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AIEEE 2002JEE Main 2018 (Online) 15th April Evening Slot
Paper was held on Sun, Apr 15, 2018 9:30 AM
Chemistry
1
The increasing order of diazotisation of the following compounds is :


2
The major product formed in the following reaction is :


3
The total number of optically active compounds formed in the following reactio is :


4
The dipeptide, Gln-Gly, on treatment with CH3COCl followed y aqueous work up gives :
5
When 2-butyne is treate with H2/Lindlar's catalyst, compound X is produced as the major product and when treated with Na/liq. NH3 it produces Y as the major product Which of the following statements is correct ?
6
Which of the following best describes the diagram below of a molecular orbital ?


7
The increasing order of the acidity of the following carboxylic acids is :


8
On treatment of the following compound with a strong acid, the most susceptible site for bond cleavage is :


9
The major product formed in the following reaction is :


10
Two compounds I and II are eluted by column chromatography (adsorption of I > II). Which one of following is a correct statement ?
11
The total number of possible isomers for square-planar [Pt(Cl)(NO2)(NO3)(SCN)]2- is :
12
Two 5 molal solutions are prepared by dissolving a non-electrolyte non-volatile solute separately in the solvents X and Y. The molecular weights of the solvents are Mx and My, respectively where Mx = $${3 \over 4}$$ My. The relative lowering of vapor pressure of the solution in X is ''m'' times that of the solution in Y. Given that the number of moles of solute is very small in comparison to that of the solvent, the value of ''m'' is :
13
$$\Delta $$fGo at 500 K for substance 'S' in liquid state and gaseous state are +100.7 kcl mol-1 and +103 kcal mol-1, respectively. Vapour pressure of liquid 'S' at 500 K is approximately equal to : ( R = 2 cal K-1 mol-1 )
14
For a first order reaction, A $$ \to $$ P, t1/2 (half-life) is 10 days The time required for $${1 \over 4}$$th conversion of A (in days) is : (ln 2 = 0.693, ln 3 = 1.1)
15
The correct order of spin-only magnetic moments among the following is :
(Atomic number : Mn = 25, Co = 27, Ni = 28, Zn = 30)
(Atomic number : Mn = 25, Co = 27, Ni = 28, Zn = 30)
16
The correct order of electron affinity is :
17
In KO2, the nature of oxygen species and the oxydation state of oxygen atom are, respectively :
18
At a certain temperature in a $$5$$ $$L$$ vessel, 2 moles of carbon monoxide and 3 moles of chlorine were allowed to reach equilibrium according to the reaction,
CO + Cl2 $$\rightleftharpoons$$ COCl2
At equilibrium, if one mole of CO is present then equilibrium constant (Kc) for the reaction is :
CO + Cl2 $$\rightleftharpoons$$ COCl2
At equilibrium, if one mole of CO is present then equilibrium constant (Kc) for the reaction is :
19
Following four solutions are prepared by mixing different volumes of NaOH and HCl of different concentrations, pH of which one of them will be equal to 1 ?
20
Given
(i) 2Fe2O3(s) $$ \to $$ 4Fe(s) + 3O2(g);
$$\Delta $$rGo = + 1487.0 kJ mol-1
(ii) 2CO(g) + O2(g) $$ \to $$ 2CO2(g);
$$\Delta $$rGo = $$-$$ 514.4 kJ mol-1
Free energy change, $$\Delta $$rGo for the reaction
2Fe2O3(s) + 6CO(g) $$ \to $$ 4Fe(s) + 6CO2(g) will be :
(i) 2Fe2O3(s) $$ \to $$ 4Fe(s) + 3O2(g);
$$\Delta $$rGo = + 1487.0 kJ mol-1
(ii) 2CO(g) + O2(g) $$ \to $$ 2CO2(g);
$$\Delta $$rGo = $$-$$ 514.4 kJ mol-1
Free energy change, $$\Delta $$rGo for the reaction
2Fe2O3(s) + 6CO(g) $$ \to $$ 4Fe(s) + 6CO2(g) will be :
21
The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is :
22
For per gram of reactant, the maximum quantity of N2 gas is produced in which of the following thermal decomposition reactions ?
(Given : Atomic wt. - Cr = 52 u, Ba = 137 u)
(Given : Atomic wt. - Cr = 52 u, Ba = 137 u)
Mathematics
1
If a, b, c are in A.P. and a2, b2, c2 are in G.P. such that
a < b < c and a + b + c = $${3 \over 4},$$ then the value of a is :
a < b < c and a + b + c = $${3 \over 4},$$ then the value of a is :
2
If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :
3
If |z $$-$$ 3 + 2i| $$ \le $$ 4 then the difference between the greatest value and the least value of |z| is :
4
The number of four letter words that can be formed using the letters of the word BARRACK is :
5
Suppose A is any 3$$ \times $$ 3 non-singular matrix and ( A $$-$$ 3I) (A $$-$$ 5I) = O where I = I3 and O = O3. If $$\alpha $$A + $$\beta $$A-1 = 4I, then $$\alpha $$ + $$\beta $$ is equal to :
