JEE Main 2024 · 30 Jan 2024 · Shift 2

Q1.If 50 Vernier divisions are equal to 49 main scale divisions of a travelling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of travelling microscope is:

Q2.A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of $60^{\circ }$ by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is: …

Q3.For the photoelectric effect, the maximum kinetic energy (${\mathrm{E}}_{\mathrm{k}}$) of the photoelectrons is plotted against the frequency (v) of the incident photons as shown in figure. The slope of the graph gives

Q4.A block of ice at $-10^{\circ }\mathrm{C}$ is slowly heated and converted to steam at $100^{\circ }\mathrm{C}$. Which of the following curves represent the phenomenon qualitatively:

Q5.In a nuclear fission reaction of an isotope of mass M, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $\Delta \mathrm{M}$ will be:

Q6.Choose the correct statement for processes A & B shown in figure.

Q7.An electron revolving in ${\mathrm{n}}^{\text{th }}$ Bohr orbit has magnetic moment ${\mu }_n$. If ${\mu }_n\alpha n^x$, the value of $x$ is:

Q8.An alternating voltage $\mathrm{V}(\mathrm{t})=220\sin 100\pi \mathrm{t}$ volt is applied to a purely resistive load of $50\Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

Q9.A block of mass $m$ is placed on a surface having vertical cross section given by $y=x^2/4$. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

Q10.If the total energy transferred to a surface in time $t$ is $6.48\times 10^5\mathrm{J}$, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

Q11.A beam of unpolarised light of intensity ${\mathrm{I}}_0$ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of $45^{\circ }$ relative to that of A. The intensity of emergent light is:

Q12.Escape velocity of a body from earth is $11.2\mathrm{km}/\mathrm{s}$. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:

Q13.A particle of charge '$-q$' and mass '$m$' moves in a circle of radius '$r$' around an infinitely long line charge of linear density '$+\lambda$'. Then time period will be given as:
(Consider k as Coulomb's constant)

Q14.If mass is written as $\mathrm{m}=\mathrm{k}{\mathrm{c}}^{\mathrm{P}}{\mathrm{G}}^{-1/2}{\mathrm{h}}^{1/2}$ then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

Q15.In the given circuit, the voltage across load resistance $({\mathrm{R}}_{\mathrm{L}})$ is:

Q16.If three moles of monoatomic gas $(\gamma =\frac{5}{3})$ is mixed with two moles of a diatomic gas $(\gamma =\frac{7}{5})$, the value of adiabatic exponent $\gamma$ for the mixture is:

Q17.Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure

The tensions ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ in the string are respectively:

Q18.When a potential difference V is applied across a wire of resistance R , it dissipates energy at a rate W . If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:

Q19.A power transmission line feeds input power at 2.3 kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V by the transformer. The current in the primary of the transformer is 5 A and its efficiency is $90\%$. The windin …

Q20.A big drop is formed by coalescing 1000 small identical drops of water. If ${\mathrm{E}}_1$ be the total surface energy of 1000 small drops of water and ${\mathrm{E}}_2$ be the surface energy of single big drop of water, the ${\mathrm{E}}_1$ : ${\mathrm{E}}_2$ is …

Q21.Two discs of moment of inertia ${\mathrm{I}}_1=4\mathrm{kg}{\mathrm{m}}^2$ and ${\mathrm{I}}_2=2\mathrm{kg}{\mathrm{m}}^2$ about their central axes & normal to their planes, rotating with angular speeds $10\mathrm{rad}/\mathrm{s}$ & …

Q22.In an experiment to measure the focal length (f) of a convex lens, the magnitude of object distance ( x ) and the image distance ( y ) are measured with reference to the focal point of the lens. The y-x plot is shown in figure.

The focal length of the lens is ______ cm .

Q23.A vector has magnitude same as that of $\overrightarrow{\mathrm{A}}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ and is parallel to $\overrightarrow{\mathrm{B}}=4\hat{\mathrm{i}}+3\hat{\mathrm{j}}$. The x and y components of this vector in first quadrant are x and 3 respectively where …

Q24.The current of 5 A flows in a square loop of sides 1 m is placed in air. The magnetic field at the centre of the loop is $\mathrm{X}\sqrt{2}\times 10^{-7}\mathrm{T}$. The value of X is

Q25.Two identical charged spheres are suspended by string of equal lengths. The string make an angle of $37^{\circ }$ with each other. When suspended in a liquid of density $0.7\mathrm{g}/{\mathrm{cm}}^3$, the angle remains same. If density of material of the sphere is …

Q26.A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillations will be $\_\_\_\_$ s. [take $\mathrm{g}={\pi }^2{\mathrm{ms}}^{-2}$]

Q27.Two resistance of $100\Omega$ and $200\Omega$ are connected in series with a battery of 4 V and negligible internal resistance. A voltmeter is used to measure voltage across $100\Omega$ resistance, which gives reading as 1 V. The resistance of voltmeter must be $\_\_\_\_$ …

Q1.Which among the following purification methods is based on the principle of "Solubility" in two different solvents?

Q2.Salicylaldehyde is synthesized from phenol, when reacted with

Q3.Given below are two statements:

Statement - I: High concentration of strong nucleophilic reagent with secondary alkyl halides which do not have bulky substituents will follow ${\mathrm{S}}_{\mathrm{N}}2$ mechanism.
Statement - II: A secondary alkyl halide when treated with a la …

Q4.m-chlorobenzaldehyde on treatment with $50\%$ KOH solution yields

Q5.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : ${\mathrm{H}}_2\mathrm{Te}$ is more acidic than ${\mathrm{H}}_2\mathrm{S}$.
Reason R: Bond dissociation enthalpy of ${\mathrm{H}}_2\mathrm{Te}$ is lower t …

Q6.Product A and B formed in the following set of reactions are:

Q7.IUPAC name of following compound is

Q8.The products A and B formed in the following reaction scheme are respectively
(i) conc. ${\mathrm{HNO}}_3/$ conc. ${\mathrm{H}}_2{\mathrm{SO}}_4$
$323-333\mathrm{K}$
(i) ${\mathrm{NaNO}}_2,\mathrm{HCl},273-278\mathrm{K}$
S)
(ii) $\mathrm{Sn}/\mathrm{HCl}$
(ii) …

Q9.The molecule/ion with square pyramidal shape is:

Q10.The orange colour of ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ and purple colour of ${\mathrm{KMnO}}_4$ is due to

Q11.Alkaline oxidative fusion of ${\mathrm{MnO}}_2$ gives "A" which on electrolytic oxidation in alkaline solution produces B . A and B respectively are:

Q12.If a substance 'A' dissolves in solution of a mixture of ' B ' and ' C ' with their respective number of moles as ${\mathrm{n}}_{\mathrm{A}},{\mathrm{n}}_{\mathrm{B}}$ and ${\mathrm{n}}_{\mathrm{C}}$, mole fraction of C in the solution is:

Q13.Given below are two statements:

Statement - I: Along the period, the chemical reactivity of the element gradually increases from group 1 to group 18.
Statement - II: The nature of oxides formed by group 1 element is basic while that of group 17 elements is acidic.
In the the lig …

Q14.The coordination geometry around the manganese in decacarbonyldimanganese(0)

Q15.Given below are two statements:

Statement-I: Since fluorine is more electronegative than nitrogen, the net dipole moment of ${\mathrm{NF}}_3$ is greater than ${\mathrm{NH}}_3$.
Statement-II: In ${\mathrm{NH}}_3$, the orbital dipole due to lone pair and the dipole moment of …

Q16.The correct stability order of carbocations is

Q17.The solution from the following with highest depression in freezing point/lowest freezing point is

Q18.A and B formed in the following reactions are: …

Q19.Choose the correct statements about the hydrides of group 15 elements.
A. The stability of the hydrides decreases in the order ${\mathrm{NH}}_3>{\mathrm{PH}}_3>{\mathrm{AsH}}_3>{\mathrm{SbH}}_3>{\mathrm{BiH}}_3$
B. The reducing ability of the hydrides increases in the order …

Q20.Reduction potential of ions are given below:


The correct orde …

Q21.Number of complexes which show optical isomerism among the following is ____.
cis $-{\left[\mathrm{Cr}(\mathrm{ox}{)}_2{\mathrm{Cl}}_2\right]}^{3-},{\left[\mathrm{Co}(\mathrm{en}{)}_3\right]}^{3+}$,
cis $-{\left[\mathrm{Pt}(\mathrm{en}{)}_2{\mathrm{Cl}}_2\right]}^{2+}$, cis …

Q22.${\mathrm{NO}}_2$ required for a reaction is produced by decomposition of ${\mathrm{N}}_2{\mathrm{O}}_5$ in ${\mathrm{CCl}}_4$ as by equation $2{\mathrm{N}}_2{\mathrm{O}}_{5(\mathrm{g})}\to 4{\mathrm{NO}}_{2(\mathrm{g})}+{\mathrm{O}}_{2(\mathrm{g})}$
The initia …

Q23.Two reactions are given below:
$2{\mathrm{Fe}}_{(\mathrm{s})}+\frac{3}{2}{\mathrm{O}}_{2(\mathrm{g})}\to {\mathrm{Fe}}_2{\mathrm{O}}_{3(\mathrm{s})},\Delta {\mathrm{H}}^{\mathrm{o}}=-822\mathrm{kJ}/\mathrm{mol}$ …

Q24.The total number of correct statements, regarding the nucleic acids is ____.
A. RNA is regarded as the reserve of genetic information.
B. DNA molecule self-duplicates during cell division
C. DNA synthesizes proteins in the cell.
D. The message for the synthesis of particular prot …

Q25.The pH of an aqueous solution containing 1 M benzoic acid $\left({\mathrm{pK}}_{\mathrm{a}}=4.20\right)$ and 1 M sodium benzoate is 4.5. The volume of benzoic acid solution in 300 mL of this buffer solution is ____ mL.

Q26.Number of geometrical isomers possible for the given structure is/are ____.

Q27.Total number of species from the following which can undergo disproportionation reaction ____.
${\mathrm{H}}_2{\mathrm{O}}_2,{\mathrm{ClO}}_3^{-},{\mathrm{P}}_4,{\mathrm{Cl}}_2,\mathrm{Ag},{\mathrm{Cu}}^{+1},{\mathrm{F}}_2,{\mathrm{NO}}_2,{\mathrm{K}}^{+}$

Q28.Number of metal ions characterized by flame test among the following is ____.
${\mathrm{Sr}}^{2+},{\mathrm{Ba}}^{2+},{\mathrm{Ca}}^{2+},{\mathrm{Cu}}^{2+},{\mathrm{Zn}}^{2+},{\mathrm{Co}}^{2+},{\mathrm{Fe}}^{2+}$

Q29.2-chlorobutane $+{\mathrm{Cl}}_2\to {\mathrm{C}}_4{\mathrm{H}}_8{\mathrm{Cl}}_2$ (isomers) Total number of optically active isomers shown by ${\mathrm{C}}_4{\mathrm{H}}_8{\mathrm{Cl}}_2$, obtained in the above reaction is ____.

Q30.Number of spectral lines obtained in ${\mathrm{He}}^{+}$spectra, when an electron makes transition from fifth excited state to first excited state will be

Q1.Consider the system of linear equations $x+y+z=5,x+2y+{\lambda }^{2}z=9$, $\mathrm{x}+3\mathrm{y}+\lambda \mathrm{z}=\mu$, where $\lambda ,\mu \in \mathrm{R}$. Then, which of the following statement is NOT correct?

Q2.Let $\mathrm{A}(\alpha ,0)$ and $\mathrm{B}(0,\beta )$ be the points on the line $5\mathrm{x}+7\mathrm{y}=50$. Let the point P divide the line segment AB internally in the ratio $7:3$. Let $3\mathrm{x}-25=0$ be a directrix of the ellipse …

Q3.Let $\vec{a}=\hat{i}+\alpha \hat{j}+\beta \hat{k},\alpha ,\beta \in R$. Let a vector $\vec{b}$ be such that the angle between $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ is $\frac{\pi }{4}$ and $|\overrightarrow{\mathrm{b}}{|}^2=6$, If …

Q4.Let $f(x)=(x+3{)}^2(x-2{)}^3,x\in [-4,4]$. If $M$ and $m$ are the maximum and minimum values of f , respectively in $[-4,4]$, then the value of $M-m$ is :

Q5.Let a and b be be two distinct positive real numbers. Let $11^{\text{th}}$ term of a GP, whose first term is $a$ and third term is $b$, is equal to $p^{\text{th}}$ term of another GP, whose first term is a and fifth term is b . Then p is equal to

Q6.If $x^2-y^2+2hxy+2gx+2fy+c=0$ is the locus of a point, which moves such that it is always equidistant from the lines $x+2y+7=0$ and $2x-y+8=0$, then the value of $\mathrm{g}+\mathrm{c}+\mathrm{h}-\mathrm{f}$ equals

Q7.Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\overrightarrow{\mathrm{b}}|=1$ and $|\overrightarrow{\mathrm{b}}\times \overrightarrow{\mathrm{a}}|=2$. Then $|(\overrightarrow{\mathrm{b}}\times \overrightarrow{\mathrm{a}})-\overrightarrow{\mathrm{b}}{|}^2$ is …

Q8.Let $y=f(x)$ be a thrice differentiable function in ( $-5,5$ ). Let the tangents to the curve $\mathrm{y}=\mathrm{f}(\mathrm{x})$ at $(1,f(1))$ and ( $3,f(3)$ ) make angles $\frac{\pi }{6}$ and $\frac{\pi }{4}$, respectively with positive x -axis. If …

Q9.Let P be a point on the hyperbola $\mathrm{H}:\frac{{\mathrm{x}}^2}{9}-\frac{{\mathrm{y}}^2}{4}=1$, in the first quadrant such that the area of triangle formed by P and the two foci of H is $2\sqrt{13}$. Then, the square of the distance of P from the origin is

Q10.Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn in white, is :

Q11.Let $f:R\to R$ be defined $f(x)=a{e}^{2x}+b{e}^x+cx$. If $f(0)=-1,f^{\prime }\left({\log }_{e}2\right)=21$ and ${\int }_0^{{\log }_{c}4}(f(x)-cx)dx=\frac{39}{2}$, then the value of $|a+b+c|$ equals :

Q12.Let $L_1:\vec{r}=(\hat{i}-\hat{j}+2\hat{k})+\lambda (\hat{i}-\hat{j}+2\hat{k}),\lambda \in R$
$L_2:\vec{r}=(\hat{j}-\hat{k})+\mu (3\hat{i}+\hat{j}+p\hat{k}),\mu \in R$ and …

Q13.Let a and b be real constants such that the function $f$ defined by $f(x)=\{\begin{array}{cc}{x}^2+3x+a,& x\le 1\\ bx+2,& x>1\end{array}$ be differentiable on $R$. Then, the value of ${\int }_{-2}^{2}f(x)dx$ equals

Q14.Let $\mathrm{f}:\mathbb{R}-\{0\}\to \mathbb{R}$ be a function satisfying
$\mathrm{f}\left(\frac{\mathrm{x}}{\mathrm{y}}\right)=\frac{\mathrm{f}(\mathrm{x})}{\mathrm{f}(\mathrm{y})}$ for all $\mathrm{x},\mathrm{y},\mathrm{f}(\mathrm{y})\ne 0$. If …

Q15.If z is a complex number, then the number of common roots of the equation $z^{1985}+z^{100}+1=0$ and $z^3+2z^2+2z+1=0$, is equal to :

Q16.If the domain of the function $\mathrm{f}(\mathrm{x})={\log }_{\mathrm{e}}\left(\frac{2x+3}{4x^2+x-3}\right)+{\cos }^{-1}\left(\frac{2x-1}{x+2}\right)$ is $(\alpha ,\beta ]$, then the value of $5\beta -4\alpha$ is equal to

Q17.Let $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ be a function defined $f(x)=\frac{x}{{\left(1+x^4\right)}^{1/4}}$ and $g(x)=f(f(f(f(x))))$ then $18{\int }_0^{\sqrt{2\sqrt{5}}}{\mathrm{x}}^2\mathrm{g}(\mathrm{x})\mathrm{dx}$

Q18.Let $\mathrm{R}=\left(\begin{array}{ccc}\mathrm{x}& 0& 0\\ 0& \mathrm{y}& 0\\ 0& 0& \mathrm{z}\end{array}\right)$ be a non-zero $3\times 3$ matrix, where …

Q19.Let $\mathrm{Y}=\mathrm{Y}(\mathrm{X})$ be a curve lying in the first quadrant such that the area enclosed by the line $Y-y=Y^{\prime }(x)(X-x)$ and the co-ordinate axes, where ( $\mathrm{x},\mathrm{y}$ ) is any point on the curve, is always …

Q20.Let a line passing through the point $(-1,2,3)$ intersect the lines $L_1:\frac{x-1}{3}=\frac{y-2}{2}=\frac{z+1}{-2}$ at $\mathrm{M}(\alpha ,\beta ,\gamma )$ and ${\mathrm{L}}_2:\frac{\mathrm{x}+2}{-3}=\frac{\mathrm{y}-2}{-2}=\frac{\mathrm{z}-1}{4}$ at …

Q21.Consider two circles ${\mathrm{C}}_1:{\mathrm{x}}^2+{\mathrm{y}}^2=25$ and ${\mathrm{C}}_2:(\mathrm{x}-\alpha {)}^2+y^2=16$, where $\alpha \in (5,9)$. Let the angle between the two radii (one to each circle) drawn from one of the intersection points of ${\mathrm{C}}_1$ …

Q22.Let $\alpha ={\sum }_{\mathrm{k}=0}^{\mathrm{n}}\left(\frac{{\left({}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{k}}\right)}^2}{\mathrm{k}+1}\right)$ and …

Q23.Let ${\mathrm{S}}_{\mathrm{n}}$ be the sum to n-terms of an arithmetic progression 3, 7, 11, ...... .
If $40<\left(\frac{6}{\mathrm{n}(\mathrm{n}+1)}{\sum }_{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{S}}_{\mathrm{k}}\right)<42$, then n equals ______.

Q24.In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : $\mathrm{A}$, $\mathrm{B}$ and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A …

Q25.The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is ______.

Q26.The number of real solutions of the equation $\mathrm{x}\left({\mathrm{x}}^2+3|\mathrm{x}|+5|\mathrm{x}-1|+6|\mathrm{x}-2|\right)=0$ is ______.

Q27.The area of the region enclosed by the parabola $(y-2{)}^2=x-1$, the line $x-2y+4=0$ and the positive coordinate axes is ______.

Q28.The variance ${\sigma }^2$ of the data

is ______.