JEE Main 2019 · 12 Apr 2019 · Shift 2

Q1.Figure shown a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6 V . If the unregulated input voltage varies between 10 V to 16 V , then what is the maximum Zener current?

Q2.Three particles of masses $50\mathrm{g}$, $100\mathrm{g}$ and $150$ g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The $(x,y)$ coordinates of the centre of mass will be :

Q3.The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is $9:4$. The mass of the planet is $\frac{1}{9}$ th of that of the Earth. If ' $R$ ' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same ma …

Q4.A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force $\mathrm{F}=$ 20 N , making an angle of $30^{\circ }$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mathrm{m}=0.2$. The difference be …

Q5.In the given circuit, the charge on $4\mu \mathrm{F}$ capacitor will be :

Q6.A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be the heat energy absorbed by the gas, in this process?

Q7.A Carnot engine has an efficiency of $1/6$. When the temperature of the sink is reduced by $62^{\circ }\mathrm{C}$, its efficiency is doubled. The temperatures of the source and the sink are, respectively

Q8.Consider an electron in a hydrogen atom, revolving in its second excited state (having radius $4.65\mathring{A}$). The de-Broglie wavelength of this electron is :

Q9.A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as $10^{-12}\mathrm{W}/{\mathrm{m}}^2$]

Q10.A system of three polarizers ${\mathrm{P}}_1,{\mathrm{P}}_2,{\mathrm{P}}_3$ is set up such that the pass axis of ${\mathrm{P}}_3$ is crossed with respect to that of ${\mathrm{P}}_1$. The pass axis of ${\mathrm{P}}_2$ is inclined at $60^{\circ }$ to the pass axis of …

Q11.Let a total charge 2 Q be distributed in a sphere of radius R , with the charge density given by $r(r)=kr$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $-Q$ each, are placed on diametrically opposite points, at equal distance, a , from the centre. If A …

Q12.An electron, moving along the $x$-axis with an initial energy of 100 eV , enters a region of magnetic field $\vec{B}=\left(1.5\times 10^{-3}T\right)\hat{k}$ at $S$ (See figure). The field extends between $x=0$ and $x=2\mathrm{cm}$. The electron is detected at the point $Q$ o …

Q13.Two particles are projected from the same point with the same speed u such that they have the same range R , but different maximum heights, ${\mathrm{h}}_1$ and ${\mathrm{h}}_2$. Which of the following is correct?

Q14.A particle is moving with speed $v=v\sqrt{x}$ along positive $x$-axis. Calculate the speed of the particle at time $\mathrm{t}=\mathrm{t}$ (assume that the particle is at origin at $\mathrm{t}=0$).

Q15.One kg of water, at $20^{\circ }\mathrm{C}$, is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20\Omega$. The rms voltage in the mains is 200 V . Ignoring heat loss from the kettle, time taken for water to evaporate fully, is …

Q16.Half lives of two radioactive nuclei $A$ and $B$ are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei $A$ and $B$ will be :

Q17.In an amplitude modulator circuit, the carrier wave is given by, $\mathrm{C}(\mathrm{t})=4\sin (20000\pi \mathrm{t})$ while modulating signal is given by, $\mathrm{m}(\mathrm{t})=2\sin (2000\pi \mathrm{t})$. The values of modulation index and lower side band frequency are:

Q18.A uniform cylindrical rod of length $L$ and radius $r$, is made from a material whose Young's modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F , its length remains unchanged. The …

Q19.Consider the LR circuit shown in the figure. If the switch S is closed at $\mathrm{t}=0$ then the amount of charge that passes through the battery between $t=0$ and $t=\frac{L}{R}$ is :

Q20.Two sources of sound $S_1$ and $S_2$ produce sound waves of same frequency 660 Hz . A listener is moving from source ${\mathrm{S}}_1$ towards ${\mathrm{S}}_2$ with a constant speed $\mathrm{um}/\mathrm{s}$ and he hears 10 beats $/\mathrm{s}$. The velo …

Q21.A plane electromagnetic wave having a frequency $\mathrm{n}=23.9\mathrm{GHz}$ propagates along the positive z-direction in free space. The peak value of the electric field is $60\mathrm{V}/\mathrm{m}$. Which among the following is the acceptable magnetic field component …

