Chemistry
1. When the expansion of a gas occurs in vacuum and at constant volume, then 2. Carbon monoxide is poisonous to human beings because 3. Which one of the following sets of monosaccharides forms sucrose? 4. Under which of the following condition, the gases does not follow Henry's law? 5. An aqueous solution of X on addition of hydrogen peroxide in ice cold conditions gives blue colour to the ethereal layer 6. Determine the specific rate constant of the reaction. If the half-life period of a first order reaction is 1402 s. 7. Which of the following amino acid (NH$$_2$$CHRCOOH) contains polar R group? 8. Find the correct order of C$$-$$O bond length among CO, CO$$_3^{2-}$$, CO$$_2$$. 9. The total number of nodes are given by 10. In the equilibrium, $$AB\rightleftharpoons A+B$$, if the equilibrium concentration of A is double, then equilibrium conc 11. The reaction $$\mathrm{ArN_2^ + C{l^ - }\buildrel {Cu/HCl} \over
\longrightarrow ArCl + {N_2} + CuCl}$$ is called as 12. In 3d-transmission series, which one has the least melting point? 13. Among the following enzymes, which one is involved in the given below catalytic reaction?
$${C_6}{H_{12}}{O_6}(aq) \to 2 14. Which of the following is correct mixture of azeotrope? 15. Rate constant (K) of a reaction has least value at 16. Arrange stability of the given carbon cation in decreasing order
17. Which of the following pairs of ions in iso-electronic and iso-structural? 18. For the equilibrium,
2NOCl(g) $$\rightleftharpoons$$ 2NO(g) + Cl$$_2$$(g),
the value of the equilibrium constant, $$K_C$ 19. Coupling reaction is an example of 20. The oxidation number of Cr in CrO$$_5$$ which has the following structure, is
21. Given that molar conductances for Ba(OH)$$_2$$, BaCl$$_2$$ and NH$$_4$$Cl are 523.28, 280.0 and 129.8 $$\Omega^{-1}$$ cm 22. Xerophthalmia disease causes by which deficiency of vitamin? 23. Find the final product for the reaction
24. The chemical formula of Hinsberg's reagent is 25. The increasing order of atomic radii of the following group 13 elements is 26. The hydrocarbon that cannot be prepared effectively by Wurtz reaction 27. Reaction
find the product B. 28. Why, ketones and carboxylic acids have higher boiling point as compared to aldehydes? 29. In the chemical reaction,
N$$_2$$ + 3H$$_2$$ $$\rightleftharpoons$$ 2NH$$_3$$ at equilibrium point. 30. The change in the energy of system if 500 cal of heat energy are added to a system and system does 350 cal of work on th 31. Which of the following is most stable? 32. Which type of ligand is EDTA? 33. Which of the following is correct order of their increasing boiling points? 34. The specific conductivity of a solution containing 1.0 g of anhydrous BaCl$$_2$$ in 200 cm$$^3$$ of the solution has bee 35. For the reaction 2N$$_2$$O$$_5$$ $$\to$$ 4NO$$_2$$ + O$$_2$$, rate constant $$k$$ is 4.48 $$\times$$ 10$$^{-5}$$ s$$^{-1 36. Calculate the difference between C$$_p$$ and C$$_V$$ for 10 moles of an ideal gas 37. What would be the molarity of one litre solution of 22.2 g of CaCl$$_2$$ ? 38. For decolourisation of 1 mole of KMnO$$_4$$, the moles of H$$_2$$O$$_2$$ required is 39. What is the IUPAC name of following compound?
40. Find the compound which have both polar and non-polar covalent bonds. 41. What is the product formed when benzene react with CO and HCl in presence of anhydrous AlCl$$_3$$? 42. Which of the following series of transitions in the spectrum of hydrogen atom fall in visible region? 43. The value of $$\Delta G^\circ$$ for the phosphorylation of glucose in glycolysis is 13.8 kJ/mol. The value of $$K_C$$ at 44. The Lyman series of hydrogen spectrum lies in which region 45. The correct IUPAC name of the coordination compound K$$_3$$[Fe(CN)$$_5$$NO] is
Mathematics
1. Shade the feasible region for the inequations $$x+y\ge2,2x+3y\le6,x\ge0,y\ge0$$ in a rough figure. 2. The maximum value of $$x+y$$ subject to $$2x+3y\le6,x\ge0,y\ge0$$ is 3. Write the solution of the following LPP
Maximize $$Z=x+y$$
Subject to $$3x+4y\le12,x\ge0,y\ge0$$.
