Chemistry
1. On the basis of crystal field theory, electronic configuration of a low spin $$\mathrm{d}^4$$ complex is: 2. In the reaction,
$$2 \mathrm{~S}_2 \mathrm{O}_3^{2-}+\mathrm{I}_2 \rightarrow \mathrm{S}_4 \mathrm{O}_6^{2-}+2 \mathrm{ 3. An aqueous solution of glucose boils at $$100.01^{\circ} \mathrm{C}$$. The number of glucose molecules in a solution con 4. The molar conductivity of the complex $$\mathrm{CoCl}_3 \cdot 4 \mathrm{NH}_3 \cdot 2 \mathrm{H}_2 \mathrm{O}$$ is found 5. $$
\text { From the following pair of compounds, identify the incorrect pair in terms of the covalent character. }
$$ 6. Arrange the following compounds in the decreasing order of reactivity towards electrophilic substitution reaction.
(I) C 7. With reference to vitamins and its deficiency diseases, the correct statements are:
(i) Cheilosis is due to the deficien 8. Predict the final major product 'S' of the following reaction
9. $$\mathrm{S}_8$$ on heating at a temperature above $$1000 \mathrm{~K}$$, changes to $$\mathrm{S}_2$$. When 1 mole of $$\ 10. Which of the following compounds will show geometrical isomerism? 11. The major product '$$\mathrm{X}$$' of the following reaction is
12. The system that forms minimum boiling azeotrope is : 13. Among the following peptides, identify the pair where the name and its structure are correctly matched. 14. The temperature $$(\mathrm{T})$$ and rate constant $$(\mathrm{k})$$ for a first order reaction $$\mathrm{R} \rightarrow 15. Names of some organic compounds are given. Which one is not in IUPAC system? 16. When $$3.92 \mathrm{~g}$$ of Mohr salt is dissolved in $$100 \mathrm{~mL}$$ of water, and titrated against $$\mathrm{KMn 17. Among the following, which is not according to the property indicated against it? 18. Arrange the following in the order of increasing reactivity towards $$\mathrm{SN}_{\mathrm{2}}$$ reactions.
$$\begin{arr 19. When 0.1 mole of $$\mathrm{MnO}_4{ }^{2-}$$ is oxidised, the quantity of electricity required to completely oxidise $$\m 20. Choose the incorrect statement from the following. 21. The correct sequence of filling of electrons in $$n=6$$ is: 22. The metallic ions that have almost same spin only magnetic moment are :
(i) $$\mathrm{Co}^{2+}$$
(ii) $$\mathrm{Mn}^{2+} 23. In a set of reactions, bromoethane yielded a final product 'S'.
The compound 'S' should be 24. Which of the following tests may be used to distinguish between phenol and cyclohexanol? 25. Which of the following compounds undergo Aldol condensation followed by dehydration to give 3-phenylprop-2-en-1-al? 26. The $$\Delta \mathrm{H}_{(\mathrm{f})}^{\mathrm{o}}$$ of $$\mathrm{NO}_2(\mathrm{~g})$$ and $$\mathrm{N}_2 \mathrm{O}_4( 27. The bond dissociation enthalpy of the species in their correct order is: 28. Identify the incorrect statement among the following. 29. At Constant volume, the heat required to raise the temperature of $$4.48 \mathrm{~L}$$ of an ideal gas at STP by $$15^{\ 30. $$
1 \mathrm{~cm}^3 \text { of } 0.01 \mathrm{~M} \mathrm{~HCl} \text { is added to } 1 \mathrm{~L} \text { of } \mathrm 31. An organic compound with molecular formula $$\mathrm{C}_3 \mathrm{H}_5 \mathrm{N}$$ on hydrolysis gives compound '$$\mat 32. Which of the following carbanions is the least stable? 33. The correct order of increasing melting point is 34. A solution of $$\mathrm{KCl}(\mathrm{M}=74.5 \mathrm{~g} \mathrm{~mol}^{-1})$$ containing $$1.9 \mathrm{~g}$$ per $$100 35. $$\mathrm{Cu}^{+}$$ undergoes disproportionation, according to the equation,
$$
2 \mathrm{Cu}^{+} \rightleftharpoons \ma 36. Arrange the following amines in the decreasing order of their solubilities in water.
