JEE Main 2019 · 12 Jan 2019 · Shift 1

Q1.An ideal gas occupies a volume of $2{\mathrm{m}}^3$ at a pressure of $3\times 10^6\mathrm{Pa}$. The energy of the gas is:

Q2.A travelling harmonic wave is represented by the equation $y(x,t)=10^{-3}\sin (50t+2x)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?

Q3.An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance $5\Omega$. The value of R, to give a difference of 5 mV across 10 cm of potentiometer wire, is:

Q4.In a meter bridge, the wire of length 1 m has a nonuniform cross-section such that, the variation $\frac{\mathrm{dR}}{\mathrm{d}\ell }$ of its resistance R with length $\ell$ is $\frac{\mathrm{dR}}{\mathrm{d}\ell }\propto \frac{1}{\sqrt{\ell }}$. Two equal resistances are connect …

Q5.A passenger train of length 60 m travels at a speed of $80\mathrm{km}/\mathrm{hr}$. Another freight train of length 120 m travels at a speed of $30\mathrm{km}/\mathrm{hr}$. The ratio of times taken by the passenger train to completely cross the freight train when:
(i) the …

Q6.Two electric bulbs, rated at $(25\mathrm{W},220\mathrm{V})$ and $(100\mathrm{W},220\mathrm{V})$, are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ respectively, then:

Q7.A straight rod of length $L$ extends from $x=a$ to $x=L+a$. The gravitational force it exerts on a point mass '$m$' at $x=0$, if the mass per unit length of the rod is $A+B{x}^2$, is given by:

Q8.What is the position and nature of image formed by lens combination shown in figure? (${\mathrm{f}}_1,{\mathrm{f}}_2$ are focal lengths)

Q9.A point source of light, S is placed at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2 L as shown below. The distance over which the man …

Q10.A light wave is incident normally on a glass slab of refractive index 1.5 . If $4\%$ of light gets reflected and the amplitude of the electric field of the incident light is $30\mathrm{V}/\mathrm{m}$, then the amplitude of the electric field for the wave propagating in t …

Q11.For the given cyclic process CAB as shown for a gas, the work done is:

Q12.Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

Q13.The position vector of the centre of mass $\overrightarrow{\mathrm{r}}\mathrm{cm}$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:

Q14.A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle $60^{\circ }$ with ground level. But he finds the aeroplane right vertically above his position. If $v$ is the speed of sound, speed of the plane is:

Q15.Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length I and mass m . the rod is pivoted at its centre '$O$' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to ri …

Q16.A simple pendulum, made of a string of length I and a bob of mass m , is released from a small angle ${\theta }_0$. It strikes a block of mass M , kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle …

Q17.A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?

Q18.A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2 R . The thermal conductivity of the material of the inner cylinder is ${\mathrm{K}}_1$ and that of the outer cylinder is ${\mathrm{K}}_2$. Assuming no loss of heat, the effective …

Q19.The least count of the main scale of a screw gauge is 1 mm . The minimum number of divisions on its circular scale required to measure $5\mu \mathrm{m}$ diameter of a wire is:

Q20.The output of the given logic circuit is:

Q21.As shown in the figure, two infinitely long, identical wires are bent by $90^{\circ }$ and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the $y$-axis. If $OP=OQ=4\mathrm{cm}$, and the magnitude of the magn …

Q22.A particle of mass $m$ moves in a circular orbit in a central potential field $U(r)=\frac{1}{2}k{r}^2$. If Bohr's quantization conditions are applied, radii of possible orbits and energy levels vary with quantum number n as:

Q23.A proton and an $\alpha$-particle (with their masses in the ratio of $1:4$ and charges in the ratio of $1:2$ are accelerated from rest through a potential difference V . If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii …

Q24.Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm ), about its axis be I . The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:

Q25.In the figure shown, a circuit contains two identical resistors with resistance $\mathrm{R}=5\Omega$ and an inductance with $\mathrm{L}=2\mathrm{mH}$. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is …

Q26.A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collis …

Q27.The galvanometer deflection, when key ${\mathrm{K}}_1$ is closed but ${\mathrm{K}}_2$ is open, equals ${\theta }_0$ (see figure). On closing $K_2$ also and adjusting ${\mathrm{R}}_2$ to $5\Omega$, the deflection in galvanometer becomes $\frac{{\theta }_0}{5}$. The …

Q28.A particle $A$ of mass ' $m$ ' and charge ' $q$ ' is accelerated by a potential difference of 50 V . Another particle B of mass ' 4 m ' and charge ' q ' is accelerated by a potential difference of 2500 V . The ratio of de-Broglie wavelength …

Q29.There is a uniform spherically symmetric surface charge density at a distance $R_0$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed $\mathrm{V}(\mathrm{R}(\mathrm{t}))$ of …

Q1.In the Hall-heroult process, aluminium is formed at the cathode. The cathode is made out of

