JEE Main 2020 · 04 Sep 2020 · Shift 1

Q1.On the $x$-axis and at a distance $x$ from the origin, the gravitational field due to a mass distribution is given by $\frac{Ax}{{\left(x^2+a^2\right)}^{3/2}}$ in the $x$-direction. The magnitude of gravitational potential on the $x$-axis at a distance $x$, taking its value …

Q2.Given figure shows few data points in a photo electric effect experiment for a certain metal. The minimum energy for ejection of electron from its surface is: (Plancks constant $\mathrm{h}=6.62\times 10^{-34}$ J.s)

Q3.A Tennis ball is released from a height $h$ and after freely falling on a wooden floor it rebounds and reaches height $\frac{\mathrm{h}}{2}$. The velocity versus height of the ball during its motion may be represented graphically by:
(graphs are drawn schematically and on not to …

Q4.Dimensional formula for thermal conductivity is (here $\mathbf{K}$ denotes the temperature):

Q5.Particle A of mass ${\mathrm{m}}_{\mathrm{A}}=\frac{\mathrm{m}}{2}$ moving along the x-axis with velocity $v_0$ collides elastically with another particle $B$ at rest having mass $m_B=\frac{m}{3}$. If both particles move along the $x$ axis after the collision, the change …

Q6.A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm , are placed as shown in the figure. The ratio of the magnetic fi …

Q7.The specific heat of water $=4200\mathrm{J}{\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ and the latent heat of ice $=3.4\times 10^5\mathrm{J}{\mathrm{kg}}^{-1}$. 100 grams of ice at $0^{\circ }\mathrm{C}$ is placed in 200 g of water at $25^{\circ }\mathrm{C}$. The amount of ice th …

Q8.Take the breakdown voltage of the zener diode used in the given circuit as 6 V . For the input voltage shown in figure below, the time variation of the output voltage is:
(Graphs drawn are schematic and not to scale)

Q9.A beam of plane polarized light of large cross-sectional area and uniform intensity of $3.3{\mathrm{Wm}}^{-2}$ falls normally on a polarizer (cross sectional area $3\times 10^{-4}{\mathrm{m}}^2$ ) which rotates about its axis with an angular speed of …

Q10.A small bar magnet placed with its axis at $30^{\circ }$ with an external field of 0.06 T experiences a torque of 0.018 Nm . The minimum work required to rotate it from its stable to unstable equilibrium position is:

Q11.A two point charges $4q$ and $-q$ are fixed on the $x$-axis at $x=-\frac{d}{2}$ and $x=\frac{d}{2}$, respectively. If a third point charge ' $q$ ' is taken from the origin to $x=d$ along the semicircle as shown in the figure, the energy of the charge will:

Q12.Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum:

Q13.Match the ${\mathrm{C}}_p/{\mathrm{C}}_{\mathrm{V}}$ ratio for ideal gases with different type of molecules:
| (B) Diatomic rigid molecule …

Q14.A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil?

Three positions shown describe:
(a) the magnet's entry
(b) magnet is completely insi …

Q15.For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5 m , while the distance between one crest and one trough is 1.5 m . The possible wavelengths (in m ) of the waves are:

Q16.A air bubble of radius 1 cm in water has an upward acceleration $9.8\mathrm{cm}{\mathrm{s}}^{-2}$. The density of water is $1\mathrm{gm}{\mathrm{cm}}^{-3}$ and water offers negligible drag force on the bubble. The mass of the bubble is: …

Q17.Starting from the origin at time $t=0$, with initial velocity $5\hat{j}{\mathrm{ms}}^{-1}$, a particle moves in the $x$ - y plane with a constant acceleration of $(10\hat{\mathrm{i}}+4\hat{\mathrm{j}}){\mathrm{ms}}^{-2}$. At time t , its coordinates are ( 20 …

Q18.Two charged thin infinite plane sheets of uniform surface charge density ${\sigma }_{+}$ and ${\sigma }_{-}$, where $\left|{\sigma }_{+}\right|>\left|{\sigma }_{-}\right|$, intersect at right angle. Which of the following best represents the electric field lines for this system.

Q19.Blocks of masses $\mathrm{m}$, $2\mathrm{m}$, $4\mathrm{m}$ and $8\mathrm{m}$ are arranged in a line on a frictionless floor. Another block of mass $\mathrm{m}$, moving with speed $v$ along the same line (see figure) collides with mass $\mathrm{m}$ in perfectly inelastic manne …

Q20.A battery of 3.0 V is connected to a resistor dissipating 0.5 W of power. If the terminal voltage of the battery is 2.5 V, the power dissipated within the internal resistance is:

Q21.A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to ____.

Q22.In a compound microscope, the magnified virtual image is formed at a distance of 25 cm from the eye-piece. The focal length of its objective lens is 1 cm. If the magnification is 100 and the tube length of the microscope is 20 cm, then the focal length of the eyepiece lens (in cm …

Q23.ABC is a plane lamina of the shape of an equilateral triangle. $\mathrm{D}$, $\mathrm{E}$ are mid points of $\mathrm{AB}$, $\mathrm{AC}$ and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is …

Q24.In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is $304\text{A˚}$. The corresponding difference for the Paschan series in Å is: ____.

Q25.A circular disc of mass M and radius R is rotating about its axis with angular speed ${\omega }_1$. If another stationary disc having radius $\frac{R}{2}$ and same mass $M$ is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed …

Q1.Among statements (a) - (d), the correct ones are:
(a) Lime stone is decomposed to CaO during the extraction of iron from its oxides.
(b) In the extraction of silver, silver is extracted as an anionic complex.
(c) Nickel is purified by Mond's process.
(d) Zr and Ti are purified by …

Q2.The decreasing order of reactivity of the following organic molecules towards $\mathrm{AgNO}{}_3$ solution is:

Q3.The region in the electromagnetic spectrum where the Balmer series lines appear is:

Q4.The pair in which both the species have the same magnetic moment (spin only) is:

Q5.On heating, lead (II) nitrate gives a brown gas (A). The gas (A) on cooling changes to a colourless solid/liquid (B). (B) on heating with NO changes to a blue solid (C). The oxidation number of nitrogen in solid (C) is:

Q6.$[\mathrm{P}]$ on treatment with ${\mathrm{Br}}_2/{\mathrm{FeBr}}_3$ in ${\mathrm{CCl}}_4$ produced a single isomer ${\mathrm{C}}_8{\mathrm{H}}_7{\mathrm{O}}_2\mathrm{Br}$ while heating $[\mathrm{P}]$ with sodalime gave toluene. The compound $[\mathrm{P}]$ is:

Q7.The ionic radii of ${\mathrm{O}}^{2-},{\mathrm{F}}^{-},{\mathrm{Na}}^{+}$ and ${\mathrm{Mg}}^{2+}$ are in the order:

Q8.The intermolecular potential energy for the molecules $\mathrm{A},\mathrm{B},\mathrm{C}$ and D given below suggest that:

Q9.An organic compound (A) (molecular formula ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_2$) was hydrolysed with dil. ${\mathrm{H}}_2{\mathrm{SO}}_4$ to give a carboxylic acid (B) and an alcohol (C). 'C' gives white turbidity immediately when treated with anhydrous …

Q10.For the equilibrium $\mathrm{A}\rightleftharpoons \mathrm{B}$, the variation of the rate of the forward (a) and reverse (B) reaction with time is given by:

Q11.The number of isomers possible for $\left[\mathrm{Pt}(\mathrm{en}){\left({\mathrm{NO}}_2\right)}_2\right]$ is:

Q12.What are the functional groups present in the structure of maltose?

Q13.

Identify the incorrect statement from the options below for the above cell:

Q14.Which of the following will react with ${\mathrm{CHCl}}_3+$ alc. KOH ?

Q15.Match the following:

Q16.For one mole of an ideal gas, which of these statements must be true?
(a) U and H each depends only on temperature
(b) Compressibility factor Z is not equal to 1
(c) ${\mathrm{C}}_{\mathrm{P},\mathrm{m}}-{\mathrm{C}}_{\mathrm{V},\mathrm{m}}=\mathrm{R}$
(d) …

Q17.On combustion of $\mathrm{Li},\mathrm{Na}$ and K in excess of air, the major oxides formed, respectively, are:

Q18.When neopentyl alcohol is heated with an acid, it slowly converted into an 85:15 mixture of alkenes A and B, respectively. What are these alkenes?

Q19.The elements with atomic numbers 101 and 104 belong to, respectively:

Q20.At 300 K, the vapour pressure of a solution containing 1 mole of $n$-hexane and 3 moles of n-heptane is 550 mm of Hg. At the same temperature, if one more mole of n-heptane is added to this solution, the vapour pressure of the solution increases by 10 mm of Hg. What is the vapour …

Q21.If $75\%$ of a first order reaction was completed in 90 minutes, $60\%$ of the same reaction would be completed in approximately (in minutes) ____.
(Take: …

Q22.The mass of ammonia in grams produced when 2.8 kg of dinitrogen quantitatively reacts with 1 kg of dihydrogen is ____.

Q23.The number of chiral centres present in [B] is ____.

Q24.At 20.0 mL solution containing 0.2 g impure ${\mathrm{H}}_2{\mathrm{O}}_2$ reacts completely with 0.316 g of ${\mathrm{KMnO}}_4$ in acid solution. The purity of ${\mathrm{H}}_2{\mathrm{O}}_2$ (in %) is ____.
(mol. wt. of ${\mathrm{H}}_2{\mathrm{O}}_2=34$; mol. wt. of …

Q1.Let $\alpha$ and $\beta$ be roots of $x^2-3x+p=0$ and $\gamma$ and $\delta$ be the roots of $x^2-6x+q=0$. If $\alpha ,\beta$, $\gamma ,\delta$, form a geometric progression. Then ratio $(2q+p):(2q-p)$ is:

Q2.Let $f(x)=|x-2|$ and $g(x)=f(f(x)),x\in [0,4]$. Then ${\int }_0^3(g(x)-f(x))dx$ is equal to:

Q3.Let $f$ be a twice differentiable function on ( 1,6 ). If $f(2)=8,f^{\prime }(2)=5,f^{\prime }(x)\ge 1$ and $f^{\prime \prime }(x)\ge 4$, for all $x\in (1,6)$, then:

Q4.Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ be given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum value of the function, $\varphi (t)=\frac{5}{12}+t-t^2$, then $a^2+b^2$ is equal to:

Q5.The mean and variance of 8 observations are 10 and 13.5 , respectively. If 6 of these observations are $5,7,10,12,14,15$, then the absolute difference of the remaining two observations is:

Q6.Let $x_0$ be the point of local maxima of $f(x)=\vec{a}\cdot (\vec{b}\times \vec{c})$ where $\vec{a}=x\hat{i}-2\hat{j}+3\hat{k},\vec{b}=-2\hat{i}+x\hat{j}-\hat{k}$ and $\vec{c}=7\hat{i}-2\hat{j}+x\hat{k}$. Then the value of …

Q7.If $(a+\sqrt{2}b\cos x)(a-\sqrt{2}b\cos y)=a^2-b^2$, where $a>b>0$, then $\frac{dx}{dy}$ at $\left(\frac{\pi }{4},\frac{\pi }{4}\right)$ is:

Q8.Two vertical poles $\mathrm{AB}=15\mathrm{m}$ and $\mathrm{CD}=10\mathrm{m}$ are standing apart on a horizontal ground with points $A$ and $C$ on the ground. If $P$ is the point of intersection of $BC$ and $AD$, then the height of $P$ (in $m$ ) above the lin …

Q9.If $1+\left(1-2^2\cdot 1\right)+\left(1-4^2\cdot 3\right)+\left(1-6^2\cdot 5\right)+\dots \dots ..+\left(1-20^2\cdot 19\right)=\alpha -220\beta$, then an ordered pair $(\alpha ,\beta )$ is equal to:

Q10.Given the following two statements:
$({\mathrm{S}}_1):(\mathrm{q}\vee \mathrm{p})\to (\mathrm{p}\leftrightarrow \sim \mathrm{q})$ is a tautology.
$({\mathrm{S}}_2):\sim \mathrm{q}\wedge (\sim \mathrm{p}\leftrightarrow \mathrm{q})$ is a fallacy. Then:

Q11.Let $\mathrm{u}=\frac{2\mathrm{z}+\mathrm{i}}{\mathrm{z}-\mathrm{ki}},\mathrm{z}=\mathrm{x}+\mathrm{iy}$ and $\mathrm{k}>0$. If the curve represented by $\mathrm{Re}(\mathrm{u})+\mathrm{Im}(\mathrm{u})=1$ intersects the $y$-axis at the points $P$ and $Q$ …

Q12.A triangle ABC lying in the first quadrant has two vertices as $\mathrm{A}(1,2)$ and $\mathrm{B}(3,1)$. If $\angle BAC=90^{\circ }$, and $\mathrm{ar}(△ABC)=5\sqrt{5}$ sq. units, then the abscissa of the vertex $C$ is:

Q13.Let $\mathrm{P}(3,3)$ be a point on the hyperbola, $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$. If the normal to it at P intersects the $x$-axis at $(9,0)$ and $e$ is its eccentricity, then the ordered pair …

Q14.The integral $\int {\left(\frac{x}{x\sin x+\cos x}\right)}^{2}dx$ is equal to (where $C$ is constant of integration):

Q15.If $A=\left[\begin{array}{cc}\cos \theta & i\sin \theta \\ i\sin \theta & \cos \theta \end{array}\right],\left(\theta =\frac{\pi }{24}\right)$ and $A^5=\left[\begin{array}{ll}a& b\\ c& d\end{array}\right]$, where $i=\sqrt{-1}$, then, which one of the following is not tr …

Q16.The value of ${\sum }_{\mathrm{r}=0}^{20}{}^{50-\mathrm{r}}{\mathrm{C}}_6$ is equal to:

Q17.Let $[t]$ denote the greatest integer $\le t$. Then the equation in $x,[x{]}^2+2[x+2]-7=0$ has:

Q18.Let $f(x)=\int \frac{\sqrt{x}}{(1+x{)}^2}dx(x\ge 0)$. Then $f(3)-f(1)$ is equal to:

Q19.A survey shows that $63\%$ of the people in a city read newspaper A whereas $76\%$ read newspaper B. if $\mathrm{x}\%$ of the people read both the newspapers, then a possible value of x can be:

Q20.Let $y=y(x)$ be the solution of the differential equation, $x{y}^{\prime }-y=x^2(x\cos x+\sin x),x>0$. If $y(\pi )=\pi$, then $y^{\prime \prime }\left(\frac{\pi }{2}\right)+y\left(\frac{\pi }{2}\right)$ is equal to:

Q21.Let ${\left(2x^2+3x+4\right)}^{10}={\sum }_{r=0}^{20}{a}_r{x}^r$. Then $\frac{a_7}{a_{13}}$ is equal to

Q22.If the equation of a plane $P$, passing through the intersection of the planes, $x+4y-z+7=0$ and $3x+y+5z=8$ is ax + by $+6z=15$ for some $a,b\in R$, then the distance of the point $(3,2,-1)$ from the plane $P$ is ____ .

Q23.If the system of equations
$x-2y+3z=9$
$2\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{b}$
$x-7y+az=24$,
has infinitely many solutions, then $\mathrm{a}-\mathrm{b}$ is equal to ____ .

Q24.Suppose a differentiable function $f(x)$ satisfies the identity $f(x+y)=f(x)+f(y)+x{y}^2+x^{2}y$, for all real $x$ and $y$. If ${\lim }_{x\to 0}\frac{f(x)}{x}=1$ then $f^{\prime }(3)$ is equal to ____ .

Q25.The probability of a man hitting a target is $\frac{1}{10}$. The least number of shots required, so that the probability of his hitting the target at least once is greater than $\frac{1}{4}$, is ______ .