37. Consider the following reaction
$$(\mathrm{CH}_3)_2 \mathrm{CHCH}_2 \mathrm{Br}+(\mathrm{CH}_3)_3 \mathrm{CCH}_2 \mathrm 38. Arrange the following compounds in the decreasing order of their acidic strength.
(I) m-cresol
(II) Phenol
(III) m-amino 39. The ratio of the first three radii of Bohr's atom is: 40. Which of the following statement is not true about glucose? 41. The type of hybridisation and the spin only magnetic moment for the complex $$[\mathrm{Ni}(\mathrm{CO})_4]$$ are respect 42. Consider the following statements in respect of lanthanides, which of the statements are incorrect?
(i) $$\mathrm{La}(\m 43. Which of the following is not aromatic?
44. Among the following compounds, the most acidic is : 45. Given below a first order reaction in the gas phase
$$\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{B}(\mathrm{g})+\mathrm{ 46. Which of the following reactions is an example for incomplete combustion? 47. The $$\mathrm{E}^{\circ}$$ values of $$\mathrm{A} . \mathrm{B}$$ and $$\mathrm{C}$$ are given. Which element/(s) is/(are 48. 4-methyl benzamide (A) on reaction with ethanolic solution of $$\mathrm{KOH}$$ and bromine gives another compound (B). T 49. Which among the following compounds has the highest freezing point of its 1 molal aqueous solution? 50. For the reaction, $$\mathrm{A}+3 \mathrm{~B} \rightarrow 2 \mathrm{C}+\mathrm{D}$$, the concentration of $$\mathrm{A}$$ 51. The major product obtained in the following reaction is :
52. In the following question a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correc 53. In the following question a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correc 54. The rate of appearance of bromine is related to the disappearance of bromide ion in the equation given below is:
$$\math 55. When 1 mole of $$\mathrm{O}_2$$ and 1 mole of ammonia are made to react in the reaction,
$$4 \mathrm{NH}_3(\mathrm{~g}) 56. The limiting molar conductivity of $$\mathrm{NH}_4 \mathrm{OH}$$ is $$238 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ 57. The half-life for a zero order reaction is 58. Identify the oxidation reaction in which acidified $$\mathrm{KMnO}_4$$ is required 59. The correct option for free expansion of an ideal gas under adiabatic condition is: 60. Which of the following compound cannot be prepared by Williamson's synthesis?
Mathematics
1. P and Q are considering to apply for a job. The probability that P applies for the job is $$\frac{1}{4}$$. The probabili 2. $$
\text { The value of } \frac{i^{1004}+i^{1006}+i^{1008}+i^{1010}+i^{1012}}{i^{510}+i^{508}+i^{506}+i^{504}+i^{502}} \ 3. There are some baskets. The chances of picking a loaded basket and choosing a red coloured one is 0.2 . For every 100 tr 4. The sum of first three terms of a geometric progression is 16 and the sum of next three terms is 128 . The sum to $$\mat 5. $$
\text { The general solution of the differential equation } \frac{d y}{d x}=\frac{x y}{x^2+y^2} \text { is }
$$ 6. The points on the ellipse $$16 x^2+9 y^2=400$$ at which the ordinate decreases at the same rate at which the abscissa in 7. $$
\text { If } a \mathcal{N}=\{a x: x \in \mathcal{N}\} \text {, then } 3 \mathcal{N} \cap 7 \mathcal{N} \text { is }
$ 8. $$
\int \frac{f^{\prime}(x)}{f(x) \log (f(x))} d x \text { is equal to }
$$ 9. $$
\text { The maximum value of } Z=3 x+4 y \text { for the given constraints } x+2 y \leq 76,2 x+y \leq 104, x \geq 0, 10. If the line $$\frac{1-x}{-3}=y=\frac{z+2}{2}$$ is perpendicular to the line $$\frac{3 x-1}{2 b}=3-y=\frac{z-1}{a}$$, the 11. The probability of inviting three friends on 5 consecutive days, exactly one friend a day and no friend is invited on mo 12. $$
\lim _\limits{x \rightarrow 0} \frac{a^x-b^x}{c^x-d^x}=
$$ 13. $$
\text { If } f(x)=\frac{a \sin x+b \cos x}{c \sin x+d \cos x} \text { is decreasing for all } x \text {, then }
$$ 14. $$
\int_\limits0^{\frac{\pi}{2}} \frac{\cos x}{1+\cos x+\sin x} d x=
$$ 15. The inequality $$4 x-3 \geq \frac{10 x-1}{3}$$ represents which of the following interval when $$x \in R$$ 16. If the distance between the foci and the distance between the two directrixes are in the ratio $$3: 2$$ for a hyperbola 17. $$
\text { If } \frac{x}{\cos \theta}=\frac{y}{\cos \left(\theta+\frac{2 \pi}{3}\right)}=\frac{z}{\cos \left(\theta-\fra 18. $$
\frac{\cos 9^{\circ}+\sin 9^{\circ}}{\cos 9^{\circ}-\sin 9^{\circ}}=
$$ 19. $$
\text { The function } y=\tan x-x \text { is }
$$ 20. If the sum of the coefficients of the first three terms in the expansion of $$\left(x-\frac{a}{x^2}\right)^{12}, x \neq 21. Evaluate :
$$ \operatorname{cosec}^{-1}\left(-\frac{2 \sqrt{3}}{3}\right)+\tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right)+\s 22. $$
\text { Integrating factor of the differential equation } \frac{d y}{d x}+y=\frac{x^3+y}{x} \text { is }
$$ 23. Let $$\mathrm{ABC}$$ be a triangle with equations of its sides $$\mathrm{AB}, \mathrm{BC}$$. $$\mathrm{CA}$$ respectivel 24. $$
\text { If } y=\sin ^{-1}(\sqrt{\sin x}) \text {, then } \frac{d y}{d x} \text { equals }
$$ 25. Let a, b, c be three vector such that $$a \neq 0$$ and $$\vec{a} \times \vec{b}=2 \vec{a} \times \vec{c},|a|=|c|=1,|b|=4 26. $$\text { Which of the following function is injective? }$$ 27. $$
\int_\limits{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sqrt{\cos x-\cos ^3 x} d x \text { is equal to }
$$ 28. $$
\int \log x(\log x+2) d x \text { equals to }
$$ 29. $$
\text { If } A=\left[\begin{array}{cc}
1 & -2 \\
4 & 5
\end{array}\right] \text { and } f(t)=t^2-3 t+7 \text { then } 30. A and B are two independent events. The probability of their simultaneous occurrence is $$\frac{1}{8}$$ and the probabil 31. A determinant of the second order is made with elements 0 and 1 . What is the probability that the determinant made is n 32. $$
\text { If } x^2+y^2=t+\frac{1}{t} \text { and } x^4+y^4=t^2+\frac{1}{t^2} \text { then } \frac{d y}{d x}=
$$ 33. The lines
$$\vec{r}=(2 \hat{\jmath}-3 \hat{k})+\lambda(\hat{\imath}+2 \hat{\jmath}+3 \hat{k})$$ and $$\vec{r}=(2 \hat{\i 34. $$
\text { If } \alpha=\tan ^{-1}\left(\tan \frac{5 \pi}{4}\right) \text { and } \beta=\tan ^{-1}\left(-\tan \frac{2 \pi 35. A line makes the same angle $$\theta$$ with each of the $$x$$ and $$z$$-axes. If the angle $$\beta$$, which it makes wit 36. $$
\text { The number of points of discontinuity of the rational function } f(x)=\frac{x^2-3 x+2}{4 x-x^3}