Q2.The correct order for acid strength of compounds:
$\mathrm{CH}\equiv \mathrm{CH},{\mathrm{CH}}_3-\mathrm{C}\equiv \mathrm{CH},{\mathrm{CH}}_2={\mathrm{CH}}_2$
is as follows:

Q3.In a chemical reaction $A+2B\rightleftharpoons 2C+D$, the initial concentration of $B$ was 1.5 times of A but the equilibrium concentrations of A and B were found to be equal. The equilibrium constant(K) for the aforesaid chemical reaction is

Q4.Given

On the basis of data given, predict which of the following gases shows least adsorpti …

Q5.${\mathrm{Mn}}_2(\mathrm{CO}{)}_{10}$ is an organometalic compound due to the presence of

Q6.A metal on combustion in excess air forms $\mathrm{X}$, $\mathrm{X}$ upon hydrolysis with water yields ${\mathrm{H}}_2{\mathrm{O}}_2$ and ${\mathrm{O}}_2$ along with another product. The metal is:

Q7.The molecules that has minimum/no role in the formation of photochemical smog is:

Q8.The pair of metal ions that can give a spin-only magnetic moment of 3.9 BM for the complex $\left[\mathrm{M}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]{\mathrm{Cl}}_2$ is

Q9.For a disatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?

Q10.Among the following compounds most basic amino acid is

Q11.The increasing order of reactivity of the following compounds towards reaction with alkyl halide directly is:

Q12.Which of the following has lowest freezing point?

Q13.The volume of gas A has is twice than that of gas B. The compressibility factor of gas $A$ is thrice that that of gas $B$ at same temperature. The pressure of gases for equal per moles are

Q14.The hardness of water sample (in terms of equivalents of $\mathrm{CaCO}{}_3$) containing $10^{-3}$ M $\mathrm{CaSO}{}_4$ is
(molar mass of CaSO${}_4$ = 136 g mol${}^{-1}$)

Q15.can not be prepared by :

Q16.Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A then molecular weight of Y is

Q17.The metal d-orbital that can directly facing the ligands in $\mathrm{K}{}_3[\mathrm{Co}(\mathrm{CN}){}_6]$ are

Q18.Decomposition of $X$ exhibits a rate constant for $0.05\mu$g/year. How many years are required for the decomposition of $5\mu$g of X into $2.5\mu$g?

Q19.The standard electrode potential $E^{\circ }$ and its temperature coefficient $\left(\frac{d{E}^{\circ }}{dT}\right)$ for a cell are 2 V and $-5\times 10^{-4}$ VK${}^{-1}$ at 300 K respectively. The cell reaction is:

Standard reacti …

Q20.The element with $Z=120$ (not yet discovered) will be an/a

Q21.In the following reaction

Aldehyde + Alcohol $\stackrel{\mathrm{HCl}}{\to }$ Acetal
Aldehyde Alcohol
HCHO ${}^t$BuOH
$\mathrm{CH}{}_3\mathrm{CHO}$ MeOH
The best combination is

Q22.Two solids dissociate as follows
$\mathrm{A}(\mathrm{s})\rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$; $K_{p_1}=x$ atm${}^2$
$\mathrm{D}(\mathrm{s})\rightleftharpoons \mathrm{C}(\mathrm{g})+\mathrm{E}(\mathrm{g})$; $K_{p_2}=y$ atm${}^2$
The total pressure when both the solids dissociate simultaneously is

Q23.In the following reactions, products A and B are:

Q24.What is the work function of the metal if the light of wavelength $4000\stackrel{\circ }{A}$ generates photoelectrons of velocity $6\times 10^5{\mathrm{ms}}^{-1}$ from it?
(Mass of electron $=9\times 10^{-31}\mathrm{kg}$
Velocity of light …

Q25.Iodine reacts with concentrated ${\mathrm{HNO}}_3$ to yield along with other products. The oxidation state of iodine in Y is

Q26.Poly - $\beta$-hydroxybutyrate-co- $\beta$-hydroxyvalerate(PHBV) is a copolymer of ____

Q27.Water sample with BOD vales of 4 ppm and 18 ppm respectively are

Q1.An ordered pair ($\alpha ,\beta$) for which the system of linear equations
$(1+\alpha )x+\beta y+z=2$
$\alpha x+(1+\beta )y+z=3$
$\alpha x+\beta y+2z=2$
has a unique solution, is:

Q2.The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is:

Q3.The Boolean expression $((p\wedge q)\vee (p\vee \sim q))\wedge (\sim p\wedge \sim q)$ is equivalent to:

Q4.Consider three boxes, each containing 10 balls labelled $1,2,\dots \dots ,10$. Suppose one ball is randomly drawn from each of the boxes. Denote by ${\mathrm{n}}_{\mathrm{i}}$, the label of the ball drawn from the $i^{\text{th }}$ box, $(i=1,2,3)$. Then, the number of w …

Q5.A tetrahedron has vertices $\mathrm{P}(1,2,1),\mathrm{Q}(2,1,3),\mathrm{R}(-1,1,2)$ and $\mathrm{O}(0,0,0)$. The angle between the faces OPQ and PQR is:

Q6.The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, $y=12-x^2$ such that the rectangle lies inside the parabola, is:

Q7.If the straight line, $2x-3y+17=0$ is perpendicular to the line passing through the points $(7,17)$ and $(15,\beta )$, then $\beta$ equals:

Q8.The sum of the distinct real values of $\mu$, for which the vectors, $\mu \hat{i}+\hat{j}+\hat{k},\hat{i}+\mu \hat{j}+\hat{k},\hat{i}+\hat{j}+\mu \hat{k}$ are co-planar, is:

Q9.Let $\mathrm{P}(4,-4)$ and $\mathrm{Q}(9,6)$ be two points on the parabola, ${\mathrm{y}}^2=4\mathrm{x}$ and let X be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of $△\mathrm{PXQ}$ is maximum. Then this m …

Q10.Let $P=\left[\begin{array}{lll}1& 0& 0\\ 3& 1& 0\\ 9& 3& 1\end{array}\right]$ and $Q=\left[q_{ij}\right]$ be two $3\times 3$ matrices such that $Q-P^5=I_3$. Then $\frac{q_{21}+q_{31}}{q_{32}}$ is equal to:

Q11.Let $y=y(x)$ be the solution of the differential equation, $x\frac{dy}{dx}+y=x{\log }_{e}x,(x>1)$. If $2y(2)={\log }_{\mathrm{e}}4-1$, then $\mathrm{y}(\mathrm{e})$ is equal to:

Q12.The area (in sq. units) of the region bounded by the parabola, $y=x^2+2$ and the lines, $y=x+1,x=0$ and $x=3$, is:

Q13.In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:

Q14.Let ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ be the centres of the circles ${\mathrm{x}}^2+{\mathrm{y}}^2-2\mathrm{x}-2\mathrm{y}-2=0$ and ${\mathrm{x}}^2+{\mathrm{y}}^2-6\mathrm{x}-6y+14=0$ respectively. If P and Q are the points of intersection of these circles, then the area …

Q15.The maximum value of $3\cos \theta +5\sin \left(\theta -\frac{\pi }{6}\right)$ for any real value of $\theta$ is:

Q16.Considering only the principal values of inverse functions, the set $A=\left\{x\ge 0:{\tan }^{-1}(2x)+{\tan }^{-1}(3x)=\frac{\pi }{4}\right\}$

Q17.If $\lambda$ be the ratio of the roots of the quadratic equation in $x,3m^2{x}^2+m(m-4)x+2=0$, then the least value of $m$ for which $\lambda +\frac{1}{\lambda }=1$ is:

Q18.If a variable line, $3x+4y-\lambda =0$ is such that the two circles $x^2+y^2-2x-2y+1=0$ and $x^2+y^2-18x-2y+78=0$ are on its opposite sides, then the set of all values of $\lambda$ is the interval:

Q19.For $x>1$, if $(2x{)}^{2y}=4e^{2x-2y}$, then ${\left(1+{\log }_{e}2x\right)}^2\frac{dy}{dx}$ is equal to:

Q20.The integral $\int \cos \left({\log }_{e}x\right)dx$ is equal to: (where $C$ is a constant of integration)

Q21.A ratio of the $5^{\text{th }}$ term from the beginning to the $5^{\text{th }}$ term from the end in the binomial expansion of ${\left(2^{1/3}+\frac{1}{2(3{)}^{1/3}}\right)}^{10}$ is:

Q22.Let ${\mathrm{S}}_{\mathrm{k}}=\frac{1+2+3+\dots ..+\mathrm{k}}{\mathrm{k}}$. If ${\mathrm{S}}_1^2+{\mathrm{S}}_2^2+\dots ..+{\mathrm{S}}_{10}^2=\frac{5}{12}\mathrm{A}$, then A equal to:

Q23.The perpendicular distance from the origin to the plane containing the two lines, $\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}$ and $\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7}$, is:

Q24.If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is:

Q25.Let S be the set of all points in $(-\pi ,\pi )$ at which the function, $f(x)=\min \{\sin x,\cos x\}$ is non-differentiable. Then S is a subset of which of the following?

Q26.Let $f$ and $g$ be continuous functions on $[0,a]$ such that $f(x)=f(a-x)$ and $g(x)+g(a-x)=4$, then ${\int }_0^{a}f(x)g(x)dx$ is equal to:

Q27.${\lim }_{x\to \pi /4}\frac{{\cot }^{3}x-\tan x}{\cos (x+\pi /4)}$ is:

Q28.If $\frac{Z-\alpha }{Z+\alpha }(\alpha \in \mathbb{R})$ is a purely imaginary number and $|Z|=2$, then a value of $\alpha$ is:

Q29.Let $S=\{1,2,3,\dots ,100\}$. The number of non-empty subsets A of S such that the product of elements in A is even is:

Q30.If the vertices of a hyperbola be at $(-2,0)$ and $(2,0)$ and one of its foci be at $(-3,0)$, then which one of the following points does not lie on this hyperbola?