Chemistry
1. The chemical formula of Lucas reagent is 2. Alkyl halides undergoing SN2 reaction do inverse 3. X and Y in the following reactions are
4. For the reaction, H$$_2$$(g) + I$$_2$$(g) $$\rightleftharpoons$$ 2HI(g) the position of equilibrium can be shifted to th 5. Which of the following are not path functions?
I. H $$-$$ TS
II. W
III. q
IV. q + W 6. The system that forms maximum boiling azeotropes is 7. KMnO$$_4$$ acts as an oxidising agent in acidic medium. The number of moles of KMnO$$_4$$ that will be required to react 8. What can be A and B in the following reaction?
9. Which of the following is a false statement? 10. Which of the following molecules does not exhibit dipole moment?
(i) CCl$$_4$$ (ii) CO$$_2$$ (iii) NH$$_3$$ (iv) CHCl$$_ 11. Which of the following is highly basic? 12. The relation between work done in reversible and irreversible process is 13. What is the function platelets? 14. The monosaccharides of maltose is 15. Which of the following does not affect solubility of a gas in liquid? 16. A newly prepared radioactive nuclide has a decay constant of 6.93 s$$^{-1}$$. What is the half-life of the nuclide? 17. The essential amino acids are
(i) Leucine (ii) Glutamic acid (iii) Asparagine (iv) Valine
correct option is 18. Increasing order of bond order of oxygen and its ions is 19. Minimum number of nodes are present in 20. pH of 10$$^{-3}$$ M solution of KOH is 21. Which of the product is not possible in Wurtz reaction? 22. On treatment of glucose with bromine water the product formed is 23. Which among the following forms minimum boiling azeotropes?
(i) Heptane + Octane
(ii) Water + Nitric acid
(iii) Ethanol 24. Which of the following statement is incorrect about activation energy? 25. The P-O bond order in PO$$_4^{3-}$$ is 26. $$\mathrm{O^{2-},F^-,Mg^{2+},Al^{3+},O_2,F_2}$$. How many of the species given above isoelectronic? 27. The equilibrium constant, $$K_C$$ for $$3C_2H_2(g) \rightleftharpoons C_6H_6(g)$$ is 4 L$$^2$$mol$$^{-2}$$. If the equil 28. Identify the product formed in the given reaction.
29. Which of the following gas readily de-colourises the acidified KMnO$$_4$$ solution? 30. What will be the emf of the following cell at 25$$^\circ$$C?
Fe/Fe$$^{2+}$$ (0.001 M) | | H$$^+$$ (0.01 M) | H$$_2$$(g) 31. Which of the following vitamin is responsible for Beri-Beri disease? 32. Find the product formed for the given reaction.
$$\mathrm{{C_6}{H_5}CHO + {H_3}C - C{H_2} - CHO\buildrel {Dil.\,NaOH/\De 33. In which of the following changes, entropy decreases? 34. Which among the following will not liberate nitrogen on reaction with nitrous acid? 35. The complex which does not show optical isomerism is 36. The solution which have lowest freezing point is 37. Calculate the molar conductance of 0.025 M aqueous solution of calcium chloride at 25$$^\circ$$C. The specific conductan 38. For the reaction 2N$$_2$$O$$_5$$ $$\to$$ 4NO$$_2$$ + O$$_2$$.
If initial pressure is 100 atm and rate constant $$k$$ is 39. The difference between heat capacity at constant pressure and heat capacity at constant volume is 40. Which of the following compound does not exists? 41. The major product in the given reaction is
42. The spectrum of He$$^+$$ is similar to 43. The Paschen series of hydrogen spectrum lies in which region? 44. The oxidation state of nickel in [Ni(CO$$_4$$)] is
Mathematics
1. The value of $${3^{{{\log }_4}5}} - {5^{{{\log }_4}3}}$$ is 2. If the tangent to the curve $$xy + ax + by = 0$$ at (1, 1) is inclined at an angle $${\tan ^{ - 1}}2$$ with X-axis, then 3. If $$\mathop {\lim }\limits_{x \to 0} {{(1 + {a^3}) + 8{e^{1/x}}} \over {1 + (1 - {b^3}){e^{1/x}}}} = 2$$, then 4. If two circles $${(x - 1)^2} + {(y - 3)^2} = {r^2}$$ and $${x^2} + {y^2} - 8x + 2y + 8 = 0$$ intersect in two distinct p 5. The approximate value of $$(0.007)^{1/3}$$ is 6. the circle $${x^2} + {y^2} + 4x - 7y + 12 = 0$$ cuts an intercept on Y-axis of length 7. Let $$f(x) = a - {(x - 3)^{8/9}}$$, then maxima of $$f(x)$$ is 8. If the derivative of the function $$f(x) = \left\{ {\matrix{
{b{x^2} + ax + 4;} & {x \ge - 1} \cr
{a{x^2} + b;} 9. If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$$, then 10. $$S\equiv x^2+y^2+2x+3y+1=0$$ and $$S'\equiv x^2+y^2+4x+3y+2=0$$ are two circles. The point $$(-3,-2)$$ lies 11. The probability of choosing randomly a number c from the set {1, 2, 3, ... 9} such that the quadratic equation $$x^2+4x+ 12. Shade the feasible region for the inequations $$6x+4y\le120, 3x+10y\le180,x,y\ge0$$ in a rough figure. 13. The maximum of Z is where, $$Z=4x+2y$$ subject to constraints $$4x+2y\ge46,x+3y\le24$$ and $$x,y\ge0$$ is 14. If for any 2 $$\times$$ 2 square matrix A,
A (adj A) = $$\left[ {\matrix{
8 & 0 \cr
0 & 8 \cr
} } \right]$$, 15. If $$A = \left[ {\matrix{
a & 0 & 0 \cr
0 & a & 0 \cr
0 & 0 & a \cr
} } \right]$$, then $$|A||adj\,A|$$ 16. If $$A = \left[ {\matrix{
{2 - k} & 2 \cr
1 & {3 - k} \cr
} } \right]$$ is a singular matrix, then the value 17. If $$\theta$$ be the angle between the vectors $$a = 2\widehat i + 2\widehat j - \widehat k$$ and $$b = 6\widehat i - 3\ 18. If x, y and z are non-zero real numbers and $$a = x\widehat i + 2\widehat j,b = y\widehat j + 3\widehat k$$ and $$c = x\ 19. Maximum value of $$z=12x+3y$$, subject to constraints $$x\ge0,y\ge0,x+y\ge5$$ and $$3x+y\le9$$ is 20. If $$\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}$$ and $$\mathbf{r}=\hat{i}+\hat{k}$$, then the unit vector 21. The line $$\frac{x-3}{4}=\frac{y-4}{5}=\frac{z-5}{6}$$ is parallel to the plane 22. $$\int \frac{1}{x \sqrt{a x-x^2}} d x$$ is 23. $$\int \frac{3^x}{\sqrt{1-9^x}} d x$$ is equal to 24. $$\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\cos x\,dx} $$ 25. The angle between the lines $${{x + 4} \over 3} = {{y - 1} \over 5} = {{z + 3} \over 4}$$ and $${{x + 1} \over 1} = {{y 26. The point of intersection of the lines $${{x - 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}$$ and $${{x -5} \over 27. Five persons A, B, C, D and E are in queue of a shop. The probability that A and B are always together is 28. If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B 29. Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability that they form 30. If A, B and C are three mutually exclusive and exhaustive events such that P(A) = 2P(B) = 3P(C). What is P(B)? 31. If $$U_{n+1}=3 U_n-2 U_{n-1}$$ and $$U_0=2, U_1=3$$, then $$U_n$$ is equal to 32. If $$4^n+15n+P$$ is divisible by 9 for all $$n\in N$$, then the least negative integral value of P is 33. $$(2^{3n}-1)$$ is divisible by 34. If $$S = {{{2^2} - 1} \over 2} + {{{3^2} - 2} \over 6} + {{{4^2} - 3} \over {12}}\, + \,...$$ upto 10 terms, then S is e 35. $$\sum\limits_{n = 1}^m {n\,.\,n!} $$ is equal to 36. The first and fifth terms of an A.P. are $$-14$$ and 2 respectively and the sum of its n terms is 40. The value of n is 37. The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ represents 38. The solution of the differential equation $$\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0$$ is 39. The solution of the differential equation $$x \frac{d y}{d x}=\cot y$$ is 40. If nC3 = 220, then n = ? 41. A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is corre 42. If $$\sin A+\sin B=a$$ and $$\cos A+\cos B=b$$, then $$\cos (A+B)$$ equals? 43. What is $${{\cos \theta } \over {1 - \tan \theta }} + {{\sin \theta } \over {1 - \cot \theta }}$$ equal to? 44. Find the general solution of $$\sin 2x + \cos x = 0$$. 