Which point the value 4. The vector that must be added to $$\widehat i - 3\widehat j + 2\widehat k$$ and $$3\widehat i + 6\widehat j - 7\widehat 5. If |a| = 8, |b| = 3 and |a $$\times$$ b| = 12, then find the angle between a and b. 6. If for $$a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k$$ and $$c = - 3\widehat i 7. If for any 2 $$\times$$ 2 square matrix A, A (adj A) = $$\left[ {\matrix{
8 & 0 \cr
0 & 8 \cr
} } \right]$$, 8. If matrix $$A = \left[ {\matrix{
2 & { - 2} \cr
{ - 2} & 2 \cr
} } \right]$$ and $${A^2} = pA$$, then the va 9. If $$A\,(adj\,A) = \left[ {\matrix{
{ - 2} & 0 & 0 \cr
0 & { - 2} & 0 \cr
0 & 0 & { - 2} \cr
} } \right 10. The coefficients a, b and c of the quadratic equation, $$ax^2+bx+c=0$$ are obtained by throwing a dice three times. The 11. $${8^{3{{\log }_8}5}}$$ is equal to 12. The equation of normal to the curve $$y = {(1 + x)^y} + {\sin ^{ - 1}}({\sin ^2}x)$$ at $$x = 0$$ is 13. If $$L = \mathop {\lim }\limits_{x \to 0} {{a - \sqrt {{a^2} - {x^2}} - {{{x^2}} \over 4}} \over {{x^4}}},a > 0$$. If L 14. What will be the equation of circle whose centre is (1, 2) and touches X-axis? 15. The approximate value of $$f(5.001)$$, where $$f(x)=x^3-7x^2+15$$ is 16. Find the centre and radius of the circle given by the equation $$2{x^2} + 2{y^2} + 3x + 4y + {9 \over 8} = 0$$. 17. Find the maximum value of $$f(x) = {1 \over {4{x^2} + 2x + 1}}$$. 18. If $$f(x) = \left\{ {\matrix{
{ax + 3,} & {x \le 2} \cr
{{a^2}x - 1} & {x > 2} \cr
} } \right.$$, then the v 19. The value of $$\mathop {\lim }\limits_{x \to 0} \left( {{{{a^x} + {b^x} + {c^x}} \over 3}} \right),(a,b,c > 0)$$ is 20. What will be the equation of the circle whose centre is (1, 2) and which passes through the point (4, 6)? 21. The line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ is parallel to the plane 22. The equation of a plane passing through the line of intersection of the planes $$x+2y+3z=2,x-y+z=3$$ and at a distance $ 23. The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is 24. The point of intersection of the lines $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}$$ and $${{x - 4} \ove 25. $$\int {{{{2^x}} \over {\sqrt {1 - {4^x}} }}dx} $$ is equal to 26. $$\int_{ - \pi /2}^{\pi /2} {\sin xdx} $$ 27. Integral of $$\int {{{dx} \over {{x^2}{{[1 + {x^4}]}^{3/4}}}}} $$. 28. Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertic 29. Five persons A, B, C, D and E are in queue of a shop. The probability that A and E are always together, is 30. If A, B and C are mutually exclusive and exhaustive events of a random experiment such that $$P(B) = {3 \over 2}P(A)$$ a 31. A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that 32. If x and y are acute angles, such that $$\cos x + \cos y = {3 \over 2}$$ and $$\sin x + \sin y = {3 \over 4}$$, then $$\ 33. The expression $${{\tan A} \over {1 - \cot A}} + {{\cot A} \over {1 - \tan A}}$$ can be written as 34. If $$\sin 2x = 4\cos x$$, then x is equal to 35. If $$f(x)$$ satisfies the relation $$2f(x) + f(1 - x) = {x^2}$$ for all real x, then $$f(x)$$ is 36. If A = {1, 2, 5, 6} and B = {1, 2, 3}, then (A $$\times$$ B) $$\cap$$ (B $$\times$$ A) is equal to 37. Total number of elements in the power set of A containing 15 elements is 38. What is the argument of the complex number $${{(1 + i)(2 + i)} \over {3 - i}}$$, where $$i = \sqrt { - 1} $$ ? 39. Evaluate $${\left[ {{i^{18}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}$$. 40. If $${(\sqrt 3 + i)^{100}} = {2^{99}}(a + ib)$$, then $${a^2} + {b^2}$$ is equal to 41. Using mathematical induction, the numbers $${a_n}$$'s are defined by $${a_0} = 1,{a_{n + 1}} = 3{n^2} + n + {a_n},(n \ge 42. If $$49^n+16n+P$$ is divisible by 64 for all $$n\in N$$, then the least negative integral value of P is 43. $${2^{3n}} - 7n - 1$$ is divisible by 44. The solution of the differential equation $${\sec ^2}x\tan ydx + {\sec ^2}y\tan xdy = 0$$ is 45. The solution of the differential equation $$y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^ 46. The solution of the differential equation $$(1 + {y^2}) + (x - {e^{{{\tan }^{ - 1}}y}}){{dy} \over {dx}} = 0$$ is 47. The value of $$1\,.\,1! + 2\,.\,2! + 3\,.\,3! + \,...\, + \,n\,.\,n!$$ is 48. The sum of the series $$(1 + 2) + (1 + 2 + {2^2}) + (1 + 2 + {2^2} + {2^3}) + ....$$ upto $$n$$ terms is 49. If a, b, c are in A.P., $$b-a,c-b$$ and a are in G.P., then a : b : c is 50. The number of triangles which can be formed by using the vertices of a regular polygon of $$(n+3)$$ sides is 220. Then, 51. Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from th 52. How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7? 53. If a polygon of n sides has 275 diagonals, then n is equal to 54. If two pairs of lines $$x^2-2mxy-y^2=0$$ and $$x^2-2nxy-y^2=0$$ are such that one of them represents the bisector of the 55. The distance of the point (1, 2) from the line $$x+y+5=0$$ measured along the line parallel to $$3x-y=7$$ is equal to 56. The slopes of the lines, which make an angle 45$$^\circ$$ with the line $$3x-y=-5$$, are 57. If 3 and 4 are intercepts of a line L = 0, then the distance of L $$\equiv$$ 0 from the origin is 58. Number of terms in the binomial expansion of $$(x+a)^{53}+(x-a)^{53}$$ is 59. The coefficient of $$x^{10}$$ in the expansion of $$1+(1+x)+...+(1+x)^{20}$$ is 60. Middle term in the expansion of $${\left( {{x^2} + {1 \over {{x^2}}} + 2} \right)^n}$$ is
Physics
1. The Lyman series of a hydrogen atom belongs
in which category 2. Insulators can be charged by which of the following process? 3. In an adiabatic process with the ratio of two specific heat, $$\gamma=\frac{3}{2}$$, pressure is increased by $$\frac{2} 4. Two converging lenses of focal length 20 cm and 40 cm are placed in contact. The effective power of the combination is 5. The formula of capacitative reactance is 6. Which graph shows the correct $$v$$ - $$x$$ graph of a freely falling body? 7. The displacement $$x$$ of a particle varies with time $$t$$, $$x=ae^{-pt}+be^{qt}$$, where a, b, p and q are positive co 8. Which of the following quantity represents the dimensions of momentum? 9. The angle of projection with the horizontal in terms of maximum height attained and horizontal range is given by 10. For the same resonant frequency, if L is changed from L to $${L \over 3}$$, then capacitance should change from C to 11. The velocity of the proton is one-fourth the velocity of the electron. What is the ratio of the de-Broglie wavelength of 12. For an ideal gas, coefficient of volume expansion is given by 13. Which of the following is not a green house gas? 14. Two particles of masses $$m_1=m,m_2=2m$$ and charges $$q_1=q,q_2=2q$$ entered into uniform magnetic field. Find $$F_1/F_ 15. Work done in moving a charge of 25C is 50 J. Calculate potential difference, between two points. 16. The correct arrangement in increasing order of wavelength of X-rays, UV rays, microwave is 17. What is the electric field near infinite plane sheet of charge density $$\sigma$$ ? 18. Which of the following waves are used to treatment of muscles ache? 19. Find the logic gate, when both the inputs are high but the output is low and vice-versa. 20. What is the minimum band-gap of the LED diode? 21. The displacement of a wave is given by
$$y = 20\cos (\omega t + 4z)$$
The amplitude of the given wave is 22. If frequencies are $$(\nu-1)$$ and $$(\nu+2)$$, then find the value of beats. 23. The function $$y = \log \omega t$$ can represent 24. Two spring of force constant $$k_1$$ and $$k_2$$ are configured as the figure given below
The angular frequency of this 25. The resistance of a wire is R ohm. If it is melted and stretched to n times its original length, its new resistance will 26. An unpolarised beam of intensity I$$_0$$ is incident on a pair of nicols making an angle of 60$$^\circ$$ with each other 27. The collision of the molecules of an ideal gas is taken as 28. The average energy associated with a monoatomic molecule is 29. For the given electrical arrangement, what is the value of current I?
30. If an electron in hydrogen atom jumps from an orbit of level $$n=3$$ to an orbit at level $$n=2$$, emitted radiation has 31. Within the elastic limit, the corresponding stress is known as 32. A wire is stretched to double of its length. The strain is 33. Kepler's second law of planetary motion corresponds to 34. A constant potential energy of a satellite is given as
$$\mathrm{PE}=r(\mathrm{KE})$$
whee, PE = potential energy
and KE 35. A long solenoid has 20 turns cm$$^{-1}$$. The current necessary to produce a magnetic field of 20 mT inside the solenoid 36. A constant current flows from A to B as shown in the figure. What is the direction of current in the circle?
37. According to Pascal's law, pressure in a fluid at rest is the same at all points, if 38. The surface tension of a liquid at its boiling point 39. Centre of mass of the given system of particles will be at
40. Newton's second law of rotational motion of a system particles having angular momentum L is given by 41. The motion of a particle of mass $$m$$ is described by $$y = ut + g{t^2}$$. The force acting on the particle will be 42. When a car of mass $$m$$ is moving with speed $$v$$ along a circle of radius $$r$$ on a level road, the centripetal forc 43. Ba-122 has half-life of 2 min. Experiment has to be done using Ba-122 and it takes 10 min to set up the experiment. It i 44. When the speed of light becomes $$\frac{2}{3}$$ of its present value, then the energy released in a given atomic explosi 45. What should be the value of self-inductance of an inductor that should be connected to 220 V 50 Hz supply, so that a max 46. The magnifying power of a telescope is 9. When it is adjusted for parallel rays, the distance between the objective and 47. Two masses of 1g and 9g are moving with equal kinetic energy. The ratio of magnitude of their momentum is 48. When two bodies collide with each other such that their kinetic energy remains constant. Their collision is said to be 49. For motion under central forces, which quantity will be conserved? 50. Which of the following statement is incorrect? 51. If impedance is $$\sqrt3$$ times of resistance, then find phase difference. 52. A bar magnet is oscillating in the earth's magnetic field with a period T. What happens to its period and motion, if its 53. The relative permeability of iron is 6000. Its magnetic susceptibility is 54. Which of the following technique is not used for measuring small time intervals? 55. The relative errors in the measurement of two lengths 1.02 cm $$\pm$$ 0.01 cm and 9.89 cm $$\pm$$ 0.01 cm is 56. In Young's double slit experiment with sodium vapour lamp of wavelength 589 nm and slit 0.589 mm apart, the half angular 57. From the figure describing photoelectric effect, we may infer correctly that
58. Carnot cycle of an engine is given below
Total work done by the gas in one cycle is
1
COMEDK 2021
MCQ (Single Correct Answer)
+1
-0
If $${(\sqrt 3 + i)^{100}} = {2^{99}}(a + ib)$$, then $${a^2} + {b^2}$$ is equal to
A
$$\sqrt2$$
B
4
C
$$\sqrt3$$
D
None of these
2
COMEDK 2021
MCQ (Single Correct Answer)
+1
-0
Using mathematical induction, the numbers $${a_n}$$'s are defined by $${a_0} = 1,{a_{n + 1}} = 3{n^2} + n + {a_n},(n \ge 0)$$. Then, $${a_n}$$ is equal to
A
$${n^3} + {n^2} + 1$$
B
$${n^3} - {n^2} + 1$$
C
$${n^3} - {n^2}$$
D
$${n^3} + {n^2}$$
3
COMEDK 2021
MCQ (Single Correct Answer)
+1
-0
If $$49^n+16n+P$$ is divisible by 64 for all $$n\in N$$, then the least negative integral value of P is
A
$$-2$$
B
$$-3$$
C
$$-4$$
D
$$-1$$
4
COMEDK 2021
MCQ (Single Correct Answer)
+1
-0
$${2^{3n}} - 7n - 1$$ is divisible by
A
64
B
36
C
49
D
25
Paper analysis
Total Questions
Chemistry
45
Mathematics
60
Physics
58
COMEDK
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