carbon and the bond dis 11. From the following compounds, identify the one which is most acidic.
12. An inorganic salt comprises of atoms of elements $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$. If the oxidation numbers 13. The rate constant for the reaction $$\mathrm{A} \rightarrow \mathrm{B}+\mathrm{C}$$ at $$500 \mathrm{~K}$$ is given as $ 14. An organic compound $$[\mathrm{A}]\left(\mathrm{C}_5 \mathrm{H}_{12} \mathrm{O}\right)$$, on reaction with conc. $$\math 15. For the reaction $$\mathrm{Cl}_{2(\mathrm{~g})}+2 \mathrm{NO}_{(\mathrm{g})} \rightarrow 2 \mathrm{NOCl}_{(\mathrm{g})}$ 16. $$\mathrm{K}_{\mathrm{H}}$$ for $$\mathrm{O}_2$$ at $$293 \mathrm{~K}$$ is $$34.86 \mathrm{~kbar}$$. What should be the 17. The permanganate ion in acid medium acts as an oxidant and gets converted to its lower oxidation state. What would be th 18. $$\mathrm{A}_3 \mathrm{~B}_4$$ is a sparingly soluble salt with a solubility of $$\mathrm{s} g / \mathrm{L}$$. If the Mo 19. Given below are 4 graphs [A], [B], [C] and [D]
Identify the 2 graphs that represent a Zero order reaction? 20. A given mass of a hydrocarbon on complete combustion produced $$176 \mathrm{~g}$$ of $$\mathrm{CO}_2$$ and $$90 \mathrm{ 21. An unsaturated hydrocarbon $$[\mathrm{A}]$$ reacts with $$\mathrm{HBr}$$ in presence of Benzoyl peroxide to yield [B]
Co 22. Match the compounds given in Column I with their characteristic features listed in Column II
.tg {border-collapse:coll 23. Choose the group of ions / molecules in which none of the species undergo Disproportionation reaction. 24. What is the amount of ice that separates out on cooling a solution containing $$60 \mathrm{~g}$$ of Ethylene glycol in $ 25. $$\text { If a compound } \mathrm{X}_3 \mathrm{Y} \text { is } 60 \% \text { ionised in aqueous medium, what is its van' 26. A Coordination compound is represented by the formula $$[\mathrm{CoBr}_3(e n) x]$$. This compound required one mole of $ 27. Propane in presence of $$\mathrm{O}_2$$ gas undergoes complete combustion to produce $$\mathrm{CO}_2$$ and $$\mathrm{H}_ 28. Arrange the following compounds in the decreasing order of reactivity towards $$\mathrm{S}_{\mathrm{N}} 1$$ reaction.
29.
Above figure represents Vapour pressure versus Temperature graphs of 2 pure volatile liquids and a solution formed by t 30. Which one of the following statements is incorrect regarding acetal and ketal formation when Propanal and Propanone are 31. Choose the incorrect statement from the following. 32. $$0.1 \mathrm{M}$$ solution of $$\mathrm{AgNO}_3$$ is taken in a Conductivity cell and a potential difference of $$40 \m 33. A statement of Assertion followed by a statement of Reason is given.
Choose the correct answer out of the following opti 34. $$300 \mathrm{ml}$$ of an aqueous solution of $$\mathrm{NaOH}$$ with $$\mathrm{pH}$$ value of 10 is mixed with $$200 \ma 35. Aniline undergoes reactions with reagents given in the order shown
(i) Aqueous $$\mathrm{Br}_2$$
(ii) $$\mathrm{NaNO}_2 36. Which one of the following shows the correct increasing order of basic nature of the given compounds?
A: Phenylmethanami 37. Given: $$\Delta \mathrm{G}^0{ }_{\mathrm{f}}$$ of $$\mathrm{C}_2 \mathrm{H}_2$$ is $$2.09 \times 10^5 \mathrm{~J} / \mat 38. A Carbonyl compound $$\mathrm{X}$$ when reacted with Methyl magnesium bromide followed by hydrolysis gave product $$\mat 39. Identify the Reagents I and II to be used in the course of the given reactions.
40. Given below are 4 species with one odd electron on the Carbon atom.
$$\begin{array}{ll}
\mathrm{A}=\left(\mathrm{CH}_3\r 41. Which one of the following compounds when reacted with $$\mathrm{NaOH}$$ (aq) undergoes Substitution Nucleophilic Bimole 42. A statement of Assertion followed by a statement of Reason is given. Choose the correct answer out of the following opti 43. Match the Hormones listed in Column I with their characteristics listed in Column II
.tg {border-collapse:collapse;bor 44. Identify the product [D] formed when Reactant [A] $$(M M 78 \mathrm{~g} / \mathrm{mol})$$ undergoes the series of reacti 45. The boiling point of a $$4 \%$$ aqueous solution of a non-volatile solute $$\mathrm{P}$$ is equal to the boiling point o 46. Given below are 4 statements about Insulin. Which of these statement/(s) is/are correct?
[A] Insulin is a globular prote 47. Given below are 4 subatomic particles travelling with the same velocity "v". Which of them will have the shortest wavele 48. The mass number of an element $$\mathrm{X}$$ is 175 with 104 neutrons in its nucleus. Into which one of the following or 49. What is the number of mono-chloro derivatives of Ethyl cyclohexane possible? 50. Which one of the following is the correct IUPAC name of the given compound?
51. An aromatic hydrocarbon $$[\mathrm{A}]\left(\mathrm{Molecular}\right.$$ formula $$\left.\mathrm{C}_9 \mathrm{H}_{12}\rig 52. A given chemical reaction is represented by the following stoichiometric equation.
$$3 X+2 Y+\frac{5}{2} Z \rightarrow P 53. Match the chemical reactions taking place at the Anode of the cell with the correct cell in which the reaction occurs.
54. If the enthalpy of formation of a diatomic molecule $$\mathrm{AB}$$ is $$-400 \mathrm{~kJ} / \mathrm{mol}$$ and the bond 55. Choose the incorrect statement from the following 56. Given below are 4 equations showing Molar conductivities at infinite dilution of various electrolytes. Which one of them 57. On the basis of VSEPR theory, match the molecules listed in Column I with their shapes given in Column II.
.tg {border 58. Match the compounds given in column I with the corresponding most stable Carbocations formed by each, as given in Column 59. Identify the pair of molecules, both of which have positive values of Dipole moment. 60. Given below are 4 molecular species/ions. Identify the species/ion which exhibits diamagnetic nature.
$$[\mathrm{A}]=\ma
Mathematics
1. The side of an equilateral triangle expands at the rate of $$\sqrt{3} \mathrm{~cm} / \mathrm{sec}$$. When the side is $$ 2. $$
\text { If } P=\left[\begin{array}{lll}
1 & \alpha & 3 \\
1 & 3 & 3 \\
2 & 4 & 4
\end{array}\right] \text { is the ad 3. $$
\text { If } f(x)=\left\{\begin{array}{cc}
\frac{1-\sin x}{(\pi-2 x)^2} & , \quad \text { if } x \neq \frac{\pi}{2} \ 4. $$\begin{aligned}
&\begin{aligned}
& \text { A, B, C are subsets of the Universal set U } \\
