JEE Main 2020 · 07 Jan 2020 · Shift 1

Q1.A polarizer-analyser set is adjusted such that the intensity of light coming out of the analyser is just 10% of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the out …

Q2.Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30^{\circ }$. The electric field in the region shown between them is given by:

Q3.A long solenoid of radius $R$ carries a time ($t$) dependent current $I(t)=I_{0}t(1-t)$. A ring of radius 2$R$ is placed coaxially near its middle. During the time interval $0\le t\le 1$, the induced current ($I_R$) and the induced EMF ($V_R$) in the ring changes as:

Q4.Visible light of wavelength $6000\times 10^{-8}$ cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at $60^{\circ }$ from the central maximum. If the first minimum is produced at ${\theta }_1$ then ${\theta }_1$ …

Q5.A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as $k(x)=K(1+\alpha x)$ where 'x' is the distance measured from one of the plates.

If $(\alpha d)\ll 1$, the total …

Q6.The current $I_1$ (in A) flowing through $1\Omega$ resistor in the following circuit is

Q7.The radius of gyration of a uniform rod of length $\ell$, about an axis passing through a point $\frac{\ell }{4}$ away from the centre of the rod, and perpendicular to it is:

Q8.Three point particles of masses $1.0\text{kg}$, $1.5\text{kg}$ and $2.5\text{kg}$ are placed at three corners of a right angle triangle of sides $4.0\text{cm}$, $3.0\text{cm}$ and $5.0\text{cm}$ as shown in the figure. The centre of mass of the system is at a point:

Q9.Consider a circular coil of wire carrying constant current $I$, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ${\varphi }_i$. The magnetic flux through the area is given by …

Q10.As shown in the figure, a bob of mass $m$ is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius $r$ and mass $m$. When released from rest the bob starts falling vertically. When it has covered a distance of $h$, the angular speed of the whe …

Q11.If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye piece should be close to

Q12.Two moles of an ideal gas with $\frac{C_P}{C_V}=\frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{C_P}{C_V}=\frac{4}{3}$. The value of $\frac{C_P}{C_V}$ for the mixture is:

Q13.Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section $1.0{\text{mm}}^2$) is $90{\text{ms}}^{-1}$. If the Young's modulus of wire is $16\times 10^{11}{\text{Nm}}^{-2}$, the extension of wire over its natural length is:

Q14.A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma =1.40$, the work done by air is: ($3^{1.4}=4.6555$) [Take air to be an ideal gas]

Q15.A satellite of mass $m$ is launched vertically upwards with an initial speed $u$ from the surface of the earth. After it reaches height $R$ ($R=$ radius of the earth), it ejects a rocket of mass $\frac{m}{10}$ so that subsequently the satellite moves in a circular orbit. The kin …

Q16.The time period of revolution of electron in its ground state orbit in a hydrogen atom is $1.6\times 10^{-16}\text{s}$. The frequency of revolution of the electron in its first excited state (in ${\text{s}}^{-1}$) is

Q17.A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be:

Q18.If the magnetic field in a plane electromagnetic wav is given by $\overrightarrow{\mathrm{B}}=3\times 10^{-8}\sin \left(1.6\times 10^3\mathrm{x}+48\times 10^{10}\mathrm{t}\right)\mathrm{jT}$, then what will be expression for electric field?

Q19.Which of the following given a reversible operation?

Q20.A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg . If the frictional force on the elevator is 4000 N , the speed of the elevator at full load is close to: $\left(1\mathrm{HP}=746\mathrm{W},\mathrm{g}=10{\mathrm{ms}}^{-2}\right)$

Q21.A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K . The engine performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle is ____.

Q22.A loop $ABCDEFA$ of straight edges has six corner points $A(0,0,0),B(5,0,0),C(5,5,0),D(0,5,0),E(0,5,5)$ and $F(0,0,5)$. The magnetic field in this region in $\vec{B}=(3\hat{i}+4\hat{k})T$. The quantity of flux through the loop ABCDEFA (in Wb ) is ____.

Q23.A non-isotropic solid metal cube has coefficients of linear expansion as: $5\times 10^{-5}/{}^{\circ }\mathrm{C}$ along the $\mathrm{x}=$ axis and $5\times 10^{-6}/{}^{\circ }\mathrm{C}$ along the y and the z -axis. If coefficient of volume expansion of the solid …

Q24.A particle ( $m=1\mathrm{kg}$ ) slides down a frictionless track (AOC) starting from rest of a point A (height 2 m ). After reaching C, the particle continues to move freely in air as a projectile. When it leading its highest point P (height 1 m ) the kinetic energy of the pa …

Q25.A beam of electromagnetic radiation of intensity $6.4\times 10^{-5}\mathrm{W}/{\mathrm{cm}}^2$ is comprised of wavelength, $\lambda =310\mathrm{nm}$. It falls normally on a metal (work function $\phi =2\mathrm{eV}$ ) of surface area $1{\mathrm{cm}}^2$. If one i …

Q1.The relative strength of interionic/intermolecular forces in decreasing order is

Q2.Oxidation number of potassium in ${\mathrm{K}}_2\mathrm{O}$, ${\mathrm{K}}_2{\mathrm{O}}_2$ and ${\mathrm{KO}}_2$ respectively is

Q3.At $35^{\circ }\mathrm{C}$, the vapour pressure of ${\mathrm{CS}}_2$ is 512 mm of Hg and that of acetone is 344 mm of Hg. A solution of ${\mathrm{CS}}_2$ in acetone has a total vapour pressure of 600 mm of Hg. The false statement among the following is

Q4.The atomic radius of Ag is closest to

Q5.The dipole moments of ${\mathrm{CCl}}_4$, ${\mathrm{CHCl}}_3$ and ${\mathrm{CH}}_4$ are in the order

Q6.In comparison to the zeolite process for the removal of permanent hardness, the synthetic resins method is

Q7.Amongst the following statements, that which was not proposed by Dalton was

Q8.The increasing order of ${\mathrm{pK}}_{\mathrm{b}}$ for the following compounds will be
(a) ${\mathrm{NH}}_2-\mathrm{CH}={\mathrm{NH}}_2$
(b) (see structure)
(c) ${\mathrm{CH}}_3{\mathrm{NHCH}}_3$

Q9.What is the product of following reaction?

Q10.The number of orbitals associated with quantum number $n=5$, $m_s=+\frac{1}{2}$ is

Q11.The purest form of commercial iron is

Q12.The theory that can completely/properly explain the nature of bonding in $\left[\mathrm{Ni}(\mathrm{CO}{)}_4\right]$ is

Q13.The IUPAC name of the complex is $\left[\mathrm{Pt}{\left({\mathrm{NH}}_3\right)}_2\mathrm{Cl}\left({\mathrm{NH}}_2{\mathrm{CH}}_3\right)\right]\mathrm{Cl}$ is

Q14.1-methyl ethylene oxide when treated with an excess of HBr, produces

Q15.Consider the following reaction:

The product 'X' is used

Q16.Match the following

Column - I
(i) Riboflamin
(ii) Thiamine
(iii) Pyridoxine
(iv) Ascorbic acid

Column - II
(a) Beriberi
(b) Scurvy
(c) Cheilosis
(d) Convulsions

Q17.Given that the standard potential (${\mathrm{E}}^{\circ }$) of ${\mathrm{Cu}}^{2+}/\mathrm{Cu}$ and ${\mathrm{Cu}}^{+}/\mathrm{Cu}$ are 0.34 V and 0.522 V respectively, the ${\mathrm{E}}^{\circ }$ of ${\mathrm{Cu}}^{2+}/{\mathrm{Cu}}^{+}$ is

Q18.A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of ${\mathrm{NaHCO}}_3$ to give fraction A. The left over organic phase was extracted with dilute NaOH solution to give fraction B. The fina …

Q19.The order of electron gain enthalpy in $\mathrm{kJ}/\mathrm{mol}$ of fluorine, chlorine, bromine and iodine, respectively are

Q20.Consider the following reactions, which of these reaction(s) will not produce Saytzeff product?

Which of these reaction(s) will not produce Saytzeff product?

Q21.Two solutions A and B, each of 100 L was made by dissolution of 4 g of NaOH and 9.8 g of ${\mathrm{H}}_2{\mathrm{SO}}_4$ in water, respectively. The pH of the resultant solution obtained from mixing 40 L of solution A and 10 L of solution B is

Q22.During the nuclear explosion, one of the product of ${}^{90}\mathrm{Sr}$ with half life of 6.93 years. If 1 $\mu \mathrm{g}$ of ${}^{90}\mathrm{Sr}$ absorbed in the bones of newly born baby in place of Ca, how much time, in years is required to reduce it by $90\%$ if …

Q23.Chlorine reacts with hot and concentrated NaOH and produces compound $(\mathrm{X})$ and $(\mathrm{Y})$. Compound(X) gives white precipitate with silver nitrate solution. The average bond order between Cl and O atoms in $(\mathrm{Y})$ is

Q24.The number of chiral carbons in chloramphenicol is

Q25.For the reaction $\mathrm{A}(\mathrm{l})⟶2\mathrm{B}(\mathrm{g})$
$\Delta \mathrm{U}=2.1\mathrm{Kcal},\Delta \mathrm{S}=20\mathrm{cal}{\mathrm{K}}^{-1}$ at 300 K
Hence $\Delta \mathrm{G}$ in Kcal is

Q1.If $f(a+b+1-x)=f(x)$, for all $x$, where $a$ and $b$ are fixed positive real numbers, then $\frac{1}{a+b}{\int }_a^{b}x(f(x)+f(x+1))dx$ is

Q2.Let the function, $f:[-7,0]\to \mathbb{R}$ be continuous on $[-7,0]$ and differentiable on $(-7,0)$. If $f(-7)=-3$ and $f^{\prime }(x)\le 2$, for all $x\in (-7,0)$, then for all such functions $f$, $f(-1)+f(0)$ lies in the interval:

Q3.If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is:

Q4.An unbiased coin is tossed 5 times. Suppose that a variable $X$ is assigned the value $k$ when $k$ consecutive heads are obtained for $k=3,4,5$, otherwise $X$ takes the value -1. Then the expected value of $X$, is

Q5.Five numbers are in A.P., whose sum is 25 and product is 2520. If one of these five numbers is $-\frac{1}{2}$, then the greatest number amongst them is:

Q6.If the system of linear equations $2x+2ay+az=0,2x+3by+bz=0,2x+4cy+cz=0$ where $a,b,c\in \mathbb{R}$ are non-zero and distinct; has a non-zero solution, then:

Q7.Let P be a plane passing through the points $(2,1,0),(4,1,1)$ and $(5,0,1)$ and R be any point $(2,1,6)$. Then the image of R in the plane P is:

Q8.If $\mathrm{Re}\left(\frac{z-1}{2z+i}\right)=1$, where $z=x+iy$, then the point $(x,y)$ lies on a:

Q9.If $y(\alpha )=\sqrt{2\left(\frac{\tan \alpha +\cot \alpha }{1+{\tan }^2\alpha }\right)+\frac{1}{{\sin }^2\alpha }},\alpha \in \left(\frac{3\pi }{4},\pi \right)$ then $\frac{dy}{d\alpha }$ at $\alpha =\frac{5\pi }{6}$ is:

Q10.Let $\alpha$ be a root of the equation $x^2+x+1=0$ and the matrix $A=\frac{1}{\sqrt{3}}\left[\begin{array}{ccc}1& 1& 1\\ 1& \alpha & {\alpha }^2\\ 1& {\alpha }^2& {\alpha }^4\end{array}\right]$, then the matrix $A^{31}$ is equal to:

Q11.If $g(x)=x^2+x-1$ and $(g\circ f)(x)=4x^2-10x+5$, then $f\left(\frac{5}{4}\right)$ is equal to

Q12.If $y=mx+4$ is a tangent to both the parabolas, $y^2=4x$ and $x^2=2by$, then $b$ is equal to:

Q13.The logical statement $(p\Rightarrow q)\wedge (q\Rightarrow \sim p)$ is equivalent to:

Q14.Let $x^k+y^k=a^k,(a,k>0)$ and $\frac{dy}{dx}+{\left(\frac{y}{x}\right)}^{\frac{1}{3}}=0$, then $k$ is:

Q15.Let $\alpha$ and $\beta$ be two real roots of the equation $(\mathrm{k}+1){\tan }^2\mathrm{x}-\sqrt{2}\cdot \lambda \tan \mathrm{x}=(1-\mathrm{k})$, where $\mathrm{k}(\ne -1)$ and $\lambda$ are real numbers. If ${\tan }^2(\alpha +\beta )=50$, then a value of …

Q16.If $\mathrm{y}=\mathrm{y}(\mathrm{x})$ is the solution of the differential equation, ${\mathrm{e}}^{\mathrm{y}}\left(\frac{\mathrm{dy}}{\mathrm{dx}}-1\right)={\mathrm{e}}^{\mathrm{x}}$ such that $y(0)=0$, then $y(1)$ is equal to:

Q17.The area of the region, enclosed by the circle $x^2+y^2=2$, which is not common to the region bounded by the parabola $y^2=x$ and the straight line $y=x$, is :

Q18.A vector $\vec{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}(\alpha ,\beta \in R)$ lies in the plane of the vectors, $\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\hat{i}-\hat{j}+4\hat{k}$. If $\vec{a}$ bisects the angle between $\vec{b}$ and $\vec{c}$, then:

Q19.The greatest positive integer k , for which $49^{\mathrm{k}}+1$ is a factor of the sum $49^{125}+49^{124}+\dots \dots +49^2+49+1$ is:

Q20.Total number of 6 - digit numbers in which only and all the five digits 1 , 3 , 5 , 7 and 9 appear, is

Q21.Let $S$ be the set of points where the function, $f(x)=|2-|x-3||,x\in R$, is not differentiable. Then ${\sum }_{x\in S}f(f(x))$ is equal to ____

Q22.If the sum of the coefficients of all even powers of $x$ in the product $\left(1+x+x^2+\dots \dots +x^{2n}\right)\left(1-x+x^2-x^3+\dots ..+x^{2n}\right)$ is 61 , then $n$ is equal to

Q23.If the variance of the first $n$ natural numbers is 10 and the variance of the first $m$ even natural numbers is 16 , then $m+n$ is equal to ____

Q24.${\lim }_{x\to 2}\frac{3^x+3^{3-x}-12}{3^{-x/2}-3^{1-x}}$ is equal to ____

Q25.Let $A(1,0),B(6,2)$ and $C\left(\frac{3}{2},6\right)$ be the vertices of a triangle $ABC$. If $P$ is a point inside the triangle ABC such that the triangles $\mathrm{APC},\mathrm{APB}$ and BPC have equal areas, then the length of the line segment PQ, where Q is the point …