JEE Main 2026 — 5 Apr Shift 1 (Previous Year Paper)

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:

1. A.160
2. B.176✓
3. C.194
4. D.187

Correct answer: B

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:

1. A.10220
2. B.12860
3. C.15220✓
4. D.19780

Correct answer: C

Let A be a $3\times3$ 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 $\det(\operatorname{adj}(A^2+A))$ is equal to:

1. A.16
2. B.25
3. C.49
4. D.64✓

Correct answer: D

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

1. A.is a constant function
2. B.is strictly increasing on $\mathbb{R}$✓
3. C.is strictly decreasing on $\mathbb{R}$
4. D.has two critical points

Correct answer: B

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

1. A.65
2. B.130✓
3. C.220
4. D.440

Correct answer: B

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

1. A.$10+\sqrt{10}$
2. B.$10-2\sqrt{10}$
3. C.$10-3\sqrt{10}$✓
4. D.$10-\sqrt{10}$

Correct answer: C

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:

1. A.$\frac{7}{10}$
2. B.$\frac{10}{17}$✓
3. C.$\frac{12}{19}$
4. D.$\frac{7}{19}$

Correct answer: B

The mean deviation about the mean for the data ($x_i$ : $f_i$) 5 : 8, 7 : 6, 9 : 2, 10 : 2, 12 : 2, 15 : 6 is equal to:

1. A.$\frac{40}{13}$
2. B.$\frac{42}{13}$
3. C.$\frac{44}{13}$✓
4. D.$\frac{46}{13}$

Correct answer: C

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 $\frac45$. If the point $P(3,\alpha)$ lies on E and O is the origin, then the area of $\triangle POS$ is equal to:

1. A.12/5
2. B.14/5
3. C.24/5✓
4. D.48/5

Correct answer: C

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:

1. A.8
2. B.10
3. C.12✓
4. D.9

Correct answer: C

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:

1. A.16
2. B.27
3. C.36
4. D.48✓

Correct answer: D

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

1. A.$-54$
2. B.$-60$
3. C.$-75$✓
4. D.$-84$

Correct answer: C

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:

1. A.3
2. B.5
3. C.6✓
4. D.8

Correct answer: C

Let $\vec a=\sqrt7\hat i+\hat j-\hat k$ and $\vec b=\hat j+2\hat k$. If $\vec r$ is a vector such that $\vec r\times\vec a+\vec a\times\vec b=\vec0$ and $\vec r\cdot\vec a=0$, then $|3\vec r|^2$ is equal to:

1. A.44✓
2. B.54
3. C.86
4. D.132

Correct answer: A

The square of the distance of the point of intersection of the lines $\vec r=\left(\hat i+\hat j-\hat k\right)+\lambda\left(a\hat i-\hat j\right)$, $a\ne0$ and $\vec r=\left(4\hat i-\hat k\right)+\mu\left(2\hat i+a\hat k\right)$ from the origin is:

1. A.5
2. B.10
3. C.17✓
4. D.26

Correct answer: C

The area of the region $R=\{(x,y) : xy\le27, 1\le y\le x^2\}$ is equal to:

1. A.$78\log_e3-\frac{52}{3}$
2. B.$54\log_e3-\frac{52}{3}$✓
3. C.$54\log_e3-\frac{26}{3}$
4. D.$54\log_e3+\frac{26}{3}$

Correct answer: B

The product of all possible values of $\alpha$, for which $\lim_{x\to0}\left(\frac{1-\cos(\alpha x)\cos((\alpha+1)x)\cos((\alpha+2)x)}{\sin^2((\alpha+1)x)}\right)=2$, is:

1. A.$-2$
2. B.1
3. C.$-1$✓
4. D.$\frac54$

Correct answer: C

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

1. A.$\frac{\pi\log_e(2)}{2}$
2. B.$\frac{\pi\log_e(2)}{4}$✓
3. C.$1+\pi\log_e(2)$
4. D.$2+\pi\log_e(2)$

Correct answer: B

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

1. A.$3\left(\frac{e+1}{e}\right)$
2. B.$3\left(\frac{e-1}{e}\right)$✓
3. C.$\frac{3-e}{e}$
4. D.$3e$

Correct answer: B

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

1. A.$\frac{11}{\sqrt3}$
2. B.$\frac{16}{\sqrt3}$
3. C.$\frac{32}{3\sqrt3}$✓
4. D.$\frac{64}{3\sqrt3}$

Correct answer: C

Let $A=\{1,2,3,4,5,6\}$. The number of one-one functions $f:A\to A$ such that $f(1)\ge3$, $f(3)\le4$ and $f(2)+f(3)=5$, is ______.

Correct answer: 72

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 ______.

Correct answer: 126

If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3}-x^4\right)^n$, $x\ne0$, is zero, then the value of $n$ is ______.

Correct answer: 21

If $\frac{\pi}{4}+\sum_{p=1}^{11}\tan^{-1}\left(\frac{2^{p-1}}{1+2^{2p-1}}\right)=\alpha$, then $\tan\alpha$ is equal to ______.

Correct answer: 2048

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 $7^{th}$ 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

1. A.0.07 cm negative zero error
2. B.0.7 cm negative zero error
3. C.0.07 cm positive zero error✓
4. D.0.7 cm positive zero error

Correct answer: C

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

1. A.$\frac{R}{\sqrt{LC}}$✓
2. B.$\frac{R}{LC}$
3. C.$\frac{C}{\sqrt{LR}}$
4. D.$\frac1R\sqrt{\frac{L}{C}}$

Correct answer: A

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.)

1. A.0.12
2. B.0.25✓
3. C.0.50
4. D.0.75

Correct answer: B

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

1. A.5/3✓
2. B.2/3
3. C.3/5
4. D.2/5

Correct answer: A

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 $\tan(37^\circ)=3/4$ and $g=10\ \mathrm{m/s^2}$)

1. A.2✓
2. B.4
3. C.$\sqrt2$
4. D.$2\sqrt2$

Correct answer: A

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

1. A.increases by two times
2. B.reduces by half
3. C.remains unchanged✓
4. D.becomes one fourth

Correct answer: C

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Statement I: Change in internal energy of a system containing $n$ mole of ideal gas can be written as $\Delta U=nC_v(T_f-T_i)=\frac{nR}{\gamma-1}(T_f-T_i)$, where $\gamma=\frac{C_p}{C_v}$, $T_i$ = initial temperature, $T_f$ = final temperature. Statement II: Relation between degree of freedom $f$ and $\gamma$ $(=C_p/C_v)$ is $\left(\gamma=1+\frac2f\right)$. Choose the correct answer from the options given below

1. A.Both A and R are true and R is the correct explanation of A
2. B.Both A and R are true but R is NOT the correct explanation of A✓
3. C.A is true but R is false
4. D.A is false but R is true

Correct answer: B

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, $\Delta Q\ne\Delta W$ 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:

1. A.C, D and E Only
2. B.A, B and C Only
3. C.A, B and D Only✓
4. D.B, C and D Only

Correct answer: C

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

1. A.$I_1=2.5$ A, $I_2=1.875$ A, $I_3=1.875$ A✓
2. B.$I_1=1.875$ A, $I_2=2.5$ A, $I_3=1.875$ A
3. C.$I_1=1.875$ A, $I_2=1.875$ A, $I_3=2.5$ A
4. D.$I_1=2.5$ A, $I_2=2.5$ A, $I_3=1.875$ A

Correct answer: A

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)

1. A.$\frac{4\lambda_0}{\left[1-\frac{E_0et}{2mv_0}\right]}$
2. B.$\frac{4\lambda_0}{\left[1+\frac{E_0et}{2mv_0}\right]}$
3. C.$\frac{4\lambda_0}{\left[1+\frac{2E_0et}{mv_0}\right]}$✓
4. D.$\frac{4\lambda_0}{\left[1-\frac{2E_0et}{mv_0}\right]}$

Correct answer: C

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 = $1.0973\times10^7$ /m)

1. A.121
2. B.242
3. C.486✓
4. D.974

Correct answer: C

A displacement current of 4.0 A can be set up in the space between two parallel plates of 6 $\mu$F capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha\times10^6$ V/s. The value of $\alpha$ is ______.

1. A.0.58
2. B.0.67✓
3. C.0.82
4. D.0.75

Correct answer: B

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

1. A.12.5
2. B.1.25✓
3. C.7.5
4. D.5

Correct answer: B

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

1. A.1.2
2. B.2✓
3. C.2.4
4. D.2.88

Correct answer: B

A ray of light passing through an equilateral prism is having velocity $2.12\times10^8$ m/s in the prism material, then the minimum angle of deviation is ______ degrees.

1. A.45
2. B.30✓
3. C.28
4. D.58

Correct answer: B

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 $\alpha\times10^{-19}$ J. The value of $\alpha$ is ______. ($h=6.62\times10^{-34}$ J s, $e=1.6\times10^{-19}$ C and $c=3\times10^8$ m/s)

1. A.3.68
2. B.4.68
3. C.5.68✓
4. D.2.68

Correct answer: C

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

1. A.increased two times✓
2. B.increased $\frac32$ times
3. C.decreased two times
4. D.decreased $\frac32$ times

Correct answer: A

Two wires as shown in the figure below, made of steel and have breaking stress of $12\times10^8\ \mathrm{N/m^2}$. Area of cross-section of upper wire is 0.008 $\mathrm{cm^2}$ and of lower wire is 0.004 $\mathrm{cm^2}$. The maximum mass that can be added to pan without breaking any wire is ______ kg. (take $g=10\ \mathrm{m/s^2}$)

1. A.56
2. B.38✓
3. C.96
4. D.5.6

Correct answer: B

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

1. A.$\sqrt{\frac67}$
2. B.$\sqrt{\frac35}$
3. C.$\sqrt{\frac78}$✓
4. D.$\sqrt{\frac34}$

Correct answer: C

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

1. A.A = 0, B = 1, C = 1
2. B.A = 1, B = 0, C = 0
3. C.A = 1, B = 0, C = 1✓
4. D.A = 1, B = 1, C = 0

Correct answer: C

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

Correct answer: 2

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 $g=10\ \mathrm{m/s^2}$ and neglect the air resistance)

Correct answer: 13

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) ($\pi=3.14$)

Correct answer: 349

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

Correct answer: 12

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)

Correct answer: 6

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 $\mathrm{mol^{-1}}$ respectively)

1. A.1.08 g
2. B.2.16 g✓
3. C.3.24 g
4. D.4.32 g

Correct answer: B

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:

1. A.C < D < B < A < E
2. B.B < A < E < C < D
3. C.E < C < D < B < A
4. D.E < B < A < D < C✓

Correct answer: D

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 [Ar] $3d^5\,4s^1$. Choose the correct answer from the options given below:

1. A.A, B and C Only
2. B.A, B and D Only✓
3. C.B, C and D Only
4. D.A, C and D Only

Correct answer: B

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 $\mathrm{mol^{-1}}$ respectively.]

1. A.0.825
2. B.0.032
3. C.0.867
4. D.0.967✓

Correct answer: D

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

1. A.$\frac{1}{54}\cdot\frac{y^4}{x^4}$✓
2. B.$\frac{y^5}{108x^4}$
3. C.$108\cdot\frac{x^5}{y^5}$
4. D.$\frac{1}{108}\frac{y^4}{x^4}$

Correct answer: A

Arrange the following resultant mixtures in increasing order of their pH values A. 10 mL 0.2 M $\mathrm{Ca(OH)_2}$ + 25 mL 0.1 M HCl B. 10 mL 0.01 M $\mathrm{H_2SO_4}$ + 10 mL 0.01 M $\mathrm{Ca(OH)_2}$ C. 10 mL 0.1 M $\mathrm{H_2SO_4}$ + 10 mL 0.1 M KOH. Choose the correct answer from the options given below:

1. A.B < C < A
2. B.C < A < B
3. C.C < B < A✓
4. D.A < C < B

Correct answer: C

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

1. A.$\frac1t\ln\frac{p_i}{2p_i-p_t}$✓
2. B.$\frac1t\ln\frac{2p_i}{p_i-p_t}$
3. C.$\frac1t\ln\frac{p_i}{3p_i-2p_t}$
4. D.$\frac1t\ln\frac{3p_i}{4p_i-p_t}$

Correct answer: A

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 $\mathrm{OF_2}$ is +2 and in $\mathrm{Na_2O}$ is $-2$. In the light of the above statements, choose the correct answer from the options given below

1. A.Both Statement I and Statement II are true✓
2. B.Both Statement I and Statement II are false
3. C.Statement I is true but Statement II is false
4. D.Statement I is false but Statement II is true

Correct answer: A

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:

1. A.B, C and D Only
2. B.C, D and E Only
3. C.A, C and E Only
4. D.A and E Only✓

Correct answer: D

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

1. A.They have high melting points, higher than those of pure metals.
2. B.They are very soft and ionic in nature.✓
3. C.They retain metallic conductivity.
4. D.They are chemically inert and usually non-stoichiometric.

Correct answer: B

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:

1. A.A and B Only
2. B.A, C and D Only✓
3. C.B and C Only
4. D.A and D Only

Correct answer: B

Given below are two statements: Statement I: Each electron in $e_g$ orbitals destabilizes the orbitals by $+0.6\Delta_0$ and each electron in the $t_{2g}$ orbitals stabilizes the orbitals by $-0.4\Delta_0$ 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

1. A.Both Statement I and Statement II are correct✓
2. B.Both Statement I and Statement II are incorrect
3. C.Statement I is correct but Statement II is incorrect
4. D.Statement I is incorrect but Statement II is correct

Correct answer: A

Given below are two statements: Statement I: On the basis of inductive effect, the order of stability of alkyl carbanions is $\mathrm{CH_3^->CH_3-CH_2^->(CH_3)_2CH^->(CH_3)_3C^-}$. 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

1. A.Both Statement I and Statement II are correct
2. B.Both Statement I and Statement II are incorrect
3. C.Statement I is correct but Statement II is incorrect✓
4. D.Statement I is incorrect but Statement II is correct

Correct answer: C

"P" is a hydrocarbon of molecular formula: $\mathrm{C_8H_{14}}$. On ozonolysis, "P" forms "Q". "Q" on treatment with alkali under reflux condition produces "R", which on treatment with $\mathrm{I_2}$/NaOH gives a yellow precipitate. Acidification of the solution gives "S". The structure of "S" is 2-methylcyclopent-1-ene-1-carboxylic acid (cyclopentene ring with $\mathrm{CH_3}$ on one alkene carbon and COOH on the other). The correct structure of "P" is

1. A.3,6-dimethylcyclohex-1-ene (CH3 on the two sp3 ring carbons that flank the ring C=C)
2. B.1-ethylcyclohex-1-ene
3. C.1-ethyl-2-methylcyclopent-1-ene
4. D.1,2-dimethylcyclohex-1-ene✓

Correct answer: D

For the following Friedel Craft's alkylation reaction, which of the statements are correct? Benzene + 1-chloropropane $\xrightarrow{\text{anhydrous }\mathrm{AlCl_3}}$ Alkylbenzene. 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:

1. A.A and D only
2. B.B and C only✓
3. C.A and C only
4. D.B and D only

Correct answer: B

Benzyl isocyanide can be obtained from A. Benzyl bromide + AgCN B. Benzylamine + $\mathrm{CHCl_3}$/aq NaOH C. Bromobenzene + AgCN D. Aniline + $\mathrm{CHCl_3}$/aq NaOH E. (2-Bromoethyl)benzene + KCN. Choose the correct answer from the options given below:

1. A.A and B Only✓
2. B.A and C Only
3. C.B and D Only
4. D.D and E Only

Correct answer: A

Consider compounds A, B and C with following structural formulae A = $\mathrm{CH_3-CH_2-CH_2-CH_2-CH_2-OH}$, B = $\mathrm{CH_2=CH-CH_2-CH_2-CH_3}$, C = $\mathrm{HO-CH_2-CH_2-CH(OH)-CH_3}$. For the conversion of B from A, reagent (D) required is ______ and structural formula of product (E) obtained when C undergoes same reaction using excess reagent (D) is ______.

1. A.D = Conc. $\mathrm{H_2SO_4}$; E = $\mathrm{CH_2=CH-CH(OH)CH_3}$
2. B.D = PCC; E = $\mathrm{HO-CH_2-CH_2-CH=CH_2}$
3. C.D = PCC; E = $\mathrm{CH_2=CH-CH=CH_2}$
4. D.D = Conc. $\mathrm{H_2SO_4}$ or $\mathrm{H_3PO_4}$; E = $\mathrm{CH_2=CH-CH=CH_2}$✓

Correct answer: D

Identify the incorrect statements. A. Benzylamine is a stronger base than aniline. B. 4-Methoxyaniline can be synthesized by Gabriel phthalimide synthesis. C. 2-Phenylacetamide ($\mathrm{C_6H_5CH_2CONH_2}$) $\xrightarrow{\mathrm{Br_2,\ NaOH}}$ primary aromatic amine. D. 4-Nitroaniline $\xrightarrow{\mathrm{(i)\ NaNO_2,\ HCl,\ 0^\circ C;\ (ii)\ \Delta}}$ product will dissolve in NaOH. Choose the correct answer from the options given below:

1. A.A and D Only
2. B.A and C Only
3. C.B and C Only✓
4. D.A and B Only

Correct answer: C

Identify the correct statements. A. Glucose exists in two anomeric forms. B. Anomers of glucose differ in configuration at C$-$1 in cyclic hemiacetal structure. C. Melting point of $\alpha$-anomer of glucose is greater than $\beta$-anomer. D. Specific rotation of $\alpha$-anomer is +19° while for $\beta$-anomer is +112° E. $\alpha$ and $\beta$-anomers of glucose are prepared by crystallization of saturated glucose solution at 303 K and 371 K respectively. Choose the correct answer from the options given below:

1. A.A and B Only
2. B.B and C Only
3. C.A, B and D Only
4. D.A, B and E Only✓

Correct answer: D

Given below are two statements: Statement I: Sodium dichromate and potassium dichromate are classified as primary standards in titrimetric analysis. Statement II: Phenolphthalein is a weak base, therefore it dissociates in acidic medium. In the light of the above statements, choose the correct answer from the options given below

1. A.Both Statement I and Statement II are true
2. B.Both Statement I and Statement II are false✓
3. C.Statement I is true but Statement II is false
4. D.Statement I is false but Statement II is true

Correct answer: B

Consider the following species: $\mathrm{BrF_5, XeF_5^-, BF_4^-, ICl_4^-, XeF_4, SF_4, NH_4^+, ClF_3, XeF_2, ICl_2^-}$. Number of species having $sp^3d$ hybridized central atom is ______.

Correct answer: 4

One mole of phenol is treated with dilute $\mathrm{HNO_3}$ at 298 K to give a mixture of products. The mixture is separated by steam distillation. The steam volatile compound (X) is separated. The increase in percentage of oxygen in (X) with respect to phenol is ______ $\times10^{-1}$ % (Given molar mass in g $\mathrm{mol^{-1}}$ H:1, C:12, N:14, O:16)

Correct answer: 175

The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below: $\mathrm{A(g)\rightleftharpoons B(g)+C(g)}$. $\frac1T$ ($\mathrm{K^{-1}}$) : $\log_{10}K_p$ = 0.05 : 3.5; 0.06 : 2.5; 0.07 : 1.5. The magnitude of $\frac{\Delta H^\circ}{R}$ calculated from the above data is ______. (Nearest integer)

Correct answer: 230

If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be ______ minutes. (Given : log 2 = 0.3010)

Correct answer: 46