JEE Main 2019 · 10 Apr 2019 · Shift 2

Q1.One mole of an ideal gas passes through a process where pressure and volume obey the relation $P=P_o\left[1-\frac{1}{2}{\left(\frac{V_o}{V}\right)}^2\right]$. Here $P_o$ and $V_o$ are constants. Calculate the change in the temperature of the gas if its volume change from …

Q2.A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let $I_1$ be the moment of inertia of the disc about …

Q3.The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz,

Q4.When heat Q is supplied to a diatomic gas of rigid molecules at constant volume its temperature increases by $\Delta T$. The heat required to produce the same change in temperature, at constant pressure is

Q5.A bullet of mass 20 g has an initial speed of $1{\mathrm{ms}}^{-1}$ just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistances of $2.5\times 10^{-2}\mathrm{N}$, the speed of the bullet after emerging from the other side of the wall i …

Q6.The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit?

Q7.A plane is inclined at an angle $\alpha =30^{\circ }$ with respect to the horizontal. A particle is projected with a speed $u=2{\mathrm{ms}}^{-1}$, from the base of the plant, making an angle $\theta =15^{\circ }$ with respect to the plane as shown in the figure. The distance from th …

Q8.The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is: [Take ${\mu }_0=4\pi \times 10^{-7}{\mathrm{NA}}^{-2}$]

Q9.Two radioactive substances A and B have decay constants $5\lambda$ and $\lambda$ respectively. At $\mathrm{t}=0$, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become ${\left(\frac{1}{\mathrm{e}}\right)}^2$ will be

Q10.Two blocks $A$ and $B$ of masses $m_A=1\mathrm{kg}$ and $m_B=3\mathrm{kg}$ are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force $F$ that can be applied on $B$ …

Q11.The formula $X=5Y{Z}^2$ $X$ and $Z$ have dimensions of capacitance and magnetic field respectively. What are the dimensions of Y in SI units?

Q12.In ${\mathrm{Li}}^{++}$, electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda$. When the ion gets deexcited to the ground state in all possible ways(including intermediate emission) a total of six spectral lines are observed. What is the value of …

Q13.The graph shows how the magnification m produced by a thin lens varies with image distance $v$. What is the focal length of the lens used?

Q14.A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the plant acts on the spaceship. What will be the number of complete revolutions made by the spaceship in 24 hours around the plane?
[Given: Mass of plane …

Q15.Light is incident normally on a completely absorbing surface with an energy flux of $25\mathrm{W}{\mathrm{cm}}^{-2}$. If the surface has an area of $25{\mathrm{cm}}^2$, the maximum transferred to the surface in 40 min time duration will be

Q16.The time dependence of the position of a particle of mass $m=2$ is given by $\vec{r}(t)=2t\hat{i}-3t^2\hat{j}$ Its angular momentum with respect to the origin at time $t=2$ is .

Q17.Water from a tap emerges vertically downwards with an initial speed of $1.0{\mathrm{ms}}^{-1}$. The cross-sectional area of the tap is $10^{-4}{\mathrm{m}}^2$. Assume that the pressure is constant throughout the stream of water and that flow is streamlined. The cross-sectional …

Q18.Space between two concentric conducting spheres of radii $a$ and $b(b>a)$ is filled with a medium of resistivity $\rho$. The resistance between the two spheres will be

Q19.A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5 s is close to

Q20.The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6 V and the load resistance is ${\mathrm{R}}_{\mathrm{L}}=4\mathrm{k}\Omega$. The series resistance of the circuit is ${\mathrm{R}}_{\mathrm{i}}=1\mathrm{k}\Omega$. …

Q21.A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass $m$ and charge $q$. The time period of the pendulum is given by

Q22.A 2 mW laser operates at a wavelength of 500 nm. The number of photons that will be emitted per second is
[Given Planck's constant $\mathrm{h}=6.6\times 10^{-34}\mathrm{Js}$, speed of light $\mathrm{c}=3.0\times 10^8\mathrm{m}/\mathrm{s}$]

Q23.A coil of self inductance 10 mH and resistance $0.1\Omega$ is connected through a switch to a battery of internal resistance $0.9\Omega$. After the switch is closed the time taken for the current to attain $80\%$ of the saturation values is: [take $\ln 5=1.6$]

Q24.A submarine experiences a pressure of $5.05\times 10^6\mathrm{Pa}$ at a depth of ${\mathrm{d}}_1$ in a sea. When it goes further to a depth of $d_2$, it experiences a pressure of $8.08\times 10^6\mathrm{Pa}$. Then $d_2-d_1$ is approximately (density of water …

Q25.A cubical block of side 0.5 m floats on water with $30\%$ of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?
[Take density of water $=10^3\mathrm{kg}/{\mathrm{m}}^3$]

Q26.In a Young's double slit experiment the ratio of the slit's width is $4:1$. The ratio of the intensity of maxima to minima, close to central fringe on the screen will be

Q27.A source of sound S is moving with the velocity of $50\mathrm{m}/\mathrm{s}$ towards a stationary observer. The observer measures the frequency of the sound as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing h …

Q28.A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m . If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be

Q1.The difference between $\Delta \mathrm{H}$ and $\Delta \mathrm{U}(\Delta \mathrm{H}-\Delta \mathrm{U})$, when the combustion of one mole of heptane(I) is carried out a temperature T is equal to

Q2.The major product obtained in the given reaction is

Q3.The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9 . The spectral series are:

Q4.The correct order of the first ionization enthalpies is

Q5.The correct statements among (a) to (b) are:
(a) saline hydrides produce ${\mathrm{H}}_2$ gas when reacted with ${\mathrm{H}}_2\mathrm{O}$.
(b) reaction of ${\mathrm{LiAH}}_4$ with ${\mathrm{BF}}_3$ leads to ${\mathrm{B}}_2{\mathrm{H}}_6$.
(c) ${\mathrm{PH}}_3$ and …

Q6.Air pollution that occurs in sunlight is:

Q7.For the re action of ${\mathrm{H}}_2$ with ${\mathrm{I}}_2$, the rate constant is $2.5\times 10^{-4}{\mathrm{dm}}^3{\mathrm{mol}}^{-1}{\mathrm{s}}^{-1}$ at $327^{\circ }\mathrm{C}$ and $1.0{\mathrm{dm}}^3{\mathrm{mol}}^{-1}{\mathrm{s}}^{-1}$ at …

Q8.In chromatography, which of the following statements is INCORRECT for ${\mathrm{R}}_f$ ?

Q9.A hydrated solid X on heating initially gives a monohydrated compound Y . Y upon heating above 373 K leads to an anhydrous white powder $\mathrm{Z}.\mathrm{X}$ and Z , respectively, are:

Q10.The INCORRECT statement is:

Q11.Which of these factors does not govern the stability of a conformation in acyclic compounds?

Q12.The correct statement is:

Q13.For the reaction,

${\Delta }_{\mathrm{H}}=-57.2\mathrm{kJ}{\mathrm{mol}}^{-1}$ and
${\mathrm{K}}_{\mathrm{C}}=1.7\times 10^{16}$
Which of the following statement is INCOR …

Q14.The increasing order of nucleophilicity of the following nucleophiles is :
(a) ${\mathrm{CH}}_3{\mathrm{CO}}_2^{-}$
(b) ${\mathrm{H}}_2\mathrm{O}$
(c) ${\mathrm{CH}}_3{\mathrm{SO}}_3^{-}$
(d) $\overline{\mathrm{O}}\mathrm{H}$

Q15.The correct match between Item-I and Item-II is:
| (c) | Novolac | (III) | Ziegler-Natta Catalys …

Q16.The major product 'Y' in the following reaction is:-

Q17.Points I, II and III in the following plot respectively correspond to ( ${\mathrm{V}}_{\mathrm{mp}}$ : most probable velocity)

Q18.The highest possible oxidation states of uranium and plutonium, respectively, are

Q19.Compound A $\left({\mathrm{C}}_9{\mathrm{H}}_{10}\mathrm{O}\right)$ shows positive iodoform test. Oxidation of A with ${\mathrm{KMnO}}_4/\mathrm{KOH}$ gives acid $\mathrm{B}\left({\mathrm{C}}_8{\mathrm{H}}_6{\mathrm{O}}_4\right)$. Anhydride of B is used for the preparation of …

Q20.The noble gas that does NOT occur in the atmosphere is:

Q21.The pH of a $0.02\mathrm{M}{\mathrm{NH}}_4\mathrm{Cl}$ solution will be [given ${\mathrm{K}}_{\mathrm{b}}\left({\mathrm{NH}}_4\mathrm{OH}\right)=10^{-5}$ and $\log 2=0.301$ ]

Q22.The crystal field stabilization energy (CFSE) of $\left[\mathrm{Fe}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]{\mathrm{Cl}}_2$ and ${\mathrm{K}}_2\left[{\mathrm{NiCl}}_4\right]$, respectively, are :-

Q23.The correct option among the following is:

Q24.Which one of the following graphs between molar conductivity $\left({\Lambda }_m\right)$ versus $\sqrt{\mathrm{C}}$ is correct?

Q25.1 g of non-volatile non-electrolyte solute is dissolved in 100 g of two different solvents A and B whose ebullioscopic constants are in the ratio of $1:5$. The ratio of the elevation in their boiling points, $\frac{\Delta T_b(A)}{\Delta T_b(B)}$ is :

Q26.Which of the following is NOT a correct method of the preparation of benzylamine from cyanobenzene?

Q27.The number of pentagons in ${\mathrm{C}}_{60}$ and trigons (triangles) in white phosphorus, respectively, are:

Q28.The minimum amount of ${\mathrm{O}}_2(\mathrm{g})$ consumed per gram of reactant is for the reaction :
(Given atomic mass: $\mathrm{Fe}=56,\mathrm{O}=16,\mathrm{Mg}=24,\mathrm{P}=31,\mathrm{C}=12,\mathrm{H}=1$ )

Q29.Number of stereo centers present in linear and cyclic structures of glucose are respectively

Q1.If ${\lim }_{\mathrm{x}\to 1}\frac{{\mathrm{x}}^2-\mathrm{ax}+\mathrm{b}}{\mathrm{x}-1}=5$, then $\mathrm{a}+\mathrm{b}$ is equal to

Q2.The sum of the real roots of the equation
$\left|\begin{array}{ccc}x& -6& -1\\ 2& -3x& x-3\\ -3& 2x& x+2\end{array}\right|=0$ is equal to

Q3.Lines are drawn parallel to the line $4x-3y+2=0$ at a distance $\frac{3}{5}$ from the origin. Then which one of the following points lies on any of these lines?

Q4.If the tangent to the curve $y=\frac{x}{x^2-3},x\in R,(x\ne \pm \sqrt{3})$ at a point $(\alpha ,\beta )\ne (0,0)$ on it is parallel to the line $2x+6y-11=0$ then

Q5.The distance of the point having position vector $-\hat{i}+2\hat{j}+6\hat{k}$ from the straight line passing through the point ( $2,3,-4$ ) and parallel to the vector $6\hat{i}+3\hat{j}-4\hat{k}$ is

Q6.If the line $ax+y=c$, touches both the curves $x^2+y^2=1$ and $y^2-4\sqrt{2}x$, then $|c|$ is equal to

Q7.Let $f(x)={\log }_e(\sin x),(0<x<\pi )$ and $g(x)={\sin }^{-1}\left(e^{-x}\right),(x\ge 0)$. If $\alpha$ is a positive real number such that $\mathrm{a}=(\mathrm{fog}{)}^{\prime }(\alpha )$ and $\mathrm{b}=(\mathrm{fog})(\alpha )$, then

Q8.If $5x+9=0$ is the directrix of the hyperbola $16x^2-9y^2=144$, then its corresponding focus is

Q9.If ${\cos }^{-1}x-{\cos }^{-1}\frac{y}{2}=\alpha$, where $-1\le x\le 1,-2\le y\le 2,x\le \frac{y}{2}$, then for all $x,y,4x^2-4xy\cos \alpha +y^2$ is equal to

Q10.The locus of the centres of the circles, which touch the circle, $x^2+y^2=1$ externally, also touch the $y$-axis and lie in the first quadrant is

Q11.Let $a_1,a_2,a_3,\dots \dots$ be and A.P with $a_6=2$. Then the common difference of this A.P., which maximizes the product ${\mathrm{a}}_1{\mathrm{a}}_4{\mathrm{a}}_5$ is

Q12.The smallest natural number n , such that the coefficient of x in the expansion of ${\left(x^2+\frac{1}{x^3}\right)}^n$ is ${}^n{\mathrm{C}}_{23}$ is

Q13.Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is

Q14.A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of $50{\mathrm{cm}}^3/\min$. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of ice decreases is

Q15.If both the means and the standard deviation of 50 observations $x_1,x_2,\dots \dots \dots ,x_{50}$ are equal to 16, then the mean of $(x_1-4{)}^2,(x_2-4{)}^2,\dots .,(x_{50}-4{)}^2$ is

Q16.The number of real roots of the equation

Q17.The tangent and normal to the ellipse $3x^2+5y^2=32$ at the point $P(2,2)$ meet the $x$-axis at $Q$ and $R$, respectively. Then the area(in sq. units) of the triangle $PQR$ is

Q18.A perpendicular is drawn from a point on the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{1}$ to the plane $x+y+z=3$ such that the foot of the perpendicular $Q$ also lies on the plane $x-y+z=3$. Then the co-ordinates of Q are

Q19.The integral ${\int }_{\pi /6}^{\pi /3}{\sec }^{2/3}x{\mathrm{cosec}}^{4/3}xdx$ is equal to

Q20.The angles $A,B$ and $C$ of a triangle $ABC$ are in $A.P$ and $a:b=1:\sqrt{3}$. If $c=4\mathrm{cm}$, then the area (in sq. cm ) of this triangle is

Q21.Let $\mathrm{a},\mathrm{b}$ and c be in G.P with common ratio r, where $\mathrm{a}\ne 0$ and $0<\mathrm{r}\le \frac{1}{2}$. If $3\mathrm{a},7\mathrm{b}$ and 15 c are the first three terms of an A.P., then the $4^{\text{th }}$ term of this A.P is

Q22.Let $\mathrm{y}=\mathrm{y}(\mathrm{x})$ be the solution of the differential equation $\frac{dy}{dx}+y\tan x=2x+x^2\tan x,x\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$, such that $y(0)=1$. Then

Q23.If the plane $2x-y+2z+3=0$ has the distances $\frac{1}{3}$ and $\frac{2}{3}$ units from the planes $4x-2y+4z+\lambda =0$ and $2x-y+2z+\mu =0$, respectively, then the maximum value of $\lambda +\mu$ us equal to

Q24.The area(in sq. units) of the region bounded by the curves $y=2^x$ and $y=|x+1|$ in the first quadrant is

Q25.Let $\lambda$ be a real number for which the system of linear equations
$x+y+z=6$
$4x+\lambda y-\lambda z=\lambda -2$
$3x+2y-4z=-5$
Has indefinitely many solutions. Then $\lambda$ is a root of the quadratic equation

Q26.The sum $1+\frac{1^3+2^3}{1+2}+\frac{1^3+2^3+3^3}{1+2+3}+\dots +\frac{1^3+2^3+3^3+\dots +15^3}{1+2+3+\dots +15}-\frac{1}{2}(1+2+3+\dots +15)$ is equal to

Q27.Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than $99\%$ is

Q28.The negation of the Boolean expression $\sim s\vee (\sim r\wedge s)$ is equivalent to

Q29.If $\int x^5{e}^{-x^2}dx=g(x)e^{-x^2}+c$, where $c$ is a constant of integration, then $g(-1)$ is equal to

Q30.If $z$ and $w$ are two complex numbers such that $|zw|=1$ and $\arg (z)-\arg (w)=\frac{\pi }{2}$, then