JEE Main 2019 · 08 Apr 2019 · Shift 1

Q1.A particle moves in one dimension from rest under the influence of a force that varies with the distance traveled by the particle as shown in the figure. The kinetic energy of the particle after it has traveled 3 m is:

Q2.An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be:

Q3.Four particles A, B, C and D with masses $m_A=m,m_B=2m,m_c=3m$ and $m_D=4m$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is:

Q4.Two identical beakers A and B contain equal volumes of two different liquids at $60^{\circ }\mathrm{C}$ each and left to cool down. Liquid in A has density of $8\times 10^2\mathrm{kg}/{\mathrm{m}}^3$ and specific heat of $2000{\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$ while liqu …

Q5.A thin strip 10 cm long is on a ∪ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5{\mathrm{Nm}}^{-1}$ (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and relea …

Q6.A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is

Q7.A wire of length 2 L is made by joining two wires A and b of same lengths but different radii $r$ and $2r$ and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire $A$ is $p$ and that in …

Q8.A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that $\mathrm{g}=3.1\pi {\mathrm{ms}}^{-2}$, what will be the tensile stress that would be developed in the wire?

Q9.Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of $10^6\frac{\mathrm{V}}{\mathrm{m}}$. The plate area is $10^{-4}{\mathrm{m}}^2$. What is the dielectric constant if the capacitance is 15 pF? (given …

Q10.An alternating voltage $\mathrm{v}(\mathrm{t})=220\sin 100\pi \mathrm{t}$ volt is applied to a purely resistive load of $50\Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

Q11.The wavelength of the carrier waves in a modern optical fiber communication network is close to:

Q12.Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of: (density of water = 1000 $\mathrm{kg}/{\mathrm{m}}^3$, coefficient of viscosity of water $=1\mathrm{mPa}\mathrm{s}$)

Q13.A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity o …

Q14.Two particles move at right angle to each other. Their de Broglie wavelengths are ${\lambda }_1$ and ${\lambda }_2$ respectively. The particles suffere perfectly inelastic collision. The de Broglie wavelength $\lambda$, of the final particle, is given by:

Q15.Four identical particles of mass M are located at the corners of a square of side '$a$'. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square?

Q16.In figure, the optical fiber is $l=2\mathrm{m}$ long and has a diameter of $d=20\mu \mathrm{m}$. If a ray of light is incident on one end of the fiber at angle ${\theta }_1=40^{\circ }$, the number of reflection it makes before emerging from the other end is close to:

Q17.A circular coil having $N$ turns and radius $r$ carries a current. It is held in the $XZ$ plane in a magnetic field $B\hat{i}$. The torque on the coil due to the magnetic field is:

Q18.Ship A is sailing towards north - east with velocity $\vec{v}=30\hat{\mathrm{i}}+50\hat{\mathrm{j}}\mathrm{km}/\mathrm{hr}$ where $\hat{\mathrm{i}}$ points east and $\hat{j}$, north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing toward …

Q19.A plane electromagnetic wave travels in free space along the x -direction. The electric field component of the wave at a particular point of space and time is $E=6{\mathrm{Vm}}^{-1}$ along y -direction. Its corresponding magnetic filed component, B would be:

Q20.A thermally insulted vessel contains 150 g of water at $0^{\circ }\mathrm{C}$. Then the air from the vessel is pumped out a adiabatically. A fraction of water turns into ice and the rest evaporates at $0^{\circ }\mathrm{C}$ itself. The mass of evaporated water will be closes …

Q21.Radiation coming from transition $\mathrm{n}=2$ to $\mathrm{n}=1$ of hydrogen atoms fall of ${\mathrm{He}}^{+}$ions in $\mathrm{n}=$ 1 and $\mathrm{n}=2$ states. The possible. Transition of helium ions as they absorb energy from the radiation is:

Q22.A $200\Omega$ resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be:

Q23.The reverse breakdown voltage of a Zener diode is 5.6 V in the given circuit .

The current ${\mathrm{I}}_{\mathrm{z}}$ through the Zener is:

Q24.A thin circular plate of mass $M$ and radius $R$ has its density varying as $p(r)=p_{0}r$ with $P_0$ as constant and $r$ is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge …

Q25.In SI units, the dimensions of $\sqrt{\frac{{ϵ}_0}{{\mu }_0}}$ is:

Q26.For the circuit shown, with ${\mathrm{R}}_1=1.0\Omega ,{\mathrm{R}}_2=2.0\Omega ,{\mathrm{E}}_1=2\mathrm{V}$ and ${\mathrm{E}}_2={\mathrm{E}}_3=4\mathrm{V}$, the potential difference between the points ' $a$ ' and ' $b$ ' is approximately (in V ):

Q27.A solid conducting sphere, having a charge Q , is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V . If the shell is now given a charge of -4 Q …

Q28.In an interference experiment the ratio of amplitudes of coherent waves is $\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{1}{3}$. The ratio of maximum and minimum intensities of fringes will be:

Q29.The bob of a simple pendulum has mass 2 g and a charge of $5.0\mu \mathrm{C}$. It is at rest in a uniform horizontal electric field of intensity $2000\frac{\mathrm{V}}{\mathrm{m}}$. At equilibrium, the angle that the pendulum makes with the vertical is: (take …

Q1.Element 'B' forms ccp structure and 'A' occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is

Q2.Coupling of benzene diazonium chloride with 1-naphthol in alkaline medium will give:

Q3.The size of the iso-electronic species ${\mathrm{Cl}}^{-}$, $\mathrm{Ar}$ and ${\mathrm{Ca}}^{2+}$ is affected by

Q4.In the following compounds, the decreasing order of basic strength will be:

Q5.The correct order of the spin only magnetic moment of metal ions in the following low spin complexes, ${\left[\mathrm{V}(\mathrm{CN}{)}_6\right]}^{4-},{\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{4-},{\left[\mathrm{Ru}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$, and …

Q6.An organic compound 'X' showing the following solubility profile is:

Q7.Diborane $\left({\mathrm{B}}_2{\mathrm{H}}_6\right)$ reacts independently with ${\mathrm{O}}_2$ and ${\mathrm{H}}_2\mathrm{O}$ to produce, respectively:

Q8.The lanthanoide that would show colour is:

Q9.The major product of the following reaction

Q10.100 mL of a water sample contains 0.81 g of calcium bicarbonate and 0.73 g of magnesium bicarbonate. The hardness of this water sample expressed in terms of equivalents of ${\mathrm{CaCO}}_3$ is:
(molar mass of calcium bicarbonate is $162{\mathrm{gmol}}^{-1}$ and magnesium bicarbo …

Q11.An organic compound neither reacts with neutral ferric chloride solution nor with Fehling solution. It however, reacts with Grignard reagent and gives positive iodoform test. The compound is:

Q12.For the reaction $2\mathrm{A}+\mathrm{B}\to \mathrm{C}$, the values of initial rate at different reactant concentrations are given in the table below: The rate law for the reaction is:

| $[\mathrm{A}]({\mathrm{molL}}^{-1})$ | $[\mathrm{B}]({\mathrm{molL}}^{-1})$ | Initial …

Q13.Which is wrong with respect to our responsibility as a human being to protect our environment?

Q14.For silver $C_P(J{K}^{-1}{\mathrm{mol}}^{-1})=23+0.01T$. If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of $\Delta H$ will be close to:

Q15.The correct order of hydration enthalpies of alkali metal ions is:

Q16.Adsorption of a gas follows Freundlich adsorption isotherm. x is the mass of the gas adsorbed on mass $m$ of the adsorbent. The plot of $\log \frac{x}{m}$ versus $\log p$ is shown in the given graph, $\frac{x}{m}$ is proportional to:

Q17.The vapour pressures of pure liquids $A$ and $B$ are 400 and 600 mm Hg, respectively at 298 K. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The mole fraction of liquid B is 0.5 in the mixture. The vapour pressure of the …

Q18.Given that ${\mathrm{E}}_{{\mathrm{O}}_2/{\mathrm{H}}_2\mathrm{O}}^0=+1.23\mathrm{V}$; ${\mathrm{E}}_{{\mathrm{S}}_2{\mathrm{O}}_8^{2-}/{\mathrm{SO}}_4^{2-}}^0=2.05\mathrm{V}$; ${\mathrm{E}}_{{\mathrm{Br}}_2/{\mathrm{Br}}^{-}}^0=+1.09\mathrm{V}$; …

Q19.The quantum number of four electrons are given below:
I. $\mathrm{n}=4,\mathrm{I}=2,{\mathrm{m}}_{\mathrm{l}}=-2,{\mathrm{m}}_{\mathrm{s}}=-1/2$
II. $\mathrm{n}=3,\mathrm{I}=2,{\mathrm{m}}_{\mathrm{l}}=1,{\mathrm{m}}_8=+1/2$
III. …

Q20.If solubility product of ${\mathrm{Zr}}_3({\mathrm{PO}}_4{)}_4$ is denoted by ${\mathrm{K}}_{\mathrm{SP}}$ and its molar solubility is denoted by S, then which of the following relation between S and ${\mathrm{K}}_{\mathrm{SP}}$ is correct?

Q21.Which of the following amines can be prepared by Gabriel phthalimide reaction?

Q22.Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non expansion work is zero)

Q23.The following ligand is:

Q24.In order to oxidize a mixture of one mole of each of ${\mathrm{FeC}}_2{\mathrm{O}}_4,{\mathrm{Fe}}_2{\left({\mathrm{C}}_2{\mathrm{O}}_4\right)}_3,{\mathrm{FeSO}}_4$ and ${\mathrm{Fe}}_2{\left({\mathrm{SO}}_4\right)}_3$ in acidic medium, the number of moles of …

Q25.Assertion : Ozone is destroyed by CFCs in the upper stratosphere.

Reason : Ozone holes increase the amount of UV radiation reaching the earth.

Q26.Maltose on treatment with dilute HCl gives:

Q27.With respect to an ore, Ellingham diagram helps to predict the feasibility of its

Q1.The magnitude of the projection of the vector $2\hat{i}+3\hat{j}+\hat{k}$ on the vector perpendicular to the plane containing the vectors $\hat{i}+\hat{j}+\hat{k}$ and $\hat{i}+2\hat{j}+3\hat{k}$, is:

Q2.The shortest distance between the line $y=x$ and the curve $y^2=x-2$ is:

Q3.If $\alpha$ and $\beta$ be the roots of the equation $x^2-2x+2=0$, then the least value of $n$ for which ${\left(\frac{\alpha }{\beta }\right)}^{\mathrm{n}}=1$ is:

Q4.All possible numbers are formed using the digits $1,1,2,2,2,2,3,4,4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is:

Q5.$\int \frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}}dx$ is equal to:
(where c is a constant of integration).

Q6.Let $\mathrm{O}(0,0)$ and $\mathrm{A}(0,1)$ be two fixed points. Then the locus of a point P such that the perimeter of $△AOP$, is 4, is:

Q7.If $\cos (\alpha +\beta )=\frac{3}{5},\sin (\alpha -\beta )=\frac{5}{13}$ and $0<\alpha ,\beta <\frac{\pi }{4}$, then $\tan (2\alpha )$ is equal to:

Q8.Let $\mathrm{A}=\left(\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{array}\right),(\alpha \in \mathrm{R})$ such that ${\mathrm{A}}^{32}=\left(\begin{array}{cc}0& -1\\ 1& 0\end{array}\right)$. Then a value of $\alpha$ is:

Q9.If $f(x)={\log }_e\left(\frac{1-x}{1+x}\right),|x|<1$, then $f\left(\frac{2x}{1+x^2}\right)$ is equal to:

Q10.If $2y={\left({\cot }^{-1}\left(\frac{\sqrt{3}\cos x+\sin x}{\cos x-\sqrt{3}\sin x}\right)\right)}^2,x\in \left(0,\frac{\pi }{2}\right)$ then $\frac{dy}{dx}$ is equal to

Q11.The sum of the solutions of the equation $|\sqrt{x}-2|+\sqrt{x}(\sqrt{x}-4)+2=0,(x>0)$ is equal to:

Q12.${\lim }_{x\to 0}\frac{{\sin }^{2}x}{\sqrt{2}-\sqrt{1+\cos x}}$ equals

Q13.$2\cdot {}^{20}{\mathrm{C}}_0+5\cdot {}^{20}{\mathrm{C}}_1+8\cdot {}^{20}{\mathrm{C}}_2+11\cdot {}^{20}{\mathrm{C}}_3+\dots \cdot +62\cdot {}^{20}{\mathrm{C}}_{20}$ is equal to

Q14.Let $y=y(x)$ be the solutions of the differential equation, ${\left(x^2+1\right)}^2\frac{dy}{dx}+2x\left(x^2+1\right)y=1$ such that $y(0)=0$. If $\sqrt{a}y(1)=\frac{\pi }{32}$, then the value of '$a$' is

Q15.If $f(x)=\frac{2-x\cos x}{2+x\cos x}$ and $g(x)={\log }_{e}x,(x>0)$ then the value of the integral ${\int }_{-\pi /4}^{\pi /4}g(f(x))dx$ is:

Q16.The area (in sq. units) of the region $\mathrm{A}=\left\{(\mathrm{x},\mathrm{y})\in \mathrm{R}\times \mathrm{R}\mid 0\le \mathrm{x}\le 3,0\le \mathrm{y}\le 4,\mathrm{y}\le {\mathrm{x}}^2+3\mathrm{x}\right\}$ is:

Q17.The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are $2,4,10,12,14$, then the product of the remaining two observations is:

Q18.The length of the perpendicular from the point $(2,-1,4)$ on the straight line, $\frac{x+3}{10}=\frac{y-2}{-7}=\frac{z}{1}$ is:

Q19.The contrapositive of the statement "If you are born in India, then you are a citizen of India", is:

Q20.The sum of all natural numbers '$n$' such that $100<n<200$ and H.C.F$(91,n)>1$ is:

Q21.If ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are respectively the sets of local minimum and local maximum points of the function. $f(x)=9x^4+12x^3-36x^2+25,x\in R$, then

Q22.The sum of the co-efficient of all even degree terms in $x$ in the expansion of ${\left(x+\sqrt{x^3-1}\right)}^6+{\left(x-\sqrt{x^3-1}\right)}^6,(x>1)$ is equal to:

Q23.A point on the straight line, $3x+5y=15$ which is equidistant from the coordinate axes will lie only in:

Q24.If the tangents on the ellipse $4x^2+y^2=8$ at the points $(1,2)$ and $(a,b)$ are perpendicular to each other, then ${\mathrm{a}}^2$ is equal to:

Q25.If $\alpha ={\cos }^{-1}\left(\frac{3}{5}\right),\beta ={\tan }^{-1}\left(\frac{1}{3}\right)$, where $0<\alpha ,\beta <\frac{\pi }{2}$, then $\alpha -\beta$ is equal to:

Q26.The equation of a plane containing the line of intersection of the planes $2x-y-4=0$ and $y+2z-4=0$ and passing through the point $(1,1,0)$ is:

Q27.The sum of the squares of the lengths of the chords intercepted on the circle, $x^2+y^2=16$, by the lines, $x+y=n,n\in N$, where $N$ is the set of all natural numbers is:

Q28.The greatest value of $\mathrm{c}\in \mathrm{R}$ for which the system of linear equations
$x-cy-cz=0$
$cx-y+cz=0$
$cx+cy-z=0$
has a non - trivial solution, is:

Q29.Let $\mathrm{f}:[0,2]\to \mathrm{R}$ be a twice differentiable function such that ${\mathrm{f}}^{\prime \prime }(\mathrm{x})>0$, for all $\mathrm{x}\in (0,2)$. If $\varphi (x)=f(x)+f(2-x)$, then $\varphi$ is:

Q30.Let A and b be two non - null events such that $\mathrm{A}\subset \mathrm{B}$. Then, which of the following statements is always correct?