JEE Main 2023 · 29 Jan 2023 · Shift 2

Q1.Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of $\frac{1}{2}$ day. If both A and B simultaneously start undergo radio activity at the same time with initial mass 320 g each, how many total atoms of A a …

Q2.At 300 K, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha +5}{\alpha }}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be (used $\pi =\frac{22}{7}$)

Q3.The ratio of de-Broglie wavelength of an $\alpha$-particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{\mathrm{m}}}$, the value of m is

Q4.For the given logic gates combination, the correct truth table will be

Q5.The time taken by an object to slide down $45^{\circ }$ rough inclined plane is $n$ times as it takes to slide down a perfectly smooth $45^{\circ }$ incline plane. The coefficient of kinetic friction between the object and the incline plane is

Q6.Force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:

Q7.A fully loaded boeing aircraft has a mass of $5.4\times 10^5\mathrm{kg}$. Its total wing area is $500{\mathrm{m}}^2$. It is in level flight with a speed of $1080\mathrm{km}/\mathrm{h}$. If the density of air $\rho$ is $1.2\mathrm{kg}{\mathrm{m}}^{-3}$, the …

Q8.Identify the correct statements from the following:
(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.
(C) Wor …

Q9.An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at $\mathrm{x}=+2\mathrm{m}$, its velocity is $-4\hat{\mathrm{j}}\mathrm{m}/\mathrm{s}$. The object's velocity (v) and acceleration (a) at …

Q10.A point charge $2\times 10^{-2}\mathrm{C}$ is moved from P to S in a uniform electric field of $30{\mathrm{NC}}^{-1}$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

Q11.The modulation index for an A.M. wave having maximum and minimum peak to peak voltages of 14 mV and 6 mV respectively is:

Q12.The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be:

Q13.With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is
(A) directly proportional to the length of the potentiometer wire
(B) directly proportional to the potential gradient of the wire
(C) inversely proportional …

Q14.A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

Q15.Given below are two statements:
Statement I: Electromagnetic waves are not deflected by electric and magnetic field.
Statement II: The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as …

Q16.Heat energy of 184 kJ is given to ice of mass 600 g at $-12^{\circ }C$. Specific heat of ice is $2222.3{\text{J kg}}^{-1\circ }{\text{C}}^{-1}$ and latent heat of ice in $336{\text{kJ/kg}}^{-1}$
(A) Final temperature of system will be $0^{\circ }C$.
(B) Final temperature of the system w …

Q17.For the given figures, choose the correct options:

Q18.The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

Q19.The equation of a circle is given by $x^2+y^2=a^2$, where a is the radius. If the equation is modified to change the origin other than $(0,0)$, then find out the correct dimensions of A and B in a new equation: $(x-At{)}^2+(y-\frac{t}{B}{)}^2=a^2$.
The dimensions of $t$ i …

Q20.A square loop of area $25{\text{cm}}^2$ has a resistance of $10\Omega$. The loop is placed in uniform magnetic field of magnitude 40.0 T. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly i …

Q21.When two resistance $R_1$ and $R_2$ connected in series and introduced into the left gap of a meter bridge and a resistance of $10\Omega$ is introduced into the right gap, a null point is found at 60 cm from left side. When $R_1$ and $R_2$ are connected in parallel and i …

Q22.A particle of mass 100 g is projected at time $t=0$ with a speed $20{\text{ms}}^{-1}$ at an angle $45^{\circ }$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $t=2\text{s}$ is found to be …

Q23.In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab at 5.00 mm. Travelling microscope has 20 divisions in one cm on m …

Q24.For a charged spherical ball, electrostatic potential inside the ball varies with r as $V=2a{r}^2+b$.
Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is $-\lambda a\epsilon$. The value of $\lambda$ is ______. …

Q25.A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of …

Q26.An inductor of inductance $2\mu \mathrm{H}$ is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x}F$, where the value of $x$ is ______.
(Tak …

Q27.A metal block of base area $0.20{\mathrm{m}}^2$ is placed on a table, as shown in figure. A liquid film of thickness 0.25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. If the viscosity of the …

Q28.A particle of mass 250 g executes a simple harmonic motion under a periodic force $\mathrm{F}=(-25\mathrm{x})\mathrm{N}$. The particle attains a maximum speed of $4\mathrm{m}/\mathrm{s}$ during its oscillation. The amplitude of the motion is ______ cm.

Q29.Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium-1) and 6.8 (medium 2), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence s …

Q30.A null point is found at 200 cm in potentiometer when cell in secondary circuit is shunted by $5\Omega$. When a resistance of $15\Omega$ is used for shunting null point moves to 300 cm. The internal resistance of the cell is ______ $\Omega$.

Q1.Given below are two statements:

Statement I: The decrease in first ionization enthalpy from B to Al is much larger than that from Al to Ga.
Statement II: The d orbitals in Ga are completely filled.
In the light of the above statements, choose the most appropriate answer from the …

Q2.Correct order of spin only magnetic moment of the following complex ions is:
(Given At. No. Fe: 26, Co:27)

Q3.The set of correct statements is:
(i) Manganese exhibits +7 oxidation state in its oxide.
(ii) Ruthenium and Osmium exhibit +8 oxidation in their oxides.
(iii) Sc shows +4 oxidation state which is oxidizing in nature.
(iv) Cr shows oxidising nature in +6 oxidation state.

Q4.An indicator 'X' is used for studying the effect of variation in concentration of iodide on the rate of reaction of iodide ion with ${\mathrm{H}}_2{\mathrm{O}}_2$ at room temp. The indicator 'X' forms blue colored complex with compound 'A' present in the solution. The indicator …

Q5.A doctor prescribed the drug Equanil to a patient. The patient was likely to have symptoms of which disease?

Q6.Find out the major product for the following reaction.

Q7.The one giving maximum number of isomeric alkenes on dehydrohalogenation reaction is (excluding rearrangement)

Q8.When a hydrocarbon A undergoes combustion in the presence of air, it requires 9.5 equivalents of oxygen and produces 3 equivalents of water. What is the molecular formula of A?

Q9.Find out the major products from the following reaction sequence.

Q10.According to MO theory the bond orders for ${\mathrm{O}}_2^{2-}$, CO and ${\mathrm{NO}}^{+}$ respectively, are

Q11.A solution of ${\mathrm{CrO}}_5$ in amyl alcohol has a....colour

Q12.The concentration of dissolved Oxygen in water for growth of fish should be more than $\underline{\mathrm{X}}$ ppm and Biochemical Oxygen Demand in clean water should be less than $\underline{Y}$ ppm. $X$ and $Y$ in ppm are, respectively.

Q13.Reaction of propanamide with ${\mathrm{Br}}_2/\mathrm{KOH}(\mathrm{aq})$ produces :

Q14.Following tetrapeptide can be represented as
(F, L, D, Y, I, Q, P are one letter codes for amino acids)

Q15.Which of the following relations are correct?
(A) $\Delta \mathrm{U}=\mathrm{q}+\mathrm{p}\Delta \mathrm{V}$
(B) $\Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T}\Delta \mathrm{S}$
(C) $\Delta \mathrm{S}=\frac{{\mathrm{q}}_{\text{rev }}}{\mathrm{T}}$
(D) …

Q16.The major component of which of the following ore is sulphide based mineral?

Q17.Given below are two statements:
Statement I : Nickel is being used as the catalyst for producing syn gas and edible fats.
Statement II : Silicon forms both electron rich and electron deficient hydrides.
In the light of the above statements, choose the most appropriate answer from …

Q18.On heating, ${\mathrm{LiNO}}_3$ gives how many compounds among the following?
${\mathrm{Li}}_2\mathrm{O},{\mathrm{N}}_2,{\mathrm{O}}_2,{\mathrm{LiNO}}_2,{\mathrm{NO}}_2$

Q19.At 298 K
${\mathrm{N}}_2(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})\rightleftharpoons 2{\mathrm{NH}}_3(\mathrm{g}),{\mathrm{K}}_1=4\times 10^5$ …

Q20.For conversion of compound $\mathrm{A}\to \mathrm{B}$, the rate constant of the reaction was found to be $4.6\times 10^{-5}\mathrm{L}{\mathrm{mol}}^{-1}{\mathrm{s}}^{-1}$. The order of the reaction is ____。

Q21.Total number of acidic oxides among
${\mathrm{N}}_2{\mathrm{O}}_3,{\mathrm{NO}}_2,{\mathrm{N}}_2\mathrm{O},{\mathrm{Cl}}_2{\mathrm{O}}_7,{\mathrm{SO}}_2,\mathrm{CO},\mathrm{CaO},{\mathrm{Na}}_2\mathrm{O}$ and NO is ____.

Q22.When 0.01 mol of an organic compound containing $60\%$ carbon was burnt completely, 4.4 g of $\mathrm{CO}{}_2$ was produced. The molar mass of compound is $\_\_\_\_$ ${\mathrm{g}\mathrm{mol}}^{-1}$ (Nearest integer)

Q23.The denticity of the ligand present in the Fehling's reagent is $\_\_\_\_$.

Q24.A metal M forms hexagonal close-packed structure. The total number of voids in 0.02 mol of it is $\_\_\_\_$ $\times 10^{21}$ (Nearest integer)
(Given ${\mathrm{N}}_{\mathrm{A}}=6.02\times 10^{23}$)

Q25.Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6\mathring{A}$. The radius of the third Bohr orbit of $\mathrm{He}{}^{+}$ is $\_\_\_\_$ picometer. (Nearest Integer)

Q26.The equilibrium constant for the reaction
$\mathrm{Zn}(\mathrm{s})+\mathrm{Sn}{}^{2+}(\mathrm{aq})\rightleftharpoons \mathrm{Zn}{}^{2+}(\mathrm{aq})+\mathrm{Sn}(\mathrm{s})$ is $1\times 10^{20}$ at 298 K. The magnitude of standard electrode potential of $\mathrm{Sn}/\mathrm{Sn}{}^{2+}$ if $E_{\mathrm{Zn}{}^{2+}/\mathrm{Zn}}^{\mathrm{o}}=-0.76\mathrm{V}$ is
$\_\_\_\_$ …

Q27.The volume of HCl, containing $73{\mathrm{g}\mathrm{L}}^{-1}$, required to completely neutralise NaOH obtained by reacting 0.69 g of metallic sodium with water, is
$\_\_\_\_$ mL. (Nearest Integer)
(Given: molar Masses of $\mathrm{Na}$, $\mathrm{Cl}$, $\mathrm{O}$, $\mathrm{H}$ are 23, 35.5, 16 and …

Q28.Match List I with List II:
List-I: A. Elastomeric polymer B. Fibre Polymer C. Thermosetting Polymer D. Thermoplastic Polymer
List-II: I. Urea formaldehyde resin II. Polystyrene III. Polyester IV. Neoprene
Choose the correct answer from the options given below:

Q1.The statement $\mathrm{B}\Rightarrow ((\sim \mathrm{A})\vee \mathrm{B})$ is equivalent to :

Q2.Shortest distance between the lines $\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}$ and $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}$ is

Q3.If $\vec{a}=\hat{i}+2\hat{k},\vec{b}=\hat{i}+\hat{j}+\hat{k},\vec{c}=7\hat{i}-3\hat{j}+4\hat{k}$,
$\overrightarrow{\mathrm{r}}\times \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}}\times \overrightarrow{\mathrm{c}}=\overrightarrow{0}$ and …

Q4.Let $\mathrm{S}=\left\{{\mathrm{w}}_1,{\mathrm{w}}_2,\dots .\right\}$ be the sample space associated to a random experiment. Let $\mathrm{P}\left({\mathrm{w}}_{\mathrm{n}}\right)=\frac{\mathrm{P}\left({\mathrm{w}}_{\mathrm{n}-1}\right)}{2},n\ge 2$. Let …

Q5.The value of the integral ${\int }_1^2\left(\frac{t^4+1}{t^6+1}\right)dt$ is :

Q6.Let K be the sum of the coefficients of the odd powers of x in the expansion of $(1+\mathrm{x}{)}^{99}$. Let a be the middle term in the expansion of ${\left(2+\frac{1}{\sqrt{2}}\right)}^{200}$. If …

Q7.Let f and g be twice differentiable functions on R such that
${\mathrm{f}}^{\prime \prime }(\mathrm{x})={\mathrm{g}}^{\prime \prime }(\mathrm{x})+6\mathrm{x}$
${\mathrm{f}}^{\prime }(1)=4{\mathrm{g}}^{\prime }(1)-3=9$
$\mathrm{f}(2)=3\mathrm{g}(2)=12$
Then which of the following i …

Q8.The set of all values of $t\in \mathbb{R}$, for which the matrix

i …

Q9.The set of all values of $\lambda$ for which the equation ${\cos }^{2}2\mathrm{x}-2{\sin }^4\mathrm{x}-2{\cos }^2\mathrm{x}=\lambda$

Q10.The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is :

Q11.The plane $2\mathrm{x}-\mathrm{y}+\mathrm{z}=4$ intersects the line segment joining the points $\mathrm{A}(\mathrm{a},-2,4)$ and $\mathrm{B}(2,\mathrm{b},-3)$ at the point C in the ratio $2:1$ and the distance of the point C from the origin is $\sqrt{5}$. If …

Q12.Let $\vec{a}=4\hat{i}+3\hat{j}$ and $\vec{b}=3\hat{i}-4\hat{j}+5\hat{k}$ and $\vec{c}$ is a vector such that $\vec{c}\cdot (\vec{a}\times \vec{b})+25=0$, $\vec{c}\cdot (\hat{i}+\hat{j}+\hat{k})=4$ and projection of $\vec{c}$ on $\vec{a}$ is 1, then the projection of …

Q13.If the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{1}$ and $\frac{x-a}{2}=\frac{y+2}{3}=\frac{z-3}{1}$ intersect at the point P, then the distance of the point P from the plane $z=a$ is:

Q14.The value of the integral ${\int }_{1/2}^2\frac{{\tan }^{-1}x}{x}dx$ is equal to

Q15.If the tangent at a point P on the parabola $y^2=3x$ is parallel to the line $x+2y=1$ and the tangents at the points Q and R on the ellipse $\frac{x^2}{4}+\frac{y^2}{1}=1$ are perpendicular to the line $x-y=2$, then the area of the triangle PQR is:

Q16.Let $y=y(x)$ be the solution of the differential equation $x{\log }_{e}x\frac{dy}{dx}+y=x^2{\log }_{e}x$, $(x>1)$. If $y(2)=2$, then $y(e)$ is equal to

Q17.The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

Q18.Let R be a relation defined on $\mathbb{N}$ as a R b if $2a+3b$ is a multiple of 5, $a,b\in \mathbb{N}$. Then R is

Q19.Consider a function $f:\mathbb{N}\to \mathbb{R}$, satisfying $f(1)+2f(2)+3f(3)+\dots +xf(x)=x(x+1)f(x)$; $x\ge 2$ with $f(1)=1$. Then $\frac{1}{f(2022)}+\frac{1}{f(2028)}$ is equal to

Q20.The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is

Q21.A triangle is formed by the tangents at the point $(2,2)$ on the curves $y^2=2x$ and $x^2+y^2=4x$, and the line $x+y+2=0$. If r is the radius of its circumcircle, then $r^2$ is equal to

Q22.A circle with centre $(2,3)$ and radius 4 intersects the line $x+y=3$ at the points P and Q. If the tangents at P and Q intersect at the point $S(\alpha ,\beta )$, then $4\alpha -7\beta$ is equal to

Q23.Let $a_1=b_1=1$ and $a_n=a_{n-1}+(n-1)$, $b_n=b_{n-1}+a_{n-1}$, $\forall n\ge 2$. If $S={\sum }_{n=1}^{10}\frac{b_n}{2^n}$ and $T={\sum }_{n=1}^8\frac{n}{2^{n-1}}$, then $2^7(2S-T)$ is equal to

Q24.If the equation of the normal to the curve $\mathrm{y}=\frac{\mathrm{x}-\mathrm{a}}{(\mathrm{x}+\mathrm{b})(\mathrm{x}-2)}$ at the point $(1,-3)$ is $\mathrm{x}-4\mathrm{y}=13$, then the value of $\mathrm{a}+\mathrm{b}$ is equal to ______.

Q25.Let A be a symmetric matrix such that $|\mathrm{A}|=2$ and $\left[\begin{array}{ll}2& 1\\ 3& \frac{3}{2}\end{array}\right]\mathrm{A}=\left[\begin{array}{ll}1& 2\\ \alpha & \beta \end{array}\right]$. If the sum of the diagonal elements of A is s, then …

Q26.Let $\{a_k\}$ and $\{b_k\}$, $k\in \mathbb{N}$, be two G.P.s with common ratio $r_1$ and $r_2$ respectively such that ${\mathrm{a}}_1={\mathrm{b}}_1=4$ and ${\mathrm{r}}_1<{\mathrm{r}}_2$. Let …

Q27.Let $\mathrm{X}=\{11,12,13,\dots ,40,41\}$ and $\mathrm{Y}=\{61,62,63,\dots ,90,91\}$ be the two sets of observations. If $\bar{x}$ and $\bar{y}$ are their respective means and ${\sigma }^2$ is the variance of all the observations in $\mathrm{X}\cup \mathrm{Y}$, …

Q28.Let $\alpha =8-14\mathrm{i}$, $\mathrm{A}=\left\{\mathrm{z}\in \mathbb{C}:\frac{\alpha \mathrm{z}-\bar{\alpha }\overline{\mathrm{z}}}{{\mathrm{z}}^2-(\overline{\mathrm{z}}{)}^2-112\mathrm{i}}=1\right\}$ and …

Q29.Let ${\alpha }_1,{\alpha }_2,\dots ,{\alpha }_7$ be the roots of the equation $x^7+3{\mathrm{x}}^5-13{\mathrm{x}}^3-15\mathrm{x}=0$ and $|{\alpha }_1|\ge |{\alpha }_2|\ge \dots \ge |{\alpha }_7|$.

Then …