& \text { If } \mathrm{A}=\ 5. The foot of the perpendicular from $$(2,4,-1)$$ to the line $$x+5=\frac{1}{4}(y+3)=-\frac{1}{9}(z-6)$$ is 6. In how many ways can the word "CHRISTMAS" be arranged so that the letters '$$\mathrm{C}$$' and '$$\mathrm{M}$$' are neve 7. $$\lim _\limits{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}$$ equals to 8. A and B each have a calculator which can generate a single digit random number from the set $$\{1,2,3,4,5,6,7,8\}$$. The 9. If $$\cos \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)$$ then $$\frac{1}{2}\left(x^2+\frac{1}{x^2}\right)=$$ 10. The probability that a randomly chosen number from one to twelve is a divisor of twelve is 11. Evaluate : $$\cos ^{-1}\left[\cos \left(-680^{\circ}\right)\right]+\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right] 12. If $$f(x)=f^{\prime}(x)$$ and $$f(1)=2$$, then $$f(3)$$ is 13. The equation of an ellipse, whose focus is $$(1,0)$$, directrix is $$x=4$$ and whose eccentricity is a root of the quadr 14. If $$A=\left[\begin{array}{ccc}-1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$ then the inverse of $$(A I)^t$$ 15. $$
\text { If } x, y, z \text { are non zero real numbers, then inverse of matrix } A=\left[\begin{array}{lll}
x & 0 & 0 16. If $$\left[{ }^{n+1} C_{r+1}\right]:\left[{ }^n C_r\right]:\left[{ }^{n-1} C_{r-1}\right]=11: 6: 3$$ then $$n r=$$ 17. If $$\int \frac{1}{\sqrt{\sin ^3 x \cos x}} d x=\frac{k}{\sqrt{\tan x}}+c$$ then the value of $$k$$ is 18. $$P$$ is a point on the line segment joining the points $$(3,2,-1)$$ and $$(6,2,-2)$$. If $$x$$ coordinate of $$\mathrm{ 19. A geometric progression consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms 20. The particular solution of $$\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0$$, when $$x=0, y=\frac{1}{2}$$ is 21. If the events A and B are mutually exclusive events such that $$P(A)=\frac{1}{3}(3 x+1)$$ and $$P(B)=\frac{1}{4}(1-x)$$ 22. The mean of the numbers $$a, b, 8,5,10$$ is 6 and the variance is 6.80 , then which of the following gives possible valu 23. If $$f(x)=2 x^3+9 x^2+\lambda x+20$$ is a decreasing function of $$x$$ in the largest possible interval $$(-2,-1)$$, the 24. $$\int \sqrt{x^2-4 x+2} d x=$$ 25. $$4\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \ 26. The minimum value of $$Z=150 x+200 y$$ for the given constraints
$$\begin{aligned}
& 3 x+5 y \geq 30 \\
& x+y \geq 8 ; x 27. The vector equation of two lines are
$$\begin{aligned}
& \vec{r}=(1-t) \hat{\imath}+(t-2) \hat{\jmath}+(3-2 t) \hat{k} \ 28. $$
\text { If the matrix } A=\left(\begin{array}{cc}
1 & -1 \\
-1 & 1
\end{array}\right) \text { then } A^{n+1}=
$$ 29. $$
\text { If } A=\{1,2,3,4,5\} \text { and } B=\{2,3,6,7\} \text { then number of elements in the set }(A \times B) \ca 30. If $$
\left[\begin{array}{lll}
1 & x & 1
\end{array}\right]\left[\begin{array}{ccc}
1 & 3 & 2 \\
2 & 5 & 1 \\
15 & 3 & 2 31. $$
\int \frac{x}{x^4-16} d x=
$$ 32. Find the direction in which a straight line must be drawn through the point $$(1,2)$$ so that its point of intersection 33. An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white it is not replaced into the urn. Ot 34. The perpendicular distance of a line from the origin is 5 units and its slope is $$-1$$.
The equation of the line is 35. Given $$a, b, c$$ are three unequal numbers such that $$\mathrm{b}$$ is arithmetic mean of $$a$$ and $$c$$ and $$(b-a),( 36. $$
\text { If } y=\log _e\left(\frac{x^2}{e^2}\right) \text {, then } \frac{d^2 y}{d x^2} \text { is equal to }
$$ 37. The equation of a circle passing through the origin is $$x^2+y^2-6 x+2 y=0$$. The equation of one of its diameter is 38. The particular solution of the differential equation $$\cos x \frac{d y}{d x}+y=\sin x$$ at $$y(0)=1$$ 39. A random variable X with probability distribution is given below
.tg {border-collapse:collapse;border-spacing:0;}
.tg 40. $$
\text { The point on the curve } x^2=x y \text { which is closest to }(0,5) \text { is }
$$ 41. $$
\text { If } y=\tan ^{-1}\left(\frac{3-2 x}{1+6 x}\right) \text { then } \frac{d y}{d x} \text { is }
$$ 42. $$
\text { The modulus of the following complex number } \frac{1+i}{1-i}-\frac{1-i}{1+i} \text { is }
$$ 43. The area (in sq units) of the minor segment bounded by the circle $$x^2+y^2=a^2$$ and the line $$x=\frac{a}{\sqrt{2}}$$ 44. Let $$f: R \rightarrow R$$ be a function defined by $$f=\frac{e^{|x|}-e^{-x}}{e^x+e^{-x}}$$ then 45. $$
\lim _\limits{x \rightarrow 0}\left(\frac{\sin a x}{\sin b x}\right)^k \text { equals }
$$ 46. $$
\text { If } \sin y=x(\cos (a+y)) \text {, then find } \frac{d y}{d x} \text { when } x=0
$$ 47. The vector $$(\vec{r})$$ whose magnitude is $$3 \sqrt{2}$$ units which makes an angle of $$\frac{\pi}{4}$$ and $$\frac{\ 48. $$
\text { The value of } \sin ^{-1}\left[\cot \left(\frac{1}{2} \tan ^{-1} \frac{1}{\sqrt{3}}+\cos ^{-1} \frac{\sqrt{12 49. For a given curve $$y=2 x-x^2$$, when $$x$$ increases at the rate of 3 units/sec, then how does the slope of the curve c 50. The coefficient of the third term in the expansion of $$\left(x^2-\frac{1}{4}\right)^n$$, when expanded in the descendin 51. $$
\text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|=
$$ 52. $$
\text { If } \sin A=\frac{4}{5} \text { and } \cos B=\frac{-12}{13} \text { where } A \text { and } B \text { lie in 53. $$
\int_\limits{-1}^1 \frac{d}{d x}\left(\tan ^{-1} \frac{1}{x}\right) d x \text { is }
$$ 54. $$
\text { If } \frac{1}{2}\left(\frac{3 x}{5}+4\right) \geq \frac{1}{3}(x-6), x \in R \text { then }
$$ 55. $$
\text { The area (in sq units) enclosed by the parabola } y^2=8 x \text {, its latus-rectum and the } x \text {-axis 56. The most economical proportion of the height of a covered box of fixed volume whose base is a rectangle with one side th 57. Express the set $$A=\{1,7,17,31,49\}$$ in set builder form 58. $$
(32) \times(32)^{\frac{1}{6}} \times(32)^{\frac{1}{36}} \times-----\infty \text { is equal to }
$$ 59. $$
\text { The value of } \int \frac{1}{x+\sqrt{x-1}} d x \text { is }
$$ 60. Which of the following is not a homogenous function of $$x$$ and $$y$$
Physics
1. The resistance of the galvanometer and shunt of an ammeter are $$90 \mathrm{~ohm}$$ and $$10 \mathrm{~ohm}$$ respectivel 2. A glass of hot water cools from $$90^{\circ} \mathrm{C}$$ to $$70^{\circ} \mathrm{C}$$ in 3 minutes when the temperature 3. When two objects are moving along a straight line in the same direction, the distance between them increases by $$6 \mat 4. In the Young's double slit experiment $$n^{\text {th }}$$ bright for red coincides with $$(n+1)^{\text {th }}$$ bright f 5. A metal ball of $$20 \mathrm{~g}$$ is projected at an angle $$30^{\circ}$$ with the horizontal with an initial velocity 6. The threshold frequency for a metal surface is '$$n_0$$'. A photo electric current '$$I$$' is produced when it is expose 7. A $$500 \mathrm{~W}$$ heating unit is designed to operate on a $$400 \mathrm{~V}$$ line. If line voltage drops to $$160 8. Current flows through uniform, square frames as shown in the figure.
In which case is the magnetic field at the centre o 9. A transformer which steps down $$330 \mathrm{~V}$$ to $$33 \mathrm{~V}$$ is to operate a device having impedance $$110 \ 10. A cell of emf E and internal resistance r is connected to two external resistances $$\mathrm{R_1}$$ and $$\mathrm{R_2}$$ 11. Select the unit of the coefficient of mutual induction from the following. 12. Steel is preferred to soft iron for making permanent magnets because, 13. A particle executes a simple harmonic motion of amplitude $$\mathrm{A}$$. The distance from the mean position at which i 14. A body of mass $$5 \mathrm{~kg}$$ at rest is rotated for $$25 \mathrm{~s}$$ with a constant moment of force $$10 \mathrm 15. In the normal adjustment of an astronomical telescope, the objective and eyepiece are $$32 \mathrm{~cm}$$ apart. If the 16. In a given semiconductor, the ratio of the number density of electron to number density of hole is $$2: 1$$. If $$\frac{ 17. If $$\mathrm{A}$$ is the areal velocity of a planet of mass $$\mathrm{M}$$, then its angular momentum is 18. When a particular wave length of light is used the focal length of a convex mirror is found to be $$10 \mathrm{~cm}$$. I 19. The mass of a particle $$\mathrm{A}$$ is double that of the particle $$\mathrm{B}$$ and the kinetic energy of $$\mathrm{ 20. A coil of inductance $$1 \mathrm{H}$$ and resistance $$100 \Omega$$ is connected to an alternating current source of fre 21. The current through a conductor is '$$\mathrm{a}$$' when the temperature is $$0^{\circ} \mathrm{C}$$. It is '$$\mathrm{b 22. Which of the following graph shows the variation of velocity with mass for the constant momentum?
23. For a $$30^{\circ}$$ prism when a ray of light is incident at an angle $$60^{\circ}$$ on one of its faces, the emergent 24. A coil offers a resistance of $$20 \mathrm{~ohm}$$ for a direct current. If we send an alternating current through the s 25. A square shaped aluminium coin weighs $$0.75 \mathrm{~g}$$ and its diagonal measures $$14 \mathrm{~mm}$$. It has equal a 26. If the earth has a mass nine times and radius four times that of planet X, the ratio of the maximum speed required by a 27. Two similar coils $A$ and $B$ of radius '$$r$$' and number of turns '$$N$$' each are placed concentrically with their pl 28. An ideal diode is connected in series with a capacitor. The free ends of the capacitor and the diode are connected acros 29. Which of the following statement is true regarding the centre of mass of a system? 30. A ray of light travelling through a medium of refractive index $$\frac{5}{4}$$ is incident on a glass of refractive inde 31. The ratio of the radii of the nucleus of two element $$\mathrm{X}$$ and $$\mathrm{Y}$$ having the mass numbers 232 and 2 32. When light wave passes from a medium of refractive index '$$\mu$$' to another medium of refractive index '$$2 \mu$$' the 33. On increasing the temperature of a conductor, its resistance increases because 34. The difference in energy levels of an electron at two excited levels is $$13.75 \mathrm{~eV}$$. If it makes a transition 35. A string of length $$25 \mathrm{~cm}$$ and mass $$10^{-3} \mathrm{~kg}$$ is clamped at its ends. The tension in the stri 36. A cubical box of side $$1 \mathrm{~m}$$ contains Boron gas at a pressure of $$100 \mathrm{~Nm}^{-2}$$. During an observa 37. Around the central part of an air cored solenoid of length $$20 \mathrm{~cm}$$ and area of cross section $$1.4 \times 10 38. A circular coil of radius $$0.1 \mathrm{~m}$$ is placed in the $$\mathrm{X}-\mathrm{Y}$$ plane and a current $$2 \mathrm 39. A body is moving along a circular path of radius '$$r$$' with a frequency of revolution numerically equal to the radius 40. Which of the given dimensional formula represents heat capacity 41. If potential (in volt) in a region is expressed as $$\mathrm{V}(\mathrm{x}, \mathrm{y}, \mathrm{z})=6 \mathrm{xy}-\mathr 42. The closest approach of an alpha particle when it make a head on collision with a gold nucleus is $$10 \times 10^{-14} \ 43. A one $\mathrm{kg}$ block of ice at $$-1.5^{\circ} \mathrm{C}$$ falls from a height of $$1.5 \mathrm{~km}$$ and is found 44. 64 rain drops of the same radius are falling through air with a steady velocity of $$0.5 \mathrm{~cm} \mathrm{~s}^{-1}$$ 45. The capacitance of a parallel plate capacitor is $$400 \mathrm{~pF}$$. It is connected to an ac source of $$100 \mathrm{ 46. Though $$\mathrm{Sn}$$ and $$\mathrm{Si}$$ are $$4^{\text {th }}$$ group elements, $$\mathrm{Sn}$$ is a metal while $$\m 47. Five charges, '$$q$$' each are placed at the comers of a regular pentagon of side '$$a$$' as shown in figure. First, cha 48. Two circular coils of radius '$$a$$' and '$$2 a$$' are placed coaxially at a distance ' $$x$$ and '$$2 x$$' respectively 49. A metallic rod of $$2 \mathrm{~m}$$ length is rotated with a frequency $$100 \mathrm{~Hz}$$ about an axis passing throug 50. The power of a gun which fires 120 bullet per minute with a velocity $$120 \mathrm{~ms}^{-1}$$ is : (given the mass of e 51. The width of the fringes obtained in the Young's double slit experiment is $$2.6 \mathrm{~mm}$$ when light of wave lengt 52. An electric bulb of volume $$300 \mathrm{~cm}^3$$ was sealed off during manufacture at a pressure of $$1 \mathrm{~mm}$$ 53. Find the binding energy of the tritium nucleus:
[Given: mass of $$1 \mathrm{H}^3=3.01605 \mathrm{~u} ; \mathrm{~m}_{\mat 54. In a single slit diffraction experiment, for slit width '$$\alpha$$' the width of the central maxima is '$$\beta$$'. If 55. Two charges '$$-q$$' each are fixed, separated by distance '$$2 d$$'. A third charge '$$q$$' of mass '$$m$$' placed at t 56. Two metal spheres, one of radius $$\frac{R}{2}$$ and the other of radius $$2 \mathrm{R}$$ respectively have the same sur 57. Find the value of '$$n$$' in the given equation $$P=\rho^n v^2$$ where '$$P$$' is the pressure, '$$\rho$$' density and ' 58. A stone of mass $$2 \mathrm{~kg}$$ is hung from the ceiling of the room using two strings. If the strings make an angle 59. A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as 60. If the ratio of lengths, radii and Young's Moduli of steel and brass wires in the figure are $$\mathrm{a}, \mathrm{b}$$
1
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $$f(x)=2 x^3+9 x^2+\lambda x+20$$ is a decreasing function of $$x$$ in the largest possible interval $$(-2,-1)$$, then $$\lambda$$ is equal to
A
$$-12$$
B
$$-6$$
C
$$12$$
D
$$6$$
2
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$\int \sqrt{x^2-4 x+2} d x=$$
A
$$
\frac{1}{2}(x-2) \sqrt{x^2-4 x+2}+\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C
$$
B
$$
(x-2) \sqrt{x^2-4 x+2}+\frac{1}{2} \log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C
$$
C
$$
\frac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\sin ^{-1} \frac{x-2}{\sqrt{2}}+C
$$
D
$$
\frac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C
$$
3
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$4\left(1+\cos \frac{\pi}{8}\right)\left(1+\cos \frac{3 \pi}{8}\right)\left(1+\cos \frac{5 \pi}{8}\right)\left(1+\cos \frac{7 \pi}{8}\right) \text { is equal to }$$
A
$$
\frac{1}{8}
$$
B
$$
\frac{1}{4}
$$
C
$$
\frac{1}{2}
$$
D
1
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The minimum value of $$Z=150 x+200 y$$ for the given constraints
$$\begin{aligned} & 3 x+5 y \geq 30 \\ & x+y \geq 8 ; x \geq 0, y \geq 0 \text { is } \end{aligned}$$
A
0
B
1600
C
1350
D
1200
Paper analysis
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60
Physics
60
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