Solved papers for JEE Main & Advanced JEE Main Paper (Held On 11-Jan-2019 Evening)
done JEE Main Paper (Held On 11-Jan-2019 Evening) Total Questions - 90
question_answer1) When 100 g of a liquid A at \[100{}^\circ C\]is added to 50 g of a liquid B at temperature\[75{}^\circ C\], the temperature of the mixture becomes\[90{}^\circ C\]. The temperature of the mixture, if 100 g of liquid A at \[100{}^\circ C\] is added to 50 g of liquid B at \[50{}^\circ C\]will b
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question_answer2) Two rods A and B of identical dimensions are at temperature \[30{}^\circ C\]. If A is heated upto \[180{}^\circ C\]and B upto \[T{}^\circ C\], then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is \[4:3\], then the value of T is
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question_answer3) A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string)
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question_answer4) If speed (V), acceleration and force (F) are considered as fundamental units, the dimension of Young's modulus will be
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question_answer5) A pendulum is executing simple harmonic motion and its maximum kinetic energy is \[{{K}_{1}}\]. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case. its maximum kinetic energy is \[{{K}_{2}}\]. Then
[JEE Main Online Paper (Held on 11-jan-2019 Evening)]
question_answer6) In a double -slit experiment, green light \[(\,5303\text{ }\overset{o}{\mathop{\text{A}}}\,)\] falls on a double slit having a separation of 19.44\[\mu m\] and a width of 4.05\[\mu m\]. The number of bright fringes between the first and the second diffraction minima is
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question_answer7) A particle of mass m is moving in a straight line with momentum p. Starting at time \[t=0,\]a force F = kt acts in the same direction on the moving particle during time interval so that its momentum changes from? to 3p. Here k is a constant. The value of T is
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question_answer8) A particle of mass m and charge q is in an electric and magnetic field given by \[\vec{E}=2\hat{i}+3\hat{j};\vec{B}=4\hat{j}+6\hat{k}.\] The charged particle is shifted from the origin to the point \[P(x=1;y=1)\]along a straight path. The magnitude of the total work done is
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question_answer9) An amplitude modulated signal is plotted below Which one of the following best describes the above signal?
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question_answer10) The region between\[y=0\]and\[y=d\]contains a magnetic field \[\vec{B}=B\overset{\wedge }{\mathop{z}}\,.\] A particle of mass m and charge q enters the region with a velocity \[\vec{v}=v\hat{i}.\] If \[d=\frac{mv}{2qB},\] the acceleration of the charged particle at the point of its emergence at the other side is
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question_answer11) A particle moves from the point \[(2.0\hat{i}+4.0\hat{j})m,\]at t = 0, with an initial velocity\[(5.0\hat{i}+4.0\hat{j})m{{s}^{-1}}\]. It is acted upon by a constant force which produces a constant acceleration \[(4.0\hat{i}+4.0\hat{j})m{{s}^{-2}}.\] What is the distance of the particle from the origin at time 2s?
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question_answer12) A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3 keeping the number of turns of the coil per unit length of the frame the same then the self-inductance of the coil
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question_answer13) A metal ball of mass 0.1 kg is heated upto \[500{}^\circ C\] and dropped into a vessel of heat capacity\[800\,\,J{{K}^{-1}}\] and containing 0.5 kg water. The initial temperature of water an d vessel is \[30{}^\circ C\]. What is the approximate percentage increment in the temperature of the water? [Specific heat capacities of water and metal are, respectively, 4200 \[Jk{{g}^{-1}}\,{{K}^{-1}}\]and 400 \[J\,k{{g}^{-1}}\,{{K}^{-1}}\]]
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question_answer14) The circuit shown below contains two ideal diodes, each with a forward resistance of \[50\Omega .\] If the battery voltage is 6 V, the current through the \[100\Omega \]resistance (in Amperes) is
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question_answer15) An electric field of 1000 V/m is applied to an electric dipole at angle of \[45{}^\circ \]. The value of electric dipole moment is \[{{10}^{-29}}Cm.\]What is the potential energy of the electric dipole?
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question_answer16) In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is\[\lambda \]. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be
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question_answer17) A circular disc \[{{D}_{1}}\] of mass M and radius R has two identical discs \[{{D}_{2}}\] and \[{{D}_{3}}\]of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO?, passing through the centre of \[{{D}_{1}}\], as shown in the figure, will be
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question_answer18) The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be
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question_answer19) In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to\[\left( \frac{hc}{e}=1240nm-V \right)\]
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question_answer20) A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of \[20\times {{10}^{-6}}J/T\] when a magnetic intensity of \[60\times {{10}^{3}}A/m\]is applied. Its magnetic susceptibility is
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question_answer21) In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process, the temperature of the gas is increased by \[\Delta T\]. The amount of heat absorbed by gas is (R is gas constant)
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question_answer23) A thermometer graduated according to a linear scale reads a value \[{{x}_{0}}\] when in. contact with boiling water, and \[{{x}_{0}}/3\] when in contact with ice. What is the temperature of an object in\[{}^\circ C\], if this thermometer in the contact with the object reads\[{{x}_{0}}/2\] ?
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question_answer24) In the experimental set up of metre bridgre shown in the figure, the null point is obtained at a distance of 40 cm from A. If a \[10\Omega \]resistor is connected in series with \[{{R}_{1}},\] the null point shifts by 10 cm. The resistance that should be connected in parallel with \[({{R}_{1}}+10)\Omega \] such that the null point shifts back to its initial position is
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question_answer25) A galvanometer having a resistance of \[20\,\Omega \]and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a voltmeter upto 15 volt, is
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question_answer26) The magnitude of torque on a particle of mass 1 kg is 2.5 N m about the origin. If the force acting on it is 1 N, and the distance of the particle from the origin is 5 m, the angle between the force and the position vector is (in radians)
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question_answer27) Seven capacitors, each of capacitance \[2\mu F,\]are to be connected in a configuration to obtain an effective capacitance of \[\left( \frac{6}{13} \right)\mu F,\]Which of the combinations, shown in figures below, will achieve the desired value?
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question_answer28) A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is \[\sqrt{3},\]then the angle of incidence is
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question_answer29) A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of \[{{10}^{-2}}\]m. The relative change in the angular frequency of the pendulum is best given by
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question_answer30) A 27 mW laser beam has a cross-sectional area of\[10\text{ }m{{m}^{2}}\]. The magnitude of the maximum electric field in this electromagnetic wave is given by [Given permittivity of space\[{{\varepsilon }_{0}}=9\times {{10}^{-12}}\] SI units, speed of light \[c=3\times {{10}^{8}}m/s\]]
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question_answer31) The number of bridging CO ligand(s) and Co-Co bond(s) in \[{{C}_{{{O}_{2}}}}{{(CO)}_{8}},\]respectively are
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question_answer33) The relative stability of +1 oxidation state of group 13 elements follows the order
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question_answer37) A compound X on treatment with \[B{{r}_{2}}/NaOH,\]provided \[{{C}_{3}}{{H}_{9}}N,\]which gives positive carbylamine test. Compound X is
question_answer38) \[{{K}_{2}}Hg{{I}_{4}}\]is 40% ionised in aqueous solution. The value of its van't Hoff factor (i) is
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question_answer39) The coordination number of Th in\[{{K}_{4}}[Th{{({{C}_{2}}{{O}_{4}})}_{4}}{{(O{{H}_{2}})}_{2}}]\]is \[({{C}_{2}}O_{4}^{2-}=oxalato)\]
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question_answer41) The reaction \[2X\to B\]is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life is 6 h. When the initial concentration of X is 0.5 M the time required to reach its final concentration of 0.2 M will be
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question_answer42) Which of the following compounds will produce a precipitate with \[AgN{{O}_{3}}\]?
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question_answer44) The standard reaction Gibbs energy for a chemical reaction at an absolute temperature T is given by \[{{\Delta }_{r}}{{G}^{o}}=A-BT,\]where A and B are non-zero constants. Which of the following is true about this reaction?
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question_answer46) The radius of the largest sphere which fits properly at the centre of the edge of a body centred cubic unit cell is (edge length is represented by a)
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question_answer47) 25 mL of the given HCl solution requires 30 mL of 0. 1 M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2 M aqueous NaOH solution?
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question_answer49) Among the colloids, cheese , milk (M) and smoke (S), the correct combination of the dispersed phase and dispersion medium, respectively is
[JEE Main Online Paper (Held on 11-jan-2019 Evening)]
A)
C : solid in liquid, M : liquid in liquid, S : gas in solid
doneclear
B)
C : solid in liquid, M : solid in liquid, S : solid in gas
doneclear
C)
C : liquid in solid, M : liquid in solid, S: solid in gas
doneclear
D)
C : liquid in solid, M : liquid in liquid, S : solid in gas
question_answer52) Which of the following compounds reacts with ethylmagnesium bromide and also decolourizes bromine water solution?
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question_answer53) The de Broglie wavelength \[(\lambda )\]associated with a photoelectron varies with the frequency \[(\upsilon )\]of the incident radiation as, [\[{{\upsilon }_{0}}\] is threshold frequency]
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question_answer55) The reaction,\[Mg{{O}_{(s)}}+{{C}_{(s)}}\to M{{g}_{s}}+C{{O}_{g}},\]for which \[{{\Delta }_{r}}{{H}^{o}}=+491.1kJ\,mo{{l}^{-1}}\] and\[{{\Delta }_{r}}{{S}^{o}}=198.0J\,{{K}^{-1}}mo{{l}^{-1}},\]is not feasible at 298 K. Temperature above which reaction will be feasible is
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question_answer56) For the equilibrium,\[2{{H}_{2}}O{{H}_{3}}{{O}^{+}}+O{{H}^{-}},\]the value of \[\Delta {{G}^{o}}\]at 298 K is approximately
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question_answer57) Given the equilibrium constant \[{{K}_{c}}\]of the reaction: \[C{{u}_{(s)}}+2A{{g}^{+}}_{(aq)}\to C{{u}^{2+}}_{(aq)}+2A{{g}_{(s)}}\]is \[10\times {{10}^{15}},\]calculate the \[E_{cell}^{o}\]of this reaction at 298 K. \[\left[ 2.303\frac{RT}{F}at\,298\,K=0.059V \right]\]
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question_answer58) Taj Mahal is being slowly disfigured and discoloured. This is primarily due to
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question_answer59) \[A\xrightarrow[{}]{4KOH,{{O}_{2}}}\underset{(green)}{\mathop{2B}}\,+2{{H}_{2}}O\] \[3B\xrightarrow[{}]{4HCl}\underset{(purple)}{\mathop{2C}}\,+Mn{{O}_{2}}+2{{H}_{2}}O\] \[2C\xrightarrow[{}]{{{H}_{2}}O,KI}2A+2KOH+D\] In the above sequence of reactions, A and D, respectively are
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question_answer61) All x satisfying the inequality\[{{(co{{t}^{-1}}x)}^{2}}-7(co{{t}^{-1}}x)+10>0,\] lie in the interval
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question_answer62) Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression \[\frac{{{x}^{m}}{{y}^{n}}}{(1+{{x}^{2m}})(1+{{y}^{2n}})}\]is
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question_answer63) Contrapositive of the statement "If two numbers are not equal, then their squares are not equal." is
[JEE Main Online Paper (Held on 11-jan-2019 Evening)]
A)
If the squares of two numbers are not equal, then the numbers are equal.
doneclear
B)
If the squares of two numbers are not equal, then the numbers are not equal.
doneclear
C)
If the squares of two numbers are equal, then the numbers are equal.
doneclear
D)
If the squares of two numbers are equal, then the numbers are not equal.
question_answer64) Let \[\sqrt{3}\hat{i}+\hat{j},\hat{i}+\sqrt{3}\hat{j}\]and \[\beta \hat{i}+(1-\beta )\hat{j}\]respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is \[\frac{3}{\sqrt{2}},\]then the sum of all possible values of \[\beta \] is
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question_answer65) Two lines \[\frac{x-3}{1}=\frac{y+1}{3}=\frac{z-6}{-1}\]and\[\frac{x+5}{7}=\frac{y-2}{-6}=\frac{z-3}{4}\]intersect at the point R. The reflection of R in the xy-plane has coordinates
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question_answer66) In a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5) then the equation of the diagonal AD is
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question_answer67) A circle cuts a chord of length 4a on the x- axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle is
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question_answer68) If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is
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question_answer69) Set \[{{S}_{n}}=1+q+{{q}^{2}}+...+{{q}^{n}}\]and \[{{T}_{n}}=1+\left( \frac{q+1}{2} \right)+{{\left( \frac{q+1}{2} \right)}^{2}}+...+{{\left( \frac{q+1}{2} \right)}^{n}}\]where q is a real number and \[q\ne 1.\] It \[^{101}{{C}_{1}}{{+}^{101}}{{C}_{2}}{{S}_{1}}+...{{+}^{101}}{{C}_{101}}{{S}_{100}}=\alpha {{T}_{100}},\]then \[\alpha \] is equal to
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question_answer70) Let \[f(x)=\frac{x}{\sqrt{{{a}^{2}}+{{x}^{2}}}}-\frac{d-x}{\sqrt{{{b}^{2}}+{{(d-x)}^{2}}}},x\in R\]where a, b and d are non-zero real constants. Then
[JEE Main Online Paper (Held on 11-jan-2019 Evening)]
A)
f' is not a continuous function of x
doneclear
B)
f is neither increasing nor decreasing function of x
question_answer71) Given:\[\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}\]for a \[\Delta ABC\]with usual notation. It \[\frac{\cos A}{\alpha }=\frac{\operatorname{cosB}}{\beta }=\frac{\operatorname{cosC}}{\gamma },\]then the ordered triad \[(\alpha ,\beta ,\gamma )\]has a value
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question_answer72) \[\underset{x\to 0}{\mathop{\lim }}\,\frac{x\cot (4x)}{{{\sin }^{2}}x{{\cot }^{2}}(2x)}\]is equal to
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question_answer73) If \[{{19}^{th}}\] term of a non-zero A.P. is zero, then it \[({{49}^{th}}\,\,term):({{29}^{th}}\,\,term)\]is
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question_answer74) If the area of the triangle whose one vertex is at the vertex of the parabola, \[{{y}^{2}}+4(x-{{a}^{2}})=0\] and the other two vertices are the points of intersection of the parabola and y-axis. is 250 sq. units, then a value of a is
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question_answer75) Let \[{{(x+10)}^{50}}+{{(x-10)}^{50}}={{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+\]\[...+{{a}_{50}}{{x}^{50}},\] for all\[x\in R;\]then \[\frac{{{a}_{2}}}{{{a}_{0}}}\]is equal to
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question_answer76) The area (in sq. units) in the first quadrant bounded by the parabola\[y={{x}^{2}}+1,\] the tangent to it at the point (2, 5) and the coordinate axes is
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question_answer78) Let A and B be two invertible matrices of order \[3\times 3.\]If \[\det (AB{{A}^{T}})=8\]and \[\det (A{{B}^{-1}})=8,\]then \[\det (B{{A}^{-1}}{{B}^{T}})\]is equal to
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question_answer79) Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?
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question_answer80) A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then \[\left( \frac{Mean\,of\,X}{S\tan dard\,Deviation\,of\,X} \right)\] is equal to
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question_answer82) Let \[\alpha \]and \[\beta \]be the roots of the quadratic equation \[{{x}^{2}}\sin \theta -x(sin\theta cos\theta +1)\]\[+(cos\theta =0({{0}^{o}}<\theta <{{45}^{o}})\]and \[\alpha <\beta .\]Then \[\sum\limits_{n=0}^{\infty }{\left( {{\alpha }^{n}}\frac{{{(-1)}^{n}}}{{{\beta }^{n}}} \right)}\]is equal to
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question_answer83) If\[\int_{{}}^{{}}{\frac{x+1}{\sqrt{2x-1}}}dx=f(x)\sqrt{2x-1}+C,\]where C is a constant of integration, then f(x) is equal to
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question_answer84) The number of functions f from {1, 2, 3,...., 20} onto {1, 2, 3,..., 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4 is
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question_answer85) The integral \[\int\limits_{\pi /6}^{\pi /4}{\frac{dx}{\sin 2x(ta{{n}^{5}}x+co{{t}^{5}}x)}}\]
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question_answer86) The solution of the differential equation,\[\frac{dy}{dx}={{(x-y)}^{2}},\]when\[y(1)=1\]is
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question_answer87) Let K be the set of all real values of x where the function\[f(x)=\sin |x|-|x|+2(x-\pi )\]is not differentiable. Then the set K is equal to
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question_answer88) Let z be a complex number such that \[|z|+z=3+i\](where \[i=\sqrt{-1})\]). Then |z| is equal to
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question_answer89) If the point \[(2,\alpha ,\beta )\]lies on the plane which passes through the points (3,4, 2) and (7,0,6) and is perpendicular to the plane \[2x-5y=15,\]then \[2\alpha -3\beta \]is equal to
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question_answer90) Let S = {1, 2, .... 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is "nice" is
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