Chemistry
1. The number of gram molecules of chlorine in $$6.02\times10^{25}$$ hydrogen chloride molecules is 2. Which one of the following has maximum
number of atoms of oxygen? 3. Which one of the following shows functional
isomerism? 4. In the ionic equation,
$$\mathrm{BiO_3^-+6H^++xe^-\rightarrow Bi^{3+}+3H_2O}$$,
the value of x is 5. Molarity of a given orthophosphoric acid
solution is 3M. It’s normality is 6. Acidified sodium fusion extract on addition of
ferric chloride solution gives blood red
colouration which confirms the p 7. A body of mass 10 mg is moving with a velocity of 100 ms$$^{-1}$$. The wavelength of de-Broglie wave associated with it 8. Mg$$^{2+}$$ is isoelectronic with 9. Presence of halogen in organic compounds can be detected using 10. The electronic configuration of Cr$$^{3+}$$ is 11. The mass of a metal, with equivalent mass 31.75, which would combine with 8 g of oxygen is 12. Benzene reacts with chlorine in sunlight to give a final product 13. In the periodic table metals usually used as catalysts belong to 14. The general formula of a cycloalkene is 15. In acetylene molecule, between the carbon atoms there are 16. Denatured alcohol is 17. During the formation of a chemical bond 18. +I-effect is shown by 19. Formation of coloured solution is possible,
when metal ion in the compound contains 20. Which of the following is an intensive property? 21. Hofmann’s bromamide reaction is to convert 22. IUPAC name of Na$$_3$$[Co(NO$$_2$$)$$_6$$] is 23. Thermodynamic standard conditions of
temperature and pressure are 24. How many chiral carbon atoms are present in
2, 3, 4-trichloropentane ? 25. The number of unidentate ligands in the
complex ion is called 26. $$2S{O_2}(g) + {O_2}(g)\buildrel {{V_2}{O_5}} \over
\rightleftharpoons $$ is an example for 27. The amino acid which is not optically active is 28. For a stable molecule the value of bond order
must be 29. Which one of the following is a second order
reaction? 30. According to Baeyer's strain theory which is highly stable? 31. The number of antibonding electron pairs in O$$_2^{2-}$$ molecular ion on the basis of molecular orbital theory is
[Atom 32. Hydroxyl ion concentration of 1M HCl is 33. Geometrical isomerism is shown by 34. The oxidation state of iron in K$$_4$$[Fe(CN)$$_6$$] is, 35. In which of the following process, a maximum
increase in entropy is observed? 36. Decomposition of benzene diazonium chloride by using Cu$$_2$$Cl$$_2$$/HCl to form chlorobenzene is 37. Which complex cannot ionise in solution? 38. Consider the reaction,
C(s) + O$$_2$$(g) $$\rightarrow$$ CO$$_2$$(g) + 393.5 kJ
The signs of $$\Delta H,\Delta S$$ and $ 39. The product formed when hydroxylamine
condenses with a carbonyl compound is called 40. Which of the following forms a colourless
solution in aqueous medium? 41. An alkyl halide reacts with alcoholic ammonia in
a sealed tube, the product formed will be 42. Entropy of the universe is 43. Which of the following salts on being dissolved in water gives pH > 7 at 25$$^\circ$$C ? 44. The reagent used in Clemmenson's reduction is 45. When KBr is dissolved in water, K$$^+$$ ions are 46. The volume of 10N and 4N HCl required to
make 1 litre of 7N HCl are 47. Carbon forms two oxides which have different
compositions. The equivalent mass of which
remains constant? 48. Maximum number of molecules of CH$$_3$$I that can react with a molecule of CH$$_3$$NH$$_2$$ are
Mathematics
1. $${7^{2{{\log }_7}5}}$$ is equal to 2. In the group $$(G\,{ \otimes _{15}})$$, where $$G = \{ 3,6,9,12\} $$, $${ \otimes _{15}}$$ is multiplication modulo 15, 3. A group (G *) has 10 elements. The minimum number of elements of G, which are their own inverses is 4. If a and b are vectors such that $$|a + b|=|a-b|$$, then the angle between a and b is 5. $${{3{x^2} + 1} \over {{x^2} - 6x + 8}}$$ is equal to 6. If $$a = 2\widehat i + 3\widehat j - \widehat k,b = \widehat i + 2\widehat j - 5\widehat k,c = 3\widehat i + 5\widehat j 7. OA and BO are two vectors of magnitudes 5 and 6 respectively. If $$\angle BOA=60^\circ$$, then OA . OB is equal to 8. A vector perpendicular to the plane containing the points $$A(1, - 1,2),B(2,0, - 1),C(0,2,1)$$ is 9. $${1 \over {2\,.\,5}} + {1 \over {5\,.\,8}} + {1 \over {8\,.\,11}} + .............
