COMEDK 2020
Paper was held on Wed, Aug 19, 2020 8:30 AM
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Chemistry

The number of gram molecules of chlorine in $$6.02\times10^{25}$$ hydrogen chloride molecules is
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Which one of the following has maximum number of atoms of oxygen?
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Which one of the following shows functional isomerism?
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In the ionic equation, $$\mathrm{BiO_3^-+6H^++xe^-\rightarrow Bi^{3+}+3H_2O}$$, the value of x is
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Molarity of a given orthophosphoric acid solution is 3M. It’s normality is
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Acidified sodium fusion extract on addition of ferric chloride solution gives blood red colouration which confirms the p
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A body of mass 10 mg is moving with a velocity of 100 ms$$^{-1}$$. The wavelength of de-Broglie wave associated with it
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Mg$$^{2+}$$ is isoelectronic with
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Presence of halogen in organic compounds can be detected using
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The electronic configuration of Cr$$^{3+}$$ is
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The mass of a metal, with equivalent mass 31.75, which would combine with 8 g of oxygen is
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Benzene reacts with chlorine in sunlight to give a final product
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In the periodic table metals usually used as catalysts belong to
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The general formula of a cycloalkene is
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In acetylene molecule, between the carbon atoms there are
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Denatured alcohol is
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During the formation of a chemical bond
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+I-effect is shown by
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Formation of coloured solution is possible, when metal ion in the compound contains
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Which of the following is an intensive property?
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Hofmann’s bromamide reaction is to convert
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IUPAC name of Na$$_3$$[Co(NO$$_2$$)$$_6$$] is
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Thermodynamic standard conditions of temperature and pressure are
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How many chiral carbon atoms are present in 2, 3, 4-trichloropentane ?
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The number of unidentate ligands in the complex ion is called
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$$2S{O_2}(g) + {O_2}(g)\buildrel {{V_2}{O_5}} \over \rightleftharpoons $$ is an example for
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The amino acid which is not optically active is
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For a stable molecule the value of bond order must be
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Which one of the following is a second order reaction?
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According to Baeyer's strain theory which is highly stable?
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The number of antibonding electron pairs in O$$_2^{2-}$$ molecular ion on the basis of molecular orbital theory is [Atom
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Hydroxyl ion concentration of 1M HCl is
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Geometrical isomerism is shown by
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The oxidation state of iron in K$$_4$$[Fe(CN)$$_6$$] is,
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In which of the following process, a maximum increase in entropy is observed?
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Decomposition of benzene diazonium chloride by using Cu$$_2$$Cl$$_2$$/HCl to form chlorobenzene is
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Which complex cannot ionise in solution?
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Consider the reaction, C(s) + O$$_2$$(g) $$\rightarrow$$ CO$$_2$$(g) + 393.5 kJ The signs of $$\Delta H,\Delta S$$ and $
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The product formed when hydroxylamine condenses with a carbonyl compound is called
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Which of the following forms a colourless solution in aqueous medium?
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An alkyl halide reacts with alcoholic ammonia in a sealed tube, the product formed will be
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Entropy of the universe is
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Which of the following salts on being dissolved in water gives pH > 7 at 25$$^\circ$$C ?
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The reagent used in Clemmenson's reduction is
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When KBr is dissolved in water, K$$^+$$ ions are
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The volume of 10N and 4N HCl required to make 1 litre of 7N HCl are
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Carbon forms two oxides which have different compositions. The equivalent mass of which remains constant?
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Maximum number of molecules of CH$$_3$$I that can react with a molecule of CH$$_3$$NH$$_2$$ are
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Mathematics

$${7^{2{{\log }_7}5}}$$ is equal to
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In the group $$(G\,{ \otimes _{15}})$$, where $$G = \{ 3,6,9,12\} $$, $${ \otimes _{15}}$$ is multiplication modulo 15,
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A group (G *) has 10 elements. The minimum number of elements of G, which are their own inverses is
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If a and b are vectors such that $$|a + b|=|a-b|$$, then the angle between a and b is
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$${{3{x^2} + 1} \over {{x^2} - 6x + 8}}$$ is equal to
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If $$a = 2\widehat i + 3\widehat j - \widehat k,b = \widehat i + 2\widehat j - 5\widehat k,c = 3\widehat i + 5\widehat j
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OA and BO are two vectors of magnitudes 5 and 6 respectively. If $$\angle BOA=60^\circ$$, then OA . OB is equal to
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A vector perpendicular to the plane containing the points $$A(1, - 1,2),B(2,0, - 1),C(0,2,1)$$ is
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$${1 \over {2\,.\,5}} + {1 \over {5\,.\,8}} + {1 \over {8\,.\,11}} + ............. + {1 \over {(3n - 1)(3n + 2)}} = $$
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The ninth term of the expansion $${\left( {3x - {1 \over {2x}}} \right)^8}$$ is
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If $$A = \left[ {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right],10B = \left[
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If $$A = \left[ {\matrix{ 0 & x & {16} \cr x & 5 & 7 \cr 0 & 9 & x \cr } } \right]$$ is singular, then
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If $$A = \left[ {\matrix{ 1 & { - 2} & 2 \cr 0 & 2 & { - 3} \cr 3 & { - 2} & 4 \cr } } \right]$$, then
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If $$f:R \to R$$ is defined by $$f(x) = |x|$$, then
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The value of $$\left| {\matrix{ x & p & q \cr p & x & q \cr p & q & x \cr } } \right|$$ is
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The number of common tangents to the circles $$x^2+y^2=4$$ and $$x^2+y^2-6x-8y-24=0$$ is,
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If $$3x+y+k=0$$ is a tangent to the circle $$x^2+y^2=10$$, the values of k are
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The equation to two circles which touch the Y-axis at (0, 3) and make an intercept of 8 units on X-axis are
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The orthocentre of the triangle with vertices A(0, 0), B(0, 3/2), C($$-$$5, 0) is
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$${x^2} + {y^2} - 6x - 6y + 4 = 0$$, $${x^2} + {y^2} - 2x - 4y + 3 = 0$$, $${x^2} + {y^2} + 2kx + 2y + 1 = 0$$. If the r
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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
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The coordinates of the foot of the perpendicular drawn from the point (3, 4) on the line $$2x+y-7=0$$ is
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The area enclosed by the pair of lines $$xy=0$$, the line $$x-4=0$$ and $$y+5=0$$ is
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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
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A graph G has m vertices of odd degree and ‘n’ vertices of even degree. Then which of the following statements is necess
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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 $$
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The value of $$\sin \left[ {2{{\cos }^{ - 1}}{{\sqrt 5 } \over 3}} \right]$$ is
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If $${{{x^2}} \over {36}} - {{{y^2}} \over {{k^2}}} = 1$$ is a hyperbola, then which of the following statements can be
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The focus of the parabola is
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The solution of $${\tan ^{ - 1}}x + 2{\cot ^{ - 1}}x = {{2\pi } \over 3}$$ is
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$${\sin ^2}17.5^\circ + \sin 72.5^\circ $$ is equal to
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The conjugate of the complex number $${{{{(1 + i)}^2}} \over {1 - i}}$$ is
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ABC is a triangle with $$\angle A=30^\circ$$ and BC = 10 cm. The area of the circumcircle of the triangle is
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If $$\sin 3\theta = \sin \theta $$, how many solutions exist such that $$ - 2\pi
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The imaginary part of $$i^i$$ is
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The amplitude of $${(1 + i)^5}$$ is
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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
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$$\mathop {\lim }\limits_{x \to 1} {{\tan ({x^2} - 1)} \over {x - 1}}$$ is equal to
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If $$y = {2^{\log x}}$$, then $${{dy} \over {dx}}$$ is
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If $${\sec ^{ - 1}}\left( {{{1 + x} \over {1 - y}}} \right) = a$$, then $${{dy} \over {dx}}$$ is
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If $$y = {\cos ^2}{{3x} \over 2} - {\sin ^2}{{3x} \over 2}$$, then $${{{d^2}y} \over {d{x^2}}}$$ is
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If the function $$f(x) = \left\{ {\matrix{ {{{1 - \cos x} \over {{x^2}}},} & {\mathrm{for}\,x \ne 0} \cr {k,} &
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If $$1,\omega ,{\omega ^2}$$ are the cube roots of unity, then $$(1 + \omega )(1 + {\omega ^2})(1 + {\omega ^4})(1 + {\o
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If $${x^x} = {y^y}$$, then $${{dy} \over {dx}}$$ is
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The point on the curve $$y^2=x$$, the tangent at which makes an angle 45$$^\circ$$ with X-axis is
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The length of the subtangent to the curve $${x^2}{y^2} = {a^4}$$ at $$( - a,a)$$ is
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The number of positive divisors of 252 is
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The remainder obtained when 5124 is divided by 124 is
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Which of the following is not a group with respect to the given operation?