$$ 37. $$
\text { The value of } \lim _\limits{x \rightarrow 0} \frac{\sin (a+x)-\sin (a-x)}{x} \text { is }
$$ 38. If $$f(x)=\log x+b x^2+a x, x \neq 0$$ has extreme values (or turning points) at $$x=-1$$ and $$x=2$$ then the values of 39. $$
\left|\begin{array}{ccc}
\cos (\alpha+\beta) & -\sin (\alpha+\beta) & \cos 2 \beta \\
\sin \alpha & \cos \alpha & \si 40. The area of the region (in sq units) bounded by the curve $$
y=\sqrt{16-x^2} \text { and } x \text {-axis is }
$$ 41. $$
\text { Let } \mathrm{A} \text { and } \mathrm{B} \text { be two sets then } A-(A \cap B) \text { is equal to }
$$ 42. The sum of four numbers in a geometric progression is 60 , and the arithmetic mean of the first and the last number is 1 43. The number of four digit numbers strictly greater than 4321 formed using the digits $$0,1,2,3,4,5$$ with repetition of d 44. Let 'P' be the mean deviation of the first five odd natural numbers about their mean and 'Q' be the mean deviation of th 45. A relation $$R$$ is defined from $$\{2,3,4\}$$ to $$\{3,6,7,10\}$$. If $$x R y \Leftrightarrow x$$ and $$y$$ are co prim 46. $$
\text { The general solution of } \frac{d y}{d x}=\sin ^{-1} x \text { is }
$$ 47. For what value of $$\mathrm{a}$$ and $$\mathrm{b}$$ the intercepts cut off on the co-ordinate axes by the line $$a x-b y 48. $$
\text { If A }(\operatorname{adj} A)=5 I \text {, where I is the identity matrix of order } 3 \text {, then }|\operat 49. A student has 3 library cards and 8 books of his interest in the library. Out of these 8 books he does not want to borro 50. The dimensions of the largest rectangle of side $$x$$ and $$y$$ that can be inscribed in the right angled triangle of si 51. $$
\text { The angle between } \hat{\imath}-\hat{\jmath} ~\&~ \hat{\jmath}-\hat{k} \text { is }
$$ 52. If $$(x-a)^2+(y-b)^2=c^2$$, where $$\mathrm{a}, \mathrm{b}, \mathrm{c}$$ are some constants, $$c>0$$ then $$\frac{\left[ 53. $$
\text { A square matrix } P \text { satisfies } P^2=I-P \text { where } I \text { is identity matrix. If } P^n=5 I-8 54. $$
\text { If } 6^{\text {th }} \text { term of a geometric progression is }-\frac{1}{32} \text { and } 9^{\text {th }} 55. $$
\left(\cos \frac{\pi}{12}-\sin \frac{\pi}{12}\right)\left(\tan \frac{\pi}{12}+\cot \frac{\pi}{12}\right)=
$$ 56. $$
\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x \text { is equal to }
$$ 57. If $$A=\left[\begin{array}{lll}5 & 0 & 4 \\ 2 & 3 & 2 \\ 1 & 2 & 1\end{array}\right] \quad B^{-1}=\left[\begin{array}{ll 58. Degree of the differential equation $$\log \left(\frac{d y}{d x}\right)^{\frac{1}{2}}=5 x+4 y$$ is 59. $$
\text { The area of the region (in square units) bounded by the line } y+3=x ; x=1 \text { and } x=5 \text { is }
$$ 60. If an ellipse has an equation in the standard form and it passes through the points $$\left(\frac{5}{2}, \frac{\sqrt{6}}
Physics
1. A transformer has 400 turns in its primary winding and 800 turns in its secondary winding. The primary voltage is $$20 \ 2. An object is placed at a distance of $$12 \mathrm{~cm}$$ from a convex lens on its principal axis and a virtual image of 3. The graph of an object moving with speed v for a time t is shown below.
