JEE Main 2020 · 08 Jan 2020 · Shift 1

Q1.The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability $\frac{4}{3}$ for this wavelength, will be

Q2.Boolean relation at the output state-Y for the following circuits is:

Q3.A thermodynamic cycle $xyzx$ is shown on a V-T diagram. The P-V diagram that best describes this cycle is: (diagrams are schematic and not to scale)

Q4.A particle of mass $m$ is fixed to one end of a light spring having force constant $k$ and unstretched length $\ell$. The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Th …

Q5.The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 kg. (the coordinates of the same are shown in figure) are:

Q6.When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy ${\mathrm{T}}_{\mathrm{A}}\mathrm{eV}$ and de-Broglie wavelength ${\lambda }_{\mathrm{A}}$. The maximum kinetic energy of photoelectrons liberated form another metal …

Q7.In finding the electric field using Gauss law the formula $|\vec{E}|=\frac{q_{\text{enc }}}{{\epsilon }_0|A|}$ is applicable. In the formula ${\epsilon }_0$ is permittivity of free space, A is the area of Gaussain surface and ${\mathrm{q}}_{\mathrm{enc}}$ is charge enclosed by …

Q8.The plot that depicts the behavior of the mean free time $\tau$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

Q9.At time $t=0$ magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced EMF in the loops is:

Q10.Consider a uniform rod of mass $\mathrm{M}=4\mathrm{m}$ and length $\ell$ pivoted about its centre. A mass m moving with velocity v making angle $\theta =\frac{\pi }{4}$ to the rod's long axis collides with one end of the rod and sticks to it. The angular sped of the rod-mass sys …

Q11.The graph which depicts the results of Rutherford gold foil experiment with $\alpha$-particles is
$\theta$ : Scattering angle
Y : Number of scattered $\alpha$-particles detected
(Plots are schematic and not to scale)

Q12.The length of a potentiometer wire is 1200 cm and it carries a current of 60 mA . For a cell of emf 5 V and internal resistance of $20\Omega$, the null point on it is found to be at 1000 cm . The resistance of whole wire is:

Q13.Proton with kinetic energy of 1 MeV moves from south the north. It gets an acceleration of $10^{12}\mathrm{m}/{\mathrm{s}}^2$ by an applied magnetic field (west to east). The value of magnetic field: (Rest mass of proton is $1.6\times 10^{-27}\mathrm{kg}$)

Q14.The magnifying power of a telescope with tube length 60 cm is 5 . What is the focal length of its eye piece?

Q15.Consider a solid sphere of radius $R$ and mass density $p(r)=p_0\left(1-\frac{r^2}{R^2}\right),0<r\le R$. The minimum density of a liquid in which it will float is

Q16.Effective capacitance of parallel combination of two capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ is $10\mu \mathrm{F}$. When these capacitor are individually connected to a voltage source of 1 V , the energy stored in the capacitor ${\mathrm{C}}_2$ is 4 times that of …

Q17.A leak proof cylinder of length 1 m , made of a metal which has very low coefficient of expansion is floating vertically in water at $0^{\circ }\mathrm{C}$ such that its height above the water surface is 20 cm . When the temperature of water is increased to …

Q18.Three charged particles $\mathrm{A},\mathrm{B}$ and C with charges $-4q,2q$ and $-2q$ are present on the circumference of a circle of radius d . The charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O …

Q19.Consider two solid spheres of radii ${\mathrm{R}}_1=1\mathrm{m}$, ${\mathrm{R}}_2=2\mathrm{m}$ and masses ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of …

Q20.Four resistances of $15\Omega ,12\Omega ,4\Omega$ and $10\Omega$ respectively in cyclic order to form Whetstone's network. The resistance that is to be connected in parallel with the resistance of $10\Omega$ to balance the network is ____ .

Q21.A particle is moving along the $x$-axis with its coordinate with time ' $t$ ' given by $x(t)=10+8t-3t^2$. Another particle is moving along the $y$-axis with its coordinate a function of time given by $y(t)=5-8t^3$. At $t=1\mathrm{s}$, the speed of the second …

Q22.A body A , of mass $\mathrm{m}=0.1\mathrm{kg}$ has an initial velocity of $3\hat{\mathrm{i}}{\mathrm{ms}}^{-1}$. It collides elastically with another body, $B$ of the same mass which has an initial velocity of $5\hat{j}{\mathrm{ms}}^{-1}$. After collision, A moves with …

Q23.A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300\mathrm{m}/\mathrm{s}$, the frequency difference between the fundamental and second harmonic of this pipe is
____ Hz …

Q24.A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the focal length of the lens (in cm ) is ____ .

Q1.The complex that can show fac- and mer-isomers is :

Q2.Arrange the following compounds in increasing order of $\mathrm{C}-\mathrm{OH}$ bond length: methanol, phenol, p-ethoxyphenol

Q3.Among the gases (a) - (e), the gases that cause greenhouse effect are :
(a) ${\mathrm{CO}}_2$
(b) ${\mathrm{H}}_2\mathrm{O}$
(c) CFCs
(d) ${\mathrm{O}}_2$
(e) ${\mathrm{O}}_3$

Q4.The third ionization enthalpy is minimum for :

Q5.A graph of vapour pressure and temperature for three different liquids $\mathrm{X},\mathrm{Y}$, and Z is shown below:

The following inferences are made :
(a) X has higher intermolecular interactions compared to Y .
(b) X has lower intermolecular interactions compared to Y .
( …

Q6.When gypsum is heated to 393 K , it forms :

Q7.The major products A and B in the following reactions are :

Q8.As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order :

Q9.The most suitable reagent for the given conversion is :

Q10.The predominant intermolecular forces present in ethyl acetate, a liquid, are:

Q11.A flask contains a mixture of isohexane and 3 -methylpentane. One of the liquids boils at $63^{\circ }\mathrm{C}$ while the other boils at $60^{\circ }\mathrm{C}$. What is the best way to separate the two liquids and which one will be distilled out first?

Q12.The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively:

Q13.The rate of a certain biochemical reaction at physiological temperature (T) occurs $10^6$ times faster with enzyme than without. The change in the activation energy upon adding enzyme is :

Q14.The strength of an aqueous NaOH solution is most accurately determined by titrating : (Note : consider that an appropriate indicator is used)

Q15.For the Balmer series in the spectrum of H atom, $\bar{v}={\mathrm{R}}_{\mathrm{H}}\left\{\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right\}$ the correct statements among (I) to (IV) are :
(I) As wavelength decreases, the lines in the series converge
(II) The integer …

Q16.The number of bonds between sulphur and oxygen atoms in ${\mathrm{S}}_2{\mathrm{O}}_8^{-}$ and the number of bonds between sulphur and sulphur atoms in rhombic sulphur, respectively, are:

Q17.Which of the following statement is not true for glucose?

Q18.The first ionization energy (in $\mathrm{kJ}/\mathrm{mol}$ ) of $\mathrm{Na},\mathrm{Mg},\mathrm{Al}$ and Si respectively, are :

Q19.The decreasing order of reactivity towards dehydrohalogenation $\left({\mathrm{E}}_1\right)$ reaction of the following compounds is :
(A)
(B)
(C)
(D)

Q20.The volume (in mL ) of $0.125\mathrm{M}{\mathrm{AgNO}}_3$ required to quantitatively precipitate chloride ions in 0.3 g of $\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]{\mathrm{Cl}}_3$ is ____ …

Q21.The number of chiral centres in penicillin is ____

Q22.The magnitude of work done by a gas that undergoes a reversible expansion along the path $ABC$ shown in the figure is ____
Pressure

Q23.Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve 10 ppm of iron in 100 kg of wheat is ______

Atomic weight : $\mathrm{Fe}=55.85;\mathrm{S}=32.00;\mathrm{O}=16.00$

Q1.Let the volume of a parallelepiped whose coterminous edges are given by $\overrightarrow{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}},\overrightarrow{\mathrm{v}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ and …

Q2.Let $f(x)=x{\cos }^{-1}(-\sin |x|),x\in \left[-\frac{\pi }{2},\frac{\pi }{2}\right]$, then which of the following is true?

Q3.Let $y=y(x)$ be a solution of the differential equation, $\sqrt{1-x^2}\frac{dy}{dx}+\sqrt{1-y^2}=0,|x|<1$. If $\mathrm{y}\left(\frac{1}{2}\right)=\frac{\sqrt{3}}{2}$, then $\mathrm{y}\left(\frac{1}{\sqrt{2}}\right)$ is equal to:

Q4.${\lim }_{x\to 0}{\left(\frac{3x^2+2}{7x^2+2}\right)}^{1/x^2}$ is equal to:

Q5.Let two points be $\mathrm{A}(1,-1)$ and $\mathrm{B}(0,2)$. If a point $\mathrm{P}\left({\mathrm{x}}^{\prime },{\mathrm{y}}^{\prime }\right)$ be such that the area of $\Delta PAB=5$ sq. units and it lies on the line, $3x+y-4\lambda =0$, then a value of $\lambda$ is:

Q6.If the equation, $x^2+bx+45=0(b\in R)$ has conjugate complex roots and they satisfy $|z+1|=2\sqrt{10}$, then:

Q7.For $\mathrm{a}>0$, let the curves ${\mathrm{C}}_1:{\mathrm{y}}^2=\mathrm{ax}$ and ${\mathrm{C}}_2:{\mathrm{x}}^2=\mathrm{ay}$ intersect at origin O and a point P . Let the line $\mathrm{x}=\mathrm{b}(0<\mathrm{b}<\mathrm{c})$ intersect the chord OP and the x - axis at points Q …

Q8.The shortest distance between the lines $\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}$ is:

Q9.Which one of the following is a tautology?

Q10.For which of the following ordered pairs $(\mu ,\delta )$, the system of linear equations
$x+2y+3z=1$
$3x+4y+5z=\mu$
$4x+4y+4z=\delta$
is inconsistent?

Q11.If $\int \frac{\cos xdx}{{\sin }^{3}x{\left(1+{\sin }^{6}x\right)}^{2/3}}=f(x){\left(1+{\sin }^{6}x\right)}^{1/\lambda }+c$ where $c$ is a constant of integration, then $\lambda \mathrm{f}\left(\frac{\pi }{3}\right)$ is equal to:

Q12.The inverse function of $f(x)=\frac{8^{2x}-8^{-2x}}{8^{2x}+8^{-2x}},x\in (-1,1)$, is

Q13.Let A and B be two independent events such that $\mathrm{P}(\mathrm{A})=\frac{1}{3}$ and $\mathrm{P}(\mathrm{B})=\frac{1}{6}$. Then, which of the following is TRUE?

Q14.The locus of a point which divides the line segment joining the point $(0,-1)$ and a point on the parabola, $x^2=4y$, internally in the ratio $1:2$, is

Q15.The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by $p$ and then reduced by $q$, where $\mathrm{p}\ne 0$ and $\mathrm{q}\ne 0$. If the new mean and new s.d. become half of their original value …

Q16.If $c$ is a point at which Rolle's theorem holds for the function, $f(x)={\log }_e\left(\frac{x^2+\alpha }{7x}\right)$ in the interval $[3,4]$, where $\alpha \in R$, then $f^{\prime \prime }(c)$ is equal to:

Q17.If $\mathrm{a},\mathrm{b}$ and c are the greatest values of ${}^{19}{\mathrm{C}}_{\mathrm{p}},{}^{20}{\mathrm{C}}_{\mathrm{q}}$ and ${}^{21}{\mathrm{C}}_{\mathrm{r}}$ respectively, then:

Q18.Let $f:R\to R$ be such that for all $x\in R\left(2^{1+x}+2^{1-x}\right),f(x)$ and $\left(3^x+3^{-x}\right)$ are in A.P., then the minimum value of $f(x)$ is:

Q19.Let the line $\mathrm{y}=\mathrm{mx}$ and the ellipse $2{\mathrm{x}}^2+{\mathrm{y}}^2=1$ intersect at a point $P$ in the first quadrant. If the normal to this ellipse at P meets the co - ordinate axes at $\left(-\frac{1}{3\sqrt{2}},0\right)$ and $(0,\beta )$ then $\beta$ is eq …

Q20.Let $\mathrm{f}(\mathrm{x})={\left(\sin \left({\tan }^{-1}\mathrm{x}\right)+\sin \left({\cot }^{-1}\mathrm{x}\right)\right)}^2-1,|\mathrm{x}|>1$. If $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{2}\frac{\mathrm{d}}{\mathrm{dx}}\left({\sin }^{-1}(\mathrm{f}(\mathrm{x}))\right)$ and …

Q21.Let the normal at a point $P$ on the curve $y^2-3x^2+y+10=0$ intersect the $y$ - axis at $\left(0,\frac{3}{2}\right)$. If m is the slope of the tangent at P to the curve, then $|\mathrm{m}|$ is equal to

Q22.An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that the most three of them are red is

Q23.The least positive value of ' $a$ ' for which the equation, $2x^2+(a-10)x+\frac{33}{2}=2a$ has real root is

Q24.The sum ${\sum }_{k=1}^{20}(1+2+3+\dots .+k)$ is

Q25.The number of all $3\times 3$ matrices, $A$, with entries from the set $\{-1,0,1\}$ such that the sum of the diagonal elements of $A{A}^{\top }$ is 3, is ____.