COMEDK 2021

The Lyman series of hydrogen spectrum lies in which region

The value of $$\Delta G^\circ$$ for the phosphorylation of glucose in glycolysis is 13.8 kJ/mol. The value of $$K_C$$ at 298 K is

Calculate the difference between C$$_p$$ and C$$_V$$ for 10 moles of an ideal gas

Which of the following series of transitions in the spectrum of hydrogen atom fall in visible region?

When the expansion of a gas occurs in vacuum and at constant volume, then

The total number of nodes are given by

Which of the following is correct mixture of azeotrope?

Under which of the following condition, the gases does not follow Henry's law?

In the equilibrium, $$AB\rightleftharpoons A+B$$, if the equilibrium concentration of A is double, then equilibrium concentration of B will be

Which of the following is correct order of their increasing boiling points?

For the equilibrium,

2NOCl(g) $$\rightleftharpoons$$ 2NO(g) + Cl$$_2$$(g),

the value of the equilibrium constant, $$K_C$$ is 3.75 $$\times$$ 10$$^{-6}$$ at 1069 K. The value of $$K_p$$ for the reaction at this temperature will be

In the chemical reaction,

N$$_2$$ + 3H$$_2$$ $$\rightleftharpoons$$ 2NH$$_3$$ at equilibrium point.

Rate constant (K) of a reaction has least value at

For decolourisation of 1 mole of KMnO$$_4$$, the moles of H$$_2$$O$$_2$$ required is

The oxidation number of Cr in CrO$$_5$$ which has the following structure, is

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$$^2$$ mol$$^{-1}$$ respectively. What is the molar conductivity ($$\Omega^{-1}$$ cm$$^2$$ mol$$^{-1}$$) of NH$$_4$$OH?

Determine the specific rate constant of the reaction. If the half-life period of a first order reaction is 1402 s.

The specific conductivity of a solution containing 1.0 g of anhydrous BaCl$$_2$$ in 200 cm$$^3$$ of the solution has been found to be 0.0058 Scm$$^{-1}$$. The molar and equivalent conductivity of the solution respectively are

Which type of ligand is EDTA?

An aqueous solution of X on addition of hydrogen peroxide in ice cold conditions gives blue colour to the ethereal layer. Then, X can be

Find the compound which have both polar and non-polar covalent bonds.

For the reaction 2N$$_2$$O$$_5$$ $$\to$$ 4NO$$_2$$ + O$$_2$$, rate constant $$k$$ is 4.48 $$\times$$ 10$$^{-5}$$ s$$^{-1}$$ and the initial pressure is 600 atm. After 10 min, determine the final pressure of N$$_2$$O$$_5$$.

Which of the following pairs of ions in iso-electronic and iso-structural?

In 3d-transmission series, which one has the least melting point?

The reaction $$\mathrm{ArN_2^ + C{l^ - }\buildrel {Cu/HCl} \over \longrightarrow ArCl + {N_2} + CuCl}$$ is called as

What is the IUPAC name of following compound?

The correct IUPAC name of the coordination compound K$$_3$$[Fe(CN)$$_5$$NO] is

What is the product formed when benzene react with CO and HCl in presence of anhydrous AlCl$$_3$$?

Arrange stability of the given carbon cation in decreasing order

Coupling reaction is an example of

Find the final product for the reaction

Why, ketones and carboxylic acids have higher boiling point as compared to aldehydes?

Which one of the following sets of monosaccharides forms sucrose?

Reaction

find the product B.

Which of the following is most stable?

The chemical formula of Hinsberg's reagent is

Among the following enzymes, which one is involved in the given below catalytic reaction?

$${C_6}{H_{12}}{O_6}(aq) \to 2{C_2}{H_5}OH(aq) + 2C{O_2}(g)$$

If A = {1, 2, 5, 6} and B = {1, 2, 3}, then (A $$\times$$ B) $$\cap$$ (B $$\times$$ A) is equal to

Carbon monoxide is poisonous to human beings because

Total number of elements in the power set of A containing 15 elements is

Which of the following amino acid (NH$$_2$$CHRCOOH) contains polar R group?

Xerophthalmia disease causes by which deficiency of vitamin?

What is the argument of the complex number $${{(1 + i)(2 + i)} \over {3 - i}}$$, where $$i = \sqrt { - 1} $$ ?

If a, b, c are in A.P., $$b-a,c-b$$ and a are in G.P., then a : b : c is

The sum of the series $$(1 + 2) + (1 + 2 + {2^2}) + (1 + 2 + {2^2} + {2^3}) + ....$$ upto $$n$$ terms is

If $${(\sqrt 3 + i)^{100}} = {2^{99}}(a + ib)$$, then $${a^2} + {b^2}$$ is equal to

$${8^{3{{\log }_8}5}}$$ is equal to

Evaluate $${\left[ {{i^{18}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}$$.

The coefficients a, b and c of the quadratic equation, $$ax^2+bx+c=0$$ are obtained by throwing a dice three times. The probability that this equation has equal roots is

The value of $$1\,.\,1! + 2\,.\,2! + 3\,.\,3! + \,...\, + \,n\,.\,n!$$ is

If a polygon of n sides has 275 diagonals, then n is equal to

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals

The number of triangles which can be formed by using the vertices of a regular polygon of $$(n+3)$$ sides is 220. Then, $$n$$ is equal to

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

Five persons A, B, C, D and E are in queue of a shop. The probability that A and E are always together, is

A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is $$p,0 < p < 1$$. If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is

If $$49^n+16n+P$$ is divisible by 64 for all $$n\in N$$, then the least negative integral value of P is

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that $$P(B) = {3 \over 2}P(A)$$ and $$P(C) = {1 \over 2}P(B)$$, then $$P(A \cup C)$$ equals

The coefficient of $$x^{10}$$ in the expansion of $$1+(1+x)+...+(1+x)^{20}$$ is

Number of terms in the binomial expansion of $$(x+a)^{53}+(x-a)^{53}$$ is

If for $$a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k$$ and $$c = - 3\widehat i + \widehat j + 2\widehat k$$, then find $$[a\,b\,c]$$.

If |a| = 8, |b| = 3 and |a $$\times$$ b| = 12, then find the angle between a and b.

Middle term in the expansion of $${\left( {{x^2} + {1 \over {{x^2}}} + 2} \right)^n}$$ is

The vector that must be added to $$\widehat i - 3\widehat j + 2\widehat k$$ and $$3\widehat i + 6\widehat j - 7\widehat k$$ so resultant vector is a unit vector along the X-axis is

$${2^{3n}} - 7n - 1$$ is divisible by

The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is

The line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ is parallel to the plane

If for any 2 $$\times$$ 2 square matrix A, A (adj A) = $$\left[ {\matrix{ 8 & 0 \cr 0 & 8 \cr } } \right]$$, then the value of det (A).

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 $$\frac{2}{\sqrt3}$$ from the point $$(3,1,-1)$$ is

The point of intersection of the lines $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}$$ and $${{x - 4} \over 5} = {{y - 1} \over 2} = z$$ is

If matrix $$A = \left[ {\matrix{ 2 & { - 2} \cr { - 2} & 2 \cr } } \right]$$ and $${A^2} = pA$$, then the value of $$p$$ is

If $$A\,(adj\,A) = \left[ {\matrix{ { - 2} & 0 & 0 \cr 0 & { - 2} & 0 \cr 0 & 0 & { - 2} \cr } } \right]$$, then $$|adj\,A|$$ equals

The expression $${{\tan A} \over {1 - \cot A}} + {{\cot A} \over {1 - \tan A}}$$ can be written as

Write the solution of the following LPP

Maximize $$Z=x+y$$

Subject to $$3x+4y\le12,x\ge0,y\ge0$$.

Which point the value of Z is maximum?

The maximum value of $$x+y$$ subject to $$2x+3y\le6,x\ge0,y\ge0$$ is

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 $$\sin (x + y)$$ equals

The slopes of the lines, which make an angle 45$$^\circ$$ with the line $$3x-y=-5$$, are

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

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 angles between the other, then

If 3 and 4 are intercepts of a line L = 0, then the distance of L $$\equiv$$ 0 from the origin is

Shade the feasible region for the inequations $$x+y\ge2,2x+3y\le6,x\ge0,y\ge0$$ in a rough figure.

If $$\sin 2x = 4\cos x$$, then x is equal to

What will be the equation of circle whose centre is (1, 2) and touches X-axis?

What will be the equation of the circle whose centre is (1, 2) and which passes through the point (4, 6)?

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 is finite, then

If $$f(x) = \left\{ {\matrix{ {ax + 3,} & {x \le 2} \cr {{a^2}x - 1} & {x > 2} \cr } } \right.$$, then the values of a for which f is continuous for all x are

If $$f(x)$$ satisfies the relation $$2f(x) + f(1 - x) = {x^2}$$ for all real x, then $$f(x)$$ is

Find the centre and radius of the circle given by the equation $$2{x^2} + 2{y^2} + 3x + 4y + {9 \over 8} = 0$$.

The value of $$\mathop {\lim }\limits_{x \to 0} \left( {{{{a^x} + {b^x} + {c^x}} \over 3}} \right),(a,b,c > 0)$$ is

Find the maximum value of $$f(x) = {1 \over {4{x^2} + 2x + 1}}$$.

The equation of normal to the curve $$y = {(1 + x)^y} + {\sin ^{ - 1}}({\sin ^2}x)$$ at $$x = 0$$ is

The approximate value of $$f(5.001)$$, where $$f(x)=x^3-7x^2+15$$ is

Integral of $$\int {{{dx} \over {{x^2}{{[1 + {x^4}]}^{3/4}}}}} $$.

$$\int {{{{2^x}} \over {\sqrt {1 - {4^x}} }}dx} $$ is equal to

The hydrocarbon that cannot be prepared effectively by Wurtz reaction

The solution of the differential equation $$y{{dy} \over {dx}} = x\left[ {{{{y^2}} \over {{x^2}}} + {{\phi \left( {{{{y^2}} \over {{x^2}}}} \right)} \over {\phi '\left( {{{{y^2}} \over {{x^2}}}} \right)}}} \right]$$ is (where, C is a constant)

The solution of the differential equation $$(1 + {y^2}) + (x - {e^{{{\tan }^{ - 1}}y}}){{dy} \over {dx}} = 0$$ is

The solution of the differential equation $${\sec ^2}x\tan ydx + {\sec ^2}y\tan xdy = 0$$ is

$$\int_{ - \pi /2}^{\pi /2} {\sin xdx} $$

How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7?

The density of a gas A is thrice that of a gas B at the same temperature. The molecular weight of gas B is twice that of A. What will be the ratio of pressure acting on B and A?

In detector, output circuit consists of $$R=10~k\Omega$$ and $$C=100~pF$$. The frequency of carrier signal which it can detect is

An optical fibre communication system works on a wavelength of 1.3 $$\mu$$m. The number of subscribers it can feed, if a channel requires 20 kHz are

Identify the pair of gases that have equal rates of diffusion

The melting of ice

Which of the following conditions are favourable for chemisorption?

How much part of any corner atom actually belongs to a particular unit cell?

Sodium metal crystallises in a body centred cubic lattice with a unit cell edge of 4.29 $$\mathop A\limits^o $$. The radius of sodium atom is

Which of the following colloids resemble to the true solutions?

The vacant space in bcc lattice cell is

Arrange the hydrides of group 15 in correct decreasing order of reducing nature.

Which of the following particulate matter is emitted from vehicles?

Which of the following options represents the correct composition of dettol?

The reducing agent which is used to reduce iron oxide in blast furnace is

Which of the following is used as a drug to reduce fever?

Which of the following is not an antacid?

Arrange the following artificial Sweetening agents in order of increasing sweetness.

Aspartame, Saccharin, Sucralose, Alitame

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 the surroundings will be

The increasing order of atomic radii of the following group 13 elements is

Which graph shows the correct $$v$$ - $$x$$ graph of a freely falling body?

Which of the following statement is incorrect?

Find the correct order of C$$-$$O bond length among CO, CO$$_3^{2-}$$, CO$$_2$$.

Which of the following technique is not used for measuring small time intervals?

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

The displacement $$x$$ of a particle varies with time $$t$$, $$x=ae^{-pt}+be^{qt}$$, where a, b, p and q are positive constant. The velocity of the particle will

For motion under central forces, which quantity will be conserved?

The angle of projection with the horizontal in terms of maximum height attained and horizontal range is given by

Two masses of 1g and 9g are moving with equal kinetic energy. The ratio of magnitude of their momentum is

When a car of mass $$m$$ is moving with speed $$v$$ along a circle of radius $$r$$ on a level road, the centripetal force is provided by $$f$$, where $$f$$ denotes

($$\mu_s$$ $$\to$$ coefficient of friction, N $$\to$$ normal reaction)

The motion of a particle of mass $$m$$ is described by $$y = ut + g{t^2}$$. The force acting on the particle will be

A wire is stretched to double of its length. The strain is

When two bodies collide with each other such that their kinetic energy remains constant. Their collision is said to be

Newton's second law of rotational motion of a system particles having angular momentum L is given by

Which of the following quantity represents the dimensions of momentum?