The graph that shows the distance s travelled b 4. An object of mass $$1 \mathrm{~kg}$$ is allowed to hang tangentially from the rim of the wheel of radius R. When release 5. A planet has double the mass of the earth and double the radius. The gravitational potential at the surface of the Earth 6. A tuning fork of unknown frequency produces 4 beats with tuning fork of frequency $$310 \mathrm{~Hz}$$. It gives the sam 7. A wire ' 1 ' $$\mathrm{cm}$$ long bent into a circular loop is placed perpendicular to the magnetic field of flux densit 8. An iron piece of mass $$200 \mathrm{~g}$$ is kept inside a furnace for some time and then put in a calorimeter of water 9. A slit of width $$10 \times 10^{-7} \mathrm{~m}$$ is illuminated by light of wavelength $$500 \mathrm{~nm}$$. Angular po 10. An ideal gas changes its state from $$\mathrm{A}$$ to $$\mathrm{C}$$ in two different paths $$\mathrm{ABC}$$ and $$\math 11. If pressure of an ideal gas is increased by keeping temperature constant the kinetic energy will 12. In Young's double slit experiment the ratio of phase difference between light waves reaching the third bright fringe and 13. An electromagnetic wave of frequency $$3 \mathrm{~MHz}$$ passes from vacuum into a dielectric medium $$(\mu_r=1)$$ of re 14. A group of devices having a total power rating of 500 watt is supplied by an $$\mathrm{AC}$$ voltage $$E=200 \sin \left( 15. $$
\text { In a p-n junction, the depletion layer of thickness } 1 \mu \mathrm{m} \text { has } 0.05 \mathrm{~V} \text { 16. A long horizontal wire $$\mathrm{P}$$ carries current of $$50 \mathrm{~A}$$ from left to right. It is rigidly fixed. Ano 17. A record player is spinning at an angular velocity of $$45 \mathrm{~rpm}$$ just before it is turned off. It then deceler 18. The resistance of a wire at room temperature $$20^{\circ} \mathrm{C}$$ is found to be $$10 \Omega$$. If resistance of th 19. The potential difference between the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ of the arrangement shown in figure is
20. If units of mass, length and gravitational constant are chosen to fundamental units, the dimensions of time would be 21. An electric motor raises a mass of $$1.5 \mathrm{~kg}$$, a distance of $$1.128 \mathrm{~m}$$ in time of $$4.79 \mathrm{~ 22. An electron starting from rest and moving with the velocity $$\mathrm{v}$$ through a potential difference $$\mathrm{V}$$ 23. In an inductor of self-inductance $$2 \mathrm{~mH}$$, current changes with time (in sec) according to the relation, $$I= 24. A tiny ball of mass $$\mathrm{m}$$ and charge $$\mathrm{q}$$ is suspended from the fixed support using an insulating str 25. To a fish under water, viewing obliquely, a fisherman standing on the bank of a lake looks 26. A cube bar slides thrice the time with friction than that without friction when it slides on an inclined plane of inclin 27. The magnetic susceptibility of an ideal diamagnetic substance is 28. Water flows from a tap with steady flow, through a cross sectional area of $$10^{-3} \mathrm{~m}^2$$ with a speed of $$0 29. The mobility of the charge carriers increases with 30. Two balls are thrown horizontally, one from the window of first floor which is $$3 \mathrm{~m}$$ high from the ground an 31. In intrinsic semiconductors at room temperature, number of electrons and holes are 32. Figure shows three arrangements of electric field lines. In each arrangement, a proton is released from rest at point $$ 33. A nucleus with mass number 190 initially at rest emits an alpha particle. If the $$\mathrm{Q}$$ value of the reaction is 34. In a container of height $$21 \mathrm{~cm}$$, certain transparent liquid is taken to a height