Q22.Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A . (See figure)
( $\mu 0=4\mathrm{p}\times 10-7\mathrm{N}-\mathrm{A}-2$ )

Q23.The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, ${\lambda }_1/{\lambda }_2$, of the photons emitted in this process is:

Q24.A smooth wire of length $2\pi \mathrm{r}$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed w about the vertical diameter AB , as shown in figure, the bead is at rest with respect to the ci …

Q25.A solid sphere, of radius R acquires a terminal velocity $v_1$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $\eta$. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, …

Q26.The number density of molecules of a gas depends on their distance $r$ from the origin as, $n(r)=n_0{e}^{-\alpha r^4}$. Then the total number of molecules is proportional to :

Q27.A transparent cube of side d , made of a material of refractive index ${\mu }_2$, is immersed in a liquid of refractive index ${\mu }_1\left({\mu }_1<{\mu }_2\right)$. A ray is incident on the face $AB$ at an angle $q$ (shown in the figure). Total internal reflection takes p …

Q28.A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, ${\ell }_1=30\mathrm{cm}$ and ${\ell }_2=70\mathrm{cm}$. Then n is equal …

Q29.A spring whose unstretched length is $\ell$ has a force constant k . The spring is cut into two pieces of unstretched lengths ${\ell }_1$ and ${\ell }_2$ where, ${\ell }_1=\mathrm{n}{\ell }_2$ and n is an integer. The ratio $k_1/k_2$ of the corresponding force consta …

Q30.A moving coil galvanometer, having a resistance G, produces full scale deflection when a current ${\mathrm{I}}_{\mathrm{g}}$ flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to ${\mathrm{I}}_0$ (${\mathrm{I}}_0>{\mathrm{I}}_{\mathrm{g}}$) by connectin …

Q1.What will be the major product when m-cresol is reacted with propargyl bromide ($\mathrm{HC}\equiv \mathrm{C}-{\mathrm{CH}}_2\mathrm{Br}$) in presence of ${\mathrm{K}}_2{\mathrm{CO}}_3$ in acetone

Q2.Which one of the following is likely to give a precipitate with ${\mathrm{AgNO}}_3$ solution?

Q3.The INCORRECT match in the following is:

Q4.Benzene diazonium chloride on reaction with aniline in the presence of dilute hydrochloric acid gives :

Q5.The INCORRECT statement is:

Q6.The $\mathrm{C}-\mathrm{C}$ bond length is maximum in

Q7.Consider the following reactions :

' $A$ ' is:

Q8.In which one of the following equilibria, ${\mathrm{K}}_{\mathrm{p}}\ne {\mathrm{K}}_{\mathrm{c}}$ ?

Q9.The coordination numbers of Co and Al in $\left[\mathrm{Co}(\mathrm{Cl})(\mathrm{en}{)}_2\right]\mathrm{Cl}$ and ${\mathrm{K}}_3\left[\mathrm{Al}{\left({\mathrm{C}}_2{\mathrm{O}}_4\right)}_3\right]$, respectively, are
(en = ethane-1,2-diamine)

Q10.Which of the given statements is INCORRECT about glycogen?

Q11.The primary pollutant that leads to photochemical smog is:

Q12.The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure are, respectively :

Q13.Thermal decomposition of a Mn compound $(\mathrm{X})$ at 513 K results in compound $\mathrm{Y}$, ${\mathrm{MnO}}_2$ and a gaseous product. ${\mathrm{MnO}}_2$ reacts with NaCl and concentrated ${\mathrm{H}}_2{\mathrm{SO}}_4$ to give a pungent gas Z. $\mathrm{X}$, …

Q14.An 'Assertion' and a 'Reason' are given below. Choose the correct answer from the following options.
Assertion (A): Vinyl halides do not undergo nucleophilic substitution easily.
Reason (R): Even though the intermediate carbocation is stabilized by loosely held p-electrons, the c …

Q15.The molar solubility of $\mathrm{Cd}(\mathrm{OH}{)}_2$ is $1.84\times 10^{-5}\mathrm{M}$ in water. The expected solubility of $\mathrm{Cd}(\mathrm{OH}{)}_2$ in a buffer solution of $\mathrm{pH}=12$ is:

Q16.The compound used in the treatment of lead poisoning is:

Q17.The pair that has similar atomic radii is:

Q18.25 g of an unknown hydrocarbon upon burning produces 88 g of ${\mathrm{CO}}_2$ and 9 g of ${\mathrm{H}}_2\mathrm{O}$. This unknown hydrocarbon contains.

Q19.The decreasing order of electrical conductivity of the following aqueous solutions is:
0.1 M Formic acid (a)
0.1 M Acetic acid (b)
0.1 M Benzoic acid (c)

Q20.Among the following, the energy of 2s orbital is lowest in:

Q21.In the following skew conformation of ethane, $\mathrm{H}\cdot -\mathrm{C}-\mathrm{C}-\mathrm{H}$" dihedral angle is:

Q22.The correct statement is:

Q23.${\mathrm{NO}}_2$ required for a reaction is produced by the decomposition of ${\mathrm{N}}_2{\mathrm{O}}_5$ in ${\mathrm{CCl}}_4$ as per the equation
$2{\mathrm{N}}_2{\mathrm{O}}_5(\mathrm{g})\to 4{\mathrm{NO}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})$
T …

Q24.The correct name of the following polymer is:

Q25.Heating of 2-chloro-1-phenylbutane with EtOK/EtOH gives $X$ as the major product. Reaction of X with $\mathrm{Hg}(\mathrm{OAc}){}_2/\mathrm{H}{}_2\mathrm{O}$ followed by $\mathrm{NaBH}{}_4$ gives Y as the major product. Y is:

Q26.Among the following, the INCORRECT statement about colloids is :

Q27.In comparison to boron, berylium has:

Q28.A solution is prepared by dissolving 0.6 g of urea (molar mass $=60{\text{ g mol}}^{-1}$) and 1.8 g of glucose (molar mass $=180{\text{ g mol}}^{-1}$) in 100 mL of water at $27^{\circ }\text{C}$. The osmotic pressure of the solution is :
( …

Q29.The temporary hardness of a water sample is due to compound X. Boiling this sample converts X to compound Y. X and Y, respectively, are :

Q1.The general solution of the differential equation $(y^2-x^3)dx-xydy=0$ $(x\ne 0)$ is : (where c is a constant of integration)

Q2.Let $\alpha \in \mathbb{R}$ and the three vectors $\vec{a}=\alpha \hat{i}+\hat{j}+3\hat{k}$, $\vec{b}=2\hat{i}+\hat{j}-\alpha \hat{k}$ and $\vec{c}=\alpha \hat{i}-2\hat{j}+3\hat{k}$. Then the set …

Q3.Let $\alpha \in (0,\pi /2)$ be fixed. If the integral $\int \frac{\tan x+\tan \alpha }{\tan x-\tan \alpha }dx=A(x)\cos 2\alpha +B(x)\sin 2\alpha +C$, where $C$ is a constant of integration, then the functions $A(x)$ and $B(x)$ are respectively:

Q4.Let S be the set of all $\alpha \in \mathbb{R}$ such that the equation, $\cos 2x+\alpha \sin x=2\alpha -7$ has a solution. Then S is equal to :

Q5.Let $f(x)=5-|x-2|$ and $g(x)=|x+1|$, $x\in \mathbb{R}$. If $f(x)$ attains maximum value at $\alpha$ and $g(x)$ attains minimum value at $\beta$, then ${\lim }_{x\to -\alpha \beta }\frac{(x-1)(x^2-5x+6)}{x^2-6x+8}$ is equal to :

Q6.Let $z\in \mathbb{C}$ with $\text{Im}(z)=10$ and it satisfies $\frac{2z-n}{2z+n}=2i-1$ for some natural number $n$. Then :

Q7.The term independent of $x$ in the expansion of $\left(\frac{1}{60}-\frac{x^8}{81}\right)\cdot {\left(2x^2-\frac{3}{x^2}\right)}^6$ is equal to:

Q8.If the area (in sq. units) bounded by the parabola $y^2=4\lambda x$ and the line $y=\lambda x$, $\lambda >0$, is $\frac{1}{9}$, then $\lambda$ is equal to :

Q9.If $[x]$ denotes the greatest integer $\le x$, then the system of linear equations
$[\sin \theta ]x+[-\cos \theta ]y=0$
$[\cot \theta ]x+y=0$

Q10.For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is $\frac{4}{5}$, then the probability that he is unable to solve less than two problems is :

Q11.If $a_1,a_2,a_3,\dots$ are in A.P. such that $a_1+a_7+a_{16}=40$, then the sum of the first 15 terms of this A.P. is:

Q12.An ellipse, with foci at $(0,2)$ and $(0,-2)$ and minor axis of length 4, passes through which of the following points?

Q13.The length of the perpendicular drawn from the point $(2,1,4)$ to the plane containing the lines $\vec{r}=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k})$ and $\vec{r}=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-2\hat{k})$ is:

Q14.Let $\mathrm{A},\mathrm{B}$ and C be sets such that $\varphi \ne \mathrm{A}\cap \mathrm{B}\subseteq \mathrm{C}$. Then which of the following statements is not true?

Q15.If $\alpha ,\beta$ and $\gamma$ are three consecutive terms of a non-constant G.P. such that the equations $\alpha x^2+2\beta x+\gamma =0$ and $x^2+x-1=0$ have a common root, then $\alpha (\beta +\gamma )$ is equal to :

Q16.The tangents to the curve $\mathrm{y}=(\mathrm{x}-2{)}^2-1$ at its points of intersection with the line $\mathrm{x}-\mathrm{y}=3$, intersect at the point :

Q17.The angle of elevation of the top of vertical tower standing on a horizontal plane is observed to be $45^{\circ }$ from a point A on the plane. Let B be the point 30 m vertically above the point A. If the angle of elevation of the top of the tower from B be $30^{\circ }$, then …

Q18.A triangle has a vertex at $(1,2)$ and the mid points of the two sides through it are $(-1,1)$ and $(2,3)$. Then the centroid of this triangle is :

Q19.A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is :

Q20.If ${}^{20}{\mathrm{C}}_1+\left(2^2\right){}^{20}{\mathrm{C}}_3+\left(3^2\right){}^{20}{\mathrm{C}}_3+\left(2^2\right)+\dots \dots +\left(20^2\right){}^{20}{\mathrm{C}}_{20}=\mathrm{A}\left(2^{\beta }\right)$, then the ordered pair ( $\mathrm{A},\beta$ ) is equ …

Q21.The derivative of ${\tan }^{-1}\left(\frac{\sin x-\cos x}{\sin x+\cos x}\right)$, with respect to $\frac{x}{2}$, where $\left(x\in \left(0,\frac{\pi }{2}\right)\right)$ is:

Q22.A circle touching the $x$-axis at $(3,0)$ and making an intercept of length 8 on the $y$-axis passes through the point :

Q23.The equation of a common tangent to the curves, $y^2=16x$ and $xy=-4$ is :

Q24.A plane which bisects the angle between the two given planes $2x-y+2z-4=0$ and $x+2y+2z-2=0$, passes through the point:

Q25.A value of $\alpha$ such that ${\int }_{\alpha }^{\alpha +1}\frac{dx}{(x+\alpha )(x+\alpha +1)}={\log }_e\left(\frac{9}{8}\right)$ is:

Q26.A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to:

Q27.A value of $\theta \in (0,\pi /3)$, for which $\left|\begin{array}{ccc}1+{\cos }^2\theta & {\sin }^2\theta & 4\cos 6\theta \\ {\cos }^2\theta & 1+{\sin }^2\theta & 4\cos 6\theta \\ {\cos }^2\theta & {\sin }^2\theta & 1+4\cos 6\theta \end{array}\right|=0$, is:

Q28.A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60^{\circ }$ with the line $x+y=0$. Then an equation of the line $L$ is:

Q29.${\lim }_{x\to 0}\frac{x+2\sin x}{\sqrt{x^2+2\sin x+1}-\sqrt{{\sin }^{2}x-x+1}}$ is:

Q30.The Boolean expression $\sim (p\Rightarrow (\sim q))$ is equivalent to: