JEE Main 2019 · 09 Jan 2019 · Shift 1

Q1.A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a dista …

Q2.A resistance is shown in the figure. Its value and tolerance are given respectively by:

Q3.Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section $5{\text{ mm}}^2$, is v. If the electron density in copper is $9\times 10^{28}/{\text{m}}^3$ the value of v in mm/s is close to (Take charge of electron to be $=1.6\times 10^{-19}$ C)

Q4.An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If $AB=BC$, and the angle made by $AB$ with downward vertical is $\theta$, then:

Q5.A particle is moving with a velocity $\vec{v}=K(y\hat{i}+x\hat{j})$, where K is a constant. The general equation for its path is:

Q6.A mixture of 2 moles of helium gas (atomic mass $=4\mathrm{u}$), and 1 mole of argon gas (atomic mass $=40\mathrm{u}$) is kept at 300 K in a container. The ratio of their rms speeds …

Q7.A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to:

Q8.A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a co …

Q9.For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance $h$ from its centre. Then value of $h$ is:

Q10.Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:

Q11.Surface of certain metal is first illuminated with light of wavelength ${\lambda }_1=350\mathrm{nm}$ and then, the light of wavelength ${\lambda }_2=540\mathrm{nm}$. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work …

Q12.Temperature difference of $120^{\circ }\mathrm{C}$ is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length $\frac{3L}{2}$, is connected across AB (See figure). In steady state, temperature difference between …

Q13.A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat flow into the system in path ADB is

Q14.Consider a tank made of glass (refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index $\mu$. A student finds that, irrespective of what the incident angle I (see figure) is for a beam of light entering the liquid, the light reflected from the …

Q15.Mobility of electron in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an $n$-type semiconductor, the density of electrons is $10^{19}{m}^{-3}$ and their mobility is $1.6{\mathrm{m}}^2/(\mathrm{V}.\mathrm{s})$ then …

Q16.A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive $x$-direction. At a particular point in space and time, $\overrightarrow{\mathrm{E}}=6.3\hat{\mathrm{j}}\mathrm{V}/\mathrm{m}$. The corresponding magnetic field …

Q17.Three charges $+\mathrm{Q},\mathrm{q},+\mathrm{Q}$ are placed respectively, at distance, $0,\mathrm{d}/2$ and d from the origin, on the $x$-axis. If the net force experienced by $+Q$, placed at $x=0$, is zero, then value of $q$ is

Q18.A copper wire is stretched to make it $0.5\%$ longer. The percentage change in its electric resistance if its volume remains unchanged is

Q19.A sample of radioactive material A , that has an activity of $10\mathrm{mCi}(1\mathrm{Ci}=3.7\times 10^{10}$ decays/s), has twice the number of nuclei as another sample of different radioactive material B which has an activity of 20 mCi . The correct choices for …

Q20.A heavy ball of mass M is suspended from the ceiling of car by a light string of mass $\mathrm{m}(\mathrm{m}\ll \mathrm{M})$. When the car is at rest, the speed of transverse waves in the string is 60 ${\mathrm{ms}}^{-1}$. When the car has acceleration a , the wave-speed incre …

Q21.An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. the radius of the loop is a and distance of its centre from the wire is $\mathrm{d}(\mathrm{d}\gg \mathrm{a})$. If the loop applies a force $F$ on the wire then …

Q22.A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6 . What should be the minimum value of force P , such that the block does not move down …

Q23.A parallel plate capacitor is made of two square plates of side ' $a$ ', separated by a distance $\mathrm{d}(\mathrm{d}\ll a$ ). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is

Q24.A rod of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having coefficient of linear expansion $\alpha /{}^{\circ }\mathrm{C}$. It is observed that an external compressive force F, is applied on each of its ends, prevents any chang …

Q25.A bar magnet is demagnetized by inserting it inside a solenoid of length $0.2\mathrm{m},100$ turns, and carrying a current of 5.2 A . The coercivity of the bar magnet is

Q26.Three blocks $\mathrm{A},\mathrm{B}$ and C are lying on a smooth horizontal surface, as shown in the figure. $A$ and $B$ have equal masses, $m$ while $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards B due to which it collides with B perfectly ine …

Q27.When the switch S , in the circuit shown, is closed, then the value of current i will be

Q28.If the angular momentum of a planet of mass m , moving a round the Sun in a circular orbit its L , about the center of the Sun, its areal velocity is:

Q29.Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $\ell$. The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rodmass system (see figure). Because of torsional constant k , the restoring tor …

Q1.Two complexes $\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]{\mathrm{Cl}}_3$ (A) and $\left[\mathrm{Cr}{\left({\mathrm{NH}}_3\right)}_6\right]{\mathrm{Cl}}_3$ (B) are violet and yellow coloured respectively. The incorrect statement regarding them is

Q2.The correct decreasing order for acidic strength is

Q3.The major product of the following reaction is

Q4.The highest value of the calculated spin-only magnetic moment (in BM) among all the transition metal complexes is

Q5.0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume $10{\mathrm{m}}^3$ at 1000 K. Given R is the gas constant in ${\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1},\mathrm{x}$ is

Q6.The one that is extensively used as a piezoelectric material is

Q7.Correct statements among a to d regarding silicones are
(i) they are polymers with hydrophobic character
(ii) they are biocompatible
(iii) in general, they have high thermal stability and low dielectric strength
(iv) usually they are resistant to oxidation and used as greases.

Q8.In general, the properties that decrease and increase down a group in the periodic table respectively are

Q9.A solution of sodium sulphate contains 92 g of ${\mathrm{Na}}^{+}$ ions per kilogram of water. The Molality of ${\mathrm{Na}}^{+}$ ions in that solution in $\mathrm{mol}{\mathrm{kg}}^{-1}$ is

Q10.The correct match between Item-I and Item-II is:
Item - I (drug) and Item - II (test)

Q11.A water sample has ppm level concentration of the following metals: $\mathrm{Fe}=0.2,\mathrm{Mn}=5.0,\mathrm{Cu}=3.0,\mathrm{Zn}=5.0$. The metal that makes the water sample unsuitable for drinking is

Q12.The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount of ${\mathrm{PbSO}}_4$ electrolyzed in g during the process is:
(Molar mass of ${\mathrm{PbSO}}_4=303\mathrm{g}{\mathrm{mol}}^{-1}$)

Q13.Which one of the following statements regarding Henry's law is not correct?

Q14.The following results were obtained during kinetic studies of the reaction $2\mathrm{A}+\mathrm{B}⟶$ products

| Experiment | $[\mathrm{A}]$ (in mol L${}^{-1}$) | $[\mathrm{B}]$ (in mol L${}^{-1}$) | Initial rate of reaction (in …

Q15.The alkaline earth metal nitrate that does not crystallise with water molecules is

Q16.20 mL of $0.1\mathrm{M}{\mathrm{H}}_2{\mathrm{SO}}_4$ is added to 30 mL of $0.2\mathrm{M}{\mathrm{NH}}_4\mathrm{OH}$ solution. The pH of the resultant mixture is [${\mathrm{pk}}_{\mathrm{b}}$ of ${\mathrm{NH}}_4\mathrm{OH}=4.7$]

Q17.Adsorption of a gas follows Freundlich adsorption isotherm. In the given plot, x is the mass of gas adsorbed on mass $m$ of the adsorbent at pressure $p$. $\frac{x}{m}$ is proportional to

Q18.Which amongst the following is the strongest acid?

Q19.The ore that contains both iron and copper is

Q20.For emission line of atomic hydrogen from ${\mathrm{n}}_{\mathrm{i}}=8$ to ${\mathrm{n}}_{\mathrm{f}}=\mathrm{n}$, the plot of wave number $(\overline{\mathrm{v}})$ against $\left(\frac{1}{{\mathrm{n}}^2}\right)$ will be (The Rydberg constant, ${\mathrm{R}}_{\mathrm{H}}$ is in wave num …

Q21.The isotopes of hydrogen are

Q22.According to molecular orbital theory, which of the following is true with respect to ${\mathrm{Li}}_2^{+}$ and ${\mathrm{Li}}_2^{-}$?

Q23.Aluminium is usually found in +3 oxidation state. In contrast, thallium exists in +1 and +3 oxidation states. This is due to

Q24.The increasing order of pKa of following amino acids in aqueous solution is Gly, Asp, Lys, Arg

Q25.Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures $T_1\&T_2\left(T_1<T_2\right)$. The correct graphical depiction of the dependence of work done(w) on the final volume(v).

Q26.Arrange the following amine in the decreasing order of basicity:

Q27.The compounds A and B in the following reaction are, respectively

Q1.The value of ${\int }_0^{\pi }|\cos x{|}^{3}dx$ is:

Q2.The maximum volume (in cu.m) of the right circular cone having slant height 3 m is

Q3.For $x^2\ne n\pi +1,n\in N$ (the set of natural numbers), the integral
$\int x\cdot \sqrt{\frac{2\sin \left(x^2-1\right)-\sin 2\left(x^2-1\right)}{2\sin \left(x^2-1\right)+\sin 2\left(x^2-1\right)}}dx$ is

Q4.If $y=y(x)$ is solution of the differential equation $x\frac{dy}{dx}+2y=x^2$ satisfying $y(1)=1$, then $y\left(\frac{1}{2}\right)$ is equal to

Q5.Axis of a parabola lies along $x$ - axis. If its vertex and focus are at distance 2 and 4 respectively from the origin, on the positive $x$ - axis then which of the following points does not lie on it?