6
Let f : A $$ \to $$ B be a function defined as f(x) = $${{x - 1} \over {x - 2}},$$ Where A = R $$-$$ {2} and B = R $$-$$ {1}. Then f is :
7
If f(x) is a quadratic expression such that f (1) + f (2) = 0, and $$-$$ 1 is a root of f (x) = 0, then the other root of f(x) = 0 is :
8
If the position vectors of the vertices A, B and C of a $$\Delta $$ ABC are respectively $$4\widehat i + 7\widehat j + 8\widehat k,$$ $$2\widehat i + 3\widehat j + 4\widehat k,$$ and $$2\widehat i + 5\widehat j + 7\widehat k,$$ then the position vectors of the point, where the bisector of $$\angle $$A meets BC is :
9
If the mean of the data : 7, 8, 9, 7, 8, 7, $$\lambda $$, 8 is 8, then the variance of this data is :
10
A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of 'p' is :
11
An angle between the lines whose direction cosines are gien by the equations,
$$l$$ + 3m + 5n = 0 and 5$$l$$m $$-$$ 2mn + 6n$$l$$ = 0, is :
$$l$$ + 3m + 5n = 0 and 5$$l$$m $$-$$ 2mn + 6n$$l$$ = 0, is :
12
Tangents drawn from the point ($$-$$8, 0) to the parabola y2 = 8x touch the parabola at $$P$$ and $$Q.$$ If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to :
13
The foot of the perpendicular drawn from the origin, on the line, 3x + y = $$\lambda $$ ($$\lambda $$ $$ \ne $$ 0) is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is :
14
The sides of a rhombus ABCD are parallel to the lines, x $$-$$ y + 2 = 0 and 7x $$-$$ y + 3 = 0. If the diagonals of the rhombus intersect P(1, 2) and the vertex A (different from the origin) is on the y-axis, then the coordinate of A is :
15
The curve satifying the differeial equation, (x2 $$-$$ y2) dx + 2xydy = 0 and passing through the point (1, 1) is :
16
If $$\int {{{2x + 5} \over {\sqrt {7 - 6x - {x^2}} }}} \,\,dx = A\sqrt {7 - 6x - {x^2}} + B{\sin ^{ - 1}}\left( {{{x + 3} \over 4}} \right) + C$$
(where C is a constant of integration), then the ordered pair (A, B) is equal to :
(where C is a constant of integration), then the ordered pair (A, B) is equal to :
17
If $${I_1} = \int_0^1 {{e^{ - x}}} {\cos ^2}x{\mkern 1mu} dx;$$
$${I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x{\mkern 1mu} dx$$ and
$${I_3} = \int_0^1 {{e^{ - {x^3}}}} dx;$$ then
$${I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x{\mkern 1mu} dx$$ and
$${I_3} = \int_0^1 {{e^{ - {x^3}}}} dx;$$ then
18
The value of integral $$\int_{{\pi \over 4}}^{{{3\pi } \over 4}} {{x \over {1 + \sin x}}dx} $$ is :
19
Let f(x) be a polynomial of degree $$4$$ having extreme values at $$x = 1$$ and $$x = 2.$$
If $$\mathop {lim}\limits_{x \to 0} \left( {{{f\left( x \right)} \over {{x^2}}} + 1} \right) = 3$$ then f($$-$$1) is equal to :
If $$\mathop {lim}\limits_{x \to 0} \left( {{{f\left( x \right)} \over {{x^2}}} + 1} \right) = 3$$ then f($$-$$1) is equal to :
20
If f(x) = sin-1 $$\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),$$ then f'$$\left( { - {1 \over 2}} \right)$$ equals :
21
Let f(x) = $$\left\{ {\matrix{
{{{\left( {x - 1} \right)}^{{1 \over {2 - x}}}},} & {x > 1,x \ne 2} \cr
{k\,\,\,\,\,\,\,\,\,\,\,\,\,\,} & {,x = 2} \cr
} } \right.$$
Thevaue of k for which f s continuous at x = 2 is :
Thevaue of k for which f s continuous at x = 2 is :
22
$$\mathop {\lim }\limits_{x \to 0} {{x\tan 2x - 2x\tan x} \over {{{\left( {1 - \cos 2x} \right)}^2}}}$$ equals :
Physics
1
A solid ball of radius R has a charge density $$\rho $$
given by $$\rho $$ = $$\rho $$o (1 $$-$$ $${\raise0.5ex\hbox{$\scriptstyle r$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle R$}}$$) for 0 $$ \le $$ r $$ \le $$ R. The electric field outside the ball is :
given by $$\rho $$ = $$\rho $$o (1 $$-$$ $${\raise0.5ex\hbox{$\scriptstyle r$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle R$}}$$) for 0 $$ \le $$ r $$ \le $$ R. The electric field outside the ball is :
2
A plane polarized monochromatic EM wave is traveling in vacuum along z direction such that at t = t1 it is found that the electric field is zero at a spatial point z1. The next zero that occurs in its neighbourhood is at z2. The frequency of the electroagnetic wave is :
3
At the center of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity $$\omega $$ about an axis along their common diameter. Calculate the emf induced in their smaller coil after a time t of its start of rotation.
4
A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 $$ \times $$ 10-2 m. The magnetic field at the center of the triangle will be :
5
Truth table for the following digital circuit will be :


