COMEDK 2022
Paper was held on Sun, Jun 19, 2022 3:30 AM
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Chemistry

The chemical formula of Lucas reagent is
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Alkyl halides undergoing SN2 reaction do inverse
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X and Y in the following reactions are
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For the reaction, H$$_2$$(g) + I$$_2$$(g) $$\rightleftharpoons$$ 2HI(g) the position of equilibrium can be shifted to th
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Which of the following are not path functions? I. H $$-$$ TS II. W III. q IV. q + W
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The system that forms maximum boiling azeotropes is
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KMnO$$_4$$ acts as an oxidising agent in acidic medium. The number of moles of KMnO$$_4$$ that will be required to react
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What can be A and B in the following reaction?
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Which of the following is a false statement?
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Which of the following molecules does not exhibit dipole moment? (i) CCl$$_4$$ (ii) CO$$_2$$ (iii) NH$$_3$$ (iv) CHCl$$_
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Which of the following is highly basic?
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The relation between work done in reversible and irreversible process is
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What is the function platelets?
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The monosaccharides of maltose is
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Which of the following does not affect solubility of a gas in liquid?
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A newly prepared radioactive nuclide has a decay constant of 6.93 s$$^{-1}$$. What is the half-life of the nuclide?
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The essential amino acids are (i) Leucine (ii) Glutamic acid (iii) Asparagine (iv) Valine correct option is
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Increasing order of bond order of oxygen and its ions is
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Minimum number of nodes are present in
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pH of 10$$^{-3}$$ M solution of KOH is
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Which of the product is not possible in Wurtz reaction?
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On treatment of glucose with bromine water the product formed is
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Which among the following forms minimum boiling azeotropes? (i) Heptane + Octane (ii) Water + Nitric acid (iii) Ethanol
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Which of the following statement is incorrect about activation energy?
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The P-O bond order in PO$$_4^{3-}$$ is
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$$\mathrm{O^{2-},F^-,Mg^{2+},Al^{3+},O_2,F_2}$$. How many of the species given above isoelectronic?
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The equilibrium constant, $$K_C$$ for $$3C_2H_2(g) \rightleftharpoons C_6H_6(g)$$ is 4 L$$^2$$mol$$^{-2}$$. If the equil
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Identify the product formed in the given reaction.
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Which of the following gas readily de-colourises the acidified KMnO$$_4$$ solution?
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What will be the emf of the following cell at 25$$^\circ$$C? Fe/Fe$$^{2+}$$ (0.001 M) | | H$$^+$$ (0.01 M) | H$$_2$$(g)
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Which of the following vitamin is responsible for Beri-Beri disease?
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Find the product formed for the given reaction. $$\mathrm{{C_6}{H_5}CHO + {H_3}C - C{H_2} - CHO\buildrel {Dil.\,NaOH/\De
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In which of the following changes, entropy decreases?
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Which among the following will not liberate nitrogen on reaction with nitrous acid?
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The complex which does not show optical isomerism is
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The solution which have lowest freezing point is
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Calculate the molar conductance of 0.025 M aqueous solution of calcium chloride at 25$$^\circ$$C. The specific conductan
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For the reaction 2N$$_2$$O$$_5$$ $$\to$$ 4NO$$_2$$ + O$$_2$$. If initial pressure is 100 atm and rate constant $$k$$ is
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The difference between heat capacity at constant pressure and heat capacity at constant volume is
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Which of the following compound does not exists?
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The major product in the given reaction is
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The spectrum of He$$^+$$ is similar to
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The Paschen series of hydrogen spectrum lies in which region?
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The oxidation state of nickel in [Ni(CO$$_4$$)] is
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Mathematics

The value of $${3^{{{\log }_4}5}} - {5^{{{\log }_4}3}}$$ is
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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
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If $$\mathop {\lim }\limits_{x \to 0} {{(1 + {a^3}) + 8{e^{1/x}}} \over {1 + (1 - {b^3}){e^{1/x}}}} = 2$$, then
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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
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The approximate value of $$(0.007)^{1/3}$$ is
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the circle $${x^2} + {y^2} + 4x - 7y + 12 = 0$$ cuts an intercept on Y-axis of length
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Let $$f(x) = a - {(x - 3)^{8/9}}$$, then maxima of $$f(x)$$ is
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If the derivative of the function $$f(x) = \left\{ {\matrix{ {b{x^2} + ax + 4;} & {x \ge - 1} \cr {a{x^2} + b;}
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If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$$, then
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$$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)$$ lies
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The probability of choosing randomly a number c from the set {1, 2, 3, ... 9} such that the quadratic equation $$x^2+4x+
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Shade the feasible region for the inequations $$6x+4y\le120, 3x+10y\le180,x,y\ge0$$ in a rough figure.
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The maximum of Z is where, $$Z=4x+2y$$ subject to constraints $$4x+2y\ge46,x+3y\le24$$ and $$x,y\ge0$$ is
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If for any 2 $$\times$$ 2 square matrix A, A (adj A) = $$\left[ {\matrix{ 8 & 0 \cr 0 & 8 \cr } } \right]$$,
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If $$A = \left[ {\matrix{ a & 0 & 0 \cr 0 & a & 0 \cr 0 & 0 & a \cr } } \right]$$, then $$|A||adj\,A|$$
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If $$A = \left[ {\matrix{ {2 - k} & 2 \cr 1 & {3 - k} \cr } } \right]$$ is a singular matrix, then the value
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If $$\theta$$ be the angle between the vectors $$a = 2\widehat i + 2\widehat j - \widehat k$$ and $$b = 6\widehat i - 3\
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If x, y and z are non-zero real numbers and $$a = x\widehat i + 2\widehat j,b = y\widehat j + 3\widehat k$$ and $$c = x\
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Maximum value of $$z=12x+3y$$, subject to constraints $$x\ge0,y\ge0,x+y\ge5$$ and $$3x+y\le9$$ is
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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
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The line $$\frac{x-3}{4}=\frac{y-4}{5}=\frac{z-5}{6}$$ is parallel to the plane
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$$\int \frac{1}{x \sqrt{a x-x^2}} d x$$ is
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$$\int \frac{3^x}{\sqrt{1-9^x}} d x$$ is equal to
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$$\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\cos x\,dx} $$
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The angle between the lines $${{x + 4} \over 3} = {{y - 1} \over 5} = {{z + 3} \over 4}$$ and $${{x + 1} \over 1} = {{y
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The point of intersection of the lines $${{x - 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}$$ and $${{x -5} \over
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Five persons A, B, C, D and E are in queue of a shop. The probability that A and B are always together is
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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
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Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability that they form
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If A, B and C are three mutually exclusive and exhaustive events such that P(A) = 2P(B) = 3P(C). What is P(B)?
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If $$U_{n+1}=3 U_n-2 U_{n-1}$$ and $$U_0=2, U_1=3$$, then $$U_n$$ is equal to
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If $$4^n+15n+P$$ is divisible by 9 for all $$n\in N$$, then the least negative integral value of P is
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$$(2^{3n}-1)$$ is divisible by
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If $$S = {{{2^2} - 1} \over 2} + {{{3^2} - 2} \over 6} + {{{4^2} - 3} \over {12}}\, + \,...$$ upto 10 terms, then S is e
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$$\sum\limits_{n = 1}^m {n\,.\,n!} $$ is equal to
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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
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The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ represents
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The solution of the differential equation $$\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0$$ is
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The solution of the differential equation $$x \frac{d y}{d x}=\cot y$$ is
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If nC3 = 220, then n = ?
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A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is corre
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If $$\sin A+\sin B=a$$ and $$\cos A+\cos B=b$$, then $$\cos (A+B)$$ equals?
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What is $${{\cos \theta } \over {1 - \tan \theta }} + {{\sin \theta } \over {1 - \cot \theta }}$$ equal to?
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Find the general solution of $$\sin 2x + \cos x = 0$$.
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If $$f(x)+2f(1-x)=x^2+5,\forall$$ real values of $$x$$, then $$f(x)$$ is given by
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If $$A=\{3,5,7\}$$ and $$B=\{1,2,3,5\}$$, then $$A \times B \cap B \times A$$ is equal to
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Total number of elements in the power set of A containing 17 elements is
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The argument of $${{1 - i\sqrt 3 } \over {1 + i\sqrt 3 }}$$ is
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Evaluate $${\left[ {{i^{22}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}$$
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$${(i + \sqrt 3 )^{100}} + {(i - \sqrt 3 )^{100}} + {2^{100}}$$ is equal to
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There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any
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A regular polygon of n sides has 170 diagonals, then n is equal to
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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
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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
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The slope of lines which makes an angle 45$$^\circ$$ with the line $$2x-y=-7$$
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If 2 and 3 are intercepts of a line L = 0, then the distance of L $$\equiv$$ 0 from the origin is
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The total number of terms in the expansion of $${(x + y)^{100}} + {(x - y)^{100}}$$ is
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The coefficient of $${x^{20}}$$ in the expansion of $${(1 + 3x + 3{x^2} + {x^3})^{20}}$$ is
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In the expansion of $${(1 - 3x + 3{x^2} - {x^3})^{2n}}$$, the middle term is
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How many 5-digit numbers greater than 50,000 can be formed using the digits 1, 2, 3, 4, 5 without repetition?
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Physics

During the phenomenon of resonance
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If the earth were to spin faster, acceleration due to gravity at the poles
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If heat engine is filled at temperature 27$$^\circ$$C and heat of 100 k cal is taken from source at temperature 677$$^\c
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During $$\alpha$$-decay, atomic mass of parent nuclei is
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A point object is placed on the optic axis of a convex lens of focal length $$f$$ at a distance of $$2f$$ to the left of
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For CE transistor amplifier, the audio signal voltage across the collector resistance of 4 k$$\Omega$$ is 5 V. If the cu
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From the following p-V diagram, an ideal gas undergoing a change of state from A to B. Four different processes I, II, I
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A copper and a steel wire of same diameter are connected end to end. A deforming force F$$_1$$ is applied to the wire wh
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If kinetic energy of a body is increased by 300%, then percentage change in momentum will be
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Which of the following diagram represents the variation of the electric field with distance r from the centre of a unifo
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A DC ammeter and a hot wire ammeter are connected to a circuit in series. When a direct current is passed through circui
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A bullet of mass $m$ hits a mass $$M$$ and gets embedded in it. If the block rises to a height $$h$$ as a result of this
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A particle of mass $$m$$ is moving in a horizontal circle of radius $$r$$ under a centripetal force given by $$\left(\fr
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The height at which the acceleration due to gravity becomes $$\frac{g}{16}$$ (where, g = acceleration due to gravity on
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Which of the following series spectrum of hydrogen atom lies in ultraviolet region?
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Speed of electromagnetic wave in a medium having relative permittivity $$\varepsilon_r$$ and relative permeability $$\mu
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The wavelength of the second line of Balmer series is 486.4 nm. What is the wavelength of the first line of Lyman series
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A bat emitting an ultrasonic wave of frequency 4.5 $$\times$$ 104 Hz at speed of 6 m/s between two parallel walls. The t
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A disc of moment of inertia 4 kg - m$$^2$$ revolving with 16 rad/s is placed on another disc of moment of inertia 8 kg -
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An electric current $I$ enters and leaves a uniform circular wire of radius $r$ through diametrically opposite points. A
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Television frequencies are of the order of 100 MHz, while radio frequencies are of the order of 1 MHz. Using these as ty
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A particle is performing simple harmonic motion. Equation of its motion is $$x = 5\sin \left( {4t - {\pi \over 6}} \rig
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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
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The displacement $$x$$ of a particle in a straight line motion is given by $$x=1-t-t^2$$. The correct representation of
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A galvanometer having a resistance of 4 $$\Omega$$ is shunted by a wire of resistance 2 $$\Omega$$. If the total current
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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
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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
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A regular hexagon of side $$m$$ which is a wire of length 24 m is coiled on that hexagon. If current in hexagon is $$I$$
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Which of the following gate give the similar output as the output of circuit diagram shown in the figure?
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Water is poured in a tank through a cylindrical tube of area of cross-section A and ejecting water at a constant speed 4
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If R and C denote resistance and capacitance of a material, then the dimension of CR will be :
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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
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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
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A bar magnet of length $$6 \mathrm{~cm}$$, is placed in the magnetic meridian with $$N$$ pole, pointing towards the geog
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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
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A 30 mW laser beam has a cross-sectional area of 15 mm2. The magnitude of the maximum electric field in this electromagn
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The average kinetic energy of a molecule in air at room temperature of 20$$^\circ$$C
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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
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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
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A plane glass mirror of thickness 3 cm of material of $$\mu=\frac{3}{2}$$ is silvered on the black surface. When a point
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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
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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
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There are two identical containers C$$_1$$ and C$$_2$$ containing to identical gases. Gas in C$$_1$$ is reduced to half
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If K$$_1$$ and K$$_2$$ are maximum kinetic energies of photoelectrons emitted when lights of wavelengths $$\lambda_1$$ a
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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
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A source of sound emits sound waves at frequency $$f_0$$. It is moving towards an observer with fixed speed $${v_s}$$ ($
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In which mode of transmission, the heat waves travel along straight line with the speed of light?
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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.
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Consider a compound slab consisting of two different materials having equal lengths, thickness and thermal conductivitie
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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
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With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is $$\frac{2}{3}$$ of
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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
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An alternating voltage = 200 $$\sin 100t$$ is applied to a series combination of $$R=30\Omega$$ and an inductor of 400 m
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In the network shown in figure, the equivalent capacitance between points P and Q is
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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
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Choose the incorrect statements.
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Charge on electron is
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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
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The AC voltage across a resistance can be measured using a
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