Q6.Let $0<\theta <\frac{\pi }{2}$. If the eccentricity of the hyperbola $\frac{x^2}{{\cos }^2\theta }-\frac{y^2}{{\sin }^2\theta }=1$ is greater than 2, then the length of its latus rectum lies in the interval:

Q7.For $\mathrm{x}\in \mathrm{R}-[0,1]$, let ${\mathrm{f}}_1(\mathrm{x})=\frac{1}{\mathrm{x}},{\mathrm{f}}_2(\mathrm{x})=1-\mathrm{x}$ and ${\mathrm{f}}_3(\mathrm{x})=\frac{1}{1-\mathrm{x}}$ be three given functions. If a function, $J(x)$ satisfies …

Q8.Let $\vec{a}=\hat{i}-\hat{j},\vec{b}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{c}$ be a vector such that $\vec{a}\times \vec{c}+\vec{b}=0$ and $\vec{a}\cdot \vec{c}=4$, then $|\vec{c}{|}^2$ is equal to:

Q9.If $\mathrm{a},\mathrm{b}$ and c be three distinct numbers in G.P. and $\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{xb}$ then x can not be

Q10.If ${\cos }^{-1}\left(\frac{2}{3x}\right)+{\cos }^{-1}\left(\frac{3}{4x}\right)=\frac{\pi }{2},x>\frac{3}{4}$ then $x$ is equal to:

Q11.Equation of a common tangent to the circle, $x^2+y^2-6x=0$ and the parabola, $y^2=4x$, is:

Q12.The system of linear equation $x+y+z=2,2x+3y+2z=5,2x+3y+\left(a^2-1\right)z=a+1$ then

Q13.If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$, then k is equal to:

Q14.The equation of line passing through $(-4,3,1)$, parallel to the plane $x+2y-z-5=0$ and intersecting the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z-2}{-1}$ is:

Q15.Consider the set of all lines $px+qy+r=0$ such that $3p+2q+4r=0$. Which one of the following statements is true?

Q17.The plane through the intersection of the plane $x+y+z=1$ and $2x+3y-z+4=0$ and parallel to $y$-axis also pass through the point:

Q18.If $\theta$ denotes the acute angle between the curves, $y=10-x^2$ and $y=2+x^2$ at a point of their intersection, then $|\tan \theta |$ is equal to

Q19.If $A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]$, then the matrix $A^{-50}$ when $\theta =\frac{\pi }{12}$, is equal to

Q20.If the Boolean expression $(p\oplus q)\wedge (\sim p\Theta q)$ is equivalent to $p\wedge q$, where $\oplus$, $\Theta \in \{\wedge ,\vee \}$, then the ordered pair $(\oplus ,\Theta )$ is :

Q21.5 students of a class have an average height 150 cm and variance $18{\mathrm{cm}}^2$. A new student, whose height is 156 cm, joined them. The variance (in ${\mathrm{cm}}^2$) of the height of these six students is:

Q22.For any $\theta \in \left(\frac{\pi }{4},\frac{\pi }{2}\right)$, the expression $3(\sin \theta -\cos \theta {)}^4+6(\sin \theta +\cos \theta {)}^2+4{\sin }^6\theta$ equals:

Q23.The area (in sq. units) bounded by the parabola $y=x^2-1$, the tangent at the point (2, 3) to it and the y - axis is:

Q24.Let $a_1,a_2,\dots ,a_{30}$ be an A.P., $S={\sum }_{i=1}^{30}{a}_i$ and $T={\sum }_{i=1}^{15}{a}_{2i-1}$. If $a_5=27$ and $S-2T=75$, then $a_{10}$ is equal to

Q25.Let $f:\mathbb{R}\to \mathbb{R}$ be a function defined as $f(x)=\{\begin{array}{ccc}5,& \text{ if }& x\le 1\\ a+bx,& \text{ if }& 1<x<3\\ b+5x,& \text{ if }& 3\le x<5\\ 30,& \text{ if }& x\ge 5\end{array}$. Then $f$ is:

Q26.Let $\mathrm{A}=\{\theta \in \left(-\frac{\pi }{2},\pi \right):\frac{3+2i\sin \theta }{1-2i\sin \theta }$ is purely imaginary $\}$. Then the sum of the elements in A is:

Q27.Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same team, is:

Q28.Let $\alpha$ and $\beta$ be two roots of the equation $x^2+2x+2=0$, then ${\alpha }^{15}+{\beta }^{15}$ is equal to:

Q29.Three circles of radii $\mathrm{a},\mathrm{b},\mathrm{c}$ $(\mathrm{a}<\mathrm{b}<\mathrm{c})$ touch each other externally. If they have x-axis as a common tangent, then:

Q30.Two cards are drawn successively with replacement from a well shuffled deck of 52 cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then $\mathrm{P}(\mathrm{X}=1)+\mathrm{P}(\mathrm{X}=2)$ equals: