2026

JEE Main 2026 (Online) 22 January Morning Shift

Full Paper Analysis & Solutions

Physics

Multiple Choice Questions

1 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#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
2 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#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
#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

NUMERICAL

1 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1216
Given $\vec{E}=10x\hat{i}+5y\hat{j}$. Potential at $(10, 20)$ is $500~V$. Find potential at origin .
HARD
2 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#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
3 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#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
4 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#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
5 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#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
#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
7 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#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
8 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#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
9 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#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

Mathematics

Multiple Choice Questions

1 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1195
If sum of first 4 terms of an A.P. is 6 and sum of first 6 terms is 4, then sum of first 12 terms of an A.P. is :
(A)
-22
(B)
-21
(C)
-23
(D)
-24
MEDIUM
2 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1196
If $xdy-ydx=\sqrt{x^{2}+y^{2}}dx$ and $y(1)=0$, then $y(3)=\_$ :
(A)
2
(B)
4
(C)
6
(D)
1
MEDIUM
3 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1198
Coefficient of $x^{48}$ in $1.(1+x)+2.(1+x)^{2}+3.(1+x)^{3}+...+100(1+x)^{100}$ is :
(A)
$^{101}C_{4\epsilon}-100$
(B)
$100(^{101}C_{49})-^{101}C_{50}$
(C)
$100(^{101}C_{46})-^{101}C_{47}$
(D)
$^{101}C_{47}-^{101}C_{46}$
HARD
4 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1200
If the domain of the function $\frac{1}{\ln(10-x)}+\sin^{-4}(\frac{x+2}{2x+3})$ is $(-\infty,-a]\cup(-1,b)\cup(b,c)$ then $b+c+3a$ is Equal to :
(A)
22
(B)
24
(C)
23
(D)
21
HARD
5 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1201
Let $M=\{1,2,3,...,16\}$ and $R=\{(x,y):4y=5x-3,x,y\in M\}$. Then the number of elements to be added in $R$ to make it symmetric is :
(A)
4
(B)
3
(C)
2
(D)
1
MEDIUM
6 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1204
Value of $\int_{-\pi/2}^{\pi/2}\frac{dx}{[x]+4}$: is $-\pi/2$ where $[.]$ is GIF .
(A)
$\frac{\pi}{20}+\frac{7}{20}$
(B)
$\frac{7\pi}{20}-\frac{7}{60}$
(C)
$\frac{7\pi}{20}-\frac{1}{60}$
(D)
$\frac{7\pi}{20}+\frac{1}{60}$
HARD
7 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1205
Two numbers '$a$' and '$b$' are chosen at random from the set $\{1,2,3,...,50\}$. The probability that $ab$ is divisible by 3, is :
(A)
664/1225
(B)
646/1225
(C)
527/1225
(D)
461/1225
MEDIUM
8 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1207
If $\frac{\cos^{2}48^{\circ}-\sin^{2}12^{\circ}}{\sin^{2}24^{\circ}-\sin^{2}6^{\circ}}=\frac{\alpha+\sqrt{5}\beta}{2}$, then $(\alpha+\beta)$ is :
(A)
3
(B)
2
(C)
4
(D)
1
MEDIUM
9 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1208
If a line $ax+y=1$ does not intersect the hyperbola $x^{2}-9y^{2}=9$, then possible value of $a$ is :
(A)
0.2
(B)
0.3
(C)
0.4
(D)
0.5
MEDIUM
10 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1210
If $\int(\cos x)^{-5/2}(\sin x)^{-11/2}dx=\frac{P_{1}}{q_{1}}(\cot x)^{9/2}+\frac{P_{2}}{q_{2}}(\cot x)^{5/2}+\frac{P_{3}}{q_{3}}(\cot x)^{1/2}-\frac{P_{4}}{q_{4}}(\cot x)^{-3/2}+C$, then $\frac{15P_{1}P_{2}P_{3}P_{4}}{q_{1}q_{2}q_{3}q_{4}}$ is equal to :
(A)
14
(B)
16
(C)
10
(D)
9
HARD

NUMERICAL

1 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1197
If probability distribution is given by : $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline X & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline P(x) & k & 2k^{2} & 6k^{2} & k^{2}+k & 3k & k & k & k & k & k^{2} \\ \hline \end{array} $$ then $P(3
HARD
2 APPLY NUMERICAL 4 Mark(s) 2026
#1199
The number of real solutions of equation $x|x+4|+3|x+2|+10=0$ is equal to .
MEDIUM
3 APPLY NUMERICAL 4 Mark(s) 2026
#1202
Let $A=\begin{bmatrix}2&3\\3&5\end{bmatrix}$ , then $|A^{2025}-3A^{2024}-A^{2023}|$ is equal to .
MEDIUM
4 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1203
Let $\int_{1}^{x}f(t)dt=3xf(x)-x^{3}+4$, then $f(2)-f(3)$ is .
HARD
5 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1206
Let $Q(5,b,c)$ be the mirror image of $P(1,3,a)$ with respect to the line $\frac{x-1}{3}=\frac{y-3}{2}=\frac{z-2}{2}$, then the value of $a^{2}+b^{2}+c^{2}$ is .
HARD
6 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1209
If the area of the region $\{(x,y):x^{2}+1\le y\le3-x\}$ is divided by the line $x=-1$ in the ratio $m : n$, where $\gcd(m,n)=1$. Then the value of $m+n$ is .
HARD
7 APPLY NUMERICAL 4 Mark(s) 2026
#1211
Find number of solutions of $\tan^{-1}4x+\tan^{-1}6x=\frac{\pi}{6}$ in $(\frac{-1}{2\sqrt{6}},\frac{1}{2\sqrt{6}})$ .
MEDIUM
8 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1212
Let $A$ satisfy the equation $\lambda\begin{bmatrix}1\\2\\3\end{bmatrix}=\begin{bmatrix}-1\\0\\3\end{bmatrix}$, and $|2\text{adj}(A+I)|=2^{\alpha}3^{\beta}11^{\gamma}$ then $\alpha+\beta+\gamma$ is equal to .
HARD
9 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1213
Chord joining at two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ on the parabola $y^{2}=12x$ intersect at right angle at the vertex, then $x_{1}x_{2}-y_{1}y_{2}=$ .
MEDIUM

Chemistry

Multiple Choice Questions

1 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1226
In adiabatic compression temperature of gas becomes $4$ times while volume decreased $1/2$ times find $\gamma$ :
(A)
1
(B)
2
(C)
3
(D)
4
HARD
2 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1227
Arrange the given metal ion in increasing order of unpaired electron in low spin complexes formed by $Mn^{3+}, Cr^{3+}, Fe^{3+}, Co^{3+}$ :
(A)
$Mn^{3+}\lt Cr^{3+}\lt Fe^{3+}\lt Co^{3+}$
(B)
$Co^{3+}\lt Fe^{3+}\lt Mn^{3+}\lt Cr^{3+}$
(C)
$Co^{3+} \lt Fe^{3+} \lt Cr^{3+} \lt Mn^{3+}$
(D)
$Fe^{3+} \lt Co^{3+} \lt Mn^{3+} \lt Cr^{3+}$
HARD
3 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1228
Arrange following in order of $S_{N}1$ reaction : (Structures A, B, C, D are given with a $Br$ atom and $Ph$ groups) .
(A)
$A>B>C>D$
(B)
$D>C>B>A$
(C)
$B>C>D>A$
(D)
$B>A>C>D$
HARD
4 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1229
What is the formal charge of atoms numbered as 1, 2, 3 and 4. In following structure :
(A)
0, +1, 0, -1
(B)
0, 0, -, +1
(C)
+1, -1, 0, 0
(D)
-1, +1, 0, 0
HARD
5 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1230
Statement-1: $NO_{2}$ is electron withdrawing group. Statement-2: Nitrobenzene is meta-directing. Statement-3: Nitrobenzene does not give Friedel Crafts alkylation :
(A)
Statement-1 and Statement-2 are correct and Statement-3 incorrect .
(B)
All Statements are wrong .
(C)
All Statements are correct .
(D)
Statement-1 and Statement-2 are incorrect and Statement-3 correct .
HARD
6 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1232
Match the following and choose the correct option : \begin{tabular}{|l|l|} \hline List-1 & List-II \\ \hline (A) $[Ag(NH_{3})_{2}]^{+}$ & (i) Fehling's solution \\ \hline (B) $Zn-Hg/HCl$ & (ii) Clemmenson's reduction \\ \hline (C) $NH_{2}-NH_{2}/KOH$ & (iii) Tollen's reagent \\ \hline (D) $Cu^{2+}/OH^{-}$ & (iv) Wolff-Kishner reduction \\ \hline \end{tabular}
(A)
(A)-(i), (B)-(ii), (C)-(iii), (D)-(iv)
(B)
(A)-(iv), (B)-(iii), (C)-(ii), (D)-(i)
(C)
(A)-(iii), (B)-(ii), (C)-(iv), (D)-(i)
(D)
(A)-(i), (B)-(ii), (C)-(iv), (D)-(iii)
HARD
7 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1233
$XF_{3}$ (Lewis Acid), $YF_{3}$ (Lewis Base) . Hybridisation of $XF_{3}$, $YF_{3}$ respectively are :
(A)
$sp^{2}, sp^{3}$
(B)
$sp^{2}, sp^{2}$
(C)
$sp^{3}, sp^{3}$
(D)
$sp^{3}, sp^{2}$
HARD
8 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1235
Calculate volume of $H_2$ gas at STP in $ml$. If $2.7~g$ of aluminium is treated with excess $HCl$. (Volume of 1 mole gas at $STP=22.4~L$) :
(A)
3.36
(B)
1.12
(C)
2.24
(D)
5.6
HARD
9 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1236
Given below are two statements . Statement-1: $HX$ bond length is higher in $HCl$ than $HF$ . Statement-2: The lowest boiling point in hydride of group 15 element is having covalency 4 .
(A)
Both Statement-1 and Statement-2 is correct .
(B)
Both Statement-1 and Statement-2 is incorrect .
(C)
Statement-1 is correct but Statement-2 is incorrect .
(D)
Statement-1 is incorrect but Statement-2 is correct .
HARD
10 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1237
Statement-1: $\text{Phenol} + CHCL_{3} \xrightarrow{KOH} \text{major} + \text{minor}$. Major product is ortho substituted and para substituted product is minor . Statement-2: Ortho \& Para product can be separated by steam distillation .
(A)
Both Statement-1 and Statement-2 is correct .
(B)
Both Statement-1 and Statement-2 is incorrect .
(C)
Statement-1 is correct but Statement-2 is incorrect .
(D)
Statement-1 is incorrect but Statement-2 is correct .
HARD
11 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1239
Which of the following is the correct order of the reactivity of given nucleophiles when treated with $CH_{3}$ in methanol? $F^{-}$, $I^{-}$, $C_{2}H_{5}O^{-}$, $C_{6}H_{5}O^{-}$ :
(A)
$I^{-}>C_{2}H_{5}O^{-}>C_{6}H_{5}O^{-}>F^{-}$
(B)
$I^{-}>F^{-}>C_{2}H_{5}O^{-}>C_{6}H_{5}O^{-}$
(C)
$I^{-}>C_{2}H_{5}O^{-}>F^{-}>C_{6}H_{5}O^{-}$
(D)
$C_{6}H_{5}O^{-}>F^{-}>I^{-}>C_{2}H_{5}O^{-}$
HARD
12 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1241
In organic compound with molecular formula ($X$) $C_{8}H_{9}NO$ when reacts with $KOH/Br_{2}$ forms '$P$' which on diazotization forms '$Q$' followed by its reaction with $CuCN$ forms '$R$' which on hydrolysis (acidic) formed '$S$' ($S$ can also be made by hydrolysis of original compound ($X$) ($C_{8}H_{9}NO$). $S$ on reaction with $KMnO_{4}/H^{+}$ forms '$T$' which has two types of hydrogen $X$ will be :
(A)
$\text{Structure 1 (with } CH \text{ and } CONH_2 \text{ groups)}$
(B)
$\text{Structure 3 (with } CH_3 \text{ and } CONH_2 \text{ groups)}$
(C)
$\text{Structure 2 (with } CONH \text{ group)}$
(D)
$\text{Structure 4 (with } CH_2-C-NH_2 \text{ group)}$
HARD
13 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1243
Consider a first order reaction: $A\to \text{products}$ . 3 different solutions are taken rate of reaction : Solution 1: $100mL~10M~'A' - r_{1}$ ; Solution 2: $200mL~10M~'A' - r_{2}$ ; Solution 3: $100mL~10M~'A' + 100ml~\text{water} - r_{3}$ . The correct order of the rates of reactions is :
(A)
$r_{1}=r_{2}=r_{3}$
(B)
$r_{1}=r_{2} \lt r_{3}$
(C)
$r_{1}=r_{2}\gt r_{3}$
(D)
$r_{1} \lt r_{2}=r_{3}$
MEDIUM

NUMERICAL

1 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1231
Statement-l: Sucrose is dextrorotatory and upon hydrolysis it becomes laevorotatory . Statement-II: Sucrose on hydrolysis gives glucose and fructose such that the laevo rotation of glucose is more than dextrorotation of fructose .
HARD
2 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1234
Find the energy to excite electron from first Bohr orbit of hydrogen atom to 2nd Bohr's orbit. (in $eV$) .
HARD
3 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1238
The $3d$-block element which does not liberate hydrogen gas on reaction with dilute $HCl$ is .
HARD
4 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1240
Which of the following graph(s) is/are correct? ($P_{\text{gas}}$ vs $X_{\text{solvent}}$ is plotted) .
HARD
5 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1242
Given below are two statements . Statement-I : $K_{H}$ is constant with change in concentration of gas till solution is dilute at given temperature . Statement II: According to Henry's Law, partial pressure of gas in vapour phase is inversely proportional to mole fraction of gas in solution .
HARD