JEE Main 2022 · 26 Jul 2022 · Shift 2

Q1.Two projectiles are thrown with same initial velocity making an angle of $45^{\circ }$ and $30^{\circ }$ with the horizontal respectively. The ratio of their respective ranges will be

Q2.A ball of mass 0.15 kg hits the wall with its initial speed of $12{\mathrm{ms}}^{-1}$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time duration of the contact of ball with the wall.

Q3.A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be:

Q4.Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere A and …

Q5.The oscillating magnetic field in a plane electromagnetic wave is given by ${\mathrm{B}}_{\mathrm{y}}=5\times 10^{-6}\sin 1000\pi \left(5\mathrm{x}-4\times 10^8\mathrm{t}\right)$ T. The amplitude of electric field will be:

Q6.Light travels in two media ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ with speeds $1.5\times 10^8{\mathrm{ms}}^{-1}$ and $2.0\times 10^8{\mathrm{ms}}^{-1}$ respectively. The critical angle between them is:

Q7.A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be:
(Take radius of earth $=6400\mathrm{km}$ and $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

Q8.The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V respectively. The percentage modulation index will be:

Q9.A nucleus of mass M at rest splits into two parts having masses $\frac{{\mathrm{M}}^{\prime }}{3}$ and $\frac{2{\mathrm{M}}^{\prime }}{3}$ (${\mathrm{M}}^{\prime }<\mathrm{M}$). The ratio of de Broglie wavelength of two parts will be:

Q10.An ice cube of dimensions $60\mathrm{cm}\times 50\mathrm{cm}\times 20\mathrm{cm}$ is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at $0^{\circ }\mathrm{C}$ of temperature is brought to a room of temperature $40^{\circ }\mathrm{C}$. The …

Q11.A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :

Q12.A transverse wave is represented by $y=2\sin (\omega t-kx)$ cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be :

Q13.A battery of 6 V is connected to the circuit as shown below. The current I drawn from the battery is :

Q14.A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key 'K' is closed, the total energy stored across the combination is $E_1$. Now key 'K' is opened and dielectric of dielectric constant 5 is introduced betw …

Q15.Two concentric circular loops of radii $r_1=30$ cm and $r_2=50$ cm are placed in X-Y plane as shown in the figure. A current $I=7$ A is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :

Q16.A velocity selector consists of electric field $\vec{E}=E\hat{k}$ and magnetic field $\vec{B}=B\hat{j}$ with $B=12$ mT. The value E required for an electron of energy 728 eV moving along the positive x-axis to pass undeflected is :
(Given, mass of electron …

Q17.Two masses $M_1$ and $M_2$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_2$ is twice that of $M_1$, the acceleration of the system is $a_1$. When the mass $M_2$ is thrice that of $M_1$, the acceleration o …

Q18.Mass numbers of two nuclei are in the ratio of $4:3$. Their nuclear densities will be in the ratio of

Q19.The area of cross section of the rope used to lift a load by a crane is $2.5\times 10^{-4}$ m${}^2$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should …

Q20.If $\vec{A}=(2\hat{i}+3\hat{j}-\hat{k})$ m and $\vec{B}=(\hat{i}+2\hat{j}+2\hat{k})$ m. The magnitude of component of vector $\vec{A}$ along vector $\vec{B}$ will be ______ m.

Q21.The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ______ m.

Given, the length of the rod is $10\sqrt{3}$ m.

Q22.In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle $60^{\circ }$ at the side AC, the refracted light beam just grazes along face AC. The refractive index of the liquid $n=\frac{\sqrt{x}}{4}$. The value of …

Q23.Two lighter nuclei combine to form a comparatively heavier nucleus by the relation given below:
${}_1^2\mathrm{X}+{}_1^2\mathrm{X}={}_2^4\mathrm{Y}$
The binding energies per nucleon ${}_1^2\mathrm{X}$ and ${}_2^4\mathrm{Y}$ are 1.1 MeV and 7.6 MeV respect …

Q24.A uniform heavy rod of mass 20 kg, Cross sectional area $0.4{\mathrm{m}}^2$ and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $\mathrm{x}\times 10^{-9}\mathrm{m}$. The value of x is ______. …

Q25.The typical transfer characteristic of a transistor in CE configuration is shown in figure. A load resistor of $2\mathrm{k}\Omega$ is connected in the collector branch of the circuit used. The input resistance of the transistor is $0.50\mathrm{k}\Omega$. The voltage gain of the …

Q26.Three point charges of magnitude $5\mu \mathrm{C}$, $0.16\mu \mathrm{C}$ and $0.3\mu \mathrm{C}$ are located at the vertices $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$ of a right angled triangle whose sides are $\mathrm{AB}=3\mathrm{cm}$, $\mathrm{BC}=3\sqrt{2}\mathrm{cm}$ a …

Q27.In a coil of resistance $8\Omega$, the magnetic flux due to an external magnetic field varies with time as $\varphi =\frac{2}{3}\left(9-t^2\right)$. The value of total heat produced in the coil, till the flux becomes zero, will be ______ J.

Q28.A potentiometer wire of length 300 cm is connected in series with a resistance $780\Omega$ and a standard cell of emf 4 V. A constant current flows through potentiometer wire. The length of the null point for cell of emf 20 mV is found to be 60 cm. The resistance of the potentio …

Q29.As per given figures, two springs of spring constants K and 2K are connected to mass m. If the period of oscillation in figure (a) is 3 s, then the period of oscillation in figure (b) will be $\sqrt{\mathrm{x}}$ s. The value of $x$ is ______.

Q1.Hemoglobin contains $0.34\%$ of iron by mass. The number of Fe atoms in 3.3 g of hemoglobin is :
(Given : Atomic mass of Fe is $56\mathrm{u}$, ${\mathrm{N}}_{\mathrm{A}}$ is $6.022\times 10^{23}{\mathrm{mol}}^{-1}$)

Q2.Arrange the following in increasing order of their covalent character.
(A) ${\mathrm{CaF}}_2$
(B) ${\mathrm{CaCl}}_2$
(C) ${\mathrm{CaBr}}_2$
(D) ${\mathrm{CaI}}_2$
Choose the correct answer from the options given below.

Q3.Class XII students were asked to prepare one litre of buffer solution of pH 8.26 by their chemistry teacher. The amount of ammonium chloride to be dissolved by the student in 0.2 M ammonia solution to make one litre of the buffer is (Given …

Q4.At $30^{\circ }\mathrm{C}$, the half life for the decomposition of ${\mathrm{AB}}_2$ is 200 s and is independent of the initial concentration of ${\mathrm{AB}}_2$. The time required for $80\%$ of the ${\mathrm{AB}}_2$ to decompose is (Given: $\log 2=0.30$; $\log 3=0.48$)

Q5.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Finest gold is red in colour, as the size of the particles increases, it appears purple then blue and finally gold.
Assertion R : The colour of the colloidal solut …

Q6.The metal that has very low melting point and its periodic position is closer to a metalloid is :

Q7.The metal that is not extracted from its sulphide ore is :

Q8.The products obtained from a reaction of hydrogen peroxide and acidified potassium permanganate are

Q9.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : LiF is sparingly soluble in water.
Reason R : The ionic radius of ${\mathrm{Li}}^{+}$ ion is smallest among its group members, hence has least hydration enthalpy.
In …

Q10.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Boric acid is a weak acid
Reason R : Boric acid is not able to release ${\mathrm{H}}^{+}$ ion on its own. It receives ${\mathrm{OH}}^{-}$ ion from water and releases …

Q11.The metal complex that is diamagnetic is (Atomic number : Fe, 26; Cu, 29)

Q12.The correct decreasing order of priority of functional groups in naming an organic compound as per IUPAC system of nomenclature is :

Q13.Which of the following is not an example of benzenoid compound?

Q14.Hydrolysis of which compound will give carbolic acid?

Q15.Consider the above reaction and predict the major product.

Q16.The correct sequential order of the reagents for the given reaction is :

Q17.Vulcanization of rubber is carried out by heating a mixture of :

Q18.Animal starch is the other name of :

Q19.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A :Phenolphthalein is a pH dependent indicator, remains colourless in acidic solution and gives pink colour in basic medium
Reason R : Phenolphthalein is a weak acid. …

Q20.A 10 g mixture of hydrogen and helium is contained in a vessel of capacity $0.0125{\mathrm{m}}^3$ at 6 bar and $27^{\circ }\mathrm{C}$. The mass of helium in the mixture is
____ g. (nearest integer)

Given : $\mathrm{R}=8.3{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$ (Atomic masse …

Q21.Consider an imaginary ion ${}_{22}^{48}{\mathrm{X}}^{3-}$. The nucleus contains ' a '% more neutrons than the number of electrons in the ion. The value of ' $a$ ' is ____ .
[nearest integer]

Q22.For the reaction
${\mathrm{H}}_2{\mathrm{F}}_2(\mathrm{g})\to {\mathrm{H}}_2(\mathrm{g})+{\mathrm{F}}_2(\mathrm{g})$
$\Delta \mathrm{U}=-59.6\mathrm{kJ}{\mathrm{mol}}^{-1}$ at $27^{\circ }\mathrm{C}$.
The enthalpy change for the above reaction is (-)
____ …

Q23.The elevation in boiling point for 1 molal solution of non-volatile solute A is 3 K . The depression in freezing point for 2 molal solution of A in the same solvent is 6 K . The ratio of ${\mathrm{K}}_{\mathrm{b}}$ and ${\mathrm{K}}_{\mathrm{f}}$ i.e., …

Q24.20 mL of 0.02 M hypo solution is used for the titration of 10 mL of copper sulphate solution, in the presence of excess of KI using starch as an indicator. The molarity of ${\mathrm{Cu}}^{2+}$ is found to be
____ $\times 10^{-2}\mathrm{M}$ [nearest integer]

Given : …

Q25.The number of non-ionisable protons present in the product B obtained from the following reaction is ____.
$\mathrm{C}{}_2\mathrm{H}{}_5\mathrm{OH}+\mathrm{PCl}{}_3\to \mathrm{C}{}_2\mathrm{H}{}_5\mathrm{Cl}+\mathrm{A}$
$\mathrm{A}+\mathrm{PCl}{}_3\to \mathrm{B}$

Q26.The spin-only magnetic moment value of the compound with strongest oxidizing ability among $\mathrm{MnF}{}_4$, $\mathrm{MnF}{}_3$ and $\mathrm{MnF}{}_2$ is ____ B.M. [nearest integer]

Q27.Total number of isomers (including stereoisomers) obtain on monochlorination of methylcyclohexane is ____.

Q28.A 100 mL solution of $\mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{MgBr}$ on treatment with methanol produces 2.24 mL of a gas at STP. The weight of gas produced is ____ mg. [nearest integer]

Q29.How many of the following drugs is/are example(s) of broad spectrum antibiotic? Ofloxacin, Penicillin G, Terpineol, Salvarsan

Q1.The minimum value of the sum of the squares of the roots of $x^2+(3-a)x+1=2a$ is:

Q2.If $z=x+iy$ satisfies $|z|-2=0$ and $|z-i|-|z+5i|=0$, then

Q3.Let $A=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}{9}^2& -10^2& 11^2\\ 12^2& 13^2& -14^2\\ -15^2& 16^2& 17^2\end{array}\right]$, then the value of $A^{\prime }BA$ is:

Q4.${\sum }_{\begin{array}{c}i,j=0\\ i\ne j\end{array}}^n{}^n{C}_i{}^n{C}_j$ is equal to

Q5.Let P and Q be any points on the curves $(x-1{)}^2+(y+1{)}^2=1$ and $y=x^2$, respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interval

Q6.If the maximum value of $a$, for which the function $f_a(x)={\tan }^{-1}2x-3ax+7$ is non-decreasing in $\left(-\frac{\pi }{6},\frac{\pi }{6}\right)$, is $\overline{a}$, then $f_{\overline{a}}\left(\frac{\pi }{8}\right)$ is equal to

Q7.Let $\beta ={\lim }_{x\to 0}\frac{\alpha x-\left(e^{3x}-1\right)}{\alpha x\left(e^{3x}-1\right)}$ for some $\alpha \in \mathbb{R}$. Then the value of $\alpha +\beta$ is:

Q8.The value of ${\log }_{e}2\frac{d}{dx}\left({\log }_{\cos x}\mathrm{cosec}x\right)$ at $x=\frac{\pi }{4}$ is

Q9.${\int }_0^{20\pi }(|\sin x|+|\cos x|{)}^{2}dx$ is equal to:

Q10.Let the solution curve $y=f(x)$ of the differential equation $\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt{1-x^2}},x\in (-1,1)$ pass through the origin. Then ${\int }_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}}f(x)dx$ is equal to

Q11.The acute angle between the pair of tangents drawn to the ellipse $2x^2+3y^2=5$ from the point $(1,3)$ is

Q12.The equation of a common tangent to the parabolas $y=x^2$ and $y=-(x-2{)}^2$ is

Q13.Let the abscissae of the two points P and Q on a circle be the roots of $x^2-4x-6=0$ and the ordinates of P and Q be the roots of $y^2+2y-7=0$. If PQ is a diameter of the circle $x^2+y^2+2ax+2by+c=0$, then the value of $(a+b-c)$ is

Q14.If the line $x-1=0$, is a directrix of the hyperbola $k{x}^2-y^2=6$, then the hyperbola passes through the point

Q15.A vector $\overrightarrow{a}$ is parallel to the line of intersection of the plane determined by the vectors $\hat{i},\hat{i}+\hat{j}$ and the plane determined by the vectors $\hat{i}-\hat{j},\hat{i}+\hat{k}$. The obtuse angle between $\vec{a}$ and the vector …

Q16.If $0<x<\frac{1}{\sqrt{2}}$ and $\frac{{\sin }^{-1}x}{\alpha }=\frac{{\cos }^{-1}x}{\beta }$, then a value of $\sin \left(\frac{2\pi \alpha }{\alpha +\beta }\right)$ is

Q17.Negation of the Boolean expression $p\iff (q\Rightarrow p)$ is

Q18.Let X be a binomially distributed random variable with mean 4 and variance $\frac{4}{3}$. Then $54P(X\le 2)$ is equal to

Q19.The integral $\int \frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}}\sin 2x\right)}dx$ is equal to

Q20.The area bounded by the curves $y=\left|x^2-1\right|$ and $y=1$ is

Q21.Let $A=\{1,2,3,4,5,6,7\}$ and $B=\{3,6,7,9\}$. Then the number of elements in the set $\{C\subseteq A:C\cap B\ne \varphi \}$ is

Q22.The largest value of a, for which the perpendicular distance of the plane containing the lines $\vec{r}=(\hat{i}+\hat{j})+\lambda (\hat{i}+a\hat{j}-\hat{k})$ and $\vec{r}=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-a\hat{k})$ from the point $(2,1,4)$ is $\sqrt{3}$, is

Q23.Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits $1,2,3,4,5$ and 6 without repetition of digits. Then the total number of such numbers is

Q24.If ${\sum }_{k=1}^{10}\frac{k}{k^4+k^2+1}=\frac{m}{n}$, where $m$ and $n$ are coprime, then $m+n$ is equal to

Q25.If the sum of solutions of the system of equations $2{\sin }^2\theta -\cos 2\theta =0$ and $2{\cos }^2\theta +3\sin \theta =0$ in the interval $[0,2\pi ]$ is $\mathrm{k}\pi$, then k is equal to ______.

Q26.The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then …

Q27.The plane passing through the line $\mathrm{L}:\ell \mathrm{x}-\mathrm{y}+3(1-\ell )\mathrm{z}=1,x+2\mathrm{y}-\mathrm{z}=2$ and perpendicular to the plane $3x+2y+z=6$ is $3x-8y+7z=4$. If $\theta$ is the acute angle between the line L and the y-axis, then …

Q28.Suppose $y=y(x)$ be the solution curve to the differential equation $\frac{dy}{dx}-y=2-e^{-x}$ such that ${\lim }_{x\to \infty }y(x)$ is finite. If $a$ and $b$ are respectively the $x$ and y-intercepts of the tangent to the curve at $\mathrm{x}=0$, then the value of …

Q29.Different A.P.'s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P's having at least 3 terms and at most 33 terms is ______.

Q30.The number of matrices $A=\left[\begin{array}{ll}a& b\\ c& d\end{array}\right]$, where $\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\in \{-1,0,1,2,3,\dots ,10\}$, such that $\mathrm{A}={\mathrm{A}}^{-1}$, is ______.