JEE Main 5 April 2026 Shift 1 Question Paper

Question 1

Let $a, b \in \mathbb{C}$. Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$. If $\beta - \alpha = \sqrt{11}$ and $\beta^2 - \alpha^2 = 3i\sqrt{11}$, then $(\beta^3 - \alpha^3)^2$ is equal to:

Accepted Answer

(B) 176

Answer

(A) 160

Answer

(C) 194

Answer

(D) 187

Question 2

Let the sum of the first $n$ terms of an A.P. be $3n^2 + 5n$. Then the sum of squares of the first 10 terms of the A.P. is:

Accepted Answer

(C) 15220

Answer

(A) 10220

Answer

(B) 12860

Answer

(D) 19780

Question 3

Let $A$ be a $3 	imes 3$ matrix such that $A^T \begin{bmatrix}1\0\1\end{bmatrix} = \begin{bmatrix}5\2\2\end{bmatrix}$, $A^T \begin{bmatrix}0\0\1\end{bmatrix} = \begin{bmatrix}3\1\1\end{bmatrix}$, $A \begin{bmatrix}1\0\1\end{bmatrix} = \begin{bmatrix}3\4\4\end{bmatrix}$ and $A \begin{bmatrix}0\0\1\end{bmatrix} = \begin{bmatrix}1\3\1\end{bmatrix}$. If $\det(A) = 1$, then $\det(\mathrm{adj}(A^2 + A))$ is equal to:

Accepted Answer

(D) 64

Answer

(A) 16

Answer

(B) 25

Answer

(C) 49

Question 4

Consider the system of linear equations in $x$, $y$, $z$:
$x + 2y + tz = 0$,
$6x + y + 5tz = 0$,
$3x + t^2 y + f(t)z = 0$,
where $f : \mathbb{R} 	o \mathbb{R}$ is a differentiable function. If this system has infinitely many solutions for all $t \in \mathbb{R}$, then $f$

Accepted Answer

(B) is strictly increasing on $\mathbb{R}$

Answer

(A) is a constant function

Answer

(C) is strictly decreasing on $\mathbb{R}$

Answer

(D) has two critical points

Question 5

$\sum_{n=1}^{10}\left(\frac{528}{n(n+1)(n+2)}\right)$ is equal to:

Accepted Answer

(B) 130

Answer

(A) 65

Answer

(C) 220

Answer

(D) 440

Question 6

Let $	an A$, $	an B$, where $A, B \in \left(-\frac{\pi}{2}, \frac{\pi}{2}ight)$, be the roots of the quadratic equation $x^2 - 2x - 5 = 0$. Then $20\sin^2\left(\frac{A+B}{2}ight)$ is equal to:

Accepted Answer

(C) $10 - 3\sqrt{10}$

Answer

(A) $10 + \sqrt{10}$

Answer

(B) $10 - 2\sqrt{10}$

Answer

(D) $10 - \sqrt{10}$

Question 7

A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:

Accepted Answer

(B) $\frac{10}{17}$

Answer

(A) $\frac{7}{10}$

Answer

(C) $\frac{12}{19}$

Answer

(D) $\frac{7}{19}$

Question 8

The mean deviation about the mean for the data is equal to:

Accepted Answer

(C) $\frac{44}{13}$

Answer

(A) $\frac{40}{13}$

Answer

(B) $\frac{42}{13}$

Answer

(D) $\frac{46}{13}$

Question 9

Let a focus of the ellipse $E : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ be $S(4,0)$ and its eccentricity be $\frac{4}{5}$. If the point $P(3, \alpha)$ lies on $E$ and $O$ is the origin, then the area of $	riangle POS$ is equal to:

Accepted Answer

(C) 24/5

Answer

(A) 12/5

Answer

(B) 14/5

Answer

(D) 48/5

Question 10

Let $P$ be a moving point on the circle $x^2 + y^2 - 6x - 8y + 21 = 0$. Then, the maximum distance of $P$ from the vertex of the parabola $x^2 + 6x + y + 13 = 0$ is equal to:

Accepted Answer

(C) 12

Answer

(A) 8

Answer

(B) 10

Answer

(D) 9

Question 11

In an equilateral triangle $PQR$, let the vertex $P$ be at $(3,5)$ and the side $QR$ be along the line $x + y = 4$. If the orthocentre of the triangle $PQR$ is $(\alpha, \beta)$, then $9(\alpha + \beta)$ is equal to:

