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Comprehensive Question Bank & Study Notes

Multiple Choice Questions

1 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1224
Detector $D$ moves from $A$ to $B$ and observe the frequencies are differing by $10~Hz$. Source is emitting frequency $f_{0}$ as shown: Speed of detector is $35$ times less than speed of sound. Then $f_{0}$ is :
(A) $400~Hz$
(B) $350~Hz$
(C) $250~Hz$
(D) $150~Hz$
HARD
2 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1215
In series R-L circuit, voltage of battery is $10~V$. Resistance and inductance are $10~\Omega$ and $10~mH$ respectively. Find energy stored in the inductor when current reaches $\frac{1}{e}$ times of maximum value :
(A) $0.67~mj$
(B) $1.33~mj$
(C) $0.33~mj$
(D) $0.50~mj$
HARD
3 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1214
Two disc having same moment of inertia about their axis. Thickness is $t_{1}$ and $t_{2}$ and they have same density. If $R_{1}/R_{2}=1/2$, then find $t_{1}/t_{2}$ :
(A) $1/16$
(B) 16
(C) $1/4$
(D) 4
MEDIUM
4 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1194
A potential energy curve U vs x is shown. If $F_{AB}, F_{BC}, F_{CD}, F_{DE}$ are forces in respective regions, arrange magnitudes in decreasing order.
(A) $F_{BC}>F_{AB}>F_{CD}>F_{DE}$
(B) $F_{BC}>F_{AB}>F_{DE}>F_{CD}$
(C) $F_{AB}>F_{BC}>F_{DE}>F_{CD}$
(D) $F_{BC}>F_{DE}>F_{AB}>F_{CD}$
MEDIUM
5 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1189
Two mechanical waves travel on strings of equal length L and equal tension T. The linear mass densities are in ratio $\frac{\mu_{1}}{\mu_{2}}=\frac{1}{2}$. Find the ratio of time taken for a wave pulse to travel from one end to the other.
(A) $\frac{1}{2}$
(B) $\frac{1}{\sqrt{2}}$
(C) $\sqrt{2}$
(D) $2$
MEDIUM
6 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1183
Two rods of equal length 60 cm each are joined together end to end. The coefficients of linear expansion are $24\times10^{-6\circ}C^{-1}$ and $1.2\times10^{-5\circ}C^{-1}$. Initial temperature $30^{\circ}C$ is increased to $100^{\circ}C$. Find final length (in cm).
(A) $120.1321$
(B) $120.1123$
(C) $120.1512$
(D) $120.1084$
MEDIUM
7 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1182
A wave propagates whose electric field is given by $\vec{E}=69~\sin(\omega t-kx)\hat{j}$. Find the direction of the magnetic field.
(A) $\hat{k}$
(B) $-\hat{k}$
(C) $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
(D) $\frac{\hat{i}-\hat{j}}{\sqrt{2}}$
MEDIUM
8 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1176
An ideal solenoid is kept with its axis vertical. A current $I_{0}$ is flowing in the solenoid. A charge q is thrown vertically downward inside the solenoid. The acceleration of the charged particle is:
(A) $g$ downward
(B) $g$ upward
(C) Zero
(D) Depends on current $I_{0}$
MEDIUM
9 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1175
Find the volume flow rate in the Venturi meter shown below in which water is flowing. Given $\frac{A}{a}=2$, $A=\sqrt{3}m^{2}$, difference in levels is 5 cm and $\rho=1000~kg~m^{-3}$.
(A) $1$
(B) $\sqrt{3}$
(C) $2\sqrt{3}$
(D) $\sqrt{2}$
MEDIUM
10 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1169
If the electric field of an EM wave is given by $60[\sin(3\times10^{14}t)+\sin(12\times10^{14}t)]$ at $x=0$ and it falls on a photosensitive material having work function $2.8 eV$, find the maximum kinetic energy (in eV) of the ejected electrons.
(A) $2.52 eV$
(B) $2.16 eV$
(C) $2.00 eV$
(D) $2.34 eV$
MEDIUM
11 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1168
Find the moment of inertia of the system formed using two identical rods about the given axis of rotation as shown in the figure. Each rod has mass M and length L.
(A) $\frac{17}{12}ML^{2}$
(B) $\frac{13}{12}ML^{2}$
(C) $\frac{2}{3}ML^{2}$
(D) $\frac{3}{4}ML^{2}$
MEDIUM
12 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1164
An air-filled capacitor of capacitance $C$ is filled with a dielectric $(k=3)$ of width $\frac{d}{3}$, where $d$ is the separation between the plates. The new capacitance is:
(A) $C$
(B) $\frac{9}{7}C$
(C) $\frac{12}{7}C$
(D) $\frac{3}{7}C$
MEDIUM
13 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1163
An $\alpha$-particle having kinetic energy $7.7 MeV$ is approaching a fixed gold nucleus (atomic number $Z=79$). Find the distance of closest approach. (Duplicate Question)
(A) $1.72 nm$
(B) $6.2 nm$
(C) $16.8 nm$
(D) $0.2 nm$
MEDIUM
14 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1161
An $\alpha$-particle having kinetic energy $7.7 MeV$ is approaching a fixed gold nucleus (atomic number $Z=79$). Find the distance of closest approach.
(A) $1.72 nm$
(B) $6.2 nm$
(C) $16.8 nm$
(D) $0.2 nm$
HARD
15 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1157
Find the heat produced in the external circuit (AB) in one second (refer to circuit diagram).
(A) $1181.25 J$
(B) $1311.25 J$
(C) $1207.50 J$
(D) $1410.50 J$
HARD
16 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1153
Find dimensions of $\frac{A}{B}$ if $(P+\frac{A^{2}}{B})+\frac{1}{2}\rho V^{2}=$ constant, where $P\rightarrow$ pressure, $\rho\rightarrow$ density, $V$ speed.
(A) $ML^{1}T^{-4}$
(B) $ML^{-1}T^{-4}$
(C) $ML^{2}T^{-4}$
(D) $ML^{-1}T^{-2}$
HARD
17 Competency APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1145
Ratio of de-Broglie wavelengths of a proton and an alpha particle accelerated through the same potential is:
(A) $1:2$
(B) $2\sqrt{2}:1$
(C) $2:1$
(D) $\sqrt{8}:1$
MEDIUM
18 Knowledge APPLY MCQ_SINGLE 4 Mark(s) 2026 JEE Main 2026 (Online) 21st January Morning Shift
#1144
Two capacitors $C$ and $2C$ charged to $V$ and $2V$ respectively are connected in parallel with opposite polarity. The common potential is:
(A) $V$
(B) $\frac{V}{2}$
(C) $2V$
(D) $3V$
MEDIUM

Multiple Selection Questions

1 Knowledge APPLY MCQ_MULTI 2 Mark(s)
#1893
what is your name
(A) 1
(B) 2
(C) 3
(D) 4

NUMERICAL

1 Competency APPLY NUMERICAL 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1225
Given $E=10~V$, $R=10$, $L=10~mH$, $\frac{N}{e}=10^{4}$. Find energy density when current is $-\frac{1}{e}$ of max. If value is $a \frac{\pi}{e^{2}}$. Find $a$ .
HARD
2 Competency APPLY NUMERICAL 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1223
A simple pendulum with bob (mass $m$ and charge $q$) is in equilibrium in presence of horizontal electric field $E$ then tension in thread is .
HARD
3 Competency APPLY NUMERICAL 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1222
Six charges (four $+q$, two $-q$) are present at circle of radius $r$ and centred at origin as shown. Electric field at origin is .
HARD
4 Competency APPLY NUMERICAL 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1221
In a potentiometer null point for two resistance $R_{1}$ and $R_{2}$ is at $40~cm$ as shown. If $16~\Omega$ is connected in parallel to $R_{2}$ then null point is at $50~cm$ then $R_{1}$ and $R_{2}$ are respectively .
HARD
5 Competency APPLY NUMERICAL 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1220
Match the following : \begin{tabular}{|l|l|} \hline List -1 & List-II \\ \hline (A) Spring constant & (i) $ML^{2}T^{-2}K^{-1}$ \\ \hline (B) Thermal conductivity & (ii) $ML^{0}T^{-2}$ \\ \hline (C) Boltzmann constant & (iii) $ML^{2}T^{-2}A^{-2}$ \\ \hline (D) inductance & (iv) $ML^{2}T^{-3}K^{-1}$ \\ \hline & (v) $M^{1}L^{-1}T^{-2}$ \\ \hline & (vi) $ML^{2}T^{-2}$ \\ \hline \end{tabular}
HARD
6 Competency APPLY NUMERICAL 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1219
A projectile is thrown upward at an angle $60^{\circ}$ with the horizontal. The speed of the projectile is $20~m/s$ when its direction of motion is $45^{\circ}$ with horizontal. The initial speed of particle is .
HARD
7 Competency APPLY NUMERICAL 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1218
If radius and density of planet $A$ are $R$ and $\rho$ respectively and escape velocity of planet $A$ is $10~km/h$. If radius of planet $B$ is $10\%$ of planet $A$ and $\rho_B = 10\%$ planet of $A$. Calculate of escape velocity of planet $B$ .
HARD
8 Competency APPLY NUMERICAL 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1217
In the given situation force at center on $1~kg$ mass is $F_{1}$. Now if $4~m$ and $3~m$ is interchanged the force is $F_{2}$ Given: $\frac{F_{1}}{F_{2}}=\frac{2}{\sqrt{\alpha}}$ Find $\alpha$ . (Diagram shows masses $4m$, $3m$, $m$, $2m$ arranged around a center point) .
HARD
9 Competency APPLY NUMERICAL 4 Mark(s) 2026 JEE Main 2026 (Online) 22 January Morning Shift
#1216
Given $\vec{E}=10x\hat{i}+5y\hat{j}$. Potential at $(10, 20)$ is $500~V$. Find potential at origin .
HARD