JEE Main 2019 · 09 Jan 2019 · Shift 2

Q1.At a given instant, say $t=0$, two radioactive substances $A$ and $B$ have equal activites. 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 $\ell n2$, the half-life of $B$ is:

Q2.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 5 A and its efficiency is $90\%$, the outp …

Q3.The energy associated with electric field is $({\mathrm{U}}_{\mathrm{E}})$ and with magnetic field is $({\mathrm{U}}_{\mathrm{B}})$ for an electromagnetic wave in free space. Then:

Q4.A force acts on a 2 kg object so that its position is given as a function of time as $\mathrm{x}=3{\mathrm{t}}^2+5$. What is the work done by this force in first 5 seconds?

Q5.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 $100\mathrm{V}/\mathrm{m}$ makes it to move in a straight path, then the mass of the particle is (given charge …

Q6.Two point charges $q_1(\sqrt{10}\mu \mathrm{C})$ and $q_2(-25\mu \mathrm{C})$ are placed on the $x$-axis at $x=1\mathrm{m}$ and $x=4\mathrm{m}$ respectively. The electric field (in $\mathrm{V}/\mathrm{m}$) at a point $y=3\mathrm{m}$ on $y$-axis is, …

Q7.Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:

Q8.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 ${\mathrm{V}}_0$ changes by: (assume that the Ge diode has large breakdown voltage)

Q9.The top of a water tank is open to air and its water level is maintained. It is giving out $0.74{\mathrm{m}}^3$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:

Q10.The energy required to take a satellite to a height ' $h$ ' above Earth surface (radius of Earth $=6.4\times 10^3\mathrm{km}$) is ${\mathrm{E}}_1$ and kinetic energy required for the satellite to be in a circular orbit at this height is ${\mathrm{E}}_2$. The value of …

Q11.Two Carnot engines A and B are operated in series. The first one, A, receives heat at ${\mathrm{T}}_1(=600\mathrm{K})$ and rejects to a reservoir at temperature ${\mathrm{T}}_2$. The second engine B receives heat rejected by the first engine and, in turns, rejects to a heat …

Q12.A series AC circuit containing an inductor ( 20 mH ), a capacitor ( $120\mu \mathrm{F}$ ) and a resistor ( $60\Omega$ ) is driven by an AC source of $24\mathrm{V}/50\mathrm{Hz}$. The energy dissipated in the circuit in 60 s is:

Q13.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

Q14.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 ( …

Q15.A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ }\mathrm{C}$. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about: [Take $\mathrm{R}=8.3\mathrm{J}/\mathrm{K}$ mole]

Q16.In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength $\lambda =500\mathrm{nm}$ 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:

Q17.Two plane mirrors are inclined to each other such that a ray of light incident to the first mirror ( $M_1$ ) and parallel to the second mirror ( $M_2$ ) is finally reflected from the second mirror ( ${\mathrm{M}}_2$ ) parallel to the first mirror ( ${\mathrm{M}}_1$ ). …

Q18.A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of $30^{\circ }$ fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad ${\mathrm{s}}^{-1}$) will be ($\mathrm{g}=10{\mathrm{ms}}^{-2}$ …

Q19.A carbon resistance has a following colour code. What is the value of the resistance?

Q20.One of the two identical conducing wires of length $L$ is bent in the form of a circular loop and the other one into a circular coil of $N$ identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop …

Q21.A rod of mass ' M ' and length ' 2 L ' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of ' $m$ ' are attached at distance ' $\mathrm{L}/2$ ' from its centre on both sides, it reduces the oscillation frequency by $20\%$. The value o …

Q22.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:

Q23.A parallel palate capacitor with square plates is filled with four dielectrics of dielectric constants ${\mathrm{K}}_1,{\mathrm{K}}_2,{\mathrm{K}}_3,{\mathrm{K}}_4$ arranged as shown in the figure. The effective dielectric constant K will be:

Q24.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 a …

Q25.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 a speed of $10\mathrm{km}/\mathrm{h}$. If the wave speed is $330\mathrm{m}/\mathrm{s}$, the frequency heard by the running …

Q26.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 ${\mathrm{a}}_1$ and ${\mathrm{a}}_2$ respectively. T …

Q27.The magnetic field associated with a light wave is given, at the origin, by


If this light falls on a silver plate having a work function of …

Q28.In the given circuit the internal resistance of the 18 V cell is negligible. If ${\mathrm{R}}_1=400\Omega ,{\mathrm{R}}_3=100\Omega$ and ${\mathrm{R}}_4=500\Omega$ and the reading of an ideal voltmeter across ${\mathrm{R}}_4$ is 5 V , then the value of ${\mathrm{R}}_2$ will b …

Q29.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 …

Q30.The position co-ordinates of a particle moving in a 3-D coordinates system is given by


The speed of the particle is:

Q1.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 vapours are $4.2\mathrm{kJ}{\mathrm{K}}^{-1}{\mathrm{kg}}^{-1}$ and $2.0\mathrm{kJ}{\mathrm{K}}^{-1}{\mathrm{kg}}^{-1}$, heat o …

Q2.For the following reaction the mass of water produced from 445 g of ${\mathrm{C}}_{57}{\mathrm{H}}_{110}{\mathrm{O}}_6$ is …

Q3.Which of the following conditions in drinking water causes methemoglobinemia?

