List of top Questions asked in JEE Main- 2023

Let $𝑎_1=𝑏_1=1$and $𝑎_𝑛=𝑎_{𝑛−1}+(𝑛−1)$, $𝑏_𝑛=𝑏_{𝑛−1}+𝑎_{𝑛−1}$, $∀𝑛≥2$. If $𝑆= \displaystyle\sum_{ 𝑛=1}^{10}\frac {𝑏_𝑛}{2^𝑛}$ and $𝑇= \displaystyle\sum_{𝑛=1}^{8} \frac {𝑛}{2^{𝑛−1}}$, then $2^7(2𝑆−𝑇)$ is equal to ____ .

A circle with centre $(2,3) $ and radius $4$ intersects the line $𝑥+𝑦=3$ at the points $𝑃$ and $𝑄$. If the tangents at $𝑃$ and $𝑄$ intersect at the point $S(α,β)$, then $4α−7β$ is equal to _____ .

Let ${a_k}$ and ${b_k}$, $𝑘∈N$, be two G.P.s with common ratios $r_1$ and $r_2$ respectively such that $a_1= b_1=4$ and $r_1<r_2$. Let $c_k=a_k+b_k$, $k∈N$. If $c_2=5$ and $c_3=\frac {13}{4}$, then $ \displaystyle\sum_{k=1}^{∞ }c_k−(12a_6+8b_4)$ is equal to _____ .

Let $α=8−14𝑖$, $𝐴=\{z∈C:\frac {αz−\bar α\bar z}{z^2−(\bar z)^2−112i }=1\}$ and $𝐵={𝑧∈C:|𝑧+3𝑖|=4}$. Then $∑_{𝑧∈𝐴∩𝐵 }(\text {𝑅𝑒}\ ⁡𝑧−\text {𝐼𝑚⁡}\ 𝑧)$ is equal to _____ .

Let $A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]$, where $i=\sqrt{-1}$ If $M = A ^{ T } B A$, then the inverse of the matrix $AM ^{2023} A ^{ T }$ is

The surface tension of a soap bubble is $2 \times 10^{-2} \, \text{N/m}$. Work done to increase the radius of the bubble from 3.5 cm to 7 cm will be:

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of the car will be, if the friction coefficient between tyres and road is 0.34. (Take g = 10 m/s²):

The magnitude of magnetic induction at the mid-point O due to the current arrangement shown in the figure is:

A stone is projected at an angle of $30\degree$ to the horizontal. The ratio of kinetic energy at projection to its kinetic energy at the highest point is:

Two particles of equal mass ‘m’ move in a circle of radius ‘r’ under the action of their mutual gravitational attraction. The speed of each particle will be :

A bicycle tyre is filled with air having pressure of 270 kPa at $27\degree C$. The approximate pressure of the air in the tyre when the temperature increases to $36\degree C$ is:

Match List I with List II:

List-I (Physical Quantity)		List-II (Dimensional Formula)
(A)	Pressure Gradient	(I)	$[M^0L^2T^{–2}]$
(B)	Energy density	(II)	$[M^1L^{–1}T^{–2}]$
(C)	Electric field	(III)	$[M^1L^{–2}T^{–2}]$
(D)	Latent heat	(IV)	$[M^1L^1T^{–3}A^{–1}]$

Choose the correct answer from the options given below:

In a Young’s double slit experiment, two slits are illuminated with light of wavelength $800 \, \text{nm}$. The first minimum is detected at $P$. The value of slit separation $a$ is:

If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be:
Given: Earth’s radius = $6.4 \times 106\text{ m}$

Find the mutual inductance in the arrangement, when a small circular loop of radius R is placed inside a large square loop of side $L$ ($L \gg R$). The loops are coplanar and their centers coincide:

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is:

The threshold wavelength for photoelectric emission from a material is $5500Å$. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a
A. 75 W infra-red lamp
B. 10 W infra-red lamp
C. 75 W ultra-violet lamp
D. 10 W ultra-violet lamp
Choose the correct answer from the options given below:

A person observes two moving trains, ‘A’ reaching the station and ‘B’ leaving the station with equal speed of 30 m/s. If both trains emit sounds with frequency 300 Hz, (Speed of sound: 330 m/s) approximate difference of frequencies heard by the person will be:

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cm/s. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be _____ mV.

A 0.4 kg mass takes 8 s to reach ground when dropped from a certain height ‘P’ above surface of earth. The loss of potential energy in the last second of fall is ____ J. (Take g = 10 m/s²)

Three identical polaroids $P_1$, $P_2$, and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclined at angles of $60^\circ$ and $90^\circ$ with respect to the axis of $P_1$. The source $S$ has an intensity of $\frac{256 \, \text{W}}{\text{m}^2}$. The intensity of light at point $O$ is _____ $\frac{\text{W}}{\text{m}^2}$.

A point charge $q_1 = 4q_0$ is placed at origin. Another point charge $q_2 = –q_0$ is placed at $x = 12\text{ cm}$. Charge of proton is q₀. The proton is placed on x axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is _____ cm.

A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ____ ms^–1.

In a metre bridge experiment, the balance point is obtained if the gaps are closed by $2 \Omega$ and $3 \Omega$. A shunt of $X \Omega$ is added to $3 \Omega$ resistor to shift the balancing point by 22.5 cm. The value of X is _______ .

A radioactive element ${}^{242}_{92}X$ emits two $\alpha$-particles, one electron, and two positrons. The product nucleus is represented by ${}^{234}_{P}Y.$ The value of $P$ is _______.