Solved papers for JEE Main & Advanced JEE Main Paper (Held On 09-Jan-2019 Evening)
done JEE Main Paper (Held On 09-Jan-2019 Evening) Total Questions - 90
question_answer1) In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of band width 6 MHz are (Take velocity of light \[c\text{ }=\text{ }3\text{ }\times \text{ }{{10}^{8}}\,m/s,\text{ }h=6.6\,\,\times \,\,{{10}^{-\,34}}J-s)\]
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question_answer2) The magnetic field associated with a light wave is given, at the origin, by \[B\text{ }=\text{ }{{B}_{0}}\] \[[sin(3.14\,\times \,\,{{10}^{7}})ct+sin(6.28\,\,\times \,{{10}^{6}})ct]\] If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the photo electrons? \[\left( c=3\text{ }\times \text{ }{{10}^{8}}\text{ }m{{s}^{-\,1}},\text{ }h\,\,=\,\,6.6\,\,\times \,\,{{10}^{-34}}\,J-s \right)\]
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question_answer3) The top of a water tank is open to air and its water level maintained. It is giving out \[0.74\text{ }{{m}^{3}}\] water per minute through a circular opening of 2 cm radius is its wall. The depth of the centre of the opening from the level of water in the tank is close to:
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question_answer4) A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by \[20%\] The value of ratio m/M is close to:
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question_answer5) A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants \[{{K}_{1}},\text{ }{{K}_{2}},\text{ }{{K}_{3}},\text{ }{{K}_{4}}\] arranged as shown in the figure. The effective dielectric constant K will be:
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question_answer6) A carbon resistance has a following colour code. What is the value of the resistance?
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question_answer7) A series AC circuit containing an inductor\[\left( 20\text{ }mH \right)\], a capacitor \[\left( 120\text{ }\mu F \right)\] and a resistor \[\left( 60\text{ }\Omega \right)\] is driven by an AC source of\[24\text{ }V/50\text{ }Hz\]. The energy dissipated in the circuit in 60 s is:
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question_answer8) A force acts on a 2 kg object so that its position is given as a function of time as\[x=3{{t}^{2}}+5\]. What is the work done by this force in first 5 seconds?
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question_answer9) One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil. If the same current is passed in both, the ratio of the magnetic field at the central of the loop \[({{B}_{L}}),\,\,\,\,i.e.\,\,\,\frac{{{B}_{L}}}{{{B}_{C}}}\]will be:
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question_answer10) In a young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength \[\lambda \text{ }=\text{ }500\text{ }nm\] is incident on the slits. The total number of bright fringes that are observed in the angular range \[-30{}^\circ \le \,\theta \le 30{}^\circ \] is:
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question_answer11) Two Carnot engines A and B are operated in series. The first one, A, receives heat at \[{{T}_{1}}\left( =600\text{ }K \right)\] and rejects to a reservoir at temperature Ta. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at\[{{T}_{3}}(=400\text{ }K)\]. Calculate the temperature \[{{T}_{2}}\] if the work outputs of the engines are equal:
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question_answer12) At a given instant, say\[t=0\], two radioactive substances A and B have equal activities. The ratio \[\frac{{{R}_{B}}}{{{R}_{A}}}\] of their activities after time t itself decays with time t as \[{{e}^{-3t}}\]. If the half-life of A is ln2, the half-life of B is-
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question_answer13) Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror \[\left( {{M}_{1}} \right)\] and parallel to the second mirror \[({{M}_{2}})\] is finally reflected from the second mirror \[({{M}_{2}})\] parallel to the first mirror\[\left( {{M}_{1}} \right)\]. The angle between the two mirrors will be:
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question_answer14) [a] In the given circuit the internal resistance of the 18 V cell is negligible. If \[{{R}_{1}}\,\,=\,\,400\,\Omega \], \[{{R}_{3}}=100\text{ }\Omega \] and \[{{R}_{4}}=500\Omega \]and the reading of an ideal voltmeter across \[{{R}_{4}}\] is 5 V, then the value of \[{{R}_{2}}\] will be:
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question_answer15) Charge is distributed within a sphere of radius R with a volume charge density\[\rho (r)=\frac{A}{{{r}^{2}}}{{e}^{{}^{-2r}/{}_{a}}}\], where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:
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question_answer16) Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:
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question_answer17) In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed 'v' more than that of car B. Both the cars start, from rest and travel with constant acceleration \[{{a}_{1}}\text{ }and\text{ }{{a}_{2}}\] respectively. Then 'v' is equal to:
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question_answer18) A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of \[45{}^\circ \] at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is \[\left( g=10\text{ }m{{s}^{-}}^{2} \right)\]
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question_answer19) The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is:
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question_answer20) A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A and its efficiency is \[90%\], the output current would be:
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question_answer21) A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature\[27{}^\circ C\]. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take\[\,R=8.3\] J/K mole]
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question_answer22) The position co-ordinates of a particle moving in a 3-D coordinate system is given by \[~x=a\text{ }cos\omega t\] \[y=a\text{ }sin\omega t\] and \[z=a\omega t\] The speed of the particle is:
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question_answer23) A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about\[x=0\]. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be:
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question_answer24) The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth \[=6.4\times {{10}^{3}}km\]) is \[{{E}_{1}}\] and kinetic energy required for the satellite to be in a circular orbit at this height is \[{{E}_{2}}\]. The value of h for which \[{{E}_{1}}\] and \[{{E}_{2}}\] are equal, is:
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question_answer25) A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at n speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to:
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question_answer26) A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle is (Given charge of electron \[=1.6\,\times \,{{10}^{-19}}C\])
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question_answer27) A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of \[30{}^\circ \]from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad \[{{s}^{-1}}\]) will be (\[g=10\text{ }m{{s}^{-2}}\])
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question_answer28) The energy associated with electric field is (\[{{U}_{E}}\]) and with magnetic field is (\[{{U}_{B}}\]) for an electromagnetic wave in free space. Then:
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question_answer29) Two point charges \[{{q}_{1}}\,(\sqrt{10}\,\mu C)\]and \[{{q}_{2}}(-25\,\,\mu C)\] are placed on the x-axis at \[x=1\,m\] and \[x=4\,m\]respectively. The electric field (in V/m) at a point \[y=3\]m on y-axis is, [take\[\frac{1}{4\pi {{\in }_{0}}}\,\,=\,\,9\,\times {{10}^{9}}\,N{{m}^{2}}{{C}^{-}}^{2}\]]
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question_answer30) Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of \[{{V}_{0}}\] changes by: (assume that the Ge diode has large breakdown voltage)
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question_answer32) A solution containing 62 g ethylene glycol in 250 g water is cooled to\[-10{}^\circ C\]. If \[{{K}_{f}}\] for water is \[1.86\text{ }K\text{ }kg\text{ }mo{{l}^{-1}}\], the amount of water (in g) separated as ice is:
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question_answer33) For coagulation of arsenious sulphide sol which one of the following salt solution will be most effective?
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question_answer34) In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?
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question_answer36) For the following reaction, the mass of water produced from 4.45 g of \[{{C}_{57}}{{H}_{110}}{{O}_{6}}\] is: \[2{{C}_{57}}{{H}_{110}}{{O}_{6}}(s)+163{{O}_{2}}(g)\to 114C{{O}_{2}}(g)+110{{H}_{2}}O(\ell )\]
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question_answer37) If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for the reaction \[Zn(s)+C{{u}^{2+}}(aq)\,\,\,\rightleftharpoons \,\,Z{{n}^{2+}}(aq)+Cu\,(s)\] At 300 K is approximately \[\left( R=8J{{K}^{-}}^{1}mo{{l}^{-1}},\text{ }F\,\,=\,\,96000\text{ }C\text{ }mo{{l}^{-1}} \right)\]
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question_answer38) The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is: (Specific heat of water liquid and water vapour are \[4.2\text{ }kJ\text{ }{{K}^{-1}}\,k{{g}^{-}}^{1}\] and \[2.0\text{ }kJ\text{ }{{K}^{-1}}\,k{{g}^{-}}^{1}\]heat of liquid fusion and vapourisation of water are \[334\text{ }kJ\text{ }k{{g}^{-1}}\] and \[2491\text{ }kJ\text{ }k{{g}^{-1}}\], respectively), \[(log\text{ }273\,\,\,=\,\,2.436\], \[log\text{ }373=2.572,\text{ }log\text{ }383\,\,\text{=}\,\,2.583)\]
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question_answer39) For the reaction, \[2A\,\,+\,\,B\,\,\to \] products, when the concentrations of A and B both were doubled, the rate of the reaction increased from \[0.3\text{ }mol\text{ }{{L}^{-1}}{{s}^{-}}^{1}\] to\[2.4\text{ }mol\text{ }{{L}^{-1}}{{s}^{-}}^{1}\]. When the concentration of A alone is doubled, the rate increased from \[0.3\text{ }mol\text{ }{{L}^{-}}^{1}\,{{s}^{-}}^{1}\] to\[0.6\text{ }mol\,\,L{{\,}^{-}}^{1}s{{\,}^{-1}}\]. Which one of the following statements is correct?
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question_answer42) Homoleptic octahedral complexes of a metal ion \[{{M}^{3+}}\] with three monodentate ligands \[{{L}_{1}},\text{ }{{L}_{2}}and\text{ }{{L}_{3}}\] absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is-
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question_answer43) When the first electron gain enthalpy \[\left( {{\Delta }_{eg}}H \right)\] of oxygen is \[-141\text{ }kJ/mol\], Its second electron gain enthalpy is:
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question_answer52) The products formed in the reaction of cumene with \[{{O}_{2}}\] followed by treatment with dil. HCl are:
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question_answer53) At\[100{}^\circ C\], copper (Cu) has FCC unit cell structure with cell edge length of x \[\overset{o}{\mathop{A}}\,\]. What is the approximate density of Cu (in\[g\text{ }c{{m}^{-}}^{3}\]) at this temperature? [Atomic Mass of \[Cu\,\,=\,\,63.55\,u\]]
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question_answer61) Let \[{{z}_{0}}\] be a root of the quadratic equation, \[{{x}^{2}}+x+1=0\]. If \[z=3+6i\,{{z}_{0}}^{81}-\,3i\,{{z}_{0}}^{93}\], then arg z is equal to:
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question_answer62) Let f: \[\left[ 0,\text{ }1 \right]\,\,\to \,\,R\] be such that\[f\left( xy \right)=f\left( x \right).f\left( y \right)\], for all \[x,\,\,y\,\,\in \,\,\,[0,\,\,\,1]\] and\[f(0)\,\,\ne \,\,0\]. If \[y\,\,=\,\,y(x)\]satisfies the differential equation, \[\frac{dy}{dx}\,\,=\,\,f(x)\,\]with \[y\left( 0 \right)\,\,=\,\,1\], then \[y\left( \frac{1}{4} \right)+y\left( \frac{3}{4} \right)\]is equal to:
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question_answer63) The coefficient of \[{{t}^{4}}\] in the expansion of \[{{\left( \frac{1-{{t}^{6}}}{1-t} \right)}^{3}}\]
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question_answer64) Let \[\overrightarrow{a}=\widehat{i}+\widehat{j}\,\,+\sqrt{2}\widehat{k},\,\,\,\overrightarrow{b}={{b}_{1}}\widehat{i}\,\,+\,{{b}_{2}}\widehat{j}\,\,+\,\,\sqrt{2}\widehat{k}\]and \[\overrightarrow{c}=5\widehat{i}\,\,+\,\,\widehat{j}\,\,+\,\,\sqrt{2}\widehat{k}\] be three vectors such that the projection vector of \[\overrightarrow{b}\] on \[\overrightarrow{a}\] is \[\overrightarrow{a}\]. If \[\overrightarrow{a}\,\,+\,\,\overrightarrow{b}\] is perpendicular to \[\overrightarrow{c}\], then \[\left| \overrightarrow{b} \right|\] is equal to:
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question_answer65) If \[f\left( x \right)\,\,=\,\int{\frac{5{{x}^{8}}+7{{x}^{6}}}{{{({{x}^{2}}+1+2{{x}^{7}})}^{2}}}}\,\,dx\,,\,\,\,(x\,\,\ge \,\,0)\,\], and \[f\left( 0 \right)\,\,\,=\,\,0\], then the value of f(1) is:
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question_answer66) If \[x\,\,=\,\,3\text{ }tan\text{ }t\] and \[y\,\,=\,\,3\text{ }sec\text{ }t\], then the value of \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\] at \[t=\frac{\pi }{4}\]is:
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question_answer67) The sum of the following series \[1+6+\frac{9({{1}^{2}}+{{2}^{2}}+{{3}^{2}})}{7}\,\,+\,\,\frac{12({{1}^{2}}+{{2}^{2}}+{{3}^{2}}+{{4}^{2}})}{9}+\] \[\frac{15({{1}^{2}}+{{2}^{2}}+......\,\,+{{5}^{2}})}{11}\,+\,.....\]up to 15 terms, is:
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question_answer68) Let a, b and c be the\[{{7}^{th}}\], \[{{11}^{th}}\] and \[{{13}^{th}}\] terms respectively of a non-constant A.P. If these are also the three consecutive terms of a G.P., then \[\frac{a}{c}\] is equal to:
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question_answer69) A hyperbola has its centre at the origin, passes through the point \[\left( 4,\text{ }2 \right)\] and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is:
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question_answer70) Let the equations of two sides of a triangle be \[3x-2y+6=0\] and\[4x+5y-20=0\]. If the orthocentre of this triangle is at \[\left( 1,\text{ }1 \right)\], then the equation of its third side is:
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question_answer71) A data consists of n observations: \[{{x}_{1}},\,\,{{x}_{2}},\,\,\,....,\,\,{{x}_{n}},\]. If \[\sum\limits_{i\,=\,1}^{n}{{{({{x}_{i}}+1)}^{2}}\,\,=\,\,9n}\] and \[\sum\limits_{i\,=\,1}^{n}{{{({{x}_{i}}-1)}^{2}}=5n}\]then the standard deviation of this data is:
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question_answer72) If \[0\,\,\le \,\,x\,<\,\,\frac{\pi }{2}\] , then the number of values of x for which \[\sin \,\,x-sin\text{ 2}x+sin\text{ }3x=0\] is
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question_answer73) If the tines \[x=ay+b,\]\[z=cy+d\]and \[x=a'z\,\,+b'\], \[y\,\,=\,\,c'z\,\,+d'\] are perpendicular then:
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question_answer74) The equation of the plane containing the straight line \[\frac{x}{2}\,\,=\,\,\frac{y}{3}\,\,=\,\,\frac{z}{4}\]and perpendicular to the plane containing the straight lines \[\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\,\,and\,\,\frac{x}{4}=\frac{y}{2}=\frac{z}{3}\]
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question_answer75) Let f be a differentiable function from, R to R such that\[\left| f(x)-f(y) \right|\,\,\le \,\,2\,\,{{\left| x-y \right|}^{3/2}}\], for all\[x,\,\,y\,\,\in \,\,\,R.\,\]. If \[f\left( 0 \right)=1\] then \[\int\limits_{0}^{1}{{{f}^{2}}\left( x \right)dx}\] is equal to:
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question_answer76) Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:
question_answer77) The area of the region \[A=\{(x,\,\,y):0\,\,\le \,\,y\,\,\le \,\,x|x|+1\,\,and\,\,-\,1\le x\le 1\}\]in sq. units, is :
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question_answer78) If the circles \[{{x}^{2}}+{{y}^{2}}-16x-20y+164={{r}^{2}}\]and \[{{\left( x-4 \right)}^{2}}+{{\left( y-7 \right)}^{2}}=36\] intersect at two distinct points, then
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question_answer79) An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:
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question_answer81) The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to:
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question_answer82) If \[\int\limits_{0}^{\pi /3}{\frac{\tan \,\theta }{\sqrt{2\,k\,\,\sec \,\theta }}}\,d\,\theta \,\,=\,\,1-\frac{1}{\sqrt{2}}\,,\text{ }\left( k\,\,>\,\,0 \right)\], then the value of k is:
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question_answer83) The number of all possible positive integral values of a for which the roots of the quadratic equation, \[6{{x}^{2}}-11x+\alpha =0\] are rational numbers is:
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question_answer84) The logical statement \[[\tilde{\ }\left( \tilde{\ }p\vee q \right)\vee (p\wedge r)]\,\,\wedge \,(\sim q\wedge r)\,\] is equivalent to:
[JEE Main Online Paper (Held On 09-Jan-2019 Evening]
A)
\[(\sim p\wedge \sim q)\wedge r\]
doneclear
B)
\[(p\wedge \sim q)\vee r\]
doneclear
C)
\[\left( p\wedge r \right)\,\,\wedge \tilde{\ }\,q\]
question_answer86) If both the roots of the quadratic equation \[{{x}^{2}}-mx+4=0\] are real and distinct and they lie in the interval \[\left[ 1,\text{ }5 \right]\], then m lies in the interval:
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question_answer87) If \[x=si{{n}^{-1}}\left( sin\text{ }10 \right)\] and \[y=co{{s}^{-1}}\,\,cos10)\], then \[y-x\] is equal to:
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question_answer88) Let \[A=\{x\text{ }\in \text{ }R:x\] is not a positive integer}. Define a function \[f:A\to R\] as \[f(x)\,\,=\,\,\frac{2x}{x-1}\], then f is:
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question_answer89) For each\[x\text{ }\in \text{ }R\], let [x] be the greatest integer less than or equal to x. Then\[\underset{x\to {{0}^{-}}}{\mathop{\lim }}\,\,\frac{x([x]+\left| x \right|)\,sin\,[x]}{\left| x \right|}\]
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question_answer90) Let A(\[4,\text{ }-4\]) and B(9, 6) be points on the parabola, \[{{y}^{2}}=4x\]. Let C be chosen on the arc AOB of the parabola, where 0 is the origin, such that the area of \[\Delta \,ACB\] is maximum. Then, the area (in sq. units) of \[\Delta \,ACB\], is:
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