6
A plane polarized light is incident on a polariser with its pass axis aking angle $$\theta $$ with x-axis, as shown in the figure. At four different values of $$\theta ,\,\theta $$ = 8o, 38o, 188o and 218o, the observed intensities are same.
What is the angle between the direction of polarization and x-axis ?

What is the angle between the direction of polarization and x-axis ?

7

A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of $$\theta $$ with the horizontal. At the bottom rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the igure. The terminal speed of the copper rod is :
8
A capacitor C1 = 1.0 $$\mu $$F is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now C1 is disconnected from battery and connected to a circuit consisting of two uncharged capacitors $${C_2} = 3.0\mu F$$ and C3 = 6.0 $$\mu $$F through switch (2), as shown in the figure. The sum of final charges on C2 and C3 is :


9
As shown in the figure, forces of 105 N each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm, shifting the upper face parallel to itself by 0.5 cm. If the side of another cube of the same material is 20 cm, then under similar conditions as above, the displacement will be :


10
A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released the speed of this end, when the rod makes an angle $$\alpha $$ with the horizontal, will be proportional to : (see figure)


11
A thin uniform bar of length $$L$$ and mass $$8$$ m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2$$\upsilon $$ and $$\upsilon $$ respectively. The masses stick to the bar after collision at a distance $${L \over 3}$$ and $${L \over 6}$$ respectively from the center of the bar. If the br starts rotating about its center of mass as a result of collision, the angular speed of the bar will be :


12
A man in a car at location Q on a straight highway is moving with speed $$\upsilon $$. He decides to reach a point P in a field at a distance d from the highway (point M) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum ?


13
A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lenses is $$2$$ cm. The focal lengths of the component lenses are :
14
A parallel plate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is $$25 \times {10^{ - 6}}N,$$ the value of V is approximately : $$\left( {{ \in _o} = 8.85 \times {{10}^{ - 12}}{{{C^2}} \over {N.{m^2}}}} \right)$$
15
A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is $$\rho $$, how long will the changes take to travel a distance d ?
16
5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :
17
Two simple harmonic motions, as shown below, are at right angles. They are combined to form Lissajous figures.
x(t) = A sin (at + $$\delta $$)
y(t) = B sin (bt)
Identify the correct match below.
x(t) = A sin (at + $$\delta $$)
y(t) = B sin (bt)
Identify the correct match below.
18
The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms-1 is :
[kB =1.4 $$ \times $$ 10-23 J/K; mHe = 7 $$ \times $$ 10 -27 kg ]
[kB =1.4 $$ \times $$ 10-23 J/K; mHe = 7 $$ \times $$ 10 -27 kg ]
19
When an air bubble of radius r rises from the bottom to the surface of a lake its radius becomes $${{5r} \over 4}.$$ Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :
20
A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $$3.5$$ revolutions per second. A coin placed at a distnce of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is : (g = 10 m/s2)
21
A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90o with respect to each other. The mass of unknown particle is :
22
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants G, h and c.
Which of the following correctly gives the Planck length ?
Which of the following correctly gives the Planck length ?
23
A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of $${30^o}$$. The external force required to take the same body up the plane with the same acceleration will be : (g = 10 m/s2)
24
A constant voltages is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :
25
Muon ($$\mu $$$$-$$) is a negatively charged (|q| = |e|) particle with a mass m$$\mu $$ = 200 me, where me is the mass of the electron and e is the electronic charge. If $$\mu $$$$-$$ is bond to a proton to form a hydrogen like atom, identify the correct statements.
(A) Radis of the muonic orbit is 200 times smaller than that of the electron.
(B) The speed of the $$\mu $$$$-$$ in the nth orbit is $${1 \over {200}}$$ times that of the electron in the nth orbit.
(C) The ionization energy of muonic atom is 200 timesmore than of an hydroen atom.
(D) The momentum of the muon in the nth orbit is 200 times more than that of the electron.
(A) Radis of the muonic orbit is 200 times smaller than that of the electron.
(B) The speed of the $$\mu $$$$-$$ in the nth orbit is $${1 \over {200}}$$ times that of the electron in the nth orbit.
(C) The ionization energy of muonic atom is 200 timesmore than of an hydroen atom.
(D) The momentum of the muon in the nth orbit is 200 times more than that of the electron.
26
An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :
27
If the de Broglie wavelengths associated with a proton and an $$\alpha $$-particle are equal, then the ratio of velocities of the proton and the $$\alpha $$-particle will be :