JEE Main 2020 · 04 Sep 2020 · Shift 2

Q1.A capacitor C is fully charged with voltage ${\mathrm{V}}_0$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $\frac{\mathrm{C}}{2}$. The energy loss in the process after the charge is distributed between the two …

Q2.In photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased:

Q3.Consider two uniform discs of the same thickness and different radii ${\mathrm{R}}_1=\mathrm{R}$ and ${\mathrm{R}}_2=\alpha \mathrm{R}$ made of the same material. If the ratio of their moments of inertia ${\mathrm{I}}_1$ and ${\mathrm{I}}_2$, respectively, about their axes is …

Q4.Find the binding energy per nucleon for ${}_{50}^{120}\mathrm{Sn}$. Mass of proton ${\mathrm{m}}_{\mathrm{p}}=1.00783\mathrm{U}$, mass of neutron $m_n=1.00867\mathrm{U}$ and mass of tin nucleus $m_{\mathrm{Sn}}=119.902199\mathrm{U}$. (take $1\mathrm{U}=931\mathrm{MeV}$)

Q5.A quantity X is given by $IF{v}^2/W{L}^4$ in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of:

Q6.For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is:

Q7.Identify the operation performed by the circuit given below:

Q8.A particle of charge $q$ and mass $m$ is subjected to an electric field $E=E_0(1-a{x}^2)$ in the x-direction, where a and $E_0$ are constants. Initially the particle was at rest at $x=0$. Other than the initial position the kinetic energy of the particle becomes zer …

Q9.The value of current $i_1$ flowing from A to C in the circuit diagram is:

Q10.Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is $x_1$ and in the other, $x_2$. When both cylinders are connected through a pipe of n …

Q11.The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is $330{\text{ ms}}^{-1}$:

Q12.A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at $t=0$, then the time at which the energy stored in the inductor reaches $(1/n)$ times of its maximum value, is:

Q13.The electric field of a plane electromagnetic wave is given by $\vec{E}=E_0(\hat{x}+\hat{y})\sin (kz-\omega t)$. Its magnetic field will be given by:

Q14.A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 …

Q15.A paramagnetic sample shows a net magnetisation of $6\text{ A/m}$ when it is placed in an external magnetic field of 0.4 T at a temperature of 4 K. When the sample is placed in an external magnetic field of 0.3 T at a temperature of 24 K, then the magnetisation will be:

Q16.A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:

Q17.A small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $mk{v}^2$ where $v$ is its speed. The maximum height attained by the ball is:

Q18.Match the thermodynamics processes taking place in a system with the correct conditions. In the table: $\Delta \mathrm{Q}$ is the heat supplied, $\Delta \mathrm{W}$ is the work done and $\Delta \mathrm{U}$ is change in internal energy of the system. Match the following:

Process: …

Q19.A cube of metal is subjected to a hydrostatic pressure 4 GPa. The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, $\mathrm{B}=8\times 10^{10}$ Pa)

Q20.The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval $\mathrm{t}=0$ to $\mathrm{t}=5\mathrm{s}$ will be ____

Q21.The distance between an object and a screen is 100 cm. A lens can produce real image of the object on the screen for two different positions between the screen and the object.

The distance between these two positions is 40 cm. If the power of the lens is close to …

Q22.The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta \mathrm{P}$ is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $\Delta \mathrm{T}$ at constant pressure. The initial …

Q23.Four resistance $40\Omega ,60\Omega ,90\Omega$, and $110\Omega$ make the arms of a quadrilateral ABCD. Across AC is a battery of emf 40 V and internal resistance negligible. The potential difference across BD in V is ____

Q24.Orange light of wavelength $6000\times 10^{-10}\mathrm{m}$ illuminates a single slit of width $0.6\times 10^{-4}\mathrm{m}$. the maximum possible number of diffraction minima produced on both sides of the central maximum is ____

Q1.The Crystal Field Stabilization Energy (CFSE) of $\left[{\mathrm{CoF}}_3{\left({\mathrm{H}}_2\mathrm{O}\right)}_3\right]\left({\Delta }_0<\mathrm{P}\right)$ is :

Q2.The processes of calcination and roasting in metallurgical industries, respectively, can lead to:

Q3.250 mL of a waste solution obtained from the workshop of a goldsmith contains 0.1 M ${\mathrm{AgNO}}_3$ and 0.1 M AuCl . The solution was electrolyzed at 2 V by passing a current of 1 A for 15 minutes. The metal/metals electrodeposited will be: …

Q4.Among the following compounds, which one has the shortest $\mathrm{C}-\mathrm{Cl}$ bond?

Q5.The process that is NOT endothermic in nature is:

Q6.If the equilibrium constant for $\mathrm{A}\rightleftharpoons \mathrm{B}+\mathrm{C}$ is ${\mathrm{K}}_{(\mathrm{eq})}^{(1)}$ and that of $\mathrm{B}+\mathrm{C}\rightleftharpoons \mathrm{P}$ is ${\mathrm{K}}_{(\mathrm{eq})}^{(2)}$, the equilibrium constant for …

Q7.Which of the following compounds will form the precipitate with aq. ${\mathrm{AgNO}}_3$ solution most readily ?

Q8.In the following reaction sequence, $[\mathrm{C}]$ is:

Q9.The major product $[R]$ in the following sequence of reactions is:

Q10.The major product $[\mathrm{C}]$ in the following reaction sequence will be: …

Q11.A sample of red ink (a colloidal suspension) is prepared by mixing eosine dye, egg white, HCHO and water. The component which ensures stability of the ink sample is :

Q12.The one that can exhibit highest paramagnetic behaviour among the following is: gly = glycinato ; bpy = 2, 2'-bipyridine

Q13.The major product [B] in the following reactions is:

(see structure) $\underset{\text{ Heat }}{\overset{\mathrm{HI}}{\to }}[\mathrm{A}]$ alcohol $\underset{\Delta }{\overset{{\mathrm{H}}_2{\mathrm{SO}}_4}{\to }}[\mathrm{B}]$

Q14.The mechanism of action of "Terfenadine" (Seldane) is :

Q15.An alkaline earth metal ' M ' readily forms water soluble sulphate and water insoluble hydroxide. Its oxide MO is very stable to heat and does not have rock-salt structure. M is:

Q16.The incorrect statement(s) among (a) - (c) is (are):
(a) $\mathrm{W}(\mathrm{VI})$ is more stable than $\mathrm{Cr}(\mathrm{VI})$.
(b) in the presence of HCl , permanganate titrations provide satisfactory results.
(c) some lanthanoid oxides can be used as phosphors.

Q17.The molecule in which hybrid MOs involve only one d-orbital of the central atom is :

Q18.The reaction in which hybridization of the underlined atom is affected is:

Q19.The shortest wavelength of H atom in the Lyman series is ${\lambda }_1$. The longest wavelength in the Balmer Series of ${\mathrm{He}}^{+}$is:

Q20.Five moles of an ideal gas at 1 bar and 298 K is expanded into vacuum to double the volume. The work done is :

Q21.The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a rise of temperature from $27^{\circ }\mathrm{C}$ to $42^{\circ }\mathrm{C}$. Its energy of activation in $\mathrm{J}/\mathrm{mol}$ is ............. (Take in …

Q22.Consider the following equations :
$2{\mathrm{Fe}}^{2+}+{\mathrm{H}}_2{\mathrm{O}}_2\to x\mathrm{A}+yB$ (in basic medium)
(in acidic medium) …

Q23.The number of chiral centres present in threonine is ____ .

Q24.A 100 mL solution was made by adding 1.43 g of ${\mathrm{Na}}_2{\mathrm{CO}}_3.\times {\mathrm{xH}}_2\mathrm{O}$. The normality of the solution is 0.1 N . The value of x is ____
(The atomic mass of Na is $23\mathrm{g}/\mathrm{mol}$ )

Q25.The osmotic pressure of a solution of NaCl is 0.10 atm and that of a glucose solution is 0.20 atm. The osmotic pressure of a solution formed by mixing 1 L of the sodium chloride solution with 2 L of the glucose solution is $x\times 10^{-3}$ atm. $x$ is ______ (nearest integer)

Q1.If a and b are real numbers such that $(2+\alpha {)}^4=a+b\alpha$, where $\alpha =\frac{-1+i\sqrt{3}}{2}$, then $a+b$ is equal to:

Q2.Contrapositive of the statement:
'If a function f is differentiable at a, then it is also continuous at a', is:

Q3.If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of $(1+x{)}^{N+5}$ are in the ratio $5:10:14$, then the largest coefficient in the expansion is:

Q4.The function $f(x)=\{\begin{array}{ll}\frac{\pi }{4}+{\tan }^{-1}x,& |x|\le 1\\ \frac{1}{2}(|x|-1),& |x|>1\end{array}$ is:

Q5.If the system of equations
$x+y+z=2$
$2x+4y-z=6$
$3x+2y+\lambda z=\mu$
has infinitely many solutions, then:

Q6.Let $\lambda \ne 0$ be in $\mathbb{R}$. If $\alpha$ and $\beta$ are the roots of the equation, $x^2-x+2\lambda =0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3x^2-10x+27\lambda =0$, then $\frac{\beta \gamma }{\lambda }$ is equal to:

Q7.The circle passing through the intersection of the circles, $x^2+y^2-6x=0$ and $x^2+y^2-4y=0$, having its centre on the line, $2x-3y+12=0$, also passes through the point:

Q8.The integral ${\int }_{\pi /6}^{\pi /3}{\tan }^{3}x\cdot {\sin }^{2}3x\left(2{\sec }^{2}x\cdot {\sin }^{2}3x+3\tan x\cdot \sin 6x\right)dx$ is

Q9.The area (in sq. units) of the largest rectangle $ABCD$ whose vertices $A$ and $B$ lie on the $x$-axis and vertices $C$ and $D$ lie on the parabola, $y=x^2-1$ below the $x$-axis, is:

Q10.Suppose the vectors $x_1$, $x_2$ and $x_3$ are the solutions of the system of linear equations, $Ax=b$ when the vector $b$ on the right side is equal to $b_1$, $b_2$ and $b_3$ respectively. If $x_1=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$, …

Q11.The solution of differential equation $\frac{dy}{dx}-\frac{y+3x}{{\log }_e(y+3x)}+3=0$ is: (where C is a constant of integration.)

Q12.The minimum value of $2^{\sin x}+2^{\cos x}$ is:

Q13.Let $\mathrm{f}:(0,\infty )\to (0,\infty )$ be a differentiable function such that $\mathrm{f}(1)=\mathrm{e}$ and ${\lim }_{t\to x}\frac{t^2{f}^2(x)-x^2{f}^2(t)}{t-x}=0$. If $f(x)=1$, then $x$ is equal to:

Q14.The distance of the point $(1,-2,3)$ from the plane $x-y+z=5$ measured parallel to the line $\frac{\mathrm{x}}{2}=\frac{\mathrm{y}}{3}=\frac{\mathrm{z}}{-6}$ is:

Q15.In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before $B$ throws a total of 7 and $B$ wins the game if he throws a total of …

Q16.The angle of elevation of a cloud C from a point $\mathrm{P},200\mathrm{m}$ above a still take is $30^{\circ }$. If the angle of depression of the image of C in the lake from the point P is $60^{\circ }$, then PC (in m ) is equal to

Q17.Let $\mathrm{x}=4$ be a directrix to an ellipse whose centre is at the origin and its eccentricity is $\frac{1}{2}$. If $\mathrm{P}(1,\beta ),\beta >0$ is a point on this ellipse, then the equation of the normal to it at P is:

Q18.Let ${\bigcup }_{i=1}^{50}{X}_i={\bigcup }_{i=1}^n{Y}_i=T$, where each $X_i$ contains 10 elements and each $Yi$ contains 5 elements. If each element of the set T is an element of exactly 20 of sets ${\mathrm{X}}_{\mathrm{i}}$'s and exactly 6 of sets $Y_i$'s then n is e …

Q19.If the perpendicular bisector of the line segment joining the points $\mathrm{P}(1,4)$ and $\mathrm{Q}(\mathrm{k},3)$ has $y$-intercept equal to -4 , then a value of $k$ is:

Q20.Let $a_1,a_2,\dots a_n$ be a given A.P. whose common difference is an integer and $S_n=a_1+a_2+\dots +a_n$. If $a_1=1,a_n=300$ and $15\le n\le 50$, then the ordered pair ( $S_{n-4},a_{n-4}$ ) is equal to:

Q21.If $\vec{a}=2\hat{i}+\hat{j}+2\hat{k}$, then the value of $|\hat{i}\times (\vec{a}\times \hat{i}){|}^2+|\hat{j}\times (\vec{a}\times \hat{j}){|}^2+|\hat{k}\times (\vec{a}\times \hat{k}){|}^2$ is equal to:

Q22.A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is

Q23.Let PQ be a diameter of the circle $x^2+y^2=9$. If $\alpha$ and $\beta$ are the lengths of the perpendiculars from P and Q on the straight line, $\mathrm{x}+\mathrm{y}=2$ respectively, then the maximum value of $\alpha \beta$ is

Q24.If the variance of the following frequency distribution :

\begin{tabular}{ccccc}
Class & $⋮$ & $10-20$ & $20-30$ & $30-40$ \\
Frequency & $⋮$ & 2 & $x$ & 2
\end{tabular}
is 50 , then x is equal to:

Q25.Let $\{\mathrm{x}\}$ and $[\mathrm{x}]$ denote the fractional part of x and the greatest integer $\le \mathrm{x}$ respectively of a real number $x$. if ${\int }_0^n\{x\}dx$, ${\int }_0^n[x]dx$ and $10\left(n^2-n\right)$, $(n\in N,n>1)$ are three consecutive terms of a …