+ {1 \over {(3n - 1)(3n + 2)}} = $$ 10. The ninth term of the expansion $${\left( {3x - {1 \over {2x}}} \right)^8}$$ is 11. If $$A = \left[ {\matrix{
1 & { - 1} & 1 \cr
2 & 1 & { - 3} \cr
1 & 1 & 1 \cr
} } \right],10B = \left[ 12. If $$A = \left[ {\matrix{
0 & x & {16} \cr
x & 5 & 7 \cr
0 & 9 & x \cr
} } \right]$$ is singular, then 13. If $$A = \left[ {\matrix{
1 & { - 2} & 2 \cr
0 & 2 & { - 3} \cr
3 & { - 2} & 4 \cr
} } \right]$$, then 14. If $$f:R \to R$$ is defined by $$f(x) = |x|$$, then 15. The value of $$\left| {\matrix{
x & p & q \cr
p & x & q \cr
p & q & x \cr
} } \right|$$ is 16. The number of common tangents to the circles $$x^2+y^2=4$$ and $$x^2+y^2-6x-8y-24=0$$ is, 17. If $$3x+y+k=0$$ is a tangent to the circle $$x^2+y^2=10$$, the values of k are 18. The equation to two circles which touch the
Y-axis at (0, 3) and make an intercept of 8 units
on X-axis are 19. The orthocentre of the triangle with vertices A(0, 0), B(0, 3/2), C($$-$$5, 0) is 20. $${x^2} + {y^2} - 6x - 6y + 4 = 0$$, $${x^2} + {y^2} - 2x - 4y + 3 = 0$$, $${x^2} + {y^2} + 2kx + 2y + 1 = 0$$. If the r 21. If the circles $${x^2} + {y^2} - 2x - 2y - 7 = 0$$ and $${x^2} + {y^2} + 4x + 2y + k = 0$$ cut orthogonally, then the le 22. The coordinates of the foot of the perpendicular drawn from the point (3, 4) on the line $$2x+y-7=0$$ is 23. The area enclosed by the pair of lines $$xy=0$$, the line $$x-4=0$$ and $$y+5=0$$ is 24. If the area of the auxillary circle of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1(a > b)$$ is t 25. A graph G has m vertices of odd degree and ‘n’
vertices of even degree. Then which of the
following statements is necess 26. If p is any point on the ellipse $${{{x^2}} \over {36}} + {{{y^2}} \over {16}} = 1$$, and S and S' are the foci, then $$ 27. The value of $$\sin \left[ {2{{\cos }^{ - 1}}{{\sqrt 5 } \over 3}} \right]$$ is 28. If $${{{x^2}} \over {36}} - {{{y^2}} \over {{k^2}}} = 1$$ is a hyperbola, then which of the following statements can be 29. The focus of the parabola is 30. The solution of $${\tan ^{ - 1}}x + 2{\cot ^{ - 1}}x = {{2\pi } \over 3}$$ is 31. $${\sin ^2}17.5^\circ + \sin 72.5^\circ $$ is equal to 32. The conjugate of the complex number $${{{{(1 + i)}^2}} \over {1 - i}}$$ is 33. ABC is a triangle with $$\angle A=30^\circ$$ and BC = 10 cm. The area of the circumcircle of the triangle is
34. If $$\sin 3\theta = \sin \theta $$, how many solutions exist such that $$ - 2\pi 35. The imaginary part of $$i^i$$ is 36. The amplitude of $${(1 + i)^5}$$ is 37. ABC is a triangle, G is the centroid, D is the mid-point of BC. If A = (2, 3) and G = (7, 5), then the point D is 38. $$\mathop {\lim }\limits_{x \to 1} {{\tan ({x^2} - 1)} \over {x - 1}}$$ is equal to 39. If $$y = {2^{\log x}}$$, then $${{dy} \over {dx}}$$ is 40. If $${\sec ^{ - 1}}\left( {{{1 + x} \over {1 - y}}} \right) = a$$, then $${{dy} \over {dx}}$$ is 41. If $$y = {\cos ^2}{{3x} \over 2} - {\sin ^2}{{3x} \over 2}$$, then $${{{d^2}y} \over {d{x^2}}}$$ is 42. If the function $$f(x) = \left\{ {\matrix{
{{{1 - \cos x} \over {{x^2}}},} & {\mathrm{for}\,x \ne 0} \cr
{k,} & 43. If $$1,\omega ,{\omega ^2}$$ are the cube roots of unity, then $$(1 + \omega )(1 + {\omega ^2})(1 + {\omega ^4})(1 + {\o 44. If $${x^x} = {y^y}$$, then $${{dy} \over {dx}}$$ is 45. The point on the curve $$y^2=x$$, the tangent at which makes an angle 45$$^\circ$$ with X-axis is 46. The length of the subtangent to the curve $${x^2}{y^2} = {a^4}$$ at $$( - a,a)$$ is 47. The number of positive divisors of 252 is 48. The remainder obtained when 5124 is divided by 124 is 49. Which of the following is not a group with
respect to the given operation? 50. The range in which $$y = - {x^2} + 6x - 3$$ is increasing, is 51. The value of the integral $$\int\limits_0^{\pi /2} {({{\sin }^{100}}x - {{\cos }^{100}}x)dx} $$ is 52. OA and OB are two roads enclosing an angle of
120$$^\circ$$. X and Y start from O at the same time. X
travels along OA w 53. If $$k\int\limits_0^1 {x\,.\,f(3x)dx = \int\limits_0^3 {t\,.\,f(t)dt} } $$, then the value of $$k$$ is 54. The value of $$\int {{1 \over {1 + \cos 8x}}dx} $$ is 55. The value of $$\int {{e^x}({x^5} + 5{x^4} + 1)\,.\,dx} $$ is 56. The value of $$\int {{{{x^2} + 1} \over {{x^2} - 1}}dx} $$ is 57. The area bounded by the curve $$x=4-y^2$$ and the Y-axis is 58. The differential equation of the family of
straight lines whose slope is equal to y-intercept
is 59. The order and degree of the differential equation $${\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^5}} \right]^{{1 \
Physics
1. Light of frequency 1015 Hz falls on a metal surface of work function 2.5 eV. The stopping potential of photoelectrons (i 2. A proton accelerated through a potential V has de-Broglie wavelength $$\lambda$$. Then, the de-Broglie wavelength of an 3. Consider a thin spherical shell of radius R
consisting of uniform surface charge density s.
The electric field at a poin 4. An electron of an atom transits from $$n_1$$ to $$n_2$$. In which of the following maximum frequency of photon will be e 5. Two protons are kept at a separation of 40 $$\mathop A\limits^o $$. F$$_n$$ is the nuclear force and F$$_e$$ is the elec 6. Two radioactive materials X$$_1$$ and X$$_2$$ have decay constant 5$$\lambda$$ and $$\lambda$$, respectively. If initial 7. The Poisson's ratio of a material is 0.1. If the longitudinal strain of a rod of this material is $$10^{-3}$$, then the 8. A satellite can be in a geostationary orbit around a planet if it is at a distance R from the centre of the planet. If t 9. When a $$p$$-$$n$$ junction diode is connected in forward bias, its barrier potential 10. A ball floats on the surface of water in a
container exposed to the atmosphere. When the
container is covered and the ai 11. A frame made of metallic wire enclosing a surface area A is covered with a soap film. If the area of the frame of metall 12. A compound slab is made of two parallel plates
of copper and brass of the same thickness and
having thermal conductiviti 13. In mm$$^3$$ of a gas is compressed at 1 atmospheric pressure and temperature 27$$^\circ$$C to 627$$^\circ$$C. What is th 14. If sink is at a temperature of $$-39\Upsilon$$C and source at 0$$^\circ$$C, then efficiency will be 15. Which of the following laws of Physics is valid
across all domains of nature? 16. A particle of mass m is moving in a horizontal
circle of radius R under a centripetal force equal
to $$-\frac{A}{R^2}$$ 17. A force of 20 N is applied on a body of mass
5 kg resting on a horizontal plane. The body
gains a kinetic energy of 10 J 18. A body under the action of a force $$F = 6\widehat i - 8\widehat j + 10\widehat k$$, acquires an acceleration of 1 m/s2. 19. A body of mass 1000 kg is moving horizontally
with a velocity 50 m/s. A mass of 250 kg is
added. Find the final velocity 20. Equal volumes of two gases, having their
densities in the ratio of 1 : 16 exert equal
pressures on the walls of two cont 21. A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $$C_p/C_V$$ of the mixture is 22. A particle executes a linear SHM with an
amplitude of 4 cm. At the mean position the
velocity of the particle is 10 cm/s 23. The equation of a progressive wave can be given by $$y=15\sin(660\pi t-0.02\pi x)$$ cm. The frequency of the wave is 24. A source of sound gives 5 beats per second, when sounded with another source of frequency 100 s$$^{-1}$$. The second har 25. A charge of 0.8 C is divided into two charges Q$$_1$$ and Q$$_2$$. These are kept at a separation of 30 cm. The force on 26. An electric dipole has a pair of equal and opposite point charges $$q$$ and $$-q$$ separated by a distance $$2x$$. The a 27. An electric dipole is placed in a uniform electric
field with the dipole axis making an angle $$\theta$$ with
the direct 28. Two point charges A = +3 nC and B = +1 nC are placed 5 cm apart in air. The work done to move charge B towards A by 1 cm 29. The potential energies associated with four
orientations of an electric dipole in an electric
field are
(i) $$-5U_0$$ (i 30. Suppose refractive index $$\alpha$$ is given as $$ \alpha = A + {B \over {{\lambda ^2}}}$$, where A and B are constants 31. If voltage $$V=(200\pm 8)V$$ and current $$I=(20\pm0.5)A$$, then the percentage error in resistance R is 32. A body is projected vertically upwards. The
times corresponding to height $$h$$, while
ascending and while descending ar 33. A particle shows distance-time curve as given in
this figure. The maximum instantaneous
velocity of the particle is arou 34. A fluid is in streamline flow across a horizontal
pipe of variable area of cross-section. For this
which of the followin 35. Two capacitors $$C_1$$ and $$C_2$$ are charged to 120 V
and 200 V, respectively. When they are
connected in parallel, it 36. Point out the right statements about the validity
of Kirchhoff’s junction rule, 37. Four particles each of the mass m are placed at
the corners of a square of side length $$l$$. The
radius of gyration of 38. A steel wire of length 4.7 m and cross-sectional area $$3.0\times10^{-5}$$ m$$^2$$ stretches by the same amount as a cop 39. The masses of 200 g and 300 g are attached to
the 20 cm and 70 cm marks of a light meter rod,
respectively. The moment o 40. Two spherical bodies of masses M and 5M and
radii R and 2R are released in free space with
initial separation between th 41. If $$P=Q=R=10\Omega$$ and $$S=20\Omega$$, then what resistance should be joined with S to balance the Wheatstone's netwo 42. To the potentiometer wire of length L and 10$$\Omega$$ resistance, a battery of emf 2.5 V and a resistance R are connect 43. An electron moves with speed of 2 $$\times$$ 10$$^5$$ m/s along the positive x-direction in a magnetic field $$B = (\wid 44. A horizontal overhead power line carries a
current of 90 A in East to West direction. What
is the magnitude and directio 45. A moving coil galvanometer has 28 turns and area of coil is $$4\times 10^{-2}$$ m$$^2$$. If the magnetic field is 0.2 T, 46. The intensity of magnetic field due to an isolated pole of strength $$m_p$$ at a point distant $$r$$ from it will be 47. The particle that cannot be accelerated by a cyclotron is 48. The angle which the total magnetic field of
earth makes with the surface of the earth is
called 49. The angle of dip of at a place where horizontal
and vertical components of earth’s magnetic
field are equal is 50. A coil of wire of a certain radius has 100 turns
and a self inductance of 15 mH. The self
inductance of a second similar 51. A coil of 100 turns carries a current of 5 mA and
creates a magnetic flux of 10$$^{-5}$$ Wb. The
inductance is 52. In step-up transformer, relation between number of turns in primary (N$$_P$$) and number of turns in secondary (N$$_S$$) 53. For a series L-C-R circuit at resonance, which statement is not true? 54. Which of the following has/have zero average
value in a plane electromagnetic wave? 55. A convex lens is made of 3 layers of glass of 3 different materials as in the figure.
A point object is placed on its a 56. A ray of light suffers minimum deviation in
equilateral prism P. Additional prisms Q and R
of identical shape and of sam 57. Two identical light waves, propagating in the
same direction, have a phase difference $$\delta$$. After
they superpose t 58. A plastic sheet (refractive index = 1 6. ) covers one
slit of a double slit arrangement for the Young’s
experiment. When 59. A particle starts moving from point (2, 10, 1). Displacement for the particle is $$8\widehat i - 2\widehat j + \widehat
1
COMEDK 2020
MCQ (Single Correct Answer)
+1
-0
If $$f:R \to R$$ is defined by $$f(x) = |x|$$, then
A
$${f^{ - 1}}(x) = {1 \over {|x|}}$$
B
$${f^{ - 1}}(x) = - x$$
C
$${f^{ - 1}}(x) = {1 \over x}$$
D
The function $${f^{ - 1}}(x)$$ does not exist.
2
COMEDK 2020
MCQ (Single Correct Answer)
+1
-0
The value of $$\left| {\matrix{ x & p & q \cr p & x & q \cr p & q & x \cr } } \right|$$ is
A
$$(x - p)(x - q)(x + p + q)$$
B
$$x(x - p)(x - q)$$
C
$$pq(x - p)(x - q)$$
D
$$(p - q)(x - q)(x - p)$$
3
COMEDK 2020
MCQ (Single Correct Answer)
+1
-0
The number of common tangents to the circles $$x^2+y^2=4$$ and $$x^2+y^2-6x-8y-24=0$$ is,
A
4
B
3
C
1
D
2
4
COMEDK 2020
MCQ (Single Correct Answer)
+1
-0
If $$3x+y+k=0$$ is a tangent to the circle $$x^2+y^2=10$$, the values of k are
A
$$\pm$$ 5
B
$$\pm$$ 7
C
$$\pm$$ 9
D
$$\pm$$ 10
Paper analysis
Total Questions
Chemistry
48
Mathematics
59
Physics
59
COMEDK
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