JEE Main 2023 · 08 Apr 2023 · Shift 2

Q1.Electric potential at a point 'P' due to a point charge of $5\times 10^{-9}\mathrm{C}$ is 50 V. The distance of 'P' from the point charge is:
(Assume, $\frac{1}{4\pi {\epsilon }_0}=9\times 10^{+9}{\mathrm{Nm}}^2{\mathrm{C}}^{-2}$)

Q2.For particle P revolving round the centre O with radius of circular path r and angular velocity $\omega$, as shown in below figure, the projection of OP on the x-axis at time t is

Q3.For a given transistor amplifier circuit in CE configuration ${\mathrm{V}}_{\mathrm{CC}}=1\mathrm{V},{\mathrm{R}}_{\mathrm{c}}=1\mathrm{k}\Omega ,{\mathrm{R}}_{\mathrm{b}}=100\mathrm{k}\Omega$ and $\beta =100$. Value of base current ${\mathrm{I}}_{\mathrm{b}}$ is

Q4.The trajectory of projectile, projected from the ground is given by $y=x-\frac{x^2}{20}$. Where $x$ and $y$ are measured in meter. The maximum height attained by the projectile will be.

Q5.A radio-active material is reduced to 1/8 of its original amount in 3 days. If $8\times 10^{-3}\mathrm{kg}$ of the material is left after 5 days. The initial amount of the material is

Q6.The equivalent resistance between A and B as shown in figure is:

Q7.A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying the load is $250{\mathrm{cm}}^2$. The maximum pressure the smaller piston would have to bear is [Assume $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$]:

Q8.The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be-

Q9.The temperature at which the kinetic energy of oxygen molecules becomes double than its value at $27^{\circ }\mathrm{C}$ is

Q10.The acceleration due to gravity at height h above the earth if $\mathrm{h}\ll \mathrm{R}$ (radius of earth) is given by

Q11.Work done by a Carnot engine operating between temperatures $127^{\circ }\mathrm{C}$ and $27^{\circ }\mathrm{C}$ is 2 kJ. The amount of heat transferred to the engine by the reservoir is:

Q12.Given below are two statements:

Statement I: Area under velocity- time graph gives the distance travelled by the body in a given time.

Statement II: Area under acceleration- time graph is equal to the change in velocity- in the given time.

In the light of given statements, cho …

Q13.The waves emitted when a metal target is bombarded with high energy electrons are

Q14.The width of fringe is 2 mm on the screen in a double slits experiment for the light of wavelength of 400 nm . The width of the fringe for the light of wavelength 600 nm will be:

Q15.Given below are two statements; one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Electromagnets are made of soft iron.

Reason R: Soft iron has high permeability and low retentivity.

In the light of above, statements, choose the most appropriate …

Q16.In photo electric effect

A. The photocurrent is proportional to the intensity of the incident radiation.

B. Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light.

C. Max. K.E with which photoelectrons are emitted depends on the …

Q17.An emf of 0.08 V is induced in a metal rod of length 10 cm held normal to a uniform magnetic field of 0.4 T , when moves with a velocity of:

Q18.A bullet of mass 0.1 kg moving horizontally with speed $400{\mathrm{ms}}^{-1}$ hits a wooden block of mass 3.9 kg kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 m before coming to rest. The coefficient of friction between the block and th …

Q19.The power radiated from a linear antenna of length $l$ is proportional to

(Given, $\lambda =$ Wavelength of wave):

Q20.A series combination of resistor of resistance 100 $\Omega$, inductor of inductance 1 H and capacitor of capacitance $6.25\mu \mathrm{F}$ is connected to an ac source. The quality factor of the circuit will be ____.

Q21.A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz . The length of the string producing a fundamental frequency of 180 Hz will be ____\ cm.

Q22.The ratio of wavelength of spectral lines ${\mathrm{H}}_{\alpha }$ and ${\mathrm{H}}_{\beta }$ in the Balmer series is $\frac{\mathrm{x}}{20}$. The value of x is

Q23.The number density of free electrons in copper is nearly $8\times 10^{28}{\mathrm{m}}^{-3}$. A copper wire has its area of cross section $=2\times 10^{-6}{\mathrm{m}}^2$ and is carrying a current of 3.2 A . The drift speed of the electrons is ____ …

Q24.A steel rod of length 1 m and cross sectional area $10^{-4}{\mathrm{m}}^2$ is heated from $0^{\circ }\mathrm{C}$ to $200^{\circ }\mathrm{C}$ without being allowed to extend or bend. The compressive tension produced in the rod is $\_\_\_\_$ $\times 10^4\mathrm{N}$.
(Given Yo …

Q25.A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\mathrm{m}/\mathrm{s}$ (as shown in figure). Maximum height with respect to the initial position covered by it will be $\_\_\_\_$ cm.

Q26.A body of mass 5 kg is moving with a momentum of $10\mathrm{kg}{\mathrm{ms}}^{-1}$. Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the body is $\_\_\_\_$ J.

Q27.A 600 pF capacitor is charged by 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. Electrostatic energy lost in the process is $\_\_\_\_$ $\mu \mathrm{J}$.

Q28.Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance o …

Q29.The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field at distance $r$ from the centre of coil on its axis is $\sqrt{x}:1$. The value of x is $\_\_\_\_$

Q1.Which of the following have same number of significant figures ?
(A) 0.00253
(B) 1.0003
(C) 15.0
(D) 163

Choose the correct answer from the options given below

Q2.Which of these reactions is not a part of breakdown of ozone in stratosphere?

Q3.The correct IUPAC nomenclature for the following compound is

Q4.Arrange the following gases in increasing order of van der Waals constant 'a'
A. Ar
B. ${\mathrm{CH}}_4$
C. ${\mathrm{H}}_2\mathrm{O}$
D. ${\mathrm{C}}_6{\mathrm{H}}_6$

Choose the correct option from the following :-

Q5.Given below are two statements :-

Statement I :- Methyl orange is a weak acid.
Statement II :- The benzenoid form of methyl orange is more intense/deeply coloured than the quinonoid form.
In the light of the above statement, choose the most appropriate answer from the options gi …

Q6.Given below are two statements :-

Statement I :- In redox titration, the indicators used are sensitive to change in pH of the solution.
Statement II :- In acid-base titration, the indicators used are sensitive to change in oxidation potential.
In the light of the above statement …

Q7.The product (P) formed from the following multistep reaction is :-

Q8.The correct reaction profile diagram for a positive catalyst reaction.

Q9.Which of the following can reduce decomposition of ${\mathrm{H}}_2{\mathrm{O}}_2$ on exposure to light

Q10.The statement/s which are true about antagonists from the following is/are :-
A. They bind to the receptor site.
B. Get transferred inside the cell for their action.
C. Inhibit the natural communication of the body.
D. Mimic the natural messenger.

Choose the correct answer from …

Q11.Major product 'P' formed in the following reaction is :-

Q12.In Hall - Heroult process, the following is used for reducing ${\mathrm{Al}}_2{\mathrm{O}}_3$ :-

Q13.Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R
Assertion A :- Sodium is about 30 times as abundant as potassium in the oceans.
Reason R :- Potassium is bigger in size than sodium.
In the light of above statements, choose the …

Q14.Henry Moseley studied characteristic X-ray spectra of elements. The graph which represents his observation correctly is : (Given $\mathrm{v}=$ frequency of X -ray emitted; $\mathrm{Z}=$ atomic number)

Q15.The descending order of acidity for the following carboxylic acid is :
A. ${\mathrm{CH}}_3\mathrm{COOH}$
B. ${\mathrm{F}}_3\mathrm{C}-\mathrm{COOH}$
C. ${\mathrm{ClCH}}_2-\mathrm{COOH}$
D. ${\mathrm{FCH}}_2-\mathrm{COOH}$
E. ${\mathrm{BrCH}}_2-\mathrm{COOH}$

Choose t …

Q16.The correct order of reactivity of following haloarenes towards nucleophilic substitution with aqueous NaOH is :
A. (see structure)
B. (see structure)
C. (see structure)
D. (see structure)

Choose the correct answer from the options given below:

Q17.For a good quality cement, the ratio of lime to the total of the oxides of $\mathrm{Si}$, $\mathrm{Al}$ and Fe should be as close as to :

Q18.A compound ' X ' when treated with phthalic anhydride in presence of concentrated ${\mathrm{H}}_2{\mathrm{SO}}_4$ yields ' Y '. ' Y ' is used as an acid/base indicator. ' X ' and ' Y ' are respectively:

Q19.The solubility product of ${\mathrm{BaSO}}_4$ is $1\times 10^{-10}$ at 298 K . The solubility of ${\mathrm{BaSO}}_4$ in $0.1\mathrm{M}{\mathrm{K}}_2{\mathrm{SO}}_4(\mathrm{aq})$ solution is ____ $\times 10^{-9}\mathrm{g}{\mathrm{L}}^{-1}$ (nearest integer).
Gi …

Q20.Coagulating value of electrolytes ${\mathrm{AlCl}}_3$ and NaCl for ${\mathrm{As}}_2{\mathrm{S}}_3$ are 0.09 and 50.04 respectively. The coagulating power of ${\mathrm{AlCl}}_3$ is $x$ times the coagulating power of NaCl . The value of $x$ is
____ :

Q21.The number of atomic orbitals from the following having 5 radial nodes is ____ .
$7\mathrm{s},7\mathrm{p},6\mathrm{s},8\mathrm{p},8\mathrm{d}$

Q22.For complete combustion of ethene.
${\mathrm{C}}_2{\mathrm{H}}_4(\mathrm{g})+3{\mathrm{O}}_2(\mathrm{g})\to 2{\mathrm{CO}}_2(\mathrm{g})+2{\mathrm{H}}_2\mathrm{O}(\mathrm{l})$ the amount of heat produced as measured in bomb calorimeter is …

Q23.The number of species from the following carrying a single lone pair on central atom Xenon is ____:
${\mathrm{XeF}}_5{}^{+},{\mathrm{XeO}}_3,{\mathrm{XeO}}_2{\mathrm{F}}_2,{\mathrm{XeF}}_5^{-},{\mathrm{XeO}}_3{\mathrm{F}}_2,{\mathrm{XeOF}}_4$, ${\mathrm{XeF}}_4$

Q24.If the boiling points of two solvents X and Y (having same molecular weights) are in the ratio 2 : 1 and their enthalpy of vaporizations are in the ratio $1:2$, then the boiling point elevation constant of X is $\underline{\mathrm{m}}$ times the boiling point elevation constant …

Q25.The sum of oxidation state of the metals in $\mathrm{Fe}(\mathrm{CO}{)}_5,{\mathrm{VO}}^{2+}$ and ${\mathrm{WO}}_3$ is ____:

Q26.The observed magnetic moment of the complex ${\left[\mathrm{Mn}(\underline{\mathrm{NCS}}{)}_6\right]}^{\mathrm{x}-}$ is 6.06 BM. The numerical value of x is ____:

Q27.The number of incorrect statements from the following is ____
A. The electrical work that a reaction can perform at constant pressure and temperature is equal to the reaction Gibbs energy.
B. ${\mathrm{E}}_{\text{cell }}^0$ is dependent on the pressure
C. …

Q28.The ratio of sigma and $\pi$ bonds present in pyrophosphoric acid is ____:

Q1.Let the mean and variance of 12 observations be $\frac{9}{2}$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $\frac{\mathrm{m}}{\mathrm{n}}$, where m and n are co-pri …

Q2.Let ${\mathrm{a}}_{\mathrm{n}}$ be the ${\mathrm{n}}^{\text{th}}$ term of the series $5+8+14+23+35+50+\dots$ and ${\mathrm{S}}_{\mathrm{n}}={\sum }_{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{k}}$. Then ${\mathrm{S}}_{30}-{\mathrm{a}}_{40}$ is equal to

Q3.Let P be the plane passing through the line $\frac{x-1}{1}=\frac{y-2}{-3}=\frac{z+5}{7}$ and the point $(2,4,-3)$. If the image of the point $(-1,3,4)$ in the plane P is $(\alpha ,\beta ,\gamma )$, then $\alpha +\beta +\gamma$ is equal to

Q4.Let $\mathrm{A}=\{\theta \in (0,2\pi ):\frac{1+2\mathrm{i}\sin \theta }{1-\mathrm{i}\sin \theta }$ is purely imaginary $\}$.

Then the sum of the elements in A is

Q5.The absolute difference of the coefficients of $x^{10}$ and $x^7$ in the expansion of ${\left(2x^2+\frac{1}{2x}\right)}^{11}$ is equal to

Q6.If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is $(6!)\mathrm{k}$, then k is equal to

Q7.Let S be the set of all values of $\theta \in [-\pi ,\pi ]$ for which the system of linear equations
$x+y+\sqrt{3}z=0$
$-x+(\tan \theta )y+\sqrt{7}z=0$
$x+y+(\tan \theta )z=0$
has non-trivial solution. Then $\frac{120}{\pi }{\sum }_{\theta \in \mathrm{s}}\theta$ is equal …

Q8.If the probability that the random variable X takes values x is given by $\mathrm{P}(\mathrm{X}=\mathrm{x})=\mathrm{k}(\mathrm{x}+1)3^{-\mathrm{x}},\mathrm{x}=0,1,2,3\dots$, where k is a constant, then $\mathrm{P}(\mathrm{X}\ge 2)$ is equal to

Q9.The value of $36\left(4{\cos }^2{9}^{\circ }-1\right)\left(4{\cos }^{2}27^{\circ }-1\right)\left(4{\cos }^{2}81^{\circ }-1\right)\left(4{\cos }^{2}243^{\circ }-1\right)$ is

Q10.The integral $\int \left({\left(\frac{x}{2}\right)}^x+{\left(\frac{2}{x}\right)}^x\right)\left(1+{\log }_e\frac{x}{2}\right)dx$ is equal to

Q11.The area of the quadrilateral ABCD with vertices $\mathrm{A}(2,1,1),\mathrm{B}(1,2,5),\mathrm{C}(-2,-3,5)$ and $\mathrm{D}(1,-6,-7)$ is equal to

Q12.For $\mathrm{a},\mathrm{b}\in \mathrm{Z}$ and $|\mathrm{a}-\mathrm{b}|\le 10$, let the angle between the plane $P$ : $ax+y-z=b$ and the line $l:\mathrm{x}-1=\mathrm{a}-\mathrm{y}=\mathrm{z}+1$ be ${\cos }^{-1}\left(\frac{1}{3}\right)$. If the distance of the point …

Q13.$25^{190}-19^{190}-8^{190}+2^{190}$ is divisible by

Q14.Let the vectors ${\overrightarrow{\mathrm{u}}}_1=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\mathrm{a}\hat{\mathrm{k}}$, ${\overrightarrow{\mathrm{u}}}_2=\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and …

Q15.Let O be the origin and OP and OQ be the tangents to the circle $x^2+y^2-6x+4y+8=0$ at the point P and Q on it. If the circumcircle of the triangle OPQ passes through the point $\left(\alpha ,\frac{1}{2}\right)$, then a value of $\alpha$ is

Q16.The negation of $(\mathrm{p}\wedge (\sim \mathrm{q}))\vee (\sim \mathrm{p})$ is equivalent to

Q17.If $\alpha >\beta >0$ are the roots of the equation $a{x}^2+bx+1=0$, and
${\lim }_{x\to \frac{1}{\alpha }}{\left(\frac{1-\cos \left(x^2+bx+a\right)}{2(1-\alpha x{)}^2}\right)}^{\frac{1}{2}}=\frac{1}{k}\left(\frac{1}{\beta }-\frac{1}{\alpha }\right)$, then $k$ is equal to

Q18.If $\mathrm{A}=\left[\begin{array}{cc}1& 5\\ \lambda & 10\end{array}\right]$, ${\mathrm{A}}^{-1}=\alpha \mathrm{A}+\beta \mathrm{I}$ and $\alpha +\beta =-2$, then $4{\alpha }^2+{\beta }^2+{\lambda }^2$ is equal to:

Q19.Let $\mathrm{A}(0,1)$, $\mathrm{B}(1,1)$ and $\mathrm{C}(1,0)$ be the mid-points of the sides of a triangle with incentre at the point D. If the focus of the parabola $y^2=4ax$ passing through D is $(\alpha +\beta \sqrt{2},0)$, where $\alpha$ and $\beta$ are rational numbers, …

Q20.Let $\mathrm{A}=\{1,2,3,4,5,6,7\}$. Then the relation $\mathrm{R}=\{(\mathrm{x},\mathrm{y})\in \mathrm{A}\times \mathrm{A}:\mathrm{x}+\mathrm{y}=7\}$ is

Q21.Let $[t]$ denote the greatest integer function. If ${\int }_0^{2.4}\left[x^2\right]dx=\alpha +\beta \sqrt{2}+\gamma \sqrt{3}+\delta \sqrt{5}$, where $\alpha ,\beta ,\gamma ,\delta$ are rational numbers, then $\alpha +\beta +\gamma +\delta$ is equal to ______.

Q22.Let k and m be positive real numbers such that the function $f(x)=\{\begin{array}{cc}3x^2+k\sqrt{x+1},& 0<x<1\\ m{x}^2+k^2,& x\ge 1\end{array}$ is differentiable for all $x>0$. Then $\frac{8f^{\prime }(8)}{f^{\prime }\left(\frac{1}{8}\right)}$ is equal to _ …

Q23.Let $0<\mathrm{z}<\mathrm{y}<\mathrm{x}$ be three real numbers such that $\frac{1}{\mathrm{x}},\frac{1}{\mathrm{y}},\frac{1}{\mathrm{z}}$ are in an arithmetic progression and $x$, $\sqrt{2}y$, $z$ are in a geometric progression. If $xy+yz+zx=\frac{3}{\sqrt{2}}xyz$, then …

Q24.If domain of the function
${\log }_e\left(\frac{6x^2+5x+1}{2x-1}\right)+{\cos }^{-1}\left(\frac{2x^2-3x+4}{3x-5}\right)$ is $(\alpha ,\beta )$
$\cup (\gamma ,\delta ]$, then $18\left({\alpha }^2+{\beta }^2+{\gamma }^2+{\delta }^2\right)$ is equal to ______.

Q25.Let m and n be the numbers of real roots of the quadratic equations $x^2-12x+[x]+31=0$ and $x^2-5|x+2|-4=0$ respectively, where $[x]$ denotes the greatest integer $\le x$. Then $m^2+mn+n^2$ is equal to ______.

Q26.The ordinates of the points P and Q on the parabola with focus $(3,0)$ and directrix $x=-3$ are in the ratio $3:1$. If $R(\alpha ,\beta )$ is the point of intersection of the tangents to the parabola at P and Q, then $\frac{{\beta }^2}{\alpha }$ is equal to ______.

Q27.Let the solution curve $x=x(y)$, $0<y<\frac{\pi }{2}$, of the differential equation $({\log }_e(\cos y){)}^2\cos ydx-(1+3x{\log }_e(\cos y))\sin ydy=0$ satisfy $x\left(\frac{\pi }{3}\right)=\frac{1}{2{\log }_{e}2}$. If $x\left(\frac{\pi }{6}\right)=\frac{1}{{\log }_{e}m-{\log }_{e}n}$, w …

Q28.Let $P_1$ be the plane $3x-y-7z=11$ and $P_2$ be the plane passing through the points $(2,-1,0)$, $(2,0,-1)$, and $(5,1,1)$. If the foot of the perpendicular drawn from the point $(7,4,-1)$ on the line of intersection of the planes $P_1$ and $P_2$ is …

Q29.Let $R=\{a,b,c,d,e\}$ and $S=\{1,2,3,4\}$. Total number of onto function $f:R\to S$ such that $f(a)\ne 1$, is equal to ______.

Q30.Let the area enclosed by the lines $x+y=2$, $y=0$, $x=0$ and the curve $f(x)=\min \left\{x^2+\frac{3}{4},1+[x]\right\}$ where $[x]$ denotes the greatest integer $\le x$, be A. Then the value of 12A is ______.