JEE Main 2022 · 25 Jul 2022 · Shift 2

Q1.In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitude are found to be 6 V and 2 V respectively. The modulation index is

Q2.The electric current in a circular coil of 2 turns produces a magnetic induction ${\mathrm{B}}_1$ at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction ${\mathrm{B}}_2$ at its centre.

The ratio of …

Q3.A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5\times 10^{-4}{\mathrm{Ncm}}^{-1}$. The radius of drop in cm will be : (Take : $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ )

Q4.Two billiard balls of mass 0.05 kg each moving in opposite directions with $10{\mathrm{ms}}^{-1}$ collide and rebound with the same speed. If the time duration of contact is $\mathrm{t}=0.005\mathrm{s}$, then what is the force exerted on the ball due to each other?

Q5.For a free body diagram shown in the figure, the four forces are applied in the ' x ' and ' y ' directions. What additional force must be applied and at what angle with positive x -axis so that the net acceleration of body is zero?

Q6.Capacitance of an isolated conducting sphere of radius $R_1$ becomes $n$ times when it is enclosed by a concentric conducting sphere of radius $R_2$ connected to earth. The ratio of their radii $\left(\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}\right)$ is:

Q7.The ratio of wavelengths of proton and deuteron accelerated by potential ${\mathrm{V}}_{\mathrm{p}}$ and ${\mathrm{V}}_{\mathrm{d}}$ is $1:\sqrt{2}$. Then, the ratio of ${\mathrm{V}}_{\mathrm{p}}$ to ${\mathrm{V}}_{\mathrm{d}}$ will be

Q8.For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces paral …

Q9.Light wave traveling in air along x -direction is given by ${\mathrm{E}}_{\mathrm{y}}=540\sin \pi \times 10^4(\mathrm{x}-\mathrm{ct}){\mathrm{Vm}}^{-1}$. Then, the peak value of magnetic field of wave will be (Given $\mathrm{c}=3\times 10^8{\mathrm{ms}}^{-1}$ )

Q10.When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on

Q11.An electron with energy 0.1 keV moves at right angle to the earth's magnetic field of $1\times 10^{-4}{\mathrm{Wbm}}^{-2}$. The frequency of revolution of the electron will be
(Take mass of electron $=9.0\times 10^{-31}\mathrm{kg}$ )

Q12.A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points $A$ and $B$ will be

Q13.The length of a seconds pendulum at a height $h=2R$ from earth surface will be:
(Given: $R=$ Radius of earth and acceleration due to gravity at the surface of earth $g={\pi }^2{m/s}^2$)

Q14.Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound, then the value of $n$ will be

Q15.Let ${\eta }_1$ is the efficiency of an engine at $T_1=447^{\circ }\mathrm{C}$ and $T_2=147^{\circ }\mathrm{C}$ while ${\eta }_2$ is the efficiency at $T_1=947^{\circ }\mathrm{C}$ and $T_2=47^{\circ }\mathrm{C}$. The ratio $\frac{{\eta }_1}{{\eta }_2}$ will be:

Q16.An object is taken to a height above the surface of earth at a distance $\frac{5}{4}R$ from the centre of the earth. Where radius of earth, $R=6400\mathrm{km}$. The percentage decrease in the weight of the object will be

Q17.A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed $10{\mathrm{ms}}^{-1}$ gets embedded in it, then loss of kinetic energy will be

Q18.A ball is projected from the ground with a speed $15{\mathrm{ms}}^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then $\tan \theta$ will be equal to

Q19.The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%, 2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be:

Q20.Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength $\lambda$. The value of principal quantum number 'n' of the excited state will be:
(R: Rydberg constant)

Q21.A particle is moving in a straight line such that its velocity is increasing at $5{\mathrm{ms}}^{-1}$ per meter. The acceleration of the particle is __________ ${\mathrm{ms}}^{-2}$ at a point where its velocity is $20{\mathrm{ms}}^{-1}$.