45. If $$f(x)+2f(1-x)=x^2+5,\forall$$ real values of $$x$$, then $$f(x)$$ is given by 46. If $$A=\{3,5,7\}$$ and $$B=\{1,2,3,5\}$$, then $$A \times B \cap B \times A$$ is equal to 47. Total number of elements in the power set of A containing 17 elements is 48. The argument of $${{1 - i\sqrt 3 } \over {1 + i\sqrt 3 }}$$ is 49. Evaluate $${\left[ {{i^{22}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}$$ 50. $${(i + \sqrt 3 )^{100}} + {(i - \sqrt 3 )^{100}} + {2^{100}}$$ is equal to 51. There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any 52. A regular polygon of n sides has 170 diagonals, then n is equal to 53. Let the equation of the pair of lines $$y=p x$$ and $$y=q x$$ can be written as $$(y-p x)(y-q x)=0$$. Then the equation 54. The distance of the point $$(1,2)$$ from the line $$x+y+2=0$$ measured along the line parallel to $$2 x-y=5$$ is equal t 55. The slope of lines which makes an angle 45$$^\circ$$ with the line $$2x-y=-7$$ 56. If 2 and 3 are intercepts of a line L = 0, then the distance of L $$\equiv$$ 0 from the origin is 57. The total number of terms in the expansion of $${(x + y)^{100}} + {(x - y)^{100}}$$ is 58. The coefficient of $${x^{20}}$$ in the expansion of $${(1 + 3x + 3{x^2} + {x^3})^{20}}$$ is 59. In the expansion of $${(1 - 3x + 3{x^2} - {x^3})^{2n}}$$, the middle term is 60. How many 5-digit numbers greater than 50,000 can be formed using the digits 1, 2, 3, 4, 5 without repetition?
Physics
1. During the phenomenon of resonance 2. If the earth were to spin faster, acceleration due to gravity at the poles 3. If heat engine is filled at temperature 27$$^\circ$$C and heat of 100 k cal is taken from source at temperature 677$$^\c 4. During $$\alpha$$-decay, atomic mass of parent nuclei is 5. A point object is placed on the optic axis of a convex lens of focal length $$f$$ at a distance of $$2f$$ to the left of 6. For CE transistor amplifier, the audio signal voltage across the collector resistance of 4 k$$\Omega$$ is 5 V. If the cu 7. From the following p-V diagram, an ideal gas undergoing a change of state from A to B. Four different processes I, II, I 8. A copper and a steel wire of same diameter are connected end to end. A deforming force F$$_1$$ is applied to the wire wh 9. If kinetic energy of a body is increased by 300%, then percentage change in momentum will be 10. Which of the following diagram represents the variation of the electric field with distance r from the centre of a unifo 11. A DC ammeter and a hot wire ammeter are connected to a circuit in series. When a direct current is passed through circui 12. A bullet of mass $m$ hits a mass $$M$$ and gets embedded in it. If the block rises to a height $$h$$ as a result of this 13. A particle of mass $$m$$ is moving in a horizontal circle of radius $$r$$ under a centripetal force given by $$\left(\fr 14. The height at which the acceleration due to gravity becomes $$\frac{g}{16}$$ (where, g = acceleration due to gravity on 15. Which of the following series spectrum of hydrogen atom lies in ultraviolet region? 16. Speed of electromagnetic wave in a medium having relative permittivity $$\varepsilon_r$$ and relative permeability $$\mu 17. The wavelength of the second line of Balmer series is 486.4 nm. What is the wavelength of the first line of Lyman series 18. A bat emitting an ultrasonic wave of frequency 4.5 $$\times$$ 104 Hz at speed of 6 m/s between two parallel walls. The t 19. A disc of moment of inertia 4 kg - m$$^2$$ revolving with 16 rad/s is placed on another disc of moment of inertia 8 kg - 20. An electric current $I$ enters and leaves a uniform circular wire of radius $r$ through diametrically opposite points. A 21. Television frequencies are of the order of 100 MHz, while radio frequencies are of the order of 1 MHz. Using these as ty 22. A particle is performing simple harmonic motion. Equation of its motion is $$x = 5\sin \left( {4t - {\pi \over 6}} \rig 23. A raft of density 600 g/m$$^3$$ and mass 120 kg floats in water. How much weight can be put on the raft to make it just 24. The displacement $$x$$ of a particle in a straight line motion is given by $$x=1-t-t^2$$. The correct representation of 25. A galvanometer having a resistance of 4 $$\Omega$$ is shunted by a wire of resistance 2 $$\Omega$$. If the total current 26. In Young's double slit experiment, the two slits are separated by 0.2 mm and they are 1 m from the screen. The wavelengt 27. A series L-C-R circuit is connected to an AC source of 220 V and 50 Hz shown in figure. If the readings of the three vol 28. A regular hexagon of side $$m$$ which is a wire of length 24 m is coiled on that hexagon. If current in hexagon is $$I$$ 29. Which of the following gate give the similar output as the output of circuit diagram shown in the figure?
