List of top Questions asked in JEE Main- 2023

If $A$ and $B$ are two events such that $P ( A )=\frac{1}{3}, P ( B )=\frac{1}{5}$ and $P ( A \cup B )=\frac{1}{2}$, then $P \left( A \mid B ^{\prime}\right)+ P \left( B \mid A ^{\prime}\right)$ is equal to

The area enclosed by the curves $y^2+4 x=4$ and $y-2 x=2$ is :

Let $\vec{a}=2 \hat{i}+\hat{j}+\hat{k}$, and $\vec{b}$ and $\vec{c}$ be two nonzero vectors such that $|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}|$ and $\vec{b} \cdot \vec{c}=0$. Consider the following two statements:

(A) $|\vec{a}+\lambda \vec{c}| \geq|\vec{a}|$ for all $\lambda \in R$

(B) $\vec{a}$ and $\vec{c}$ are always parallel. Then. is

The foot of perpendicular from the origin $O$ to a plane $P$ which meets the co-ordinate axes at the points $A , B , C$ is $(2, a , 4), a \in N$ If the volume of the tetrahedron $OABC$ is 144 unit $^3$, then which of the following points is NOT on $P$ ?

If $ y(x) = x^x, \, x > 0 $, then $ y''(2) - 2y'(2) $ is equal to:

Let $a, b$ be two real numbers such that $a b<$ If the complex number $\frac{1+ai}{b+i}$ is of unit modulus and $a$ $+i b$ lies on the circle $|z-I|=|2 z|$, then a possible value of $\frac{1+[a ]}{4 b}$, where $[t]$ is greatest integer function, is :

If the solution of the equation $\log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right)$, is $\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$, where $\alpha$, $\beta$ are integers, then $\alpha+\beta$ is equal to :

If $f(x) + f(\pi-x) = \pi^{2}$ then $_{0}\int^{\pi}f(x) sinx dx$ ?

Find the sum of series: $2*2^2 - 2*3^2 + 2*4^2 +$ $….(20 \,terms)$

Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least 3 and at most 6 elements is:

If all the particles have same kinetic energy, The relation between the wavelengths of alpha particle, electron and proton is:

Let the shortest distance between the lines $L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$ and $L_1: x+1=y-1=4-z$ be $2 \sqrt{6}$ If $(\alpha, \beta, \gamma)$ lies on $L$, then which of the following is NOT possible?

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:

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 most appropriate answer from the options given below.

If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}$ and $g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b$ have a common extreme point, then $a+2 b+7$ is equal to:

Let $a,b,c>1,a^3,b^3 \text{ and } c^3$ be in A.P., and $log_ab, log_ca \text{ and } log_bc$ be in G.P. If the sum of first 20 terms of an A.P., whose first term is $\frac{a+4b+c}{3}$ and the common difference is $\frac{a−8b+c}{10}$ is −444, then abc is equal to:

Let $N$ denote the number that turns up when a fair die is rolled If the probability that the system of equations$ x+y+z=1 $ $ 2 x + Ny +2 z=2 $ $ 3 x +3 y+ N z=3$ has unique solution is $\frac{k}{6}$, then the sum of value of $k$ and all possible values of $N$ is

Choose the correct representation of conductometric titration of benzoic acid vs sodium hydroxide

For an object placed at a distance $24\, m$ from a lens, a sharp focused image is observed on a screen placed at a distance $12\, cm$ from the lens A glass plate of refractive index $15$ and thickness $1 \,cm$ is introduced between lens and screen such that the glass plate plane faces parallel to the screen By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

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

Electron beam used in an electron microscope, when accelerated by a voltage of $20 kV$, has a de-Broglie wavelength of $\lambda_0$. If the voltage is increased to $40 kV$, then the de-Broglie wavelength associated with the electron beam would be:

For the system of linear equations$\alpha x+y+z=1, x+\alpha y+z=1, x+y+\alpha z=\beta$ which one of the following statements is NOT correct ?

The tangents at the point $A (1,3)$ and $B (1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$ Then the area (in unit $^2$ ) of $\triangle PAB$ is :-

Let αx=exp(x^βy^γ) be the solution of the differential equation 2x²ydy−(1−xy²) dx = 0, x>0 , y(2)=$\sqrt {log_e2}$. Then α+β−γ equals :

If $A=\frac{1}{2}\begin{bmatrix}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{bmatrix}$, then :