Centre of mass of the given system of particles will be at

Within the elastic limit, the corresponding stress is known as

The surface tension of a liquid at its boiling point

According to Pascal's law, pressure in a fluid at rest is the same at all points, if

In an adiabatic process with the ratio of two specific heat, $$\gamma=\frac{3}{2}$$, pressure is increased by $$\frac{2}{3}$$%, then decrease in the volume will be

Which of the following is not a green house gas?

The average energy associated with a monoatomic molecule is

For an ideal gas, coefficient of volume expansion is given by

The collision of the molecules of an ideal gas is taken as

The function $$y = \log \omega t$$ can represent

A constant potential energy of a satellite is given as

$$\mathrm{PE}=r(\mathrm{KE})$$

whee, PE = potential energy

and KE = kinetic energy.

The value of $$r$$ will be

Carnot cycle of an engine is given below

Total work done by the gas in one cycle is

Kepler's second law of planetary motion corresponds to

Two spring of force constant $$k_1$$ and $$k_2$$ are configured as the figure given below

The angular frequency of this configuration is

The displacement of a wave is given by

$$y = 20\cos (\omega t + 4z)$$

The amplitude of the given wave is

The magnifying power of a telescope is 9. When it is adjusted for parallel rays, the distance between the objective and eyepiece is 20 cm. The focal length of lenses are

In Young's double slit experiment with sodium vapour lamp of wavelength 589 nm and slit 0.589 mm apart, the half angular width of the central maxima is

An unpolarised beam of intensity I$$_0$$ is incident on a pair of nicols making an angle of 60$$^\circ$$ with each other. The intensity of light emerging from the pair is

If frequencies are $$(\nu-1)$$ and $$(\nu+2)$$, then find the value of beats.

Two converging lenses of focal length 20 cm and 40 cm are placed in contact. The effective power of the combination is

Insulators can be charged by which of the following process?

The resistance of a wire is R ohm. If it is melted and stretched to n times its original length, its new resistance will be

Work done in moving a charge of 25C is 50 J. Calculate potential difference, between two points.

Two particles of masses $$m_1=m,m_2=2m$$ and charges $$q_1=q,q_2=2q$$ entered into uniform magnetic field. Find $$F_1/F_2$$ (force ratio).

A long solenoid has 20 turns cm$$^{-1}$$. The current necessary to produce a magnetic field of 20 mT inside the solenoid is approximately

What is the electric field near infinite plane sheet of charge density $$\sigma$$ ?

For the given electrical arrangement, what is the value of current I?

The relative permeability of iron is 6000. Its magnetic susceptibility is

The formula of capacitative reactance is

For the same resonant frequency, if L is changed from L to $${L \over 3}$$, then capacitance should change from C to

A bar magnet is oscillating in the earth's magnetic field with a period T. What happens to its period and motion, if its mass is quadrupled?

If impedance is $$\sqrt3$$ times of resistance, then find phase difference.

A constant current flows from A to B as shown in the figure. What is the direction of current in the circle?

The correct arrangement in increasing order of wavelength of X-rays, UV rays, microwave is

What should be the value of self-inductance of an inductor that should be connected to 220 V 50 Hz supply, so that a maximum current of 0.9 A flows through it?

Which of the following waves are used to treatment of muscles ache?

The Lyman series of a hydrogen atom belongs in which category

What is the minimum band-gap of the LED diode?

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 initially 80 g at Ba-122 was taken, how much Ba was left when experiment was started?

If an electron in hydrogen atom jumps from an orbit of level $$n=3$$ to an orbit at level $$n=2$$, emitted radiation has a frequency of

(R = Rydberg's constant and c = velocity of light)

Find the logic gate, when both the inputs are high but the output is low and vice-versa.

When the speed of light becomes $$\frac{2}{3}$$ of its present value, then the energy released in a given atomic explosion would

The velocity of the proton is one-fourth the velocity of the electron. What is the ratio of the de-Broglie wavelength of an electron to that of a proton?

What would be the molarity of one litre solution of 22.2 g of CaCl$$_2$$ ?

From the figure describing photoelectric effect, we may infer correctly that