JEE Main 2020 · 07 Jan 2020 · Shift 2

Q1.An emf of 20 V is applied at time $t=0$ to a circuit containing in series 10 mH inductor and $5\Omega$ resistor. The ratio of the currents at time $t=\infty$ and at $t=40$ s is close to: (take $e^2=7.389$)

Q2.A particle of mass $m$ and charge $q$ has an initial velocity $\vec{v}=v_0\hat{j}$. If an electric field $\vec{E}=E_0\hat{i}$ and magnetic field $\vec{B}=B_0\hat{i}$ act on the particle, its speed will double after a time:

Q3.In a building there are 15 bulbs of $45\mathrm{W}$, 15 bulbs of $100\mathrm{W}$, 15 small fans of 10 W and 2 heaters of 1 kW. The voltage of electric main is 220 V. The minimum fuse capacity (rated value) of the building will be

Q4.An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is ($c=$ speed of light in vacuum)

Q5.A thin lens made of glass (refractive index $=1.5$) of focal length $f=16\mathrm{cm}$ is immersed in a liquid of refractive index 1.42. If its focal length in liquid is $f_{\ell }$, then the ratio $f_{\ell }/f$ is closest to the integer:

Q6.A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observers hears 2 beats/sec. The oscillation frequency of each tuning fork is …

Q7.Mass per unit area of a circular disc of radius a depends on the distance $r$ from its centre as $\sigma (r)=A+Br$. The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:

Q8.A planar loop of wire rotates in a uniform magnetic field. Initially, at $t=0$, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively …

Q9.Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, $T_1$ and $T_2$. The temperature of the hot reservoir of the first engine is ${\mathrm{T}}_1$ and the temperature of the cold reserv …

Q10.A box weighs 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take $\mathrm{g}=10{\mathrm{ms}}^{-2}$ at the north pole and the radius of the earth $=6400\mathrm{km}$)

Q11.The dimension of $\frac{B^2}{2{\mu }_0}$, where $B$ is magnetic field and ${\mu }_0$ is the magnetic permeability of vacuum, is

Q12.In a Young's double slit experiment, the separation between the slits is 0.15 mm. In the experiment, a source of light of wavelength 589 nm is used and the interference pattern is observed on a screen kept 1.5 m away. The separation between the successive bright fringes on the sc …

Q13.The figure gives experimentally measured B vs H variation in a ferromagnetic material. The retentivity, coercivity and saturation, respectively, of the material are

Q14.The activity of a radioactive sample falls from $700{\mathrm{s}}^{-1}$ to $500{\mathrm{s}}^{-1}$ in 30 minutes. Its half life is close to

Q15.An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is

Q16.A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ }$ with the vertical. Then F equals: (Take $\mathrm{g}=10{\mathrm{ms}}^{-2}$ and t …

Q17.The electric field of a plane electromagnetic wave is given by

At $t=0$, a positively charged particle is at the point …

Q18.Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from ${\tau }_1$ to ${\tau }_2$. If $\frac{{\mathrm{C}}_{\mathrm{p}}}{{\mathrm{C}}_{\mathrm{v}}}=\gamma$ for the gas then a good estimate for …

Q19.An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed of $3\mathrm{m}/\mathrm{s}$. the frictional force opposing the motion is 6000 N. If the …

Q20.In the figure, potential difference between A and B is:

Q21.Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force $F$ at a point $b$ above its centre of mass (see figure). If the coefficient of friction is $\mu =0.4$, the maximum possible value of $100\times \frac{b}{a}$ for box n …

Q22.M grams of steam at $100^{\circ }\mathrm{C}$ is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produces liquid water at $40^{\circ }\mathrm{C}$ [heat of vaporization of water is $540\mathrm{cal}/\mathrm{g}$ and heat of fusion of ice is …

Q23.A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) __ …

Q24.The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of $10\Omega$ is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the cell is $\frac{\mathrm{N}}{10}\Omega$, where N is an …

Q25.The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $|\vec{R}|=|\vec{P}|$. The angle $\theta$ (in degrees) that the resultant of $2\vec{P}$ and $\vec{Q}$ will make with $\vec{Q}$ is, ______.

Q1.In the following reactions, products(A) and (B) respectively are …

Q2.The refining method used when the metal and the impurities have low and high melting temperatures, respectively is

Q3.The redox reaction among the following is

Q4.Within each pair of elements $\mathrm{F}\&\mathrm{Cl},\mathrm{S}\&\mathrm{Se}$ and $\mathrm{Li}\&\mathrm{Na}$, respectively, the elements that release more energy upon an electron gain are

Q5.Identify the correct labels of $\mathrm{A},\mathrm{B}$ and C in the following graph from the options given below

Root mean square speed $({\mathrm{V}}_{\mathrm{rms}})$; most probable speed $({\mathrm{V}}_{\mathrm{mp}})$; Average speed $({\mathrm{V}}_{\mathrm{av}})$

Q6.For the reaction
$2{\mathrm{H}}_2(\mathrm{g})+2\mathrm{NO}(\mathrm{g})⟶{\mathrm{N}}_2(\mathrm{g})+2{\mathrm{H}}_2\mathrm{O}$, the observed rate expression is, rate $={\mathrm{k}}_{\mathrm{f}}[\mathrm{NO}{]}^2\left[{\mathrm{H}}_2\right]$. The rate expression f …

Q7.In the following reaction sequence

The major product B is

Q8.Which of the following statements is correct?

Q9.The equation that is incorrect is

Q10.Consider the following reactions:
(a)
(b)
(c)
(d)

Which of these reactions are possible?

Q11.The number of possible optical isomers for the complexes ${\mathrm{MA}}_2{\mathrm{B}}_2$ with ${\mathrm{sp}}^3$ and ${\mathrm{dsp}}^2$ hybridized metal atom, respectively is:
[Note: A and B are unidentate neutral and unidentate monoanionnic ligands, respectively]

Q12.In the following reaction sequence, structures of A and B respectively will be

Q13.The bond order and the magnetic characteristics of ${\mathrm{CN}}^{-}$ are

Q14.For the following reactions:

where,

${\mathrm{k}}_{\mathrm{s}}$ and ${\mathrm{k}}_{\mathrm{e}}$ are respectively, the rate constant for substitution and elimination, and $\mu =\frac{{\mathrm{k}}_{\mathrm{s}}}{{\mathrm{k}}_{\mathrm{e}}}$, the correct option is ____

Q15.Among the statements $(\mathrm{a}-\mathrm{d})$, the incorrect ones are:
(a) Octahedral Co (III) complexes with strong field ligands have very high magnetic moments
(b) When ${\Delta }_0<\mathrm{P}$, the d-electron configuration of Co (III) in an octahedral complex is …

Q16.A Chromatography column, packed with silica gel as stationary phase, was used to separate a mixture of compounds consisting of (a) benzanilide, (b) aniline and (c) acetophenone. When the column is eluted with a mixture of solvents, hexane; ethyl acetate(20:80), the sequence of ob …

Q17.The correct order of stability for the following alkoxides is

Q18.Among statements (a) - (d), the correct ones are
(a) decomposition of hydrogen peroxide gives dioxygen.
(b) like hydrogen peroxide, compounds such as ${\mathrm{KCIO}}_3,\mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2$ and ${\mathrm{NaNO}}_3$ when heated liberated dioxygen.
(c) …

Q19.The ammonia $\left({\mathrm{NH}}_3\right)$ released on quantitative reaction of 0.6 g urea $\left({\mathrm{NH}}_2{\mathrm{CONH}}_2\right)$ with sodium hydroxide(NaOH) can be neutralized by

Q20.Two open beakers one containing a solvent and the other containing a mixture of that solvent with a non-volatile solute are together sealed in a container. Over time

Q21.Consider the following reactions:
$\mathrm{NaCl}+{\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7+\underset{\text{ (Conc.) }}{{\mathrm{H}}_2{\mathrm{SO}}_4}⟶(\mathrm{A})+$ side products
$(\mathrm{A})+\mathrm{NaOH}⟶(\mathrm{B})+$ Side products …

Q22.The standard heat of formation $\left({\Delta }_{\mathrm{f}}{\mathrm{H}}_{298}^0\right)$ of ethane (in $\mathrm{kJ}/\mathrm{mol}$ ), if the heat of combustion of ethane, hydrogen and graphite are $-1560,-393.5$ and $-286\mathrm{kJ}/\mathrm{mol}$ respectively is ___ …

Q23.The flocculation value of HCl for arsenic sulphide sol is $30\mathrm{m}\mathrm{mol}{\mathrm{L}}^{-1}$. If ${\mathrm{H}}_2{\mathrm{SO}}_4$ is used for the flocculation of arsenic sulphide, the amount, in grams of ${\mathrm{H}}_2{\mathrm{SO}}_4$ in 250 mL required for t …

Q24.The number of ${\mathrm{sp}}^2$-hybridized carbons present in "Aspartame" is ____

Q25.3 g of acetic acid is added to 250 mL of 0.1 M HCl and the solution made up to 500 mL. To 20 mL of this solution $\frac{1}{2}$ mL of 5 M NaOH is added. The pH of the solution is ______
[Given: ${\mathrm{pK}}_{\mathrm{a}}$ of acetic acid $=4.75$, molar mass of acetic acid …

Q1.The number of ordered pairs $(r,k)$ for which $6.{}^{35}{C}_r=\left(k^2-3\right)\cdot {}^{36}{C}_{r+1}$, where $k$ is an integer, is:

Q2.If $3x+4y=12\sqrt{2}$ is a tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{9}=1$ for some $a\in R$, then the distance between the foci of the ellipse is:

Q3.If the sum of the first 40 terms of the series, $3+4+8+9+13+14+18+19+\dots$. is $(102)\mathrm{m}$, then m is equal to:

Q4.Let $\mathrm{A}=\left[{\mathrm{a}}_{\mathrm{ij}}\right]$ and $\mathrm{B}=\left[{\mathrm{b}}_{\mathrm{ij}}\right]$ be two $3\times 3$ real matrices such that ${\mathrm{b}}_{\mathrm{ij}}=(3{)}^{(\mathrm{i}+\mathrm{j}-2)}{\mathrm{a}}_{\mathrm{ji}}$, where $i,j=1,2,3$. If the dete …

Q5.The value of $c$ in the Lagrange's mean value theorem for the function $f(x)=x^3-4x^2+8x+11$, when $x\in [0,1]$ is:

Q6.The value of $\alpha$ for which $4\alpha {\int }_{-1}^2{e}^{-\alpha |x|}dx=5$, is

Q7.Let $y=y(x)$ be a function of $x$ satisfying $y\sqrt{1-x^2}=k-x\sqrt{1-y^2}$ where $k$ is a constant and $\mathrm{y}\left(\frac{1}{2}\right)=-\frac{1}{4}$. Then $\frac{\mathrm{dy}}{\mathrm{dx}}$ at $\mathrm{x}=\frac{1}{2}$, is equal to:

Q8.Let $y=y(x)$ be the solution curve of the differential equation, $\left(y^2-x\right)\frac{dy}{dx}=1$, satisfying $y(0)=1$. This curve intersects the $x$-axis at a point whose abscissa is:

Q9.Let $f(x)$ be a polynomial of degree 5 such that $x=\pm 1$ are its critical points. If ${\lim }_{x\to 0}\left(2+\frac{f(x)}{x^3}\right)=4$, then which one of the following is not true?

Q10.The area (in sq. units of the region $\left\{(x,y)\in R^2\mid 4x^2\le y\le 8x+12\right\}$ is:

Q11.Let $\vec{a},\vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$. If $\lambda =\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a}$ and …

Q12.The locus of the mid - points of the perpendiculars drawn from points on the line, $x=2y$ to the line $x=y$ is:

Q13.Let $a_1,a_2,a_3,\dots$ be a G.P. such that $a_1<0$, $a_1+a_2=4$ and $a_3+a_4=16$. If ${\sum }_{i=1}^9{a}_i=4\lambda$, then $\lambda$ is equal to:

Q14.Let $\alpha$ and $\beta$ be the roots of the equation $x^2-x-1=0$. If $P_k=(\alpha {)}^k+(\beta {)}^k$, $k\ge 1$, then which one of the following statements is not true?

Q15.If $\frac{3+i\sin \theta }{4-i\cos \theta }$, $\theta \in [0,2\pi ]$, is a real number, then an argument of $\sin \theta +i\cos \theta$ is:

Q16.In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $\frac{1}{4}$. If the probability that at most two machines will be out of service on the same day is ${\left(\frac{3}{4}\right)}^{3}k$, then k is equal to:

Q17.Let the tangents drawn from the origin to the circle, $x^2+y^2-8x-4y+16=0$ touch it at the points $A$ and $B$. Then $(AB{)}^2$ is equal to:

Q18.If ${\theta }_1$ and ${\theta }_2$ be respectively the smallest and the largest values of $\theta$ in $(0,2\pi )-\{\pi \}$ which satisfy the equation, $2{\cot }^2\theta -\frac{5}{\sin \theta }+4=0$, then ${\int }_{{\theta }_1}^{{\theta }_2}{\cos }^{2}3\theta d\theta$ is equal to:

Q19.The coefficient of $x^7$ in the expression $(1+x{)}^{10}+x(1+x{)}^9+x^2(1+x{)}^8+\dots +x^{10}$ is:

Q20.Let $A,B,C$ and $D$ be four non-empty sets. The contrapositive statement of "If $A\subseteq B$ and $B\subseteq D$, then $A\subseteq C$" is:

Q21.If the function $f$ defined on $\left(-\frac{1}{3},\frac{1}{3}\right)$ by $f(x)=\{\begin{array}{l}\frac{1}{x}{\log }_e\left(\frac{1+3x}{1-2x}\right),\text{ when }x\ne 0\\ k\text{, when }x=0\end{array}$ is continuous, then k is equal to ____

Q22.If the system of linear equations,

has more than two solutions, then $\mu -{\lambda }^2$ is equal to ____

Q23.If the mean and variance of eight numbers $3,7,9,12,13,20,x$ and $y$ be 10 and 25 respectively, then xy is equal to ____

Q24.If the foot of the perpendicular drawn from the point $(1,0,3)$ on a line passing through $(\alpha ,7,1)$ is $\left(\frac{5}{3},\frac{7}{3},\frac{17}{3}\right)$, then $\alpha$ is equal to ____

Q25.Let $X=\{n\in N:1\le n\le 50\}$. If $A=\{n\in X:n$ is a multiple of 2$\}$ and $B=\{n\in X,n$ is a multiple of 7$\}$, then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is ____