List of top Questions asked in JEE Main- 2023

An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force $F=2 N$ In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as $\theta=k x$, where $k$ is a constant and $x$ is the distance covered by the object from its initial position The expression of kinetic energy of the object will be $E=\frac{n}{k} \sin \theta$ The valte of $n$ is

An object of mass m initially at rest on a smooth horizontal plane starts moving

The energy of one mole of photons of radiation of frequency 2 $\times$10¹²H_z in Jmol^-1 is ________ (Nearest integer)

[Given : $h=6.626\times10^{-34}Js$

$N_{A}=6.022\times10^{23}mol^{-1}$]

If $\vec{P}=3 \hat{i}+\sqrt{3} \hat{j}+2 \hat{k}$ and $\vec{Q}=4 \hat{i}+\sqrt{3} \hat{j}+25 \hat{k}$ then, The unit vector in the direction of $\vec{P} \times \vec{Q}$ is $\frac{1}{x}(\sqrt{3} i+\hat{j}-2 \sqrt{3} \hat{k})$ The value of $x$ is

600 mL of 0.01M HCl is mixed with 400 mL of 0.01 M H₂SO₄.The pH of the mixture is ______ × 10^-2(Nearest integer)
[Given log 2 =0.30 , log 3 =0.48 log 5 =0.69 log 7 -0.84 log 11 =1.04 ]

Some amount of dichloromethane $\left( CH _2 Cl _2\right)$ is added to $671.141 \,mL$ of chloroform $\left( CHCl _3\right)$ to prepare $2.6 \times 10^{-3} M$ solution of $CH _2 Cl _2$ (DCM) The concentration of DCM is ______$ppm$ (by mass) Given: atomic mass : $C =12$ $H =1$ $Cl =35.5$ density of $CHCl _3=1.49\, g \,cm ^{-3}$

If compound A reacts with B following first-order kinetics with rate constant $2.011 \times 10^{-3} \, \text{s}^{-1}$, the time taken by A (in seconds) to reduce from 7 g to 2 g will be ------- (Nearest Integer).
Given: \[\log 5 = 0.698, \, \log 7 = 0.845, \, \log 2 = 0.301.\]

The wavelength of the radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of hydrogen atom If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $\frac{20}{x} \lambda_0$ The value of $x$ is

The number of electrons involved in the reduction of permanganate to manganese dioxide in acidic medium is _______

A $300\, mL$ bottle of soft drink has $0.2 \,M\, CO _2$ dissolved in it Assuming $CO _2$ behaves as an ideal gas, the volume of the dissolved $CO _2$ at STP is ______$mL$ (Nearest integer) Given : At STP, molar volume of an ideal gas is $227\, L \,mol ^{-1}$

A litre of buffer solution contains $01$ mole of each of $NH _3$ and $NH _4 CL$ On the addition of $002$ mole of $HCl$ by dissolving gaseous $HCl$, the $pH$ of the solution is found to be ____ $\times 10^{-3}$ (Nearest integer) [Given : $pK _5\left( NH _3\right)=4745$ $ \log 2=0301$ $\log 3=0477$ $T =298 K ]$

$\displaystyle\lim _{x \rightarrow 0} \frac{48}{x^4} \int_0^x \frac{ t ^3}{ t ^6+1} d t$ is equal to

Let $\alpha$ be the area of the larger region bounded by the curve $y^2=8 x$ and the lines $y=x$ and $x=2$, which lies in the first quadrant Then the value of $3 \alpha$ is equal to _____

Let $\sum_{n=0}^{\infty }\frac{n^{3}((2n)!+(2n-1)(n!))}{(n!)((2n)!)}=ae+\frac{b}{e}+c$, where $a, b, c \in Z$ and $e=\displaystyle\sum_{n=0}^{\infty} \frac{1}{n !}$ Then $a^2-b+c$ is equal to _______

Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1,2 , 3 and 5 , and are divisible by 15 , is equal to _____

The osmotic pressure of solutions of PVC in cyclohexanone at $300 K$ are plotted on the graph The molar mass of $PVC$ is ____$g \,mol ^{-1}$ (Nearest integer)

( Given : R = 0.083 L atm K^-1 mol^-1 )

If the equation of the plane passing through the point $(1,1,2)$ and perpendicular to the line $x-3 y+$ $2 z-1=0=4 x-y+z$ is $A t+ B y+ C z=1$, then $140( C - B + A )$ is equal to______

For the first order reaction $A \rightarrow B$, the half life is $30 min$ The time taken for $75 \%$ completion of the reaction is min (Nearest integer) Given : $\log _g 2=03010$ $ \log 3=04771 $ $ \log 5=06989$

The mean and variance of 7 observations are 8 and 16 respectively If one observation 14 is omitted and $a$ and $b$ are respectively mean and variance of remaining 6 observation, then $a+3 b-5$ is equal to ______

Let $z=1+i$ and $z_1=\frac{1+i \bar{z}}{\bar{z}(1-z)+\frac{1}{z}}$ Then $\frac{12}{\pi} \arg \left(z_1\right)$ is equal to________

$Pt(s) ∣ H2(g)(1atm) ∣ H+(aq, [H+]=1)\, ∥\, Fe3+(aq), Fe2+(aq) ∣ Pt(s)$
Given$ E^∘_{Fe^{3+}Fe^{2+}}$$=0.771V$ and $E^∘_{H^{+1/2}H_2}=0\,V,T=298K$
If the potential of the cell is 0.712V, the ratio of concentration of $Fe2+$ to $Fe3+$ is

In sulphur estimation, $0471 \,g$ of an organic compound gave $14439 \,g$ of barium sulphate The percentage of sulphur in the compound is ___(Nearest Integer) (Grven: Atomic mass Ba: $137 \,u , S : 32\, u , O : 16 \,u$ )

How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? (Given: Atomic number: $V, 23; Cr, 24; Fe, 26; Ni, 28$) $V ^{3+} \cdot Ci ^{3+} \cdot Fe ^{2+} \cdot Ni ^{3+}$

Let $f^1(x)=\frac{3 x+2}{2 x+3}, x \in R -\left\{\frac{-3}{2}\right\}$ For $n \geq 2$, define $f^{ n }(x)=f^1 o f^{ n -1}(x)$ if $f^5(x)=\frac{ a x+ b }{ b x+ a }, \operatorname{gcd}( a , b )=1$, then $a + b$ is equal to ______ .

As shown in figure, a cuboid lies in a region with electric field $E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} N / C$. The magnitude of charge within the cuboid is $n \epsilon_0 C$. The value of $n$ is _____. (if dimension of cuboid is $1 \times 2 \times 3 m ^3$ )

A uniform disc of mass $0.5\, kg$ and radius $r$ is projected with velocity $18 \,m / s$ at $t=0$ s on a rough horizontal surface It starts off with a purely sliding motion at $t=0\, s$ After $2\, s$ it acquires a purely rolling motion (see figure) The total kinetic energy of the disc after $2 \,s$ will be ______ $J$ (given, coefficient of friction is $0.3$ and g=10m/s²⁾