JEE Main 2019 · 08 Apr 2019 · Shift 2

Q1.A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{\mathrm{sph}}$ and $h_{\mathrm{cyl}}$ on the incline. The radio …

Q2.In the circuit shown, a four wire potentiometer is made of a 400 cm long wire, which extends between $A$ and $B$. The resistance per unit length of the potentiometer wire is $r=0.01\Omega /\mathrm{cm}$. If an ideal voltmeter is connected as shown with jockey J at 50 cm from e …

Q3.A parallel plate capacitor has $1\mu \mathrm{F}$ capacitance. One of its two plates is given $+2\mu \mathrm{C}$ charge and the other plate, $+4\mu \mathrm{C}$ charge. The potential difference developed across the capacitor is:

Q4.If Surface tension (S), Moment of Inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be:

Q5.Two magnetic dipoles X and Y are placed at a separation $d$, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge $q$ is passing through their mid-point P, at angle $\theta =45^{\circ }$ with the horizontal line as shown in th …

Q6.A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to $\frac{1}{1000}$ of the original amplitude is close to:

Q7.A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, …

Q8.A cell of internal resistance $r$ drives current through an external resistance $R$. The power delivered by the cell to the external resistance will be maximum when:

Q9.In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale …

Q10.The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to:
[Boltzmans Constant $k_B=1.38\times 10^{-23}$ J/K
Avogadro number $N_A=6.02\times 10^{26}$/kg
Radius of Earth: $6.4\times 10^6$ m
Gravitat …

Q11.A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. ($a=$ acceleration, $v=$ velocity, $x=$ displacement, $t=$ time)

Q12.The election field in a region is given by $\vec{E}=(Ax+B)\hat{i}$ where $E$ is in $N{C}^{-1}$ and $x$ in meters. The values of constants are $A=20$ SI unit and $B=10$ SI unit. If the potential at $x=1$ is $V_1$ and that at $x=-5$ is $V_2$ then $V_1-V_2$ is:

Q13.Young's moduli of two wires $A$ and $B$ are in the ratio $7:4$. Wire $A$ is 2 m long and has radius $R$. Wire $B$ is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of $R$ is close to:

Q14.A body of mass $m_1$ moving with an unknown velocity of $v_1\hat{i}$ undergoes a collinear collision with a body of mass $m_2$ moving with a velocity $v_2\hat{i}$. After collision $m_1$ and $m_2$ move with velocities of $v_3\hat{i}$ and $v_4\hat{i}$ respectively. If $m_2=0.5m_1$ …

Q15.The ratio of mass densities of nuclei of ${}^{40}Ca$ and ${}^{16}O$ is close to:

Q16.A rectangles solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5 m. When released, it slips off the table in a very short time $\tau =0.01$ s, remaining essentially horizontal. The angle by which it would rotate when it hits …

Q17.An electric dipole is formed by two equal and opposite charges $q$ with separation $d$. The charges have the same mass $m$. It is kept in a uniform electric field $E$. If it is slightly rotated from its equilibrium orientation, then its angular frequency $\omega$ is:

Q18.The magnetic field of an electromagnetic wave is given by:

The associated electric field will be:

Q19.A common emitter amplifier circuit, built using an npn transistor, is shown in the figure. Its dc current gain is $250,R_C=1k\Omega$ and $V_{CC}=10V$. What is the minimum base current for $V_{CE}$ to reach saturation?

Q20.A positive point charge is released from rest at a distance $r_0$ from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance $r$ from line charge, is proportional to

Q21.Let $|{\vec{A}}_1|=3$, $|{\vec{A}}_2|=5$, and $|{\vec{A}}_1+{\vec{A}}_2|=5$. The value of $(2{\vec{A}}_1+3{\vec{A}}_2)\cdot (3{\vec{A}}_1-2{\vec{A}}_2)$ is:

Q22.In the figure shown, what is the current (in Ampere) drawn from the battery? You are given

Q23.In a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the height of the receiving antenna is 70 m, then the minimum height of the transmitting antenna should be: (Radius of the Earth $=6.4\times 10^{6}m$)

Q24.A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon? Assume that …

Q25.A circuit connected to an ac source of emf $e=e_0\sin (1000t)$ with t in seconds, gives a phase difference of $\frac{\pi }{4}$ between the emf e and current i. Which of the following circuits will exhibit this?

Q26.A nucleus A, with a finite de-broglie wavelength ${\lambda }_A$, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de-Broglie wavele …

Q27.Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star.

Q28.Two very long, straight and insulated wires are kept at $90^{\circ }$ angle from each other in xy plane as shown in the figure.

These wires carry current of equal magnitude I, whose directions are shown in the figure. The net magnetic field at point P will be:

Q29.The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by:

Q30.A uniform rectangular thin sheet $ABCD$ of mass $M$ has length $a$ and breadth $b$, as shown in the figure. If the shaded portion HBGO is cut off, the coordinates of the centre of mass of the remaining portion will be:

Q1.The statement that is INCORRECT about the interstitial compound is:

Q2.If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength $\lambda$, then for $1.5p$ momentum of the photoelectron, the wavelength of the light should be:
(Assume kinetic energy of ejected photoelectron to be very h …

Q3.The ion that has ${\mathrm{sp}}^3{\mathrm{d}}^2$ hybridization for the central atom is:

Q4.The major product obtained in the following reaction is:

Q5.For a reaction scheme. $A\stackrel{k_1}{\to }B\stackrel{k_2}{\to }C$ if the rate of formation of $B$ is set to be zero then the concentration of $B$ is given by

Q6.For the following reactions, equilibrium constants are given:
$\mathrm{S}(\mathrm{s})+{\mathrm{O}}_2(\mathrm{g})\rightleftharpoons {\mathrm{SO}}_2(\mathrm{g});{\mathrm{K}}_1=10^{52}$ …

Q7.Calculate the standard cell potential (in V ) of the cell in which following reaction takes place:
${\mathrm{Fe}}^2+(\mathrm{aq})+{\mathrm{Ag}}^{+}(\mathrm{aq})\to {\mathrm{Fe}}^{3+}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s})$
Given that: …

Q8.The covalent alkaline earth metal halide
( $\mathrm{X}=\mathrm{Cl},\mathrm{Br},\mathrm{I}$ ) is:

Q9.The structure of Nylon - 6 is:

Q10.The IUPAC symbols for the element with atomic number 119 would be:

Q11.Which of the following compounds will show the maximum 'enol' content?

Q12.$0.27\mathrm{g}$ of a long chain fatty acid was dissolved in $100{\mathrm{cm}}^3$ of hexane. 10 mL of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch gl …

Q13.The percentage composition of carbon by mole in methane is:

Q14.The Mond process is used for the:

Q15.Which one of the following alkenes when treated with HCl yields majorly an anti Markovnikov product?

Q16.5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K. If ${\mathrm{C}}_{\mathrm{v}}=28{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$, calculate $\Delta \mathrm{U}$ and $\Delta \mathrm{pV}$ for this process. ( …

Q17.The calculated spin only magnetic moments (BM) of the anionic and cationic species of ${\left[\mathrm{Fe}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}_2$ and $\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]$, respectively, are:

Q18.Fructose and glucose can be distinguished by:

Q19.The major product in the following reaction is:

Q20.Polysubstitution is a major drawback in:

Q21.The strength of 11.2 volume solution of ${\mathrm{H}}_2{\mathrm{O}}_2$ is:
[Given that molar mass of $\mathrm{H}=1\mathrm{g}{\mathrm{mol}}^{-1}$ and $\mathrm{O}=16\mathrm{g}{\mathrm{mol}}^{-1}$]

Q22.For the solution of the gases $\mathrm{w},\mathrm{x},\mathrm{y}$ and z in water at 298 K, the Henrys law constants $\left({\mathrm{K}}_{\mathrm{H}}\right)$ are $0.5,2,35$ and 40 kbar, respectively. The correct plot for the given data is:

Q23.Among the following molecules / ions ${\mathrm{C}}_2^{2-},{\mathrm{N}}_2^{2-},{\mathrm{O}}_2^{2-},{\mathrm{O}}_2$ which one is diamagnetic and has the shortest bond length?

Q24.The major product obtained in the following reactions is:

Q25.The maximum prescribed concentration of copper in drinking water is:

Q26.The correct statement about ${\mathrm{ICl}}_5$ and ${\mathrm{ICl}}_4^{-}$is:

Q27.The compound that inhibits the growth of tumors is:

Q28.Consider the bcc unit cells of the solid 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A . The unit cell edge length is $50\%$ more in solid 2 than in 1 . What is the approximate packing efficiency in solid 2 ?

Solid 1

Solid 2

Q1.Let $S(\alpha )=\left\{(x,y):y^2\le x,0\le x\le \alpha \right\}$ and $A(\alpha )$ is area of the region $S(\alpha )$. If for a $\lambda ,0<\lambda <4,\mathrm{A}(\lambda ):\mathrm{A}(4)=2:5$ then $\lambda$ equals:

Q2.Let $f(x)={\int }_0^{x}g(t)dt$, where $g$ is a non zero even function. If $f(x+5)=g(x)$, then ${\int }_0^{x}f(t)dt$ equals

Q3.Suppose that the points $(h,k),(1,2)$ and $(-3,4)$ lie on the line $L_1$. If a line $L_2$ passing through the points $(h,k)$ and $(4,3)$ is perpendicular to $L_1$, then $\frac{k}{h}$ equals:

Q4.Let $f(x)=a^x(a>0)$ be written as $f(x)=f_1(x)+f_2(x)$, where $f_1(x)$ is an even function and $f_2(x)$ is an odd function. Then $f_1(x+y)+f_1(x-y)$ equals

Q5.Let $f:[-1,3]\to R$ be defined as

where $[t]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is discontinuous at:

Q6.If $z=\frac{\sqrt{3}}{2}+\frac{i}{2}(i=\sqrt{-1})$, then ${\left(1+iz+z^5+i{z}^8\right)}^9$ is equal to:

Q7.Which one of the following statements is not a tautology:

Q8.Given that the slope of the tangent to a curve $y=y(x)$ at any point $(x,y)$ is $\frac{2y}{x^2}$. If the curve passes through the centre of the circle $x^2+y^2-2x-2y=0$, then its equation is:

Q9.If $f(1)=1,f^{\prime }(1)=3$, then the derivative of $f(f(f(x)))+{\left(f(x)\right)}^2$ at $x=1$ is:

Q10.The number of four-digit numbers strictly greater than 4321 that can be formed using the digits $0,1,2,3,4,5$ (repetition of digits is allowed) is:

Q11.If a point $\mathrm{R}(4,\mathrm{y},\mathrm{z})$ lies on the line segment joining the points $\mathrm{P}(2,-3,4)$ and $\mathrm{Q}(8,0,10)$, then the distance of $R$ from the origin is:

Q12.If the system of linear equations
$\mathrm{x}-2\mathrm{y}+\mathrm{kz}=1$
$2\mathrm{x}+\mathrm{y}+\mathrm{z}=2$
$3x-y-kz=3$
has a solution $(x,y,z),z\ne 0$, then $(x,y)$ lies on the straight line whose equation is:

Q13.A student score the following marks in five tests : $45,54,41,57,43$. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:

Q14.The vector equation of the plane through the line of intersection of the planes $x+y+z=1$ and $2x+3y+4z=5$ which is perpendicular to the plane $x-y+z=0$ is:

Q15.If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle:

Q16.In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at $(0,5\sqrt{3})$, then the length of its latus rectum is:

Q17.The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least $90\%$ is:

Q18.If the eccentricity of the standard hyperbola passing through the point $(4,6)$ is 2, then the equation of the tangent to the hyperbola at $(4,6)$ is:

Q19.The number of integral values of $m$ for which the equation $\left(1+m^2\right)x^2-2(1+3m)x+(1+8m)=0$ has no real root is:

Q20.The sum ${\sum }_{k=1}^{20}k\frac{1}{2^k}$ is equal to:

Q21.Let $\vec{a}=3\hat{i}+2\hat{j}+x\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$, for some real $x$. Then $|\vec{a}\times \vec{b}|=r$ is possible if:

Q22.The tangent and the normal lines at the point $(\sqrt{3},1)$ to the circle $x^2+y^2=4$ and the $x$-axis form a triangle. The area of this triangle (in square units) is:

Q23.The tangent to the parabola $y^2=4x$ at the point where it intersects the circle $x^2+y^2=5$ in the first quadrant, passes through the point:

Q24.The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is:

Q25.Let the numbers $2,b,c$ be in an A.P and $A=\left[\begin{array}{ccc}1& 1& 1\\ 2& b& c\\ 4& b^2& c^2\end{array}\right]$. If $\det (A)\in [2,16]$ then $c$ lies in the interval

Q26.Let $f:R\to R$ be a differentiable function satisfying $f^{\prime }(3)+f^{\prime }(2)=0$. Then ${\lim }_{x\to \infty }{\left(\frac{1+f(3+x)-f(3)}{1+f(2-x)-f(2)}\right)}^{\frac{1}{x}}$ is equal to:

Q27.If $\int \frac{dx}{x^3{\left(1+x^6\right)}^{2/3}}=xf(x){\left(1+x^6\right)}^{\frac{1}{3}}+C$ where $C$ is a constant of integration, then the function $f(x)$ is equal to:

Q28.Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is:

Q29.If three distinct numbers $a,b,c$ are in G.P. and the equations $a{x}^2+2bx+c=0$ and $d{x}^2+2ex+f=0$ have a common root, then which one of the following statements is correct?