JEE Main 2019 · 12 Apr 2019 · Shift 1

Q1.The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength $5000\mathring{A}$ is used, the minimum separation between two points, to be seen as distinct, will be :

Q2.The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the network is 4 Watt. The value of $R$ is:

Q3.The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of $1{\mathrm{cms}}^{-1}$. At some instant, a part of L is in a uniform magnetic field of 1 T, perpendicular to the plane of …

Q4.A circular disc of radius $b$ has a hole of radius $a$ at its centre (see figure). If the mass per unit area of the disc varies as $\left(\frac{{\sigma }_0}{r}\right)$, then the radius of gyration of the disc about its axis passing through the centre is :

Q5.A man (mass $=50\mathrm{kg}$) and his son (mass $=20\mathrm{kg}$) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 ${\mathrm{ms}}^{-1}$ with respect to the man. The speed of the man with respect to the …

Q6.Two identical parallel plate capacitors, of capacitance C each, have plates of area A , separated by a distance d . The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants ${\mathrm{K}}_1,{\mathrm{K}}_2$ …

Q7.Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? ( $\mathrm{R}=8.3\mathrm{J}/\mathrm{mol}\mathrm{K}$ )

Q8.The stopping potential ${\mathrm{V}}_0$ (in volt) as a function of frequency ( $v$ ) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be :
(Given : Planck's constant …

Q9.At $40^{\circ }\mathrm{C}$, a brass wire of 1 mm diameter is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from $40^{\circ }\mathrm{C}$ to $20^{\circ }\mathrm{C}$ it regains its original length of 0.2 m . The value of M …

Q10.A magnetic compass needle oscillates 30 times per minute at a place where the dip is $45^{\circ }$, and 40 times per minute where the dip is $30^{\circ }$. If ${\mathrm{B}}_1$ and ${\mathrm{B}}_2$ are respectively the total magnetic field due to the earth at the two places, then th …

Q11.An excited ${\mathrm{He}}^{+}$ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm , in making a transition to ground state. The quantum number n , corresponding to its initial excited state is (for photon of wavelength $\lambda$, energy …

Q12.When ${\mathrm{M}}_1$ gram of ice at $-10^{\circ }\mathrm{C}$ (specific heat $=0.5\mathrm{cal}{\mathrm{g}}^{-1\circ }{\mathrm{C}}^{-1}$ ) is added to ${\mathrm{M}}_2$ gram of water at $50^{\circ }\mathrm{C}$, finally no ice is left and the water is at $0^{\circ }\mathrm{C}$. The v …

Q13.A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance R from it. If ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$ are the values of the time taken by it to hit the target in two possible ways, the product …

Q14.The transfer characteristic curve of a transistor, having input and output resistance 100 $\Omega$ and $100\mathrm{k}\Omega$ respectively, is shown in the figure. The Voltage and Power gain, are respectively :

Q15.Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius $b$, and carries charge $Q$. At its centre is a dipole $\overrightarrow{\mathrm{P}}$ as shown. In this case :

Q16.Which of the following combinations has the dimension of electrical resistance ( ${ϵ}_0$ is the permittivity of vacuum and ${\mu }_0$ is the permeability of vacuum)?

Q17.A galvanometer of resistance $100\Omega$ has 50 divisions on its scale and has sensitivity of $20\mu \mathrm{A}/$ division. It is to be converted to a voltmeter with three ranges, of $0-2\mathrm{V},0-10\mathrm{V}$ and $0-20\mathrm{V}$. The appropriate circuit to do so …

Q18.In a double slit experiment, when a thin film of thickness t having refractive index $\mu$ is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of $t$ is ( $\lambda$ is the wavelength of the light …

Q19.A progressive wave travelling along the positive $x$-direction is represented by $y(x,t)=A$ sin $(\mathrm{kx}-\omega \mathrm{t}+\varphi )$. Its snapshot at $\mathrm{t}=0$ is given in the figure:

For this wave, the phase $\varphi$ is :

Q20.A uniform rod of length $\ell$ is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is $\mathrm{T}(\mathrm{x})$ at a distance x from the axis, then which of the …

Q21.A point dipole $\overrightarrow{\mathrm{p}}=-{\mathrm{p}}_0\hat{\mathrm{x}}$ is kept at the origin. The potential and electric field due to this dipole on the y -axis at a distance d are, respectively : (Take $\mathrm{V}=0$ at infinity)

Q22.An electromagnetic wave is represented by the electric field $\vec{E}=E_0\hat{n}\sin [\omega t+(6y-8z)]$. Taking unit vectors in $x$, $y$ and $z$ directions to be $\hat{i},\hat{j},\hat{k}$, the direction of propogation $\hat{s}$, is

Q23.A submarine (A) travelling at $18\mathrm{km}/\mathrm{hr}$ is being chased along the line of its velocity by another submarine (B) travelling at $27\mathrm{km}/\mathrm{hr}$. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency $v$. …

Q24.The trajectory of a projectile near the surface of the earth is given as $y=2x-9x^2$. If it were launched at an angle ${\theta }_0$ with speed $v_0$, then $(g=10\mathrm{m}{\mathrm{s}}^{-2})$:

Q25.A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40\pi \mathrm{rad}{\mathrm{s}}^{-1}$ about its axis, perpendicular to its plane. If the magnetic field at its centre is $3.8\times 10^{-9}\mathrm{T}$, then …

Q26.The truth table for the circuit given in the fig is :

Q27.A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J . The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path …

Q28.A concave mirror has radius of curvature of 40 cm . It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance $d$ from the surface of …

Q29.To verify Ohm's law, a student connects the voltmeter across the battery as, shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained:

If ${\mathrm{V}}_0$ is almost zero, identify the correct statement:

Q30.A person of mass $M$ is, sitting on a swing of length $L$ and swinging with an angular amplitude ${\theta }_0$. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance $\ell (\ell \ll L)$, is …

Q1.The mole fraction of a solvent in aqueous solution of a solute is 0.8. The molality (in mol ${\mathrm{kg}}^{-1}$) of the aqueous solution is

Q2.The correct statement among the following is

Q3.The complex ion that will lose its crystal field stabilization energy upon oxidation of its metal to +3 state is
(Phen = (see structure) and ignore pairing energy)

Q4.The correct set of species responsible for the photochemical smog is :

Q5.The major product(s) obtained in the following reaction is/ are:

Q6.The major product of the following addition reaction is:

Q7.The correct sequence of thermal stability of the following carbonates is :

Q8.The group number, number of valence electrons and valency of an element with atomic number 15, respectively, are:

Q9.Peptization is a :

Q10.The metal that gives hydrogen gas upon treatment with both acid as well as base is:

Q11.The electrons are more likely to be found:

Q12.An example of a disproportionation reaction is :

Q13.5 moles of $A{B}_2$ weigh $125\times 10^{-3}\mathrm{kg}$ and 10 moles of $A_2{B}_2$ weigh $300\times 10^{-3}\mathrm{kg}$. The molar mass of $A\left(M_A\right)$ and molar mass of $B\left(M_B\right)$ in $\mathrm{kg}{\mathrm{mol}}^{-1}$ are :

Q14.The basic structural unit of feldspar, zeolites, mica and asbestos is :

Q15.Enthalpy of sublimation of iodine is $24\mathrm{cal}{\mathrm{g}}^{-1}$ at $200^{\circ }\mathrm{C}$. If specific heat of ${\mathrm{I}}_2(\mathrm{s})$ and ${\mathrm{I}}_2$ (vap) are 0.055 and $0.031\mathrm{cal}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ respectively, then enthalpy of subl …

Q16.Which of the following is a thermosetting polymer?

Q17.An element has a face-centred cubic (fcc) structure with a cell edge of a. The distance between the centres of two nearest tetrahedral voids in the lattice is:

Q18.An organic compound 'A' is oxidized with ${\mathrm{Na}}_2{\mathrm{O}}_2$ followed by boiling with ${\mathrm{HNO}}_3$. The resultant solution is then treated with ammonium molybdate to yield a yellow precipitate. Based on above observation, the element present in the given compou …

Q19.The idea of froth floatation method came from a person $X$ and this method is related to the process $Y$ of ores. $X$ and $Y$, respectively, are:

Q20.In the following reaction; $xA⟶yB$
${\log }_{10}\left[-\frac{\mathrm{d}[\mathrm{A}]}{\mathrm{dt}}\right]={\log }_{10}\left[\frac{\mathrm{d}[\mathrm{B}]}{\mathrm{dt}}\right]+0.3010$
'A' and 'B' respectively can be :

Q21.Glucose and Galactose are having identical configuration in all the positions except position.

Q22.Which of the following statements is not true about RNA?

Q23.What is the molar solubility of $\mathrm{Al}(\mathrm{OH}{)}_3$ in 0.2 M NaOH solution? Given that, solubility product of $\mathrm{Al}(\mathrm{OH}{)}_3=2.4\times 10^{-24}$ :

Q24.The increasing order of the ${\mathrm{pK}}_{\mathrm{b}}$ of the following compound is :

Q25.Given :
${\mathrm{Co}}^{3+}{\mathrm{e}}^{-}⟶{\mathrm{Co}}^{2+};{\mathrm{E}}^{\circ }=1.81\mathrm{V}$
${\mathrm{Pb}}^4+2{\mathrm{e}}^{-}⟶{\mathrm{Pb}}^{2+};{\mathrm{E}}^{\circ }=+1.67\mathrm{V}$ …

Q26.But-2-ene on reaction with alkaline ${\mathrm{KMnO}}_4$ at elevated temperature followed by acidification will give :

Q27.Complete removal of both the axial ligands (along the z -axis) from an octahedral complex leads to which of the following splitting patterns? (relative orbital energies not on scale).

Q28.An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1bar. The work done in kJ is:

Q1.Let $P$ be the point of intersection of the common tangents to the parabola $y^2=12x$ and the hyperbola $8x^2-y^2=8$. If $S$ and $S^{\prime }$ denote the foci of the hyperbola where $S$ lies on the positive $x$-axis then $P$ divides $S{S}^{\prime }$ in a ra …

Q2.If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:

Q3.Let $f:R\to R$ be a continuously differentiable function such that $f(2)=6$ and $f^{\prime }(2)=\frac{1}{48}$. If ${\int }_6^{f(x)}4t^{3}dt=(x-2)g(x)$, then ${\lim }_{x\to 2}g(x)$ is equal to:

Q4.The integral $\int \frac{2x^3-1}{x^4+x}dx$ is equal to:
(Here C is a constant of integration)

Q5.The coefficient of $x^{18}$ in the product $(1+x)(1-x{)}^{10}{\left(1+x+x^2\right)}^9$ is:

Q6.The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:

Q7.Let a random variable $X$ have a binomial distribution with mean 8 and variance 4. If $\mathrm{P}(\mathrm{X}\le 2)=\frac{\mathrm{k}}{2^{16}}$, then k is equal to:

Q8.The equation $|z-i|=|z-1|,i=\sqrt{-1}$, represents:

Q9.If $m$ is the minimum value of $k$ for which the function $f(x)=x\sqrt{kx-x^2}$ is increasing in the interval $[0,3]$ and $M$ is the maximum value of $f$ in $[0,3]$ when $k=m$, then the ordered pair $(\mathrm{m},\mathrm{M})$ is equal to:

Q10.If the data $x_1,x_2,\dots .,x_{10}$ is such that the mean of first four of these is 11 , the mean of the remaining six is 16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is:

Q11.If the area (in sq. units) of the region $\left\{(x,y):y^2\le 4x,x+y\le 1,x\ge 0,y\ge 0\right\}$ is $a\sqrt{2}+b$, then $\mathrm{a}-\mathrm{b}$ is equal to:

Q12.Consider the differential equation, $y^{2}dx+\left(x-\frac{1}{y}\right)dy=0$. If value of $y$ is 1 when $x=1$, then the value of x for which $\mathrm{y}=2$, is:

Q13.If $\alpha$ and $\beta$ are the roots of the equation $375x^2-25x-2=0$, then ${\lim }_{n\to \infty }{\sum }_{r=1}^n{\alpha }^r+{\lim }_{n\to \infty }{\sum }_{r=1}^n{\beta }^r$ is equal to :

Q14.A 2 m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate $25\mathrm{cm}/\sec$., then the rate (in $\mathrm{cm}/\sec$.) at which the bottom of the ladder slides away from the wall on the horizontal gro …

Q15.The number of solutions of the equation $1+{\sin }^{4}x={\cos }^{2}3x,x\epsilon \left[-\frac{5\pi }{2},\frac{5\pi }{2}\right]$ is :

Q16.If $e^y+xy=e$, the ordered pair $\left(\frac{dy}{dx},\frac{d^{2}y}{d{x}^2}\right)$ at $x=0$ is equal to :

Q17.The value of ${\sin }^{-1}\left(\frac{12}{13}\right)-{\sin }^{-1}\left(\frac{3}{5}\right)$ is equal to :

Q18.If the normal to the ellipse $3x^2+4y^2=12$ at a point $P$ on it is parallel to the line, $2x+y=4$ and the tangent to the ellipse at $P$ passes through $Q(4,4)$ then $PQ$ is equal to :

Q19.Let $\vec{a}=3\hat{i}+2\hat{j}+2\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}-2\hat{k}$ be two vectors. If a vector perpendicular to both the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$ has the magnitude 12 then one such vector is:

Q20.The equation $\mathrm{y}=\sin \mathrm{x}\sin (\mathrm{x}+2)-{\sin }^2(\mathrm{x}+1)$ represents a straight line lying in :

Q21.For $x\in \left(0,\frac{3}{2}\right)$, let $f(x)=\sqrt{x},g(x)=\tan x$ and $h(x)=\frac{1-x^2}{1+x^2}$. If $\varphi (x)=((h\mathrm{of})\mathrm{og})(x)$, then $\varphi \left(\frac{\pi }{3}\right)$ is equal to :

Q22.If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is $90^{\circ }$, then the length (in cm ) of their common chord is :

Q23.If ${\int }_0^{\frac{\pi }{2}}\frac{\cot x}{\cot x+\cos ecx}dx=m(\pi +n)$, then $m\cdot n$ is equal to

Q24.Let $S_n$ denote the sum of the first $n$ terms of an A.P.. If $S_4=16$ and $S_6=-48$, then $S_{10}$ is equal to :

Q25.If $B=\left[\begin{array}{ccc}5& 2\alpha & 1\\ 0& 2& 1\\ \alpha & 3& -1\end{array}\right]$ is the inverse of a $3\times 3$ matrix $A$, then the sum of all values of $\alpha$ for which $\det (A)+1=0$, is :

Q26.If the line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects the plane $2x+3y-z+13=0$ at a point $P$ and the plane $3x+y+4z=16$ at a point $Q$, then $PQ$ is equal to :

Q27.If $A$ is a symmetric matrix and $B$ is a skew-symmetric matrix such that $A+B=\left[\begin{array}{cc}2& 3\\ 5& -1\end{array}\right]$, then $AB$ is equal to :

Q28.If the truth value of the statement $p\to (\sim q\vee r)$ is false (F), then the truth values of the statement $p,q,r$ are respectively :

Q29.For $\mathrm{x}\in \mathrm{R}$, let $[\mathrm{x}]$ denote the greatest integer $\le \mathrm{x}$, then the sum of the series …