Q22.Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the syste …

Q23.A block of ice of mass 120 g at temperature $0^{\circ }\mathrm{C}$ is put in 300 gm of water at $25^{\circ }\mathrm{C}$. The xg of ice melts as the temperature of the water reaches $0^{\circ }\mathrm{C}$. The value of x is
[Use: Specific heat capacity of water …

Q24.$\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its
(i) third permitted energy level to the second level and
(ii) the highest permitted energy level to the second permitted level.
The value of $x$ will be

Q25.In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be ______ cm.

Q26.Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between A and B is ______ $\Omega$.

Q27.Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is ______ (deg …

Q28.Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric …

Q29.A convex lens of focal length 20 cm is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combin …

Q30.Magnetic flux (in weber) in a closed circuit of resistance $20\Omega$ varies with time $t(s)$ as $\varphi =8t^2-9t+5$. The magnitude of the induced current at $t=0.25$ s will be ______ mA

Q1.Match List I with List II :
| C. ${\mathrm{XeOF}}_4$ | III. …

Q2.Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y . respectively in 1 kg of water. The ratio of depression in freezing points for A and B is found to be $1:4$. The ratio of molar masses of X and Y is :

Q3.${\mathrm{Ka}}_1,{\mathrm{Ka}}_2$ and ${\mathrm{Ka}}_3$ are the respective ionization constants for the following reactions (a),(b), and (c).
(a) ${\mathrm{H}}_2{\mathrm{C}}_2{\mathrm{O}}_4\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{HC}}_2{\mathrm{O}}_4^{-}$
(b) …

Q4.The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is ${\Lambda }_{\mathrm{m}1}$ and that of 20 moles another identical cell heaving 80 mL NaCl solution is ${\Lambda }_{\mathrm{m}2}$, The conductivities exhibited by these two cells are same. …

Q5.For micelle formation, which of the following statements are correct?
(A) Micelle formation is an exothermic process.
(B) Micelle formation is an endothermic process.
(C) The entropy change is positive.
(D) The entropy change is negative.

Q6.The first ionization enthalpies of $\mathrm{Be},\mathrm{B},\mathrm{N}$ and O follow the order

Q7.Given below are two statements.

Statement I: Pig iron is obtained by heating cast iron with scrap iron.
Statement II: Pig iron has a relatively lower carbon content than that of cast iron. In the light of the above statements, choose the correct answer from the options given bel …

Q8.High purity (>99.95%) dihydrogen is obtained by

Q9.The correct order of density is

Q10.The total number of acidic oxides from the following list is: NO, ${\mathrm{N}}_2\mathrm{O},{\mathrm{B}}_2{\mathrm{O}}_3,{\mathrm{N}}_2{\mathrm{O}}_5,\mathrm{CO}$, ${\mathrm{SO}}_3,{\mathrm{P}}_4{\mathrm{O}}_{10}$

Q11.The correct order of energy of absorption for the following metal complexes is
A: ${\left[\mathrm{Ni}(\mathrm{en}{)}_3\right]}^{2+}$, B:${\left[\mathrm{Ni}{\left({\mathrm{NH}}_3\right)}_6\right]}^{2+}$, C:${\left[\mathrm{Ni}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}$

Q12.Match List I with List II.

Choose the correct answer from the options given below:

Q13.What is the major product of the following reaction?

Q14.Arrange the following in decreasing acidic strength.
(A) (see structure)
(B) (see structure)
(C) (see structure)
(D) (see structure)

Q15.$\mathrm{CH}{}_3-\mathrm{CH}{}_2-\mathrm{CN}\underset{\text{Ether}}{\overset{\mathrm{CH}{}_3\mathrm{MgBr}}{\to }}\mathrm{A}\stackrel{\mathrm{H}{}_3\mathrm{O}{}^{+}}{\to }\mathrm{B}\underset{\text{HCl}}{\overset{\mathrm{Zn}-\mathrm{Hg}}{\to }}\mathrm{C}$

The correct structure of C is

Q16.Glycosidic linkage between $\mathrm{C}{}_1$ of $\alpha$-glucose and $\mathrm{C}{}_2$ of $\beta$-fructose is found in

Q17.Some drugs bind to a site other than, the active site of an enzyme. This site is known as

Q18.In base vs. Acid titration, at the end point methyl orange is present as

Q19.56.0 L of nitrogen gas is mixed with excess of hydrogen gas and it is found that 20 L of ammonia gas is produced. The volume of unused nitrogen gas is found to be _____ L.

Q20.A sealed flask with a capacity of $2{\mathrm{dm}}^3$ contains 11 g of propane gas. The flask is so weak that it will burst if the pressure becomes 2 MPa . The minimum temperature at which the flask will burst is _____ ${}^{\circ }$C. [Nearest integer]
(Given: …

Q21.When the excited electron of a H atom from $\mathrm{n}=5$ drops to the ground state, the maximum number of emission lines observed are _____

Q22.While performing a thermodynamics experiment, a student made the following observations, $\mathrm{HCl}+\mathrm{NaOH}\to \mathrm{NaCl}+\mathrm{H}{}_2\mathrm{O}$ $\Delta \mathrm{H}=-57.3\mathrm{kJ}{\mathrm{mol}}^{-1}$ $\mathrm{CH}{}_3\mathrm{COOH}+\mathrm{NaOH}\to \mathrm{CH}{}_3\mathrm{COONa}+\mathrm{H}{}_2\mathrm{O}$ $\Delta \mathrm{H}=-55.3\mathrm{kJ}{\mathrm{mol}}^{-1}$.

T …

Q23.For the decomposition of azomethane.
${\mathrm{CH}}_3{\mathrm{N}}_2{\mathrm{CH}}_3(\mathrm{g})\to {\mathrm{CH}}_3{\mathrm{CH}}_3(\mathrm{g})+{\mathrm{N}}_2(\mathrm{g})$ a first order reaction, the variation in partial pressure with time at 600 K is given as

The …

Q24.The sum of number of lone pairs of electrons present on the central atoms of ${\mathrm{XeO}}_3$, ${\mathrm{XeOF}}_4$ and ${\mathrm{XeF}}_6$ is ____

Q25.The spin-only magnetic moment value of ${\mathrm{M}}^{3+}$ ion (in gaseous state) from the pairs ${\mathrm{Cr}}^{3+}/{\mathrm{Cr}}^{2+}$, ${\mathrm{Mn}}^{3+}/{\mathrm{Mn}}^2$, ${\mathrm{Fe}}^{3+}/{\mathrm{Fe}}^{2+}$ and ${\mathrm{Co}}^{3+}/{\mathrm{Co}}^{2+}$ that has negative …

Q26.A sample of 4.5 mg of an unknown monohydric alcohol, $\mathrm{R}-\mathrm{OH}$ was added to methylmagnesium iodide. A gas is evolved and is collected and its volume measured to be 3.1 mL. The molecular weight of the unknown alcohol is ____ g/mol. [Nearest integer]

Q27.The separation of two coloured substances was done by paper chromatography. The distances travelled by solvent front, substance A and substance B from the base line are 3.25 cm, 2.08 cm and 1.05 cm respectively. The ratio of $R_f$ values of A to B is ____

Q28.The total number of monobromo derivatives formed by the alkanes with molecular formula ${\mathrm{C}}_5{\mathrm{H}}_{12}$ is (excluding stereo isomers) ____

Q1.For $z\in \mathbb{C}$ if the minimum value of $(|z-3\sqrt{2}|+|z-p\sqrt{2}i|)$ is $5\sqrt{2}$, then a value of $p$ is

Q2.The number of real values $\lambda$, such that the system of linear equations
$2\mathrm{x}-3\mathrm{y}+5\mathrm{z}=9$
$\mathrm{x}+3\mathrm{y}-\mathrm{z}=-18$
$3x-y+\left({\lambda }^2-|\lambda |\right)z=16$
has no solution, is :-