30. Water is poured in a tank through a cylindrical tube of area of cross-section A and ejecting water at a constant speed 4 31. If R and C denote resistance and capacitance of a material, then the dimension of CR will be : 32. An ideal gas is taken through the cycle A $$\to$$ B $$\to$$ C $$\to$$ A, as shown in the figure. If the net heat supplie 33. From a circular disc of radius R, a square is cut out with a radius as its diagonal. The centre of mass of remaining por 34. A bar magnet of length $$6 \mathrm{~cm}$$, is placed in the magnetic meridian with $$N$$ pole, pointing towards the geog 35. A force F applied on the wire of radius r and length L and change in the length of the wire is $$l$$. If the same force 36. A 30 mW laser beam has a cross-sectional area of 15 mm2. The magnitude of the maximum electric field in this electromagn 37. The average kinetic energy of a molecule in air at room temperature of 20$$^\circ$$C 38. Two guns P and Q can fire bullets at speeds 2 km/s and 4 km/s, respectively. From a point on a horizontal ground, they a 39. A cell of emf 2 V is connected with a load of resistance 1.5 $$\Omega$$. The power delivered by the cell to the load is 40. A plane glass mirror of thickness 3 cm of material of $$\mu=\frac{3}{2}$$ is silvered on the black surface. When a point 41. Ultraviolet light of wavelength 99 mm falls on a metal plate of work function 1.0 eV. If the mass of the electron is 9.1 42. In Young's double slit experiment, the fringe width is found to be 0.4 mm. If the whole apparatus is immersed in a liqui 43. There are two identical containers C$$_1$$ and C$$_2$$ containing to identical gases. Gas in C$$_1$$ is reduced to half 44. If K$$_1$$ and K$$_2$$ are maximum kinetic energies of photoelectrons emitted when lights of wavelengths $$\lambda_1$$ a 45. A car is moving with a speed of 54 km/h. If after 3 s, the driver applies brakes and it stops, then how much distance is 46. A source of sound emits sound waves at frequency $$f_0$$. It is moving towards an observer with fixed speed $${v_s}$$ ($ 47. In which mode of transmission, the heat waves travel along straight line with the speed of light? 48. The escape velocity of a projectile on the earth's surface is 11.2 km/s. A body is projected out with thrice this speed. 49. Consider a compound slab consisting of two different materials having equal lengths, thickness and thermal conductivitie 50. A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the 51. With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $$\frac{2}{3}$$ of 52. The string of length 2 m is fixed at both ends. If the string vibrates in its fourth normal mode with a frequency of 500 53. An alternating voltage = 200 $$\sin 100t$$ is applied to a series combination of $$R=30\Omega$$ and an inductor of 400 m 54. In the network shown in figure, the equivalent capacitance between points P and Q is
55. The resultant of two forces acting at an angle of 120$$^\circ$$ is 10 kg-W and is perpendicular to one of the forces. Th 56. Choose the incorrect statements. 57. Charge on electron is 58. Two charged spheres of $$-20\mu$$C and $$60\mu$$C are kept at a certain distance. They are touched and kept again at the 59. The AC voltage across a resistance can be measured using a
1
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0
The argument of $${{1 - i\sqrt 3 } \over {1 + i\sqrt 3 }}$$ is
A
$${\pi \over 3}$$
B
$${{2\pi } \over 3}$$
C
$${{4\pi } \over 3}$$
D
$${{ - 2\pi } \over 3}$$
2
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0
Evaluate $${\left[ {{i^{22}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}$$
A
$$4 - (i - 1)$$
B
$$2 - 7i$$
C
$$i - 1$$
D
$$2(1 - i)$$
3
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0
$${(i + \sqrt 3 )^{100}} + {(i - \sqrt 3 )^{100}} + {2^{100}}$$ is equal to
A
0
B
1
C
$$-$$1
D
2101
4
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0
There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?
A
60
B
64
C
72
D
84
Paper analysis
Total Questions
Chemistry
44
Mathematics
60
Physics
59
COMEDK
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