Accepted Answer

(D) 48

Answer

(A) 16

Answer

(B) 27

Answer

(C) 36

Question 12

The sum of all the integral values of $p$ such that the equation $3\sin^2 x + 12\cos x - 3 = p$, $x \in \mathbb{R}$, has at least one solution, is:

Accepted Answer

(C) $-75$

Answer

(A) $-54$

Answer

(B) $-60$

Answer

(D) $-84$

Question 13

The square of the distance of the point $P(5,6,7)$ from the line $\frac{x-2}{2} = \frac{y-5}{3} = \frac{z-2}{4}$ is equal to:

Accepted Answer

(C) 6

Answer

(A) 3

Answer

(B) 5

Answer

(D) 8

Question 14

Let $\vec{a} = \sqrt{7}\hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = \hat{j} + 2\hat{k}$. If $\vec{r}$ is a vector such that $\vec{r} 	imes \vec{a} + \vec{a} 	imes \vec{b} = \vec{0}$ and $\vec{r} \cdot \vec{a} = 0$, then $|3\vec{r}|^2$ is equal to:

Accepted Answer

(A) 44

Answer

(B) 54

Answer

(C) 86

Answer

(D) 132

Question 15

The square of the distance of the point of intersection of the lines $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(a\hat{i} - \hat{j})$, $a 
eq 0$ and $\vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + a\hat{k})$ from the origin is:

Accepted Answer

(C) 17

Answer

(A) 5

Answer

(B) 10

Answer

(D) 26

Question 16

The product of all possible values of $\alpha$, for which $\lim\limits_{x 	o 0} \left( \frac{1 - \cos(\alpha x)\cos((\alpha + 1)x)\cos((\alpha + 2)x)}{\sin^2((\alpha + 1)x)} ight) = 2$, is:

Accepted Answer

(C) $-1$

Answer

(A) $-2$

Answer

(B) 1

Answer

(D) $\frac{5}{4}$

Question 17

The value of the integral $\int_0^\infty \frac{\log_e(x)}{x^2 + 4}\,dx$ is:

Accepted Answer

(B) $\frac{\pi \log_e(2)}{4}$

Answer

(A) $\frac{\pi \log_e(2)}{2}$

Answer

(C) $1 + \pi \log_e(2)$

Answer

(D) $2 + \pi \log_e(2)$

Question 18

Let $f : \mathbb{R} 	o \mathbb{R}$ be a differentiable function such that $f\left(\frac{x + y}{3}ight) = \frac{f(x) + f(y)}{3}$ for all $x, y \in \mathbb{R}$, and $f'(0) = 3$. Then the minimum value of the function $g(x) = 3 + e^x f(x)$, is:

Accepted Answer

(B) $3\left(\frac{e - 1}{e}\right)$

Answer

(A) $3\left(\frac{e + 1}{e}\right)$

Answer

(C) $\frac{3 - e}{e}$

Answer

(D) $3e$

Question 19

The value of the integral $\int_{\pi/6}^{\pi/3} \left( \frac{4 - \csc^2 x}{\cos^4 x} \right) dx$ is:

Accepted Answer

(C) $\frac{32}{3\sqrt{3}}$

Answer

(A) $\frac{11}{\sqrt{3}}$

Answer

(B) $\frac{16}{\sqrt{3}}$

Answer

(D) $\frac{64}{3\sqrt{3}}$

Question 20

Let $A = \{1, 2, 3, 4, 5, 6\}$. The number of one-one functions $f : A 	o A$ such that $f(1) \geq 3$, $f(3) \leq 4$ and $f(2) + f(3) = 5$, is __________.

Accepted Answer

72

Question 21

Two players $A$ and $B$ play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player $A$ wins the series is __________.

Accepted Answer

126

Question 22

If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3} - x^4ight)^n$, $x 
eq 0$, is zero, then the value of $n$ is __________.

Accepted Answer

21

Question 23

If $\frac{\pi}{4} + \sum\limits_{p=1}^{11} 	an^{-1}\left(\frac{2^{p-1}}{1 + 2^{2p-1}}ight) = \alpha$, then $	an\alpha$ is equal to __________.

Accepted Answer

2048

Question 24

Let $y = y(x)$ be the solution of the differential equation $x\sin\left(\frac{y}{x}\right) dy = \left(y\sin\left(\frac{y}{x}\right) - x\right) dx$, $y(1) = \frac{\pi}{2}$ and let $\alpha = \cos\left(\frac{y(e^{12})}{e^{12}}\right)$. Then the number of integral values of $p$, for which the equation $x^2 + y^2 - 2px + 2py + \alpha + 2 = 0$ represents a circle of radius $r \leq 6$, is __________.

Accepted Answer

6

Question 25

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and 7$^{	ext{th}}$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has

Accepted Answer

(C) 0.07 cm positive zero error

Answer

(A) 0.07 cm negative zero error

Answer

(B) 0.7 cm negative zero error

Answer

(D) 0.7 cm positive zero error

Question 26

$L$, $C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $ML^2T^{-4}A^{-2}$ corresponds to __________.

Accepted Answer

(A) $\frac{R}{\sqrt{LC}}$

Answer

(B) $\frac{R}{LC}$

Answer

(C) $\frac{C}{\sqrt{LR}}$

Answer

(D) $\frac{1}{R}\sqrt{\frac{L}{C}}$

Question 27

When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in $g$ is approximately $\alpha$ %. The value of $\alpha$ is ______.
(Take radius of the earth $=$ 6400 km.)

Accepted Answer

(B) 0.25

Answer

(A) 0.12

Answer

(C) 0.50

Answer

(D) 0.75

Question 28

Three masses $m_1 = 4$ kg, $m_2 = 4$ kg and $m_3 = 6$ kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of $T_1/T_2$ is ______.
(take $g = 10$ m/s$^2$)

Accepted Answer

(A) $5/3$

Answer

(B) $2/3$

Answer

(C) $3/5$

Answer

(D) $2/5$

Question 29

A wedge $Y$ with mass of 10 kg and all frictionless surfaces and the inclined surface making 37° with horizontal. A block $X$ with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $t = 0$ wedge $(Y)$ is pulled toward right with constant force $(f)$ of 24 N. Taking the block $X$ at rest at $t = 0$, the time taken by it to slide down 8.8 m on the slope, while $Y$ is on the move, is ______ s.
(take $	an(37°) = 3/4$ and $g = 10$ m/s$^2$)

Accepted Answer

(A) 2

Answer

(B) 4

Answer

(C) $\sqrt{2}$

Answer

(D) $2\sqrt{2}$

Question 30

The Young's modulus of steel wire of radius $r$ and length $L$ is $Y$. If the radius $r$ and length $L$ of the wire are doubled then the value of $Y$

Accepted Answer

(C) remains unchanged

Answer

(A) increases by two times

Answer

(B) reduces by half

Answer

(D) becomes one fourth

Question 31

Consider the following statements:
A. Zeroth law of thermodynamics gives concept of temperature
B. First law of thermodynamics gives concept of internal energy
C. In isothermal expansion of ideal gas, $\Delta Q 
eq \Delta W$
D. Product of intensive and extensive variables is extensive
E. The ratio of any extensive variable to mass will be an extensive variable
Choose the correct combination of statements from the options given below:

Accepted Answer

(C) A, B and D Only

Answer

(A) C, D and E Only

Answer

(B) A, B and C Only

Answer

(D) B, C and D Only

Question 32

Refer to the figure given below. The values of $I_1$, $I_2$ and $I_3$ are __________.

Accepted Answer

(A) $I_1 = 2.5$ A, $I_2 = 1.875$ A, $I_3 = 1.875$ A

Answer

(B) $I_1 = 1.875$ A, $I_2 = 2.5$ A, $I_3 = 1.875$ A

Answer

(C) $I_1 = 1.875$ A, $I_2 = 1.875$ A, $I_3 = 2.5$ A

Answer

(D) $I_1 = 2.5$ A, $I_2 = 2.5$ A, $I_3 = 1.875$ A

Question 33

An electron of mass $m$ is moving in an electric field $\vec{E} = -2E_0\hat{i}$ ($E_0 =$ constant $> 0$), with an initial velocity $\vec{V} = v_0\hat{i}$ ($v_0 =$ constant $> 0$). If $\lambda_0 = \frac{h}{4mv_0}$, its de Broglie wavelength at time $t$ is __________.
($e =$ charge of electron)

Accepted Answer

(C) $\frac{4\lambda_0}{\left[1 + \frac{2E_0e}{m}\frac{t}{v_0}\right]}$

Answer

(A) $\frac{4\lambda_0}{\left[1 - \frac{E_0e}{2m}\frac{t}{v_0}\right]}$

Answer

(B) $\frac{4\lambda_0}{\left[1 + \frac{E_0e}{2m}\frac{t}{v_0}\right]}$

Answer

(D) $\frac{4\lambda_0}{\left[1 - \frac{2E_0e}{m}\frac{t}{v_0}\right]}$

Question 34

In the hydrogen atom, the electron makes a transition from the higher orbit $(i)$ to a lower orbit $(f)$. The ratio of the radius of the orbits in given by $r_i : r_f = 16 : 4$. The wavelength of photon emitted due to this transition is ______ nm.
(Given Rydberg constant $= 1.0973 	imes 10^7$ /m)

Accepted Answer

(C) 486

Answer

(A) 121

Answer

(B) 242

Answer

(D) 974

Question 35

A displacement current of 4.0 A can be set up in the space between two parallel plates of 6 μF capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha 	imes 10^6$ V/s. The value of $\alpha$ is __________.

Accepted Answer

(B) 0.67

Answer

(A) 0.58

Answer

(C) 0.82

Answer

(D) 0.75

Question 36

Refer to the figure given below, current between terminals $A$ and $B$ is ______ A.

Accepted Answer

(B) 1.25

Answer

(A) 12.5

Answer

(C) 7.5

Answer

(D) 5

Question 37

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is 2.4 μm. If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be _____ μm.

Accepted Answer

(B) 2

Answer

(A) 1.2

Answer

(C) 2.4

Answer

(D) 2.88

Question 38

A ray of light passing through an equilateral prism is having velocity $2.12 	imes 10^{8}$ m/s in the prism material, then the minimum angle of deviation is _____ degrees.

Accepted Answer

(B) 30

Answer

(A) 45

Answer

(C) 28

Answer

(D) 58

Question 39

Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is $\alpha 	imes 10^{-19}$ J. The value of $\alpha$ is _____.
($h = 6.62 	imes 10^{-34}$ J s, $e = 1.6 	imes 10^{-19}$ C and $c = 3 	imes 10^{8}$ m/s)

Accepted Answer

(C) 5.68

Answer

(A) 3.68

Answer

(B) 4.68

Answer

(D) 2.68

Question 40

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

Accepted Answer

(A) increased two times

Answer

(B) increased $\frac{3}{2}$ times

Answer

(C) decreased two times

Answer

(D) decreased $\frac{3}{2}$ times

Question 41

Two wires as shown in the figure below, made of steel and have breaking stress of $12 	imes 10^{8}$ N/m$^{2}$. Area of cross-section of upper wire is 0.008 cm$^{2}$ and of lower wire is 0.004 cm$^{2}$. The maximum mass that can be added to pan without breaking any wire is _____ kg.
(take $g = 10$ m/s$^{2}$)

Accepted Answer

(B) 38

Answer

(A) 56

Answer

(C) 96

Answer

(D) 5.6

Question 42

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is

Accepted Answer

(C) $\sqrt{\frac{7}{8}}$

Answer

(A) $\sqrt{\frac{6}{7}}$

Answer

(B) $\sqrt{\frac{3}{5}}$

Answer

(D) $\sqrt{\frac{3}{4}}$

Question 43

For the given logic circuit, which of the following inputs combination will make both LED−1 and LED−2 to glow?

Accepted Answer

(C) $A = 1, B = 0, C = 1$

Answer

(A) $A = 0, B = 1, C = 1$

Answer

(B) $A = 1, B = 0, C = 0$

Answer

(D) $A = 1, B = 1, C = 0$

Question 44

A cube has side length 5 cm and modulus of rigidity $10^{5}$ N/m$^{2}$. The displacement produced by a force of 10 N in the upper face of cube is _____ mm.

Accepted Answer

2

Question 45

From 18 m height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is _____ m.
(Take $g = 10$ m/s$^{2}$ and neglect the air resistance)

Accepted Answer

13

Question 46

A transverse wave on a string is described by $y = 3\sin(36t + 0.018x + \pi/4)$, where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer)
($\pi = 3.14$)

Accepted Answer

349

Question 47

The charged particle moving in a uniform magnetic field of $(3\hat{i} + 2\hat{j})$ T has an acceleration $\left(4\hat{i} - \frac{x}{2}\hat{j}\right)$ m/s$^{2}$. The value of $x$ is _____.

Accepted Answer

12

Question 48

In the given circuit below inductance values of $L_1$, $L_2$ and $L_3$ are same. The magnetic energy stored in the entire circuit is $(U_t)$ and that stored in the $L_2$ inductor is $(U_l)$. $U_t/U_l$ is _____.
(Ignore the mutual inductance if any)

Accepted Answer

6

Question 49

How many grams of residue is obtained by heating 2.76 g of silver carbonate?
(Given: Molar mass of C, O and Ag are 12, 16 and 108 g mol$^{-1}$ respectively)

Accepted Answer

(B) 2.16 g

Answer

(A) 1.08 g

Answer

(C) 3.24 g

Answer

(D) 4.32 g

Question 50

Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.
A. $n = 3, l = 2, m = +1$
B. $n = 4, l = 0, m = 0$
C. $n = 6, l = 1, m = 0$
D. $n = 5, l = 1, m = +1$
E. $n = 2, l = 1, m = +1$
Choose the correct answer from the options given below:

Accepted Answer

(D) $E < B < A < D < C$

Answer

(A) $C < D < B < A < E$

Answer

(B) $B < A < E < C < D$

Answer

(C) $E < C < D < B < A$

Question 51

Identify the correct statements from the following:
A. Heisenberg uncertainty principle is applicable to electrons.
B. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital.
C. The energy of $2s$ orbital of H atom is equal to the energy of $2s$ orbital of Li.
D. The electronic configuration of Cr is $[\mathrm{Ar}]3d^5 4s^1$
Choose the correct answer from the options given below:

Accepted Answer

(B) A, B and D Only

Answer

(A) A, B and C Only

Answer

(C) B, C and D Only

Answer

(D) A, C and D Only

Question 52

What is the mole fraction of water in 10% by weight (w/w) of aqueous urea solution?
[Given: Molar mass of H, O, C and N are 1, 16, 12 and 14 g mol$^{-1}$ respectively.]

Accepted Answer

(D) 0.967

Answer

(A) 0.825

Answer

(B) 0.032

Answer

(C) 0.867

Question 53

$M_3A_2$ is a sparingly soluble salt of molar mass $y$ g mol$^{-1}$ and solubility $x$ g L$^{-1}$. The ratio of the molar concentration of the anion ($A^{3-}$) to the solubility product of the salt is

Accepted Answer

(A) $\frac{1}{54} \cdot \frac{y^4}{x^4}$

Answer

(B) $\frac{y^5}{108x^4}$

Answer

(C) $108 \cdot \frac{x^5}{y^5}$

Answer

(D) $\frac{1}{108} \cdot \frac{y^4}{x^4}$

Question 54

Arrange the following resultant mixtures in increasing order of their pH values
A. 10 mL 0.2 M Ca(OH)$_2$ + 25 mL 0.1 M HCl
B. 10 mL 0.01 M H$_2$SO$_4$ + 10 mL 0.01 M Ca(OH)$_2$
C. 10 mL 0.1 M H$_2$SO$_4$ + 10 mL 0.1 M KOH
Choose the correct answer from the options given below:

Accepted Answer

(C) $C < B < A$

Answer

(A) $B < C < A$

Answer

(B) $C < A < B$

Answer

(D) $A < C < B$

Question 55

First order gas phase reaction $A \rightarrow B + C$
$p_i$ = initial pressure of gas A, $p_t$ = total pressure of the reaction mixture at time $t$
Expression of rate constant ($k$) is

Accepted Answer

(A) $\frac{1}{t} \ln \frac{p_i}{2p_i - p_t}$

Answer

(B) $\frac{1}{t} \ln \frac{2p_i}{p_i - p_t}$

Answer

(C) $\frac{1}{t} \ln \frac{p_i}{3p_i - 2p_t}$

Answer

(D) $\frac{1}{t} \ln \frac{3p_i}{4p_i - p_t}$

Question 56

Given below are two statements:
Statement I: The correct order of electronegativity of fluorine, oxygen and nitrogen is $F > O > N$.
Statement II: The oxidation state of oxygen in OF$_2$ is $+2$ and in Na$_2$O is $-2$.
In the light of the above statements, choose the correct answer from the options given below

Accepted Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

(C) Statement I is true but Statement II is false

Answer

(D) Statement I is false but Statement II is true

Question 57

Correct statements from the following are:
A. Nitrogen in oxidation states from $+1$ to $+4$ disproportionates in acid medium.
B. Nitrogen has the ability to form $d\pi - p\pi$ multiple bonds with itself and other elements with small size and high electronegativity.
C. N-N single bond is stronger than P-P single bond.
D. Nitrogen has highest density in its group due to small size.
E. The maximum covalency of nitrogen is four since it has only four valence orbitals for bonding.
Choose the correct answer from the options given below:

Accepted Answer

(D) A and E Only

Answer

(A) B, C and D Only

Answer

(B) C, D and E Only

Answer

(C) A, C and E Only

Question 58

Which of the following is NOT a physical or chemical characteristics of interstitial compounds?

Accepted Answer

(B) They are very soft and ionic in nature.

Answer

(A) They have high melting points, higher than those of pure metals.

Answer

(C) They retain metallic conductivity.

Answer

(D) They are chemically inert and usually non-stoichiometric.

Question 59

The correct statements about metal carbonyls are
A. The metal-carbon bonds in metal carbonyls possess both $\sigma$ and $\pi$-character.
B. Due to synergic bonding interactions between metal and CO ligand, the metal-carbon bond becomes weak.
C. The metal-carbon $\sigma$ bond is formed by the donation of lone pair of electrons on the carbonyl carbon into a vacant orbital of metal.
D. The metal-carbon $\pi$ bond is formed by the donation of electrons from filled d-orbital of metal into vacant $\pi^*$ orbital of CO.
Choose the correct answer from the options given below:

Accepted Answer

(B) A, C and D Only

Answer

(A) A and B Only

Answer

(C) B and C Only

Answer

(D) A and D Only

Question 60

Given below are two statements:
Statement I: Each electron in $e_g$ orbitals destabilizes the orbitals by $+0.6\Delta_o$ and each electron in the $t_{2g}$ orbitals stabilizes the orbitals by $-0.4\Delta_o$ in an octahedral field on the basis of crystal field theory.
Statement II: All the d-orbitals of the transition metals have the same energy in their free atomic state but when a complex is formed the ligands destroy the degeneracy of these orbitals on the basis of crystal field theory.
In the light of the above statements, choose the correct answer from the options given below

Accepted Answer

(A) Both Statement I and Statement II are correct

Answer

(B) Both Statement I and Statement II are incorrect

Answer

(C) Statement I is correct but Statement II is incorrect

Answer

(D) Statement I is incorrect but Statement II is correct

Question 61

Given below are two statements:
Statement I: On the basis of inductive effect, the order of stability of alkyl carbanions is $\mathrm{CH_3^-} > \mathrm{CH_3	ext{-}CH_2^-} > \mathrm{(CH_3)_2CH^-} > \mathrm{(CH_3)_3C^-}$.
Statement II: Allyl and benzyl carbanions are more stabilised by inductive effect and not by resonance effect.
In the light of the above statements, choose the correct answer from the options given below

Accepted Answer

(C) Statement I is correct but Statement II is incorrect

Answer

(A) Both Statement I and Statement II are correct

Answer

(B) Both Statement I and Statement II are incorrect

Answer

(D) Statement I is incorrect but Statement II is correct

Question 62

"P" is a hydrocarbon of molecular formula: C$_8$H$_{14}$. On ozonolysis, "P" forms "Q". "Q" on treatment with alkali under reflux condition produces "R", which on treatment with I$_2$/NaOH gives a yellow precipitate. Acidification of the solution gives "S". The structure of "S" is given below:

The correct structure of "P" is

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 63

For the following Friedel Craft's alkylation reaction, which of the statements are correct?

A. Major product is n-propyl benzene.
B. iso-propyl carbocation intermediate is also generated.
C. Multiple substitution is inevitable.
D. Introducing electron-donating substituent on benzene will not produce any alkyl benzene.
Choose the correct answer from the options given below:

Accepted Answer

(B) B and C only

Answer

(A) A and D only

Answer

(C) A and C only

Answer

(D) B and D only

Question 64

Benzyl isocyanide can be obtained from

Choose the correct answer from the options given below:

Accepted Answer

(A) A and B Only

Answer

(B) A and C Only

Answer

(C) B and D Only

Answer

(D) D and E Only

$\frac{1}{T}$ (K $^{-1}$ )	$\log_{10} K_p$
0.05	3.5
0.06	2.5
0.07	1.5

JEE Main 5 April 2026 Shift 1 Question Paper with Answers

Physics — JEE Main 5 April 2026 Shift 1

Chemistry — JEE Main 5 April 2026 Shift 1

Mathematics — JEE Main 5 April 2026 Shift 1

Chapters tested in this paper

Attempt this paper under exam timing.

$x_i$	$f_i$
5	8
7	6
9	2
10	2
12	2
15	6