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The range in which $$y = - {x^2} + 6x - 3$$ is increasing, is
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The value of the integral $$\int\limits_0^{\pi /2} {({{\sin }^{100}}x - {{\cos }^{100}}x)dx} $$ is
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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
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If $$k\int\limits_0^1 {x\,.\,f(3x)dx = \int\limits_0^3 {t\,.\,f(t)dt} } $$, then the value of $$k$$ is
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The value of $$\int {{1 \over {1 + \cos 8x}}dx} $$ is
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The value of $$\int {{e^x}({x^5} + 5{x^4} + 1)\,.\,dx} $$ is
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The value of $$\int {{{{x^2} + 1} \over {{x^2} - 1}}dx} $$ is
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The area bounded by the curve $$x=4-y^2$$ and the Y-axis is
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The differential equation of the family of straight lines whose slope is equal to y-intercept is
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The order and degree of the differential equation $${\left[ {1 + {{\left( {{{dy} \over {dx}}} \right)}^5}} \right]^{{1 \
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Physics

Light of frequency 1015 Hz falls on a metal surface of work function 2.5 eV. The stopping potential of photoelectrons (i
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A proton accelerated through a potential V has de-Broglie wavelength $$\lambda$$. Then, the de-Broglie wavelength of an
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Consider a thin spherical shell of radius R consisting of uniform surface charge density s. The electric field at a poin
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An electron of an atom transits from $$n_1$$ to $$n_2$$. In which of the following maximum frequency of photon will be e
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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
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Two radioactive materials X$$_1$$ and X$$_2$$ have decay constant 5$$\lambda$$ and $$\lambda$$, respectively. If initial
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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
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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
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When a $$p$$-$$n$$ junction diode is connected in forward bias, its barrier potential
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A ball floats on the surface of water in a container exposed to the atmosphere. When the container is covered and the ai
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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
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A compound slab is made of two parallel plates of copper and brass of the same thickness and having thermal conductiviti
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In mm$$^3$$ of a gas is compressed at 1 atmospheric pressure and temperature 27$$^\circ$$C to 627$$^\circ$$C. What is th
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If sink is at a temperature of $$-39\Upsilon$$C and source at 0$$^\circ$$C, then efficiency will be
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Which of the following laws of Physics is valid across all domains of nature?
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A particle of mass m is moving in a horizontal circle of radius R under a centripetal force equal to $$-\frac{A}{R^2}$$
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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
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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.
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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
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Equal volumes of two gases, having their densities in the ratio of 1 : 16 exert equal pressures on the walls of two cont
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A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $$C_p/C_V$$ of the mixture is
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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
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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
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A source of sound gives 5 beats per second, when sounded with another source of frequency 100 s$$^{-1}$$. The second har
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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
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An electric dipole has a pair of equal and opposite point charges $$q$$ and $$-q$$ separated by a distance $$2x$$. The a
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An electric dipole is placed in a uniform electric field with the dipole axis making an angle $$\theta$$ with the direct
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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
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The potential energies associated with four orientations of an electric dipole in an electric field are (i) $$-5U_0$$ (i
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Suppose refractive index $$\alpha$$ is given as $$ \alpha = A + {B \over {{\lambda ^2}}}$$, where A and B are constants
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If voltage $$V=(200\pm 8)V$$ and current $$I=(20\pm0.5)A$$, then the percentage error in resistance R is
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A body is projected vertically upwards. The times corresponding to height $$h$$, while ascending and while descending ar
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A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is arou
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A fluid is in streamline flow across a horizontal pipe of variable area of cross-section. For this which of the followin
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Two capacitors $$C_1$$ and $$C_2$$ are charged to 120 V and 200 V, respectively. When they are connected in parallel, it
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Point out the right statements about the validity of Kirchhoff’s junction rule,
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Four particles each of the mass m are placed at the corners of a square of side length $$l$$. The radius of gyration of
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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
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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
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Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between th
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If $$P=Q=R=10\Omega$$ and $$S=20\Omega$$, then what resistance should be joined with S to balance the Wheatstone's netwo
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To the potentiometer wire of length L and 10$$\Omega$$ resistance, a battery of emf 2.5 V and a resistance R are connect
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An electron moves with speed of 2 $$\times$$ 10$$^5$$ m/s along the positive x-direction in a magnetic field $$B = (\wid
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A horizontal overhead power line carries a current of 90 A in East to West direction. What is the magnitude and directio
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A moving coil galvanometer has 28 turns and area of coil is $$4\times 10^{-2}$$ m$$^2$$. If the magnetic field is 0.2 T,
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The intensity of magnetic field due to an isolated pole of strength $$m_p$$ at a point distant $$r$$ from it will be
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The particle that cannot be accelerated by a cyclotron is
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The angle which the total magnetic field of earth makes with the surface of the earth is called
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The angle of dip of at a place where horizontal and vertical components of earth’s magnetic field are equal is
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A coil of wire of a certain radius has 100 turns and a self inductance of 15 mH. The self inductance of a second similar
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A coil of 100 turns carries a current of 5 mA and creates a magnetic flux of 10$$^{-5}$$ Wb. The inductance is
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In step-up transformer, relation between number of turns in primary (N$$_P$$) and number of turns in secondary (N$$_S$$)
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For a series L-C-R circuit at resonance, which statement is not true?
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Which of the following has/have zero average value in a plane electromagnetic wave?
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A convex lens is made of 3 layers of glass of 3 different materials as in the figure. A point object is placed on its a
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A ray of light suffers minimum deviation in equilateral prism P. Additional prisms Q and R of identical shape and of sam
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Two identical light waves, propagating in the same direction, have a phase difference $$\delta$$. After they superpose t
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A plastic sheet (refractive index = 1 6. ) covers one slit of a double slit arrangement for the Young’s experiment. When
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A particle starts moving from point (2, 10, 1). Displacement for the particle is $$8\widehat i - 2\widehat j + \widehat
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