of $$12 \mathrm{~cm}$$. Wh 35. A man standing in a truck moving with constant velocity throws a ball vertically into air, ball falls 36. A charge of $$+1 \mathrm{C}$$ is moving with velocity $$\vec{V}=(2 \mathrm{i}+2 \mathrm{j}-\mathrm{k}) \mathrm{ms}^{-1}$ 37. Modulus of rigidity of an incompressible liquid is 38. In a hydrogen atom, if electron is replaced by a particle which is 40 times heavier but has the same charge, then, the r 39. An AC voltage source of variable angular frequency $$\omega$$ and fixed amplitude $$\mathrm{V}_0$$ is connected in serie 40. 3 point charges each of $$-\mathrm{q}$$ are placed on the circumference of a circle of diameter $$2 \mathrm{a}$$ at $$\m 41. To increase the current sensitivity of a moving coil galvanometer by $$25 \%$$, its resistance is increased so that the 42. A uniformly charged solid sphere of radius $$\mathrm{R}$$ has potential $$\mathrm{V}_0$$ (measured with respect to infin 43. Energy required for moving a body of mass $$\mathrm{m}$$ from a circular orbit of radius 3R to a higher orbit of radius 44. The shortest wavelengths of Paschen, Lymen and Balmer series are in the ratio 45. Two identical moving coil galvanometers have $$10 \Omega$$ resistance and full-scale deflection at $$2 \mu \mathrm{A}$$ 46. The velocity of an electron so that its momentum is equal to that of a photon of wavelength $$660 \mathrm{~nm}$$ is 47. A wire of uniform cross section and resistance 4 ohms is bent in the shape of square ABCD. Point A is connected to a poi 48. The percentage increase in magnetic field $$\mathrm{B}$$ when the space within a current carrying solenoid is filled wit 49. A storage battery of emf $$28.0 \mathrm{~V}$$ and internal resistance $$0.5 \Omega$$ is being charged by a $$140 \mathrm 50. A metallic rod of length '$$a$$' is rotated with an angular frequency of $$0.2 \mathrm{~rads}^{-1}$$ about an axis norma 51. A semiconductor $$\mathrm{X}$$ is made by doping silicon with phosphorous. A second semiconductor $$\mathrm{Y}$$ is made 52. If $$\alpha, \beta$$ and $$\gamma$$ are the angles between the vectors $$\overrightarrow{\mathrm{P}}, \overrightarrow{\m 53. In Young's double slit experiment, the ratio of intensities of light from one slit to the other is $$9: 1$$. If Im is th 54. In Young's double slit experiment, the intensity of light at a point on the screen where the path difference is $$\lambd 55. $$\mathrm{K}_1$$ and $$\mathrm{K}_2$$ are maximum kinetic energies of photoelectrons emitted when lights of wavelength $ 56. An object of mass $$3 \mathrm{~kg}$$ moves due to an applied constant force such that its position along $$\mathrm{X}$$ 57. The radius of a nucleus as measured by electron scattering is $$4.8 \mathrm{~fm}$$. The mass number of nucleus is most l 58. Light enters at an angle of incidence in a transparent rod of refractive index '$$n$$'. The least value of '$$n$$' for w 59. A cubical box of side $$2 \mathrm{~m}$$ contains helium gas. It was observed that in a time of 1 second, an atom travell 60. A circular disc of mass $$20 \mathrm{~kg}$$, having radius $$10 \mathrm{~cm}$$ is suspended by a wire attached to its ce
1
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
A circular disc of mass $$20 \mathrm{~kg}$$, having radius $$10 \mathrm{~cm}$$ is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The time period of torsional oscillations is found to be $$1 \mathrm{~s}$$. The torsional spring constant of the wire is
A
$$6 \mathrm{~N~m} \mathrm{~rad}^{-1}$$
B
$$9.86 \mathrm{~N~m} \mathrm{~rad}^{-1}$$
C
$$3.94 \mathrm{~N~m} \mathrm{~rad}^{-1}$$
D
$$1.264 \mathrm{~N~m} \mathrm{~rad}^{-1}$$
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