JEE Main 2024 · 05 Apr 2024 · Shift 2

Q1.Given below are two statements :

Statement I: When the white light passed through a prism, the red light bends lesser than yellow and violet.

Statement II : The refractive indices are different for different wavelengths in dispersive medium. In the light of the above statements …

Q2.Which of the following statement is not true about stopping potential ( ${\mathrm{V}}_0$ )?

Q3.The angular momentum of an electron in a hydrogen atom is proportional to : (Where r is the radius of orbit of electron)

Q4.A galvanometer of resistance $100\Omega$ when connected in series with $400\Omega$ measures a voltage of upto 10 V . The value of resistance required to convert the galvanometer into ammeter to read upto 10 A is $\mathrm{x}\times 10^{-2}\Omega$. The value of x is :

Q5.The vehicles carrying inflammable fluids usually have metallic chains touching the ground :

Q6.If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

Q7.A particle moves in $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\overrightarrow{\mathrm{P}}(\mathrm{t})=\hat{\mathrm{i}}\cos (\mathrm{kt})-\hat{\mathrm{j}}\sin (\mathrm{kt})$. If k is constant, the angle between …

Q8.The electrostatic force $({\overrightarrow{\mathrm{F}}}_1)$ and magnetic force ( ${\overrightarrow{\mathrm{F}}}_2$ ) acting on a charge q moving with velocity v can be written :

Q9.A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $\mathrm{m}/{\mathrm{s}}^2$ ) :

Q10.A series LCR circuit is subjected to an AC signal of $200\mathrm{V},50\mathrm{Hz}$. If the voltage across the inductor $(\mathrm{L}=10\mathrm{mH})$ is 31.4 V , then the current in this circuit is ______ :

Q11.What is the dimensional formula of ${\mathrm{ab}}^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual meaning.

Q12.The output (Y) of logic circuit given below is 0 only when :

Q13.A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :

Q14.During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_P}{C_V}$ for the gas is :

Q15.A vernier callipers has 20 divisions on the vernier scale, which coincides with $19^{\text{th}}$ division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to ______ mm.

Q16.A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

Q17.A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : (Given = Radius of geo-stationary orbit for earth is $4.2\times 10^4$ km)

Q18.The ratio of heat dissipated per second through the resistance $5\Omega$ and $10\Omega$ in the circuit given below is :

Q19.A solenoid of length 0.5 m has a radius of 1 cm and is made up of 'm' number of turns. It carries a current of 5 A. If the magnitude of the magnetic field inside the solenoid is $6.28\times 10^{-3}$ T, then the value of m is :

Q20.The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $915\text{A˚}$. The longest wavelength of spectral lines in the Balmer series will be ______ Å.

Q21.In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm. The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be $x\times 10^{-5}$ m. The value …

Q22.A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension ______ cm.

Q23.A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{X}{5}$. The value of $x$ is ____.

Q24.A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is ____ N …

Q25.The electric field at point p due to an electric dipole is E. The electric field at point R on equitorial line will be $\frac{E}{x}$. The value of $x$:

Q26.The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is ____ m.

Q27.A wire of resistance $20\Omega$ is divided into 10 equal parts. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is ____ $\Omega$.

Q28.The current in an inductor is given by $I=(3t+8)$ where $t$ is in second. The magnitude of induced emf produced in the inductor is 12 mV. The self-inductance of the inductor ____ mH.

Q1.Match List - I with List - II.

List - I (Molecules)
(A) ICl
(B) ClF₃
(C) IF₅
(D) IF₇

List - II (Shapes)
(I) T -Shape
(II) Square pyramidal
(III) Pentagonal bipyramidal
(IV) Linear

Choose the correct answer from the options given below:

Q2.While preparing crystals of Mohr's salt, dil. ${\mathrm{H}}_2{\mathrm{SO}}_4$ is added to a mixture of ferrous sulphate and ammonium sulphate, before dissolving this mixture in water, dil. ${\mathrm{H}}_2{\mathrm{SO}}_4$ is added here to:

Q3.Identify the major product in the following reaction.

Q4.The correct nomenclature for the following compound is:

Q5.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : ${\mathrm{NH}}_3$ and ${\mathrm{NF}}_3$ molecule have pyramidal shape with a lone pair of electrons on nitrogen atom. The resultant dipole moment of …

Q6.Given below are two statements:

Statement I: On passing ${\mathrm{HCl}}_{(\mathrm{g})}$ through a saturated solution of ${\mathrm{BaCl}}_2$, at room temperature white turbidity appears.

Statement II : When HCl gas is passed through a saturated solution of NaCl, sodium chlorid …

Q7.The metal atom present in the complex MABXL (where $\mathrm{A},\mathrm{B},\mathrm{X}$ and L are unidentate ligands and M is metal) involves ${\mathrm{sp}}^3$ hybridization. The number of geometrical isomers exhibited by the complex is:

Q8.Match List - I with List - II.

List - I (Pair of Compounds)
(A) n-propanol and Isopropanol
(B) Methoxypropane and ethoxyethane
(C) Propanone and propanal
(D) Neopentane and Isopentane

List - II (Isomerism)
(I) Metamerism
(II) Chain Isomerism
(III) Position Isomerism
(IV) Functi …

Q9.The quantity of silver deposited when one coulomb charge is passed through ${\mathrm{AgNO}}_3$ solution:

Q10.Which one of the following reactions is NOT possible?

Q11.Given below are two statements :

Statement I : The metallic radius of Na is $1.86{\mathrm{A}}^{\circ }$ and the ionic radius of ${\mathrm{Na}}^{+}$is lesser than $1.86{\mathrm{A}}^{\circ }$.

Statement II : Ions are always smaller in size than the corresponding elements.

In t …

Q12.Consider the above reaction sequence and identify the major product P.

Q13.Consider the given chemical reaction :

Product " A " is :

Q14.For the electro chemical cell
$\mathrm{M}\left|{\mathrm{M}}^{2+}\Vert \mathrm{X}\right|{\mathrm{X}}^{2-}$
If ${\mathrm{E}}_{\left({\mathrm{M}}^{2+}/\mathrm{M}\right)}^0=0.46\mathrm{V}$ and ${\mathrm{E}}_{\left(\mathrm{X}/{\mathrm{X}}^{2-}\right)}^0=0.34\mathrm{V}$.
Which of …

Q15.The number of moles of methane required to produce $11\mathrm{g}{\mathrm{CO}}_2(\mathrm{g})$ after complete combustion is:
(Given molar mass of methane in $\mathrm{g}{\mathrm{mol}}^{-1}:16$)

Q16.The number of complexes from the following with no electrons in the ${\mathrm{t}}_2$ orbital is ____.
${\mathrm{TiCl}}_4,{\left[{\mathrm{MnO}}_4\right]}^{-},{\left[{\mathrm{FeO}}_4\right]}^{2-},{\left[{\mathrm{FeCl}}_4\right]}^{-},{\left[{\mathrm{CoCl}}_4\right]}^{2-}$

Q17.The number of ions from the following that have the ability to liberate hydrogen from a dilute acid is ____.
${\mathrm{Ti}}^{2+},{\mathrm{Cr}}^{2+}$ and ${\mathrm{V}}^{2+}$

Q18.Identify A and B in the given chemical reaction sequence :-

Q19.The correct statements from the following are :
(A) The decreasing order of atomic radii of group 13 elements is $\mathrm{Tl}>\mathrm{In}>\mathrm{Ga}>\mathrm{Al}>\mathrm{B}$.
(B) Down the group 13 electronegativity decreases from top to bottom.
(C) Al dissolves in dil. HCl and …

Q20.Coagulation of egg, on heating is because of :

Q21.Combustion of 1 mole of benzene is expressed at
${\mathrm{C}}_6{\mathrm{H}}_6(1)+\frac{15}{2}{\mathrm{O}}_2(\mathrm{g})\to {\mathrm{CO}}_2(\mathrm{g})+3{\mathrm{H}}_2\mathrm{O}(1)$.
The standard enthalpy of combustion of 2 mol of benzene is …

Q22.The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products A and B along with the evolution of ${\mathrm{CO}}_2$. The sum of spin-only magnetic moment values of $A$ and $B$ is ____ B.M. (Nearest integer)
(Given atomic number : …

Q23.X of enthanamine was subjected to reaction with ${\mathrm{NaNO}}_2/\mathrm{HCl}$ followed by hydrolysis to liberate ${\mathrm{N}}_2$ and HCl . The HCl generated was completely neutralised by 0.2 moles of NaOH . X is ____ g.

Q24.In an atom, total number of electrons having quantum numbers $n=4,\left|m_1\right|=1$ and $m_s=-\frac{1}{2}$ is

Q25.Using the given figure, the ratio of $R_f$ values of sample A and sample C is $\mathrm{x}\times 10^{-2}$. Value of x is

Q26.In the Claisen-Schmidt reaction to prepare 351 g of dibenzalacetone using 87 g of acetone, the amount of benzaldehyde required is ______ g. (Nearest integer)

Q27.Consider the following single step reaction in gas phase at constant temperature.
$2{\mathrm{A}}_{(\mathrm{g})}+{\mathrm{B}}_{(\mathrm{g})}\to {\mathrm{C}}_{(\mathrm{g})}$
The initial rate of the reaction is recorded as $r_1$ when the reaction starts with 1.5 atm press …

Q28.The product © in the following sequence of reactions has ______ $\pi$ bonds.

Q29.Considering acetic acid dissociates in water, its dissociation constant is $6.25\times 10^{-5}$. If 5 mL of acetic acid is dissolved in 1 litre water, the solution will freeze at $-\mathrm{x}\times 10^{-2}{}^{\circ }\mathrm{C}$, provided pure water freezes at …

Q30.Number of compounds from the following with zero dipole moment is ______.
$\mathrm{HF},{\mathrm{H}}_2,{\mathrm{H}}_2\mathrm{S},{\mathrm{CO}}_2,{\mathrm{NH}}_3,{\mathrm{BF}}_3,{\mathrm{CH}}_4,{\mathrm{CHCl}}_3,{\mathrm{SiF}}_4$, …

Q1.If $y(\theta )=\frac{2\cos \theta +\cos 2\theta }{\cos 3\theta +4\cos 2\theta +5\cos \theta +2}$, then at $\theta =\frac{\pi }{2}$, $y^{\prime \prime }+y^{\prime }+y$ is equal to

Q2.Let the set $S=\{2,4,8,16,\dots ,512\}$ be partitioned into 3 sets $A,B,C$ with equal number of elements such that $A\cup B\cup C=S$ and $A\cap B=B\cap C=A\cap C=\varphi$. The maximum number of such possible partitions of $S$ is equal to

Q3.Let the circle $C_1:x^2+y^2-2(x+y)+1=0$ and $C_2$ be a circle having centre at $(-1,0)$ and radius 2. If the line of the common chord of $C_1$ and $C_2$ intersects the y-axis at the point $P$, then the square of the distance of $P$ from the centre of …

Q4.Let $\vec{a}=2\hat{i}+5\hat{j}-\hat{k}$, $\vec{b}=2\hat{i}-2\hat{j}+2\hat{k}$ and $\vec{c}$ be three vectors such that $(\vec{c}+\hat{i})\times (\vec{a}+\vec{b}+\hat{i})=\vec{a}\times (\vec{c}+\hat{i})$. If $\vec{a}\cdot \vec{c}=-29$, then …

Q5.For $x\ge 0$, the least value of $K$, for which $4^{1+x}+4^{1-x},\frac{K}{2},16^x+16^{-x}$ are three consecutive terms of an A.P., is equal to :

Q6.Let $\alpha \beta \ne 0$ and $A=\left[\begin{array}{ccc}\beta & \alpha & 3\\ \alpha & \alpha & \beta \\ -\beta & \alpha & 2\alpha \end{array}\right]$. If $B=\left[\begin{array}{ccc}3\alpha & -9& 3\alpha \\ -\alpha & 7& -2\alpha \\ -2\alpha & 5& -2\beta \end{array}\right]$ is the matrix of cofactors …

Q7.The coefficients $a,b,c$ in the quadratic equation $a{x}^2+bx+c=0$ are from the set $\{1,2,3,4,5,6\}$. If the probability of this equation having one real root bigger than the other is $p$, then $216p$ equals :

Q8.Let $f,g:R\to R$ be defined as: $f(x)=|x-1|$ and $g(x)=\{\begin{array}{ll}{e}^x,& x\ge 0\\ x+1,& x\le 0\end{array}$. Then the function $f(g(x))$ is

Q9.Let $f:[-1,2]\to R$ be given by $f(x)=2x^2+x+[x^2]-[x]$, where $[t]$ denotes the greatest integer less than or equal to $t$. The number of points, where $f$ is not continuous, is

Q10.If the constant term in the expansion of ${\left(\frac{\sqrt[5]{3}}{x}+\frac{2x}{\sqrt[3]{5}}\right)}^{12},x\ne 0$, is $\alpha \times 2^8\times \sqrt[5]{3}$, then $25\alpha$ is equal to

Q11.The values of $m,n$, for which the system of equations $x+y+z=4$, $2x+5y+5z=17$, $x+2y+mz=n$ has infinitely many solutions, satisfy the equation :

Q12.Consider three vectors $\vec{a},\vec{b},\vec{c}$. Let $|\vec{a}|=2,|\vec{b}|=3$ and $\vec{a}=\vec{b}\times \vec{c}$. If $\alpha \in \left[0,\frac{\pi }{3}\right]$ is the angle between the vectors $\vec{b}$ and $\vec{c}$, then the minimum value of …

Q13.Let $(\alpha ,\beta ,\gamma )$ be the image of the point $(8,5,7)$ in the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}$. Then $\alpha +\beta +\gamma$ is equal to

Q14.Let $\beta (m,n)={\int }_0^1{x}^{m-1}(1-x{)}^{n-1}dx,m,n>0$. If ${\int }_0^1(1-x^{10}{)}^{20}dx=a\times \beta (b,c)$, then $100(a+b+c)$ equals ____ .

Q15.The differential equation of the family of circles passing through the origin and having centre at the line $y=x$ is

Q16.Let $a>0$ be a root of the equation $2x^2+x-2=0$. If ${\lim }_{x\to \frac{1}{a}}\frac{16(1-\cos (2+x-2x^2))}{(1-ax{)}^2}=\alpha +\beta \sqrt{17}$, where $\alpha ,\beta \in Z$, then $\alpha +\beta$ is equal to ____ .

Q17.If $1+\frac{\sqrt{3}-\sqrt{2}}{2\sqrt{3}}+\frac{5-2\sqrt{6}}{18}+\frac{9\sqrt{3}-11\sqrt{2}}{36\sqrt{3}}+\frac{49-20\sqrt{6}}{180}+\dots$ upto $\infty =2+\left(\sqrt{\frac{b}{a}}+1\right){\log }_e\left(\frac{a}{b}\right)$, where $a$ and $b$ are integers with …

Q18.If $f(t)={\int }_0^{\pi }\frac{2xdx}{1-{\cos }^{2}t{\sin }^{2}x},0<t<\pi$, then the value of ${\int }_0^{\frac{\pi }{2}}\frac{{\pi }^{2}dt}{f(t)}$ equals ____ .

Q19.The number of real solutions of the equation $x|x+5|+2|x+7|-2=0$ is ____ .

Q20.Let the mean and the standard deviation of the probability distribution $x:\alpha ,1,0,-3$; $P(x):\frac{1}{3},K,\frac{1}{6},\frac{1}{4}$ be $\mu$ and $\sigma$, respectively. If $\sigma -\mu =2$, then $\sigma +\mu$ is equal to ____ .

Q21.Let a line perpendicular to the line $2x-y=10$ touch the parabola $y^2=4(x-9)$ at the point $P$. The distance of the point $P$ from the centre of the circle $x^2+y^2-14x-8y+56=0$ is ____ .