JEE Main 2019 · 12 Jan 2019 · Shift 2

Q1.The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I(x)'. Which one of the graphs represents the variation of I(x) with x correctly?

Q2.A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of lo …

Q3.An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is $6\times 10^{-8}s$. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be c …

Q4.In the figure, given that $V_{BB}$ supply can vary from 0 to 5.0 V, $V_{cc}=5V$, ${\beta }_{dc}=200$, $R_B=100k\Omega$, $R_C=1k\Omega$ and $V_{BE}=1.0V$. The minimum base current and the input voltage at which the transistor will go to saturation, will be respectively:

Q5.In the circuit shown, find C if the effective capacitance of the whole circuit is to be $0.5\mu F$. All values in the circuit are in $\mu F$.

Q6.An alpha-particle of mass $m$ suffers 1-deminsional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is :

Q7.A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of $5.0{\mathrm{ms}}^{-1}$, at right angles to the horizontal component of the earth's magnetic field, $0.3\times 10^{-4}\mathrm{Wb}/{\mathrm{m}}^2$. The value of the induced em …

Q8.To double the covering range of a TV transition tower, its height should be multiplied by :

Q9.A plano-convex lens (focal length $f_2$, refractive index ${\mu }_2$, radius of curvature $R$) fits exactly into a plano-concave lens (focal length ${\mathrm{f}}_1$, refractive index ${\mu }_1$, radius of curvature R). Their plane surfaces are parallel to each other. Th …

Q10.A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is ${\mathrm{l}}_1$, and that below the piston is …

Q11.Two satellites, $A$ and $B$, have masses $m$ and $2m$ respectively. $A$ is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, $T_A/T_B$, is :

Q12.A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the ce …

Q13.A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the pl …

Q14.In a Frank-hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to :

Q15.A particle of mass 20 g is released with an initial velocity $5\mathrm{m}/\mathrm{s}$ along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, it …

Q16.A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of $4\times 10^{-4}\mathrm{A}$ passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range 2.5 V, it should be connected to a resistance …

Q17.In the given circuit diagram, the currents, $I_1=-0.3\mathrm{A},I_4=0.8\mathrm{A}$ and $I_5=0.4\mathrm{A}$, are flowing as shown. The currents $I_2,I_3$ and $I_6$, respectively are:

Q18.A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tub …

Q19.A paramagnetic material has $10^{28}$ atoms $/{\mathrm{m}}^3$. Its magnetic susceptibility at temperature 350 K is $2.8\times 10^{-4}$. Its susceptibility at 300 K is :

Q20.In a radioactive decay chain, the initial nucleus is ${}_{90}^{232}\mathrm{Th}$. At the end there are $6\alpha$ particles and $4\beta$-particles which are emitted. If the end nucleus is ${}_Z^{A}X,A$ and $Z$ are given by :

Q21.Let $L$, $R$, $C$ and $V$ represent inductance, resistance, capacitance and voltage, respectively. The dimension of $\frac{L}{RCV}$ in SI units will be :

Q22.Formation of real image using a biconvex lens is shown below :

If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?

Q23.When a certain photosensitive surface is illuminated with monochromatic light of frequency v , the stopping potential for the photo current is $-{\mathrm{V}}_0/2$. When the surface is illuminated by monochromatic light of frequency $\mathrm{v}/2$, the stopping potential is …

Q24.A simple harmonic motion is represented by :
$\mathrm{y}=5(\sin 3\pi \mathrm{t}+\sqrt{3}\cos 3\pi \mathrm{t})\mathrm{cm}$
The amplitude and time period of the motion are :

Q25.Two particles $A,B$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega$. At $\mathrm{t}=0$, their positions and direction of motion are shown in the figure :

The relative velocity $\overrightarrow{V_A}-\overrightarrow{V_B}$ at …

Q26.The mean intensity of radiation on the surface of the Sun is about $10^8\mathrm{W}/{\mathrm{m}}^2$. The rms value of the corresponding magnetic field is closet to :

Q27.A parallel plate capacitor with plates of area $1{\mathrm{m}}^2$ each, are at a separation of 0.1 m . If the electric field between the plates is $100\mathrm{N}/\mathrm{C}$, the magnitude of charge on each plate is:

Q28.The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure :

What is the value of current at $t=4s$ ?

Q1.8 g of NaOH is dissolved in 18 g of ${\mathrm{H}}_2\mathrm{O}$. Mole fraction of NaOH in solution and molality (in $\mathrm{mol}{\mathrm{kg}}^{-1}$) of the solution respectively are :

Q2.The magnetic moment of an octahedral homoleptic Mn (II) complex is 5.9 BM. The suitable ligand for this complex is :

Q3.The element that does NOT show catenation is :

Q4.Among the following, the false statement is :

Q5.The correct structure of histidine in a strongly acidic solution $(\mathrm{pH}=2)$ is :

Q6.The major product of the following reaction is:

(i) ${\mathrm{NaNO}}_2/{\mathrm{H}}^{+}$
(ii) ${\mathrm{CrO}}_3/{\mathrm{H}}^{+}$
(iii) ${\mathrm{H}}_2{\mathrm{SO}}_4$ (conc.), $\Delta$

Q7.${\wedge }_{\mathrm{m}}^{\circ }$ for $\mathrm{NaCl}$, $\mathrm{HCl}$ and NaA are $126.4,425.9$ and $100.5\mathrm{S}{\mathrm{cm}}^2{\mathrm{mol}}^{-1}$, respectively. If the conductivity of 0.001 M HA is $5\times 10^{-5}{\mathrm{Scm}}^{-1}$, degree of dissociation of HA is :

Q8.Molecules of benzoic acid $({\mathrm{C}}_6{\mathrm{H}}_5\mathrm{COOH})$ dimerise in benzene. 'w' g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w i …

Q9.Chlorine on reaction with hot and concentrated sodium hydroxide gives :

Q10.The combination of plots which do not represent isothermal expansion of an ideal gas is:

Q11.The major product in the following conversion is :

Q12.The correct order of atomic radii is :

Q13.The element that shows greater ability to form $p\pi -p\pi$ multiple bonds, is:

Q14.The two monomers for the synthesis of Nylon 6, 6 are :

Q15.The aldehydes which will not form Grignard product with one equivalent Grignard reagents are:

Q16.Given :
(i) C (graphite) $+{\mathrm{O}}_2(\mathrm{g})\to {\mathrm{CO}}_2(\mathrm{g});\Delta {\mathrm{rH}}^{\circ }=\mathrm{x}\mathrm{kJ}{\mathrm{mol}}^{-1}$
(ii) C (graphite) …

Q17.The volume strength of $1\mathrm{M}{\mathrm{H}}_2{\mathrm{O}}_2$ is : (Molar mass of ${\mathrm{H}}_2{\mathrm{O}}_2=34\mathrm{g}{\mathrm{mol}}^{-1}$ )

Q18.The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are :
I. They activate many enzymes
II. They participate in the oxidation of glucose to produce ATP
III. Along with sodium ions, they are responsible for the transmi …

Q19.The compound that is NOT a common component of photochemical smog is :

Q20.For a certain reaction consider the plot of $\ell \mathrm{nk}$ versus $1/\mathrm{T}$ given in the figure. If the rate constant of this reaction at 400 K is $10^{-5}{\mathrm{s}}^{-1}$, then the rate constant at 500 K is:
$\ln \mathrm{k}$ Slope $=-4606\mathrm{K}$

Q21.An open vessel at $27^{\circ }\mathrm{C}$ is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at which the vessel has been heated is :

Q22.The increasing order of the reactivity of the following with ${\mathrm{LiAlH}}_4$ is :
(a)
(see structure)
(b)
(see structure)
(c)
(see structure)
(d)
(see structure)

Q23.The pair that does NOT require calcination is :

Q24.If ${\mathrm{K}}_{\mathrm{sp}}$ of ${\mathrm{Ag}}_2{\mathrm{CO}}_3$ is $8\times 10^{-12}$, the molar solubility of ${\mathrm{Ag}}_2{\mathrm{CO}}_3$ in $0.1\mathrm{M}{\mathrm{AgNO}}_3$ is :

Q25.The upper stratosphere consisting of the ozone layer protects us from the sun's radiation that falls in the wavelength region of :

Q26.If the de Brogile wavelength of the electron in ${\mathrm{n}}^{\text{th }}$ Bohr orbit in a hydrogenic atom is equal to $1.5\pi {\mathrm{a}}_0$ ( ${\mathrm{a}}_0$ is Bohr radius), then the value of $\mathrm{n}/\mathrm{z}$ is :

Q1.${\lim }_{x\to 1^{-}}\frac{\sqrt{\pi }-\sqrt{2{\sin }^{-1}x}}{\sqrt{1-x}}$ is equal to :

Q2.Let $f$ be a differentiable function such that $f(1)=2$ and $f^{\prime }(x)=f(x)$ for all $x\in R$. If $h(x)=f(f(x))$, then $h^{\prime }(1)$ is equal to :

Q3.The integral ${\int }_1^e\left\{{\left(\frac{x}{e}\right)}^{2x}-{\left(\frac{e}{x}\right)}^x\right\}{\log }_{e}xdx$ is equal to :

Q4.Let $\vec{a},\vec{b}$, and $\vec{c}$ be three unit vectors, out of which vectors $\vec{b}$ and $\vec{c}$ are non-parallel. If $\alpha$ and $\beta$ are the angles which vector $\vec{a}$ makes with vectors $\vec{b}$ and $\vec{c}$ respectively and …

Q5.The integral $\int \frac{3x^{13}+2x^{11}}{{\left(2x^4+3x^2+1\right)}^4}dx$ is equal to (where $C$ is a constant of integration)

Q6.If ${\sin }^4\alpha +4{\cos }^4\beta +2=4\sqrt{2}\sin \alpha \cos \beta$; $\alpha ,\beta \in [0,\pi ]$, then $\cos (\alpha +\beta )-\cos (\alpha -\beta )$ is equal to :

Q7.If a curve passes through the point ( $1,-2$ ) and has slope of the tangent at any point ( x , $y)$ on it as $\frac{x^2-2y}{x}$, then the curve also passes through the point :

Q8.If an angle between the line, $\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}$ and the plane, $x-2y-kz=3$ is ${\cos }^{-1}\left(\frac{2\sqrt{2}}{3}\right)$, then a value of k is :

Q9.${\lim }_{n\to \infty }\left(\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\frac{n}{n^2+3^2}+\dots +\frac{1}{5n}\right)$ is equal to

Q10.In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

Q11.If a straight line passing through the point $\mathrm{P}(-3,4)$ is such that its intercepted portion between the coordinate axes is bisected at P , then its equation is:

Q12.There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84 , then the value of …

Q13.The tangent to the curve $y=x^2-5x+5$, parallel to the line $2y=4x+1$, also passes through the point :

Q14.Let S be the set of all real values of $\lambda$ such that a plane passing through the points $\left(-{\lambda }^2,1,1\right),\left(1,-{\lambda }^2,1\right)$ and $\left(1,1,-{\lambda }^2\right)$ also passes through the point $(-1,-1,1)$. Then $S$ is equal to:

Q15.Let $z_1$ and $z_2$ be two complex numbers satisfying $\left|z_1\right|=9$ and $\left|z_2-3-4i\right|=4$. Then the minimum value of $\left|z_1-z_2\right|$ is :

Q16.The total number or irrational terms in the binomial expansion of ${\left(7^{\frac{1}{5}}-3^{\frac{1}{10}}\right)}^{60}$ is :

Q17.The equation of a tangent to the parabola, $x^2=8y$, which makes an angle $\theta$ with the positive direction of $x$-axis, is :

Q18.In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :

Q19.The mean and the variance of five observations are 4 and 5.20 , respectively. If three of the observations are 3,4 and 4 ; then the absolute value of the difference of the other two observations, is :

Q20.If $\mathrm{A}=\left[\begin{array}{ccc}1& \sin \theta & 1\\ -\sin \theta & 1& \sin \theta \\ -1& -\sin \theta & 1\end{array}\right]$; then for all $\theta \in \left(\frac{3\pi }{4},\frac{5\pi }{4}\right)$, $\det (\mathrm{A})$ lies in the interval :

Q21.If a circle of radius R passes through the origin O and intersects the coordinate axes at A and $B$, then the locus of the foot of perpendicular from $O$ on $AB$ is :

Q22.The set of all values of $\lambda$ for which the system of linear equations
$x-2y-2z=\lambda x$
$x+2y+z=\lambda y$
$-x-y=\lambda z$

Q23.If the function $f$ given by $f(x)=x^3-3(a-2)x^2+3ax+7$, for some $a\in R$ is increasing in ( 0 , $1]$ and decreasing in $[1,5)$, then a root of the equation, $\frac{f(x)-14}{(x-1{)}^2}=0(x\ne 1)$ is :

Q24.Let Z be the set of integers. If
$A=\left\{x\in Z:2^{(x+2)\left(x^2-5x+6\right)}=1\right\}$ and $B=\{x\in Z:-3<2x-1<9\}$, then the number of subsets of the set $A\times B$, is :

Q25.If ${}^n{\mathrm{C}}_4,{}^n{\mathrm{C}}_5$ and ${}^n{\mathrm{C}}_6$ are in A.P., then n can be :

Q26.Let $S$ and $S^{\prime }$ be the foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $\Delta {\mathrm{S}}^{\prime }\mathrm{BS}$ is a right angled triangle with right angle at B and area ($\Delta {\mathrm{S}}^{\prime }\mathrm{BS}$) $=8$ sq. units, then the leng …

Q27.If the angle of elevation of a cloud from a point P which is 25 m above a lake be $30^{\circ }$ and the angle of depression of reflection of the cloud in the lake from P be $60^{\circ }$, then the height of the cloud (in meters) from the surface of the lake is :

Q28.The expression $\sim (\sim p\to q)$ is logically equivalent to :

Q29.If the sum of the first 15 terms of the series ${\left(\frac{3}{4}\right)}^3+{\left(1\frac{1}{2}\right)}^3+{\left(2\frac{1}{4}\right)}^3+3^3+{\left(3\frac{3}{4}\right)}^3+\dots .$ is equal to 225 k , then k is equal to :

Q30.The number of integral values of $m$ for which the quadratic expression, $(1+2m)x^2-2(1+3m)x+4(1+m),x\in R$, is always positive, is :