JEE Main 2023 · 31 Jan 2023 · Shift 2

Q1.The H amount of thermal energy is developed by a resistor in 10 s when a current of 4A is passed through it. If the current is increased to 16 A, the thermal energy developed by the resistor in 10 s will be:

Q2.A body is moving with constant speed, in a circle of radius 10 m. The body completes one revolution in 4 s. At the end of 3rd second, the displacement of body (in m) from its starting point is:

Q3.A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The height of the liquid in the bucket is:

Q4.A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the string is 400 N, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

Q5.For a solid rod, the Young's modulus of elasticity is $3.2\times 10^{11}{\mathrm{Nm}}^{-2}$ and density is $8\times 10^3\mathrm{kg}{\mathrm{m}}^{-3}$. The velocity of longitudinal wave in the rod will be.

Q6.A long conducting wire having a current I flowing through it, is bent into a circular coil of N turns. Then it is bent into a circular coil of $n$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to th …

Q7.Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:

Q8.Given below are two statements

Statement I: For transmitting a signal, size of antenna ( $l$ ) should be comparable to wavelength of signal (at least $l=\frac{\lambda }{4}$ in dimension).

Statement II: In amplitude modulation, amplitude of carrier wave remains constant (unchange …

Q9.The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by $50\%$. The percentage change in voltage sensitivity of the galvanometer will be:

Q10.If the two metals A and B are exposed to radiation of wavelength 350 nm. The work functions of metals A and B are 4.8 eV and 2.2 eV. Then choose the correct option

Q11.A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:

Q12.An alternating voltage source $V=260\sin (628t)$ is connected across a pure inductor of 5 mH. Inductive reactance in the circuit is:

Q13.Match List-I with List-II.

List-I:
A. Microwaves
B. UV rays
C. Infra-red rays
D. X-rays

List-II:
I. Physiotherapy
II. Treatment of cancer
III. Lasik eye surgery
IV. Aircraft navigation

Choose the correct answer from the option given below:

Q14.The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

Q15.Under the same load, wire A having length 5.0 m and cross section $2.5\times 10^{-5}{\mathrm{m}}^2$ stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of $3.0\times 10^{-5}{\mathrm{m}}^2$ stretches. The ratio of the Young's modulus …

Q16.Considering a group of positive charges, which of the following statements is correct?

Q17.A body of mass 10 kg is moving with an initial speed of $20m/s$. The body stops after 5 s due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity $g=10{\mathrm{ms}}^{-2}$)

Q18.A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$. Then the ratio of $\frac{C_P}{C_V}$ will be.

Q19.Given below are two statements:

Statement I: In a typical transistor, all three regions emitter, base and collector have same doping level.
Statement II: In a transistor, collector is the thickest and base is the thinnest segment.
In the light of the above statements, choose the …

Q20.A series LCR circuit consists of $R=80\Omega$, $X_L=100\Omega$, and $X_C=40\Omega$. The input voltage is $2500\cos (100\pi t)$ V. The amplitude of current, in the circuit, is ______ A.

Q21.Two light waves of wavelengths 800 and 600 nm are used in Young's double slit experiment to obtain interference fringes on a screen placed 7 m away from plane of slits. If the two slits are separated by 0.35 mm, then shortest distance from the central bright maximum to the point …

Q22.A water heater of power 2000 W is used to heat water. The specific heat capacity of water is 4200 J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$. The efficiency of heater is $70\%$. Time required to heat 2 kg of water from $10^{\circ }\mathrm{C}$ to $60^{\circ }\mathrm{C}$ is ______ s.
(Assu …

Q23.A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision between ball and floor is 0.5, after hitting the floor, the ball rebounds to a height of ______ m.

Q24.Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0.5 cm respectively. The densities of materials are in the ratio 3:5. The moment of inertia of these discs respectively about their diameters will be in the ratio o …

Q25.If the binding energy of ground state electron in a hydrogen atom is 13.6 eV, then, the energy required to remove the electron from the second excited state of ${\mathrm{Li}}^{2+}$ will be: $x\times 10^{-1}$ eV. The value of $x$ is ____.

Q26.For the given circuit, in the steady state, $|{\mathrm{V}}_{\mathrm{B}}-{\mathrm{V}}_{\mathrm{D}}|=$ ____ V.

Q27.Two parallel plate capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ each having capacitance of $10\mu \mathrm{F}$ are individually charged by a 100 V D.C. source. Capacitor ${\mathrm{C}}_1$ is kept connected to the source and a dielectric slab is inserted between it plates. Cap …

Q28.The displacement equations of two interfering waves are given by


respectively. The amplitude of the resultant wave is ____ cm.

Q29.Two bodies are projected from ground with same speeds $40{\mathrm{ms}}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^{\circ }$, with horizontal then sum of the maximum heights …

Q1.In the following halogenated organic compounds the one with maximum number of chlorine atoms in its structure is :

Q2.Incorrect statement for the use of indicators in acid-base titration is :

Q3.Which of the following compounds are not used as disinfectants?
(A) Chloroxylenol
(B) Bithional
(C) Veronal
(D) Prontosil
(E) Terpineol

Choose the correct answer from the options given below:

Q4.A hydrocarbon ' X ' with formula $\mathrm{C}{}_6\mathrm{H}{}_8$ uses two moles of $\mathrm{H}{}_2$ on catalytic hydrogenation of its one mole. On ozonolysis, 'X' yields two moles of methane dicarbaldehyde. The hydrocarbon ' X ' is :

Q5.Cyclohexylamine when treated with nitrous acid yields (P). On treating (P) with PCC results in (Q). When ( Q ) is heated with dil. NaOH we get ( R ) The final product $(\mathrm{R})$ is :

Q6.Given below are two statements :

Statement I: Upon heating a borax bead dipped in cupric sulphate in a luminous flame, the colour of the bead becomes green.
Statement II : The green colour observed is due to the formation of copper(I) metaborate.
In the light of the above statem …

Q7.Evaluate the following statements for their correctness.
(A) The elevation in boiling point temperature of water will be same for 0.1 M NaCl and 0.1 M urea.
(B) Azeotropic mixtures boil without change in their composition
(C) Osmosis always takes place from hypertonic to hypotoni …

Q8.Compound A, ${\mathrm{C}}_5{\mathrm{H}}_{10}{\mathrm{O}}_5$, given a tetraacetate with ${\mathrm{Ac}}_2\mathrm{O}$ and oxidation of A with ${\mathrm{Br}}_2-{\mathrm{H}}_2\mathrm{O}$ gives an acid, ${\mathrm{C}}_5{\mathrm{H}}_{10}{\mathrm{O}}_6$. Reduction of A with HI gives iso …

Q9.Arrange the following orbitals in decreasing order of energy ?
(A) $\mathrm{n}=3,\mathrm{l}=0,\mathrm{m}=0$
(B) $\mathrm{n}=4,\mathrm{l}=0,\mathrm{m}=0$
(C) $\mathrm{n}=3,\mathrm{l}=1,\mathrm{m}=0$
(D) $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=1$

The correct option for t …

Q10.The Lewis acid character of boron tri halides follows the order :

Q11.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : The first ionization enthalpy of 3d series elements is more than that of group 2 metals

Reason (R) : In 3d series of elements successive filling of d-orbital …

Q12.The element playing significant role in neuromuscular function and interneuronal transmission is :

Q13.Given below are two statements :

Statement I: ${\mathrm{H}}_2{\mathrm{O}}_2$ is used in the synthesis of Cephalosporin
Statement II : ${\mathrm{H}}_2{\mathrm{O}}_2$ is used for the restoration of aerobic conditions to sewage wastes.
In the light of the above statements, choose …

Q14.The normal rain water is slightly acidic and its pH value is 5.6 because of which one of the following?

Q15.When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of A ?

Q16.An organic compound $[\mathrm{A}]\left({\mathrm{C}}_4{\mathrm{H}}_{11}\mathrm{N}\right)$, shows optical activity and gives ${\mathrm{N}}_2$ gas on treatment with ${\mathrm{HNO}}_2$. The compound [A] reacts with ${\mathrm{PhSO}}_2\mathrm{Cl}$ producing a compound which is solubl …

Q17.Which one of the following statements is incorrect?

Q18.Which of the following elements have half-filled f-orbitals in their ground state ?
(Given : atomic number
$\mathrm{Sm}=62;\mathrm{Eu}=63;\mathrm{Tb}=65;\mathrm{Gd}=64,\mathrm{Pm}=61$ )
A. Sm
B. Eu
C. Tb
D. Gd
E. Pm

Choose the correct answer from the options given below:

Q19.In Dumas method for the estimation of ${\mathrm{N}}_2$, the sample is heated with copper oxide and the gas evolved is passed over :

Q20.If the CFSE of ${\left[\mathrm{Ti}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}$ is $-96.0\mathrm{kJ}/\mathrm{mol}$, this complex will absorb maximum at wavelength ____ nm. (nearest integer)
Assume Planck's constant $(\mathrm{h})=6.4\times 10^{-34}$ Js Speed …

Q21.Amongst the following, the number of species having the linear shape is ______.

$\mathrm{Xe}{\mathrm{F}}_2,{\mathrm{I}}_3^{+},{\mathrm{C}}_3{\mathrm{O}}_2,{\mathrm{I}}_3^{-},\mathrm{C}{\mathrm{O}}_2,\mathrm{S}{\mathrm{O}}_2,\mathrm{BeC}{\mathrm{l}}_2$ and $\mathrm{BC}{\mathrm{l}}_2^{-}$

Q22.The resistivity of a 0.8 M solution of an electrolyte is $5\times 10^{-3}\Omega \mathrm{cm}$. Its molar conductivity is
____ $\times 10^4{\Omega }^{-1}{\mathrm{cm}}^2{\mathrm{mol}}^{-1}$. (Nearest integer)

Q23.At 298 K, the solubility of silver chloride in water is $1.434\times 10^{-3}\mathrm{g}{\mathrm{L}}^{-1}$. The value of $-\log {\mathrm{K}}_{\mathrm{sp}}$ for silver chloride is ____.
(Given mass of Ag is $107.9\mathrm{g}{\mathrm{mol}}^{-1}$ and mass of Cl is …

Q24.A sample of a metal oxide has formula ${\mathrm{M}}_{0.83}{\mathrm{O}}_{1.00}$. The metal M can exist in two oxidation states +2 and +3. In the sample of ${\mathrm{M}}_{0.83}{\mathrm{O}}_{1.00}$, the percentage of metal ions existing in +2 oxidation state is ____ % (nearest in …

Q25.Assume carbon burns according to following equation :
$2{\mathrm{C}}_{(\mathrm{s})}+{\mathrm{O}}_{2(\mathrm{g})}\to 2\mathrm{CO}(\mathrm{g})$
When 12 g carbon is burnt in 48 g of oxygen, the volume of carbon monoxide produced is ____
$\times 10^{-1}\mathrm{L}$ a …

Q26.The number of alkali metal(s), from $\mathrm{Li},\mathrm{K},\mathrm{Cs},\mathrm{Rb}$ having ionization enthalpy greater than $400\mathrm{kJ}{\mathrm{mol}}^{-1}$ and forming stable super oxide is ____.

Q27.Enthalpies of formation of ${\mathrm{CCl}}_4(\mathrm{g}),{\mathrm{H}}_2\mathrm{O}(\mathrm{g}),{\mathrm{CO}}_2(\mathrm{g})$ and
$\mathrm{HCl}(\mathrm{g})$ are $-105,-242,-394$ and $-92\mathrm{kJ}{\mathrm{mol}}^{-1}$ respectively. The magnitude of enthalpy of the rea …

Q28.The number of molecules which gives haloform test among the following molecules is ____.

Q29.The rate constant for a first order reaction is $20{\min }^{-1}$. The time required for the initial concentration of the reactant to reduce to its $\frac{1}{32}$ level is ____ $\times 10^{-2}\min$. (Nearest integer)
(Given : $\ln 10=2.303$
$\log 2=0.3010$)

Q1.If $\varphi (\mathrm{x})=\frac{1}{\sqrt{\mathrm{x}}}{\int }_{\frac{\pi }{4}}^{\mathrm{x}}\left(4\sqrt{2}\sin \mathrm{t}-3{\varphi }^{\prime }(\mathrm{t})\right)\mathrm{dt},\mathrm{x}>0$, then ${\varphi }^{\prime }\left(\frac{\pi }{4}\right)$ is equal to :

Q2.If a point $\mathrm{P}(\alpha ,\beta ,\gamma )$ satisfying $(\alpha \beta \gamma )\left(\begin{array}{ccc}2& 10& 8\\ 9& 3& 8\\ 8& 4& 8\end{array}\right)=\left(\begin{array}{lll}0& 0& 0\end{array}\right)$ lies on the plane $2\mathrm{x}+4\mathrm{y}+3\mathrm{z}=5$, …

Q3.Let ${\mathrm{a}}_1,{\mathrm{a}}_2,{\mathrm{a}}_3,\dots$ be an A.P. If ${\mathrm{a}}_7=3$, the product ${\mathrm{a}}_1{\mathrm{a}}_4$ is minimum and the sum of its first n terms is zero, then $\mathrm{n}!-4{\mathrm{a}}_{\mathrm{n}(\mathrm{n}+2)}$ is equal to :

Q4.Let $(\mathrm{a},\mathrm{b})\subset (0,2\pi )$ be the largest interval for which
${\sin }^{-1}(\sin \theta )-{\cos }^{-1}(\sin \theta )>0,\theta \in (0,2\pi )$, holds. If …

Q5.Let $\mathrm{y}=\mathrm{y}(\mathrm{x})$ be the solution of the differential equation
$\left(3y^2-5x^2\right)ydx+2x\left(x^2-y^2\right)dy=0$ such that $\mathrm{y}(1)=1$. then $\left|(\mathrm{y}(2){)}^3-12\mathrm{y}(2)\right|$ is equal to:

Q6.Among the relations
$\mathrm{S}=\left\{(\mathrm{a},\mathrm{b}):\mathrm{a},\mathrm{b}\in \mathbb{R}-\{0\},2+\frac{\mathrm{a}}{\mathrm{b}}>0\right\}$
And …

Q7.The equation
${\mathrm{e}}^{4\mathrm{x}}+8{\mathrm{e}}^{3\mathrm{x}}+13{\mathrm{e}}^{2\mathrm{x}}-8{\mathrm{e}}^{\mathrm{x}}+1=0,\mathrm{x}\in \mathrm{R}$ has:

Q8.The number of values of $\mathrm{r}\in \{\mathrm{p},\mathrm{q},\sim \mathrm{p},\sim \mathrm{q}\}$ for which $((\mathrm{p}\wedge \mathrm{q})\Rightarrow (\mathrm{r}\vee \mathrm{q}))\wedge ((\mathrm{p}\wedge \mathrm{r})\Rightarrow \mathrm{q})$ is a tautology, is:

Q9.Let $\mathrm{f}:\mathbb{R}-\{2,6\}\to \mathbb{R}$ be real valued function defined as $f(x)=\frac{x^2+2x+1}{x^2-8x+12}$. Then range of $f$ is

Q11.Let P be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$ and $(2,4,3)$. Then the distance of P from the point $(3,-2,2)$ is

Q12.The absolute minimum value, of the function $\mathrm{f}(\mathrm{x})=\left|{\mathrm{x}}^2-\mathrm{x}+1\right|+\left[{\mathrm{x}}^2-\mathrm{x}+1\right]$, where $[\mathrm{t}]$ denotes the greatest integer function, in the interval $[-1,2]$, is :

Q13.Let the plane P : $8\mathrm{x}+{\alpha }_1\mathrm{y}+{\alpha }_2\mathrm{z}+12=0$ be parallel to the line $\mathrm{L}:\frac{\mathrm{x}+2}{2}=\frac{\mathrm{y}-3}{3}=\frac{\mathrm{z}+4}{5}$. If the intercept of P on the y-axis is 1, then the distance between P and L is :

Q14.The foot of perpendicular from the origin O to a plane P which meets the co-ordinate axes at the points $\mathrm{A},\mathrm{B},\mathrm{C}$ is $(2,\mathrm{a},4),\mathrm{a}\in \mathrm{N}$. If the volume of the tetrahedron OABC is 144 unit${}^3$, then which of the follow …

Q15.Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and $\alpha (>0)$, and the mean and standard deviation of marks of class B of n students be respectively 55 and $30-\alpha$. If the mean and variance of the marks of the combined class o …

Q16.Let : $\vec{a}=\hat{i}+2\hat{j}+3\hat{k},\vec{b}=\hat{i}-\hat{j}+2\hat{k}$ and $\overrightarrow{\mathrm{c}}=5\hat{\mathrm{i}}-3\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ be three vectors. If $\overrightarrow{\mathrm{r}}$ is a vector such that, …

Q17.Let H be the hyperbola, whose foci are $(1\pm \sqrt{2},0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum is

Q18.Let $\alpha >0$. If ${\int }_0^{\alpha }\frac{\mathrm{x}}{\sqrt{\mathrm{x}+\alpha }-\sqrt{\mathrm{x}}}\mathrm{dx}=\frac{16+20\sqrt{2}}{15}$, then $\alpha$ is equal to :

Q19.The complex number $z=\frac{i-1}{\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}}$ is equal to:

Q20.The Coefficient of $x^{-6}$, in the expansion of ${\left(\frac{4\mathrm{x}}{5}+\frac{5}{2{\mathrm{x}}^2}\right)}^9$, is

Q21.Let the area of the region $\left\{(\mathrm{x},\mathrm{y}):|2\mathrm{x}-1|\le \mathrm{y}\le \left|{\mathrm{x}}^2-\mathrm{x}\right|,0\le \mathrm{x}\le 1\right\}$ be A. Then $(6\mathrm{A}+11{)}^2$ is equal to

Q22.If the constant term in the binomial expansion of ${\left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^{\ell }}\right)}^9$ is -84 and the Coefficient of $x^{-3\ell }$ is $2^{\alpha }\beta$, where $\beta <0$ is an odd number, Then $|\alpha \ell -\beta |$ is equal to

Q23.Let $\vec{a},\vec{b},\vec{c}$ be three vectors such that $|\overrightarrow{\mathrm{a}}|=\sqrt{31},4|\overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{c}}|=2$ and …

Q24.The sum
$1^2-2.3^2+3.5^2-4.7^2+5.9^2-\dots \dots \dots +15.29^2$ is ______.

Q25.Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ is less than or equal to a. If $\mathrm{P}(A)=\frac{11}{36}$, then a is equal to ______.

Q26.Let $\mathrm{A}=[{\mathrm{a}}_{\mathrm{ij}}],{\mathrm{a}}_{\mathrm{ij}}\in \mathrm{Z}\cap [0,4],1\le \mathrm{i},\mathrm{j}\le 2$. The number of matrices A such that the sum of all entries is a prime number $\mathrm{p}\in (2,13)$ is ______.

Q27.Let A be a $\mathrm{n}\times \mathrm{n}$ matrix such that $|\mathrm{A}|=2$. If the determinant of the matrix $\mathrm{Adj}\left(2.\mathrm{Adj}\left(2{\mathrm{A}}^{-1}\right)\right)$ is $2^{84}$, then n is equal to ______.

Q28.If ${}^{2n+1}{P}_{n-1}:{}^{2n-1}{P}_n=11:21$, then $n^2+n+15$ is equal to ______