Q4.The correct match between item I and item II is
Item I
Item II
(a) Benzaldehyde
(b) Alumina
(c) Acetonitrile
(p) Mobile phase
(q) Adsorbent
(r) Adsorbate

Q5.The metal that forms nitride by reacting directly with ${\mathrm{N}}_2$ of air is

Q6.For coagulation of arsenious sulphide sol, which one of the following salt solution will be most effective?

Q7.The complex that has highest crystal field splitting energy( $\Delta$ ) is

Q8.The pH of rain water is approximately

Q9.Consider the following reversible chemical reactions:


The relation between ${\mathrm{K}}_1$ and …

Q10.The correct sequence of amino acids present in the tripeptide given below is

Q11.For the reaction, $2\mathrm{A}+\mathrm{B}⟶$ products , when the concentrations of A and B both were doubled, the rate of the reaction increased from $0.3\mathrm{mol}{\mathrm{L}}^{-1}{\mathrm{s}}^{-1}$ to …

Q12.The products formed in the reaction of cumene with ${\mathrm{O}}_2$ followed by treatment with dil. HCl are:

Q13.The tests performed on compound $X$ and their inferences are:

\begin{tabular}{lcl}
& \multicolumn{1}{c}{ Test } & \multicolumn{1}{c}{ Interference } \\
(a) & 2, 4-DNP test & Colorued precipitate \\
(b) & Iodoform test & Yellow precipitate \\
(c) & Azo-dye test & No dye formati …

Q14.If the standard electrode potential for a cell is 2 V at 300 K , the equilibrium constant $(\mathrm{K})$ for the reaction
$\mathrm{Zn}(\mathrm{s})+{\mathrm{Cu}}^{2+}(\mathrm{aq})\rightleftharpoons {\mathrm{Zn}}^{2+}(\mathrm{aq})+\mathrm{Cu}(\mathrm{s})$
At 300 K is approximately …

Q15.The temporary hardness of water is due to

Q16.In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?

Q17.Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?
(1) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum.
(2) For a given value of the …

Q18.Which of the following compounds is not aromatic?

Q19.Good reducing nature of ${\mathrm{H}}_3{\mathrm{PO}}_2$ is attributed to the presence of

Q20.The correct statement regarding the given Ellingham diagram is

Q21.The transition element that has lowest enthalpy of atomisation is

Q22.The increasing basicity order of the following compounds is
(1) $\mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{NH}{}_2$
(2) (see structure)
(3) (see structure)
(4) (see structure)

Q23.When the first electron gain enthalpy $({\Delta }_{\mathrm{eg}}\mathrm{H})$ of oxygen is $-141\mathrm{kJ}/\mathrm{mol}$, its second electron gain enthalpy is

Q24.At $100^{\circ }\mathrm{C}$, copper(Cu) has FCC unit cell structure with cell edge length $x\stackrel{\circ }{\mathrm{A}}$. What is the approximate density of $\mathrm{Cu}$ (in ${\mathrm{g}\mathrm{cm}}^{-3}$) at this temperature?
[Atomic mass of $\mathrm{Cu}=63.55\mathrm{u}$]

Q25.A solution containing 62 g ethylene glycol in 250 g water is cooled to $-10^{\circ }\mathrm{C}$. If ${\mathrm{K}}_{\mathrm{f}}$ for water is $1.86{\mathrm{K}\mathrm{kg}\mathrm{mol}}^{-1}$, the amount of water(in g) separated as ice is

Q26.Homoleptic octahedral complexes of a metal ion '${\mathrm{M}}^{3+}$' with three monodentate ligands ${\mathrm{L}}_1$, ${\mathrm{L}}_2$ and ${\mathrm{L}}_3$ absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is

Q1.The sum of the following series $1+6+\frac{9\left(1^2+2^2+3^2\right)}{7}+\frac{12\left(1^2+2^2+3^2+4^2\right)}{9}+\frac{15\left(1^2+2^2+\dots .+5^2\right)}{11}+\dots$ up to 15 terms, is:

Q2.For each $x\in R$, let $[x]$ be the greatest integer less than or equal to $x$. Then ${\lim }_{x\to 0^{+}}\frac{x([x]+|x|)\sin [x]}{|x|}$ is equal to

Q3.Let $f:[0,1]\to R$ be such that $f(xy)=f(x)f(y)$ 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 $y(0)=1$, then $y\left(\frac{1}{4}\right)+y\left(\frac{3}{4}\right)$ is equal to

Q4.If $x={\sin }^{-1}(\sin 10)$ and $y={\cos }^{-1}(\cos 10)$, then $y-x$ is equal to:

Q5.If $0\le x<\frac{\pi }{2}$, then the number of values of $x$ for which $\sin x-\sin 2x+\sin 3x=0$, is

Q6.Let ${\mathrm{z}}_0$ be a root of the quadratic equation, ${\mathrm{x}}^2+\mathrm{x}+1=0$. If $\mathrm{z}=3+6{\mathrm{iz}}_0^{81}-3{\mathrm{iz}}_0^{93}$, then $\arg \mathrm{z}$ is equal to

Q7.The area of the region $\mathrm{A}\{(\mathrm{x},\mathrm{y}):0\le \mathrm{y}\le \mathrm{x}|\mathrm{x}|+1$ and $-1\le \mathrm{x}\le 1\}$ in sq. units, is:

Q8.If the system of linear equation $x-4y+7z=g,3y-5z=h,-2x+5y-9z=k$ is consistent, then:

Q9.The coefficient of $t^4$ in the expansion of ${\left(\frac{1-t^6}{1-t}\right)}^3$ is

Q10.If both the roots of the quadratic equation $x^2-mx+4=0$ are real and distinct and they lie in the interval $[1,5]$, then $m$ lies in the interval.

Q11.Let S be the set of all triangle 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:

Q12.Let $\mathrm{a},\mathrm{b}$ and c be the $7^{\text{th }},11^{\text{th }}$ and $13^{\text{th }}$ 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:

Q13.The logical statement $[\sim (\sim p\vee q)\vee (p\wedge r)\wedge (\sim q\wedge r)]$ is equivalent to:

Q14.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 $\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$ is:

Q15.A data consists of $n$ observations: ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots \dots ,{\mathrm{x}}_{\mathrm{n}}$. If ${\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}+1\right)}^2=9\mathrm{n}$ and …

Q16.If $\mathrm{A}=\left[\begin{array}{ccc}{e}^t& e^{-t}\cos t& e^{-t}\sin t\\ e^t& -e^{-t}\cos t-e^{-t}\sin t& -e^{-t}\sin t+e^{-t}\cos t\\ e^t& 2e^{-t}\sin t& -2e^{-t}\cos t\end{array}\right]$ Then $A$ is

Q17.If $f(x)=\int \frac{5x^8+7x^6}{{\left(x^2+1+2x^7\right)}^2}dx,(x\ge 0)$ and $f(0)=0$, then the value of $f(1)$ is:

Q18.Let $f$ be a differentiable function $R$ to $R$ such that $|f(x)-f(y)|\le 2|x-y{|}^{\frac{3}{2}}$, for all $x,y\in R$. If $f(0)=1$ then ${\int }_0^1{f}^2(x)dx$ is equal to

Q19.If $x=3\tan t$ and $y=3\sec t$, then the value of $\frac{d^{2}y}{d{x}^2}$ at $t=\frac{\pi }{4}$, is:

Q20.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:

Q21.If the circles $x^2+y^2-16x-20y+164=r^2$ and $(x-4{)}^2+(y-7{)}^2=36$ intersect at two distinct points, then:

Q22.A hyperbola has its centre at the origin, passes through the point ( 4,2 ) and has transverse axis of length 4 along the x -axis. Then the eccentricity of the hyperbola is:

Q23.Let $A(4,-4)$ and $B(9,6)$ be points on the parabola $y^2=4x$. Let $C$ be chosen on the $\mathrm{arc}AOB$ of the parabola, where $O$ is the origin, such that the area of $△ACB$ is maximum. Then, the area (in sq. units) of …

Q24.Let the equation of two sides of a triangle be $3x-2y+6=0$ and $4x+5y-20=0$. If the orthocentre of this triangle is at $(1,1)$, then the equation of its third side is:

Q25.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 i …

Q26.If the lines $x=ay+b,z=cy+d$ and $x=a^{\prime }z+b^{\prime },y=c^{\prime }z+d^{\prime }$ are perpendicular, then:

Q27.Let $\vec{a}=\hat{i}+\hat{j}+\sqrt{2}\hat{k},\vec{b}=b_1\hat{i}+b_2\hat{j}+\sqrt{2}\hat{k}$ and $\vec{c}=5\hat{i}+\hat{j}+\sqrt{2}\hat{k}$ be three vectors such that the projection vector of $\vec{b}$ on $\vec{a}$ is $\vec{a}$. If $\vec{a}+\vec{b}$ is perpendicular to …

Q28.The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation, $6x^2-11x+\alpha =0$ are rational numbers is:

Q29.Let $A=\{x\in R:x$ is not a positive integer $\}$ Define a function $f:A\to R$ as $f(x)=\frac{2x}{x-1}$ then $f$ is

Q30.If ${\int }_0^{\frac{\pi }{3}}\frac{\tan \theta }{\sqrt{2\mathrm{k}\sec \theta }}\mathrm{d}\theta =1-\frac{1}{\sqrt{2}},(\mathrm{k}>0)$, then the value of k is: