Solved papers for JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Morning)
done JEE Main Paper (Held on 10-4-2019 Morning) Total Questions - 90
question_answer1) Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are: [JEE Main 10-4-2019 Morning]
question_answer2) A current of 5 A passes through a copper conductor (resistivity\[=1.7\times {{10}^{-8}}\Omega m\]) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is \[=1.1\times {{10}^{-3}}m/s.\] [JEE Main 10-4-2019 Morning]
question_answer4) One plano-convex and one plano-concave lens of same radius of curvature 'R' but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is \[{{\mu }_{1}}\]and that of 2 is \[{{\mu }_{2}}\], then the focal length of the combination is : [JEE Main 10-4-2019 Morning]
question_answer5) A ball is thrown upward with an initial velocity \[{{V}_{0}}\]from the surface of the earth. The motion of the ball is affected by a drag force equal to \[m\gamma {{\upsilon }^{2}}\] (where m is mass of the ball, \[\upsilon \]is its instantaneous velocity and \[\gamma \] is a constant). Time taken by the ball to rise to its zenith is : [JEE Main 10-4-2019 Morning]
question_answer6) A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by \[20{}^\circ C\] is : [Given that \[R=8.31\text{ }J\text{ }mo{{l}^{1}}\text{ }{{K}^{1}}\]] [JEE Main 10-4-2019 Morning]
question_answer7) A thin disc of mass M and radius R has mass per unit area \[\sigma (r)=k{{r}^{2}}\] where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is : [JEE Main 10-4-2019 Morning]
question_answer8) Two coaxial discs, having moments of inertia \[{{I}_{1}}\]and \[\frac{{{I}_{1}}}{2},\]are rotating with respective angular velocities \[{{\omega }_{1}}\]and \[\frac{{{\omega }_{1}}}{2},\]about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \[{{E}_{f}}\]and\[{{E}_{i}}\]are the final and initial total energies, then \[({{E}_{f}}-{{E}_{i}})\]is : [JEE Main 10-4-2019 Morning]
question_answer10) A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let \[{{r}_{p}},{{r}_{e}}\]and \[{{r}_{He}}\] be their respective radii, then, [JEE Main 10-4-2019 Morning]
question_answer11) The electric field of a plane electromagnetic wave is given by \[\vec{E}={{E}_{0}}\hat{i}\cos (kz)cos(\omega t)\] The corresponding magnetic field \[\vec{B}\]is then given by: [JEE Main 10-4-2019 Morning]
question_answer12) Two wires A & B are carrying currents \[{{I}_{1}}\And {{I}_{2}}\]as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are: [JEE Main 10-4-2019 Morning]
question_answer13) A message signal of frequency 100 MHz and peak voltage 100 V is used to execute amplitude modulation on a carrier wave of frequency 300 GHz and peak voltage 400 V. The modulation index and difference between the two side band frequencies are : [JEE Main 10-4-2019 Morning]
question_answer14) In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that : [JEE Main 10-4-2019 Morning]
question_answer15) A ray of light AO in vacuum is incident on a glass slab at angle \[60{}^\circ \] and refracted at angle \[30{}^\circ \] along OB as shown in the figure. The optical path length of light ray from A to B is: [JEE Main 10-4-2019 Morning]
question_answer16) A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coil is 10A, then the input voltage and current in the primary coil are: [JEE Main 10-4-2019 Morning]
question_answer17) In a photoelectric effect experiment the threshold wavelength of the light is 380 nm. If the wavelength of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be:
Given E (in eV) \[=\frac{1237}{\lambda (in\,nm)}\]
question_answer18) The displacement of a damped harmonic oscillator is given by \[x(t)={{e}^{-01.1t}}\cos (10\pi t+\phi ).\]Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to: [JEE Main 10-4-2019 Morning]
question_answer19) A moving coil galvanometer allows a full scale current of \[{{10}^{-4}}A\]. A series resistance of \[2M\Omega \] is required to convert the above galvanometer into a voltmeter of range 0-5 V. Therefore the value of shunt resistance required to convert the above galvanometer into an ammeter of range 0-10 mA is : [JEE Main 10-4-2019 Morning]
question_answer20) A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in \[m{{s}^{-1}},\]
question_answer21) Two radioactive materials A and B have decay constants\[10\lambda \]and\[\lambda ,\]respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time : [JEE Main 10-4-2019 Morning]
question_answer22) An npn transistor operates as a common emitter amplifier, with a power gain of 60 dB. The input circuit resistance is \[100\Omega \]and the output load resistance is \[10k\Omega .\]The common emitter current gain b is : [JEE Main 10-4-2019 Morning]
question_answer23) In the given circuit, an ideal voltmeter connected across the \[10\Omega \]resistance reads 2V. The internal resistance r, of each cell is: [JEE Main 10-4-2019 Morning]
question_answer24) A \[25\times {{10}^{-3}}{{m}^{3}}\]volume cylinder is filled with 1 mol of \[{{O}_{2}}\]gas at room temperature (300K). The molecular diameter of \[{{O}_{2}}\], and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an \[{{O}_{2}}\] molecule? [JEE Main 10-4-2019 Morning]
question_answer25) n moles of an ideal gas with constant volume heat capcity \[{{C}_{V}}\]undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is: [JEE Main 10-4-2019 Morning]
question_answer26) A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = 4a. The minimum value of u such that it crosses the origin is : [JEE Main 10-4-2019 Morning]
question_answer27) The value of acceleration due to gravity at Earth's surface is \[9.8m{{s}^{-2}}\]. The altitude above its surface at which the acceleration due to gravity decreases to \[4.9\,m{{s}^{-2}}\], is close to :
question_answer29) The radtio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to\[135{}^\circ \]and\[0{}^\circ ,\]respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius \[{{r}_{1}},\] while water rises by the same amount h in a capillary tube of radius \[{{r}_{2}}.\]The ratio, \[({{r}_{1}}/{{r}_{2}}),\]is then close to: [JEE Main 10-4-2019 Morning]
question_answer30) Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds\[{{\upsilon }_{1}}\]and \[{{\upsilon }_{2}}\], respectively. The values of \[{{\upsilon }_{1}}\]and \[{{\upsilon }_{2}}\] are nearly: [JEE Main 10-4-2019 Morning]
question_answer31) The major product of the following reaction is: \[C{{H}_{3}}\overset{\begin{smallmatrix} OH \\ | \end{smallmatrix}}{\mathop{C}}\,HC{{H}_{2}}C{{H}_{2}}N{{H}_{2}}\xrightarrow[triethyla\min e]{ehtyl\,formate\,(lequiv.)}\] [JEE Main 10-4-2019 Morning]
question_answer32) SOLUTION A bacterial infection in an internal wound grows as \[N'(t)={{N}_{0}}\] exp(t), where the time t is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as \[\frac{dN}{dt}=-5{{N}^{2}}.\]What will be the plot of \[\frac{{{N}_{0}}}{N}\]vs. t after 1 hour ? [JEE Main 10-4-2019 Morning]
question_answer37) At 300 K and 1 atmospheric pressure, 10 Ml of a hydrocarbon required 55 mL of \[{{O}_{2}}\] for complete combustion and 40 mL of \[C{{O}_{2}}\] is formed. The formula of the hydrocarbon is : [JEE Main 10-4-2019 Morning]
question_answer38) Ethylamine \[({{C}_{2}}{{H}_{5}}N{{H}_{2}})\]can be obtained from N-ethylphthalimide on treatment with : [JEE Main 10-4-2019 Morning]
question_answer47) Consider the hydrates ions of \[T{{i}^{2+}},{{V}^{2+}},T{{i}^{3+}}\]and \[S{{c}^{3+}}.\]The correct order of their spin-only magnetic moments is : [JEE Main 10-4-2019 Morning]
question_answer48) A gas undergoes physical adsorption on a surface and follows the given Freundlich adsorption isotherm equation\[\frac{x}{m}=k{{p}^{0.5}}\] Adsorption of the gas increases with : [JEE Main 10-4-2019 Morning]
question_answer53) The increasing order of the reactivity of the following compounds towards electrophilic aromatic substitution reactions is :- [JEE Main 10-4-2019 Morning]
question_answer55) At room temperature, a dilute soluton of urea is prepared by dissolving 0.60 g of urea in 360 g of water. If the vapour pressure of pure water at this temperature is 35 mmHg, lowering of vapour pressure will be (molar mass of urea \[=60g\,mo{{l}^{-1}}\]):- [JEE Main 10-4-2019 Morning]
question_answer63) If\[\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{4}}-1}{x-1}=\underset{x\to k}{\mathop{\lim }}\,\frac{{{x}^{3}}-{{k}^{3}}}{{{x}^{2}}-{{k}^{2}}},\]then k is: [JEE Main 10-4-2019 Morning]
question_answer65) If the circles \[{{x}^{2}}+{{y}^{2}}+5Kx+2y+K=0\]and \[2\left( {{x}^{2}}+{{y}^{2}} \right)+2Kx+3y1=0,(K\in R),\] intersect at the points P and Q, then the line \[4x+5yK=0\] passes through P and Q for : [JEE Main 10-4-2019 Morning]
question_answer66) Le \[f(x)={{x}^{2}},x\in R.\]For any \[A\subseteq R,\]define\[g(A)=\{x\in R,f(x)\in A\}\]If \[S=\left[ 0,4 \right],\] then which one of the following statements is not true? [JEE Main 10-4-2019 Morning]
question_answer69) All the pairs (x, y) that satisfy the inequality \[2\sqrt{{{\sin }^{2}}x-2\sin x+5}.\]\[\frac{1}{{{4}^{{{\sin }^{2}}y}}}\le 1\]also satisfy the equation. [JEE Main 10-4-2019 Morning]
question_answer70) The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is : [JEE Main 10-4-2019 Morning]
question_answer71) Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is : [JEE Main 10-4-2019 Morning]
question_answer72) The sum \[=\frac{3\times {{1}^{3}}}{{{1}^{2}}}+\frac{5\times \left( {{1}^{3}}+{{2}^{3}} \right)}{{{1}^{2}}+{{2}^{2}}}+\frac{7\times \left( {{1}^{3}}+{{2}^{3}}+{{3}^{3}} \right)}{{{1}^{2}}+{{2}^{2}}+{{3}^{2}}}+......\] [JEE Main 10-4-2019 Morning]
question_answer73) If a directrix of a hyperbola centred at the origin and passing through the point \[\left( 4,-2\sqrt{3} \right)\]is \[5x=4\sqrt{5}\]and its eccentricity is e, then : [JEE Main 10-4-2019 Morning]
question_answer74) If\[f(x)=\left\{ \begin{align} & \frac{\sin (p+1)+sin\,x}{x}\,\,\,\,,\,\,\,\,x<0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,q\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,x=0 \\ & \frac{\sqrt{x+{{x}^{2}}}-\sqrt{x}}{{{x}^{{}^{3}/{}_{2}}}}\,\,\,\,\,\,\,\,,\,\,\,\,x>0 \\ \end{align} \right.\] is continuous at x = 0, then the ordered pair (p,q) is equal to : [JEE Main 10-4-2019 Morning]
question_answer75) If \[y=y\left( x \right)\]is the solution of the differential equation \[\frac{dy}{dx}=(tanx-y)se{{c}^{2}}x,x\in \left( -\frac{\pi }{2},\frac{\pi }{2} \right),\]such that\[y(0)=0,\]then \[y\left( -\frac{\pi }{4} \right)\]is equal to : [JEE Main 10-4-2019 Morning]
question_answer76) If the line \[x2y=12\]is tangent to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]at the point \[\left( 3,\frac{-9}{2} \right),\]then the length of the latus recturm of the ellipse is : [JEE Main 10-4-2019 Morning]
question_answer77) The value of \[\int\limits_{0}^{2\pi }{\left[ \sin 2x(1+cos3x) \right]}dx,\]where [t] denotes the greatest integer function, is : [JEE Main 10-4-2019 Morning]
question_answer79) The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, -3), then its radius is : [JEE Main 10-4-2019 Morning]
question_answer80) Let \[A\left( 3,0,1 \right),B\left( 2,10,6 \right)\]and \[C\left( 1,2,1 \right)\]be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the ratio, 2 : 1, then \[\cos \left( \angle GOA \right)\](O being the origin) is equal to: [JEE Main 10-4-2019 Morning]
question_answer81) Let \[f:R\to R\]be differentiable at \[c\in R\]and \[f(c)=0\]. If \[g(x)=|f(x)|,\]then at \[x=c,g\]is : [JEE Main 10-4-2019 Morning]
question_answer82) If \[\alpha \] and \[\beta \] are the roots of the quadratic equation, \[{{x}^{2}}+x\sin \theta -2\sin \theta =0,\theta \in \left( 0,\frac{\pi }{2} \right),\] then \[\frac{{{\alpha }^{12}}+{{\beta }^{12}}}{\left( {{\alpha }^{-12}}+{{\beta }^{-12}} \right){{\left( \alpha -\beta \right)}^{24}}}\]is equal to : [JEE Main 10-4-2019 Morning]
question_answer83) If the length of the perpendicular from the point \[(\beta ,0,\beta )(\beta \ne 0)\] to the line,\[\frac{x}{1}=\frac{y-1}{0}=\frac{z+1}{-1}\] is \[\sqrt{\frac{3}{2}},\]then \[\beta \]is equal to : [JEE Main 10-4-2019 Morning]
question_answer84) If \[\int_{{}}^{{}}{\frac{dx}{{{\left( {{x}^{2}}-2x+10 \right)}^{2}}}}\]\[=A\left( {{\tan }^{-1}}\left( \frac{x-1}{3} \right)+\frac{f(x)}{{{x}^{2}}-2x+10} \right)+C\] where C is a constant of integration, then : [JEE Main 10-4-2019 Morning]
question_answer85) ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are \[{{\cot }^{-1}}\left( 3\sqrt{2} \right)\] and \[\cos e{{c}^{-1}}\left( 2\sqrt{2} \right)\] respectively, then the height of the tower (in metres) is : [JEE Main 10-4-2019 Morning]
question_answer86) If \[{{a}_{1}},{{a}_{2}},{{a}_{3}},\]........., \[{{a}_{n}}\]are in A.P. and \[{{a}_{1}}+{{a}_{4}}+{{a}_{7}}+\]......... \[+{{a}_{16}}=114,\]then \[{{a}_{1}}+{{a}_{6}}+{{a}_{11}}+{{a}_{16}}\]is equal to : [JEE Main 10-4-2019 Morning]
question_answer87) \[\underset{n\to \infty }{\mathop{\lim }}\,\left( \frac{{{(n+1)}^{{}^{1}/{}_{3}}}}{{{n}^{{}^{4}/{}_{3}}}}+\frac{{{(n+2)}^{{}^{1}/{}_{3}}}}{{{n}^{{}^{4}/{}_{3}}}}+......+\frac{{{(2n)}^{{}^{1}/{}_{3}}}}{{{n}^{{}^{4}/{}_{3}}}} \right)\] is equal to: [JEE Main 10-4-2019 Morning]
question_answer88) If \[Q\left( 0,1,3 \right)\]is the image of the point P in the plane \[3xy+4z=2\]and R is the point (3, -1, -2), then the area (in sq. units) of \[\Delta PQR\]is: [JEE Main 10-4-2019 Morning]
question_answer89) If the coefficients of \[{{x}^{2}}\]and \[{{x}^{3}}\]are both zero, in the expansion of the expression \[(1+ax+b{{x}^{2}})\]\[{{(1-3x)}^{15}}\]in powers of x, then the ordered pair (a, b) is equal to: [JEE Main 10-4-2019 Morning]
question_answer90) If \[a>0\]and \[z=\frac{{{\left( 1+i \right)}^{2}}}{a-i},\]has magnitude\[\sqrt{\frac{2}{5},}\]then \[\overline{z}\]is equal to : [JEE Main 10-4-2019 Morning]