Q3.The number of bijective functions $\mathrm{f}:\{1,3,5,7,\dots ,99\}\to \{2,4,6,8,\dots ,100\}$, such that $\mathrm{f}(3)\ge \mathrm{f}(9)\ge \mathrm{f}(15)\ge \mathrm{f}(21)\ge \dots \ge \mathrm{f}(99)$, is

Q4.The remainder when $(11{)}^{1011}+(1011{)}^{11}$ is divided by 9 is

Q5.The sum ${\sum }_{n=1}^{21}\frac{3}{(4n-1)(4n+3)}$ is equal to

Q6.${\lim }_{x\to \frac{\pi }{4}}\frac{8\sqrt{2}-(\cos x+\sin x{)}^7}{\sqrt{2}-\sqrt{2}\sin 2x}$ is equal to

Q7.${\lim }_{n\to \infty }\frac{1}{2^n}\left(\frac{1}{\sqrt{1-\frac{1}{2^n}}}+\frac{1}{\sqrt{1-\frac{2}{2^n}}}+\frac{1}{\sqrt{1-\frac{3}{2^n}}}+\dots +\frac{1}{\sqrt{1-\frac{2^n-1}{2^n}}}\right)$ is equal to

Q8.If A and B are two events such that $\mathrm{P}(\mathrm{A})=\frac{1}{3},\mathrm{P}(\mathrm{B})=\frac{1}{5}$ and $\mathrm{P}(\mathrm{A}\cup \mathrm{B})=\frac{1}{2}$, then …

Q9.Let $[t]$ denote the greatest integer less than or equal to $t$. Then the value of the integral ${\int }_{-3}^{101}\left([\sin (\pi \mathrm{x})]+{\mathrm{e}}^{[\cos (2\pi \mathrm{x})]}\right)\mathrm{dx}$ is equal to

Q10.Let the point $\mathrm{P}(\alpha ,\beta )$ be at a unit distance from each of the two lines $L_1:3x-4y+12=0$, and ${\mathrm{L}}_2:8\mathrm{x}+6\mathrm{y}+11=0$. If P lies below ${\mathrm{L}}_1$ and above $L_2$, then $100(\alpha +\beta )$ is equal to

Q11.Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point ( $\mathrm{x},\mathrm{y}$ ) on it is directly proportional to $\left(\frac{-y}{x}\right)$. If the curve passes through the point $(1,2)$ and $(8,1)$, then …

Q12.If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the line $\frac{x}{7}+\frac{y}{2\sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2\sqrt{6}}=1$ on the $y$-axis, then the eccentricity of the ellipse is

Q13.The tangents at the point $\mathrm{A}(1,3)$ and $\mathrm{B}(1,-1)$ on the parabola $y^2-2x-2y=1$ meet at the point P . Then the area (in unit ${}^2$ ) of the triangle PAB is :-

Q14.Let the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{7}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{\alpha }=\frac{1}{25}$ coincide. Then the length of the latus rectum of the hyperbola is:-

Q15.A plane E is perpendicular to the two planes $2\mathrm{x}-2\mathrm{y}+\mathrm{z}=0$ and $\mathrm{x}-\mathrm{y}+2\mathrm{z}=4$, and passes through the point $\mathrm{P}(1,-1,1)$. If the distance of the plane E from the point $\mathrm{Q}(\mathrm{a},\mathrm{a},2)$ is …

Q16.The shortest distance between the lines $\frac{x+7}{-6}=\frac{y-6}{7}=z$ and $\frac{7-x}{2}=y-2=z-6$ is

Q17.Let $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$ and $\vec{b}$ be a vector such that $\vec{a}\times \vec{b}=2\hat{i}-\hat{k}$ and $\vec{a}\cdot \vec{b}=3$. Then the projection of $\vec{b}$ on the vector $\vec{a}-\vec{b}$ is :-

Q18.If the mean deviation about median for the number 3, 5, 7, 2k, 12, 16, 21, 24 arranged in the ascending order, is 6 then the median is

Q19.$2\sin \left(\frac{\pi }{22}\right)\sin \left(\frac{3\pi }{22}\right)\sin \left(\frac{5\pi }{22}\right)\sin \left(\frac{7\pi }{22}\right)\sin \left(\frac{9\pi }{22}\right)$ is equal to

Q20.Consider the following statements :
P : Ramu is intelligent
Q : Ramu is rich
R : Ramu is not honest
The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as :

Q21.Let $\mathrm{A}:\{1,2,3,4,5,6,7\}$. Define $\mathrm{B}=\{\mathrm{T}\subseteq \mathrm{A}$ : either $1\notin \mathrm{T}$ or $2\in \mathrm{T}\}$ and $\mathrm{C}=\mathrm{T}\subseteq \mathrm{A}:\mathrm{T}$ the sum of all the elements of T is a prime number}. Then the …

Q22.Let $\mathrm{f}(\mathrm{x})$ be a quadratic polynomial with leading coefficient 1 such that $f(0)=p,p\ne 0$ and $\mathrm{f}(1)=\frac{1}{3}$. If the equation $\mathrm{f}(\mathrm{x})=0$ and $\mathrm{fofofof}(\mathrm{x})=0$ have a common real root, then …

Q23.Let $\mathrm{A}=\left[\begin{array}{ccc}1& \mathrm{a}& \mathrm{a}\\ 0& 1& \mathrm{b}\\ 0& 0& 1\end{array}\right],\mathrm{a},\mathrm{b}\in \mathbb{R}$. If for some $\mathrm{n}\in \mathrm{N}$, …

Q24.The sum of the maximum and minimum values of the function $\mathrm{f}(\mathrm{x})=|5\mathrm{x}-7|+\left[{\mathrm{x}}^2+2\mathrm{x}\right]$ is the interval $\left[\frac{5}{4},2\right]$, where $[t]$ is the greatest integer $\le \mathrm{t}$ is

Q25.Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=\frac{4y^3+2y{x}^2}{3x{y}^2+x^3},y(1)=1$. If for some $n\in N,y(2)\in [n-1,n)$, then $n$ is equal to

Q26.Let f be a twice differentiable function on R. If ${\mathrm{f}}^{\prime }(0)=4$ and
$f(x)+{\int }_0^x(x-t)f^{\prime }(t)dt=\left(e^{2x}+e^{-2x}\right)\cos 2x+\frac{2}{a}x$, then $(2\mathrm{a}+1{)}^5{\mathrm{a}}^2$ is equal to

Q27.Let $a_n={\int }_{-1}^n\left(1+\frac{x}{2}+\frac{x^2}{3}+\frac{x^3}{4}+\dots +\frac{x^{n-1}}{n}\right)dx$ for $n\in N$. Then the sum of all the elements of the set $\{n\in N:a_n\in (2,30)\}$ is

Q28.If the circles $x^2+y^2+6x+8y+16=0$ and $x^2+y^2+2(3-\sqrt{3})x+2(4-\sqrt{6})y=\mathrm{k}+6\sqrt{3}+8\sqrt{6},\mathrm{k}>0$, touch internally at the point $P(\alpha ,\beta )$, then $(\alpha +\sqrt{3}{)}^2+(\beta +\sqrt{6}{)}^2$ is equal to

Q29.Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve $4x^3-3x{y}^2+6x^2-5xy-8y^2+9x+14=0$ at the point $(-2,3)$ be A. Then 8A is equal to

Q30.Let $x=\sin \left(2{\tan }^{-1}\alpha \right)$ and $y=\sin \left(\frac{1}{2}{\tan }^{-1}\frac{4}{3}\right)$. If $S=\left\{\alpha \in R:y^2=1-x\right\}$, then ${\sum }_{\alpha \in S}16{\alpha }^3$ is equal to