JEE Main 2026 — 6 Apr Shift 2 (Previous Year Paper)

Let $f:\mathbb{R}\to\mathbb{R}$ be defined as $f(x)=\frac{2x^2-3x+2}{3x^2+x+3}$. Then $f$ is :

1. A.both one-one and onto
2. B.one-one but not onto
3. C.onto but not one-one
4. D.neither one-one nor onto✓

Correct answer: D

Consider the quadratic equation $(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0$, $n\in\mathbb{R}$. Let $\alpha$ be the minimum value of the product of its roots and $\beta$ be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is $\alpha$ and the common ratio is $\frac{\alpha}{\beta}$, is :

1. A.$\frac{61}{37}$
2. B.$\frac{121}{81}$
3. C.$\frac{364}{243}$✓
4. D.$\frac{1093}{729}$

Correct answer: C

Let $S=\{z\in\mathbb{C} : z^2+\sqrt6\,iz-3=0\}$. Then $\sum_{z\in S}z^8$ is equal to :

1. A.162✓
2. B.184
3. C.262
4. D.324

Correct answer: A

The sum of all possible values of $\theta\in[0,2\pi]$, for which the system of equations : $x\cos3\theta-8y-12z=0$, $x\cos2\theta+3y+3z=0$, $x+y+3z=0$ has a non-trivial solution, is equal to :

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

Correct answer: D

Let $A=\begin{bmatrix}1&0&0\\3&1&0\\9&3&1\end{bmatrix}$ and $B=[b_{ij}]$, $1\le i,j\le3$. If $B=A^{99}-I$, then the value of $\frac{b_{31}-b_{21}}{b_{32}}$ is :

1. A.99
2. B.199
3. C.149✓
4. D.159

Correct answer: C

The sum $1+\frac12\left(1^2+2^2\right)+\frac13\left(1^2+2^2+3^2\right)+\dots$ upto 10 terms is equal to :

1. A.130
2. B.155
3. C.$\frac{315}{2}$✓
4. D.$\frac{325}{2}$

Correct answer: C

A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the $10^{th}$ floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :

1. A.2184
2. B.3064
3. C.7056✓
4. D.11340

Correct answer: C

Let the mean and the variance of seven observations $2, 4, \alpha, 8, \beta, 12, 14$, $\alpha<\beta$, be 8 and 16 respectively. Then the quadratic equation whose roots are $3\alpha+2$ and $2\beta+1$ is :

1. A.$x^2-35x+306=0$
2. B.$x^2-41x+420=0$✓
3. C.$x^2-45x+506=0$
4. D.$x^2-37x+342=0$

Correct answer: B

A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :

1. A.$\frac{63}{925}$
2. B.$\frac{17}{231}$
3. C.$\frac{16}{231}$✓
4. D.$\frac{64}{925}$

Correct answer: C

Let C be a circle having centre in the first quadrant and touching the $x$-axis at a distance of 3 units from the origin. If the circle C has an intercept of length $6\sqrt3$ on $y$-axis, then the length of the chord of the circle C on the line $x-y=3$ is :

1. A.8
2. B.6
3. C.$6\sqrt2$✓
4. D.$8\sqrt2$

Correct answer: C

The eccentricity of an ellipse E with centre at the origin O is $\frac{\sqrt3}{2}$ and its directrices are $x=\pm\frac{4\sqrt6}{3}$. Let $H : \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be a hyperbola whose eccentricity is equal to the length of semi-major axis of E, and whose length of latus rectum is equal to the length of minor axis of E. Then the distance between the foci of H is :

1. A.$\frac{4\sqrt2}{\sqrt7}$
2. B.$\frac{4\sqrt2}{7}$
3. C.$\frac{4}{\sqrt7}$
4. D.$\frac87$✓

Correct answer: D

Let $x=9$ be a directrix of an ellipse E, whose centre is at the origin and eccentricity is $\frac13$. Let $P(\alpha,0)$, $\alpha>0$, be a focus of E and AB be a chord passing through P. Then the locus of the mid point of AB is :

1. A.$9y^2=8x(1-x)$✓
2. B.$3y^2=4x(1-x)$
3. C.$9y^2=8x(x-1)$
4. D.$3y^2=4x(x-1)$

Correct answer: A

If $\sin\left(\tan^{-1}\left(x\sqrt2\right)\right)=\cot\left(\sin^{-1}\sqrt{1-x^2}\right)$, $x\in(0,1)$, then the value of $x$ is :

1. A.$\frac12$✓
2. B.$\frac13$
3. C.$\frac23$
4. D.$\frac58$

Correct answer: A

The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is :

1. A.$\frac{5\sqrt6}{6}$
2. B.$2\sqrt5$
3. C.$3\sqrt5$✓
4. D.$4\sqrt5$

Correct answer: C

Let $\vec a=2\hat i+3\hat j+3\hat k$ and $\vec b=6\hat i+3\hat j+3\hat k$. Then the square of the area of the triangle with adjacent sides determined by the vectors $\left(2\vec a+3\vec b\right)$ and $\left(\vec a-\vec b\right)$ is :

1. A.450
2. B.900
3. C.1800✓
4. D.2400

Correct answer: C

Let $\lim_{x\to2}\frac{(\tan(x-2))\left(rx^2+(p-2)x-2p\right)}{(x-2)^2}=5$ for some $r,p\in\mathbb{R}$. If the set of all possible values of $q$, such that the roots of the equation $rx^2-px+q=0$ lie in $(0,2)$, be the interval $(\alpha,\beta]$, then $4(\alpha+\beta)$ equals :

1. A.11
2. B.13
3. C.17✓
4. D.21

Correct answer: C

Let $A=\begin{bmatrix}1&3&-1\\2&1&\alpha\\0&1&-1\end{bmatrix}$ be a singular matrix. Let $f(x)=\int_0^x\left(t^2+2t+3\right)dt$, $x\in[1,\alpha]$. If M and m are respectively the maximum and the minimum values of $f$ in $[1,\alpha]$, then $3(M-m)$ is equal to :

1. A.64
2. B.68✓
3. C.72
4. D.76

Correct answer: B

Let $f:\mathbb{R}\to\mathbb{R}$ be such that $f(xy)=f(x)f(y)$, for all $x,y\in\mathbb{R}$ and $f(0)\ne0$. Let $g:[1,\infty)\to\mathbb{R}$ be a differentiable function such that $x^2g(x)=\int_1^x\left(t^2f(t)-tg(t)\right)dt$. Then $g(2)$ is equal to :

1. A.$\frac{13}{8}$
2. B.$\frac{11}{16}$
3. C.$\frac{15}{32}$✓
4. D.$\frac{17}{64}$

Correct answer: C

The area of the region $\{(x,y) : x^2-8x\le y\le-x\}$ is :

1. A.$\frac{343}{6}$✓
2. B.$\frac{637}{6}$
3. C.$\frac{437}{6}$
4. D.$\frac{523}{6}$

Correct answer: A

The value of the integral $\int_{-1}^{1}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx$ is equal to :

1. A.$3\log_e2$
2. B.$2\log_e2$✓
3. C.$5\log_e3$
4. D.$3\log_e3$

Correct answer: B

Let $R=\{(x,y)\in\mathbb{N}\times\mathbb{N} : \log_e(x+y)\le2\}$. Then the minimum number of elements, required to be added in R to make it a transitive relation, is ______.

Correct answer: 15

If $(1-x^3)^{10}=\sum_{r=0}^{10}a_rx^r(1-x)^{30-2r}$, then $\frac{9a_9}{a_{10}}$ is equal to ______.

Correct answer: 30

Let the line $x-y=4$ intersect the circle $C : (x-4)^2+(y+3)^2=9$ at the points Q and R. If $P(\alpha,\beta)$ is a point on C such that $PQ=PR$, then $(6\alpha+8\beta)^2$ is equal to ______.

Correct answer: 18

Let the image of the point $P(0,-5,0)$ in the line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2}$ be the point R and the image of the point $Q\left(0,\frac{-1}{2},0\right)$ in the line $\frac{x-1}{-1}=\frac{y+9}{4}=\frac{z+1}{1}$ be the point S. Then the square of the area of the parallelogram PQRS is ______.

Correct answer: 162

Let $f(x)=\begin{cases}x^3+8; & x<0,\\ x^2-4; & x\ge0,\end{cases}$ and $g(x)=\begin{cases}(x-8)^{1/3}; & x<0,\\ (x+4)^{1/2}; & x\ge0.\end{cases}$ Then the number of points, where the function $g\circ f$ is discontinuous, is ______.

Correct answer: 3

The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is ______.

1. A.1
2. B.2
3. C.6✓
4. D.8

Correct answer: C

Match List - I with List - II. List - I : A. Boltzmann constant B. Stefan's constant C. Planck's constant D. Gravitational constant. List - II : I. $[M^{-1}L^3T^{-2}]$ II. $[ML^2T^{-1}]$ III. $[ML^2T^{-2}K^{-1}]$ IV. $[ML^0T^{-3}K^{-4}]$. Choose the correct answer from the options given below :

1. A.A-I, B-II, C-III, D-IV
2. B.A-IV, B-III, C-II, D-I
3. C.A-III, B-IV, C-II, D-I✓
4. D.A-II, B-I, C-IV, D-III

Correct answer: C

A solid sphere (A) of mass $5m$ and a spherical shell (B) of mass $m$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of $a_A$ and $a_B$, respectively. The ratio of $a_A$ and $a_B$ is ______.

1. A.5 : 21✓
2. B.6 : 10
3. C.21 : 25
4. D.1 : 5

Correct answer: A

A body of mass 1 kg moves along a straight line with a velocity $v=2x^2$. The work done by the body during displacement from $x=0$ to 5 m is ______ J.

1. A.0
2. B.250
3. C.1250✓
4. D.1000

Correct answer: C

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same P, V, T. Heating is started from left side until pressure changes to $27P/8$. If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is ______ litres. (for this ideal gas $C_P/C_V=1.5$)

1. A.3
2. B.4✓
3. C.14
4. D.9

Correct answer: B

For an electromagnetic wave propagating through vacuum, $\vec k$, $\vec E$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by :

1. A.$\frac{\vec E\times\vec k}{\omega}$
2. B.$\frac{\vec k\times\vec E}{\omega}$✓
3. C.$\omega\left(\vec E\times\vec k\right)$
4. D.$\omega\left(\vec k\times\vec E\right)$

Correct answer: B

Two identical bodies A and B of equal masses have initial velocities $\vec v_1=4\hat i$ m/s and $\vec v_2=4\hat j$ m/s respectively. The body A has acceleration $\vec a_1=6\hat i+6\hat j\ \mathrm{m/s^2}$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in ______ path.

1. A.circular
2. B.parabolic
3. C.straight line✓
4. D.elliptical

Correct answer: C

Figure represents the extension ($\Delta l$) of a wire of length 1 meter, suspended from the ceiling of the room at one end with a load W connected to the other end. If the cross-sectional area of the wire is $10^{-5}\ \mathrm{m^2}$ then the Young's modulus of the wire is ______ $\mathrm{N/m^2}$.

1. A.$1.0\times10^{11}$
2. B.$2.0\times10^{10}$
3. C.$1.0\times10^{10}$✓
4. D.$2.0\times10^{11}$

Correct answer: C

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 $\mathrm{dm^3}$ (dm : decimeter) The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is ______ cm.

1. A.$120\sqrt2$
2. B.$140\sqrt2$✓
3. C.$140\sqrt3$
4. D.$120\sqrt3$

Correct answer: B

If 2 mole of an ideal monoatomic gas at temperature T, is mixed with 6 mole of another ideal monoatomic gas at temperature 2T then the temperature of mixture is :

1. A.$\frac52T$
2. B.$\frac54T$
3. C.$\frac72T$
4. D.$\frac74T$✓

Correct answer: D

A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maxmimum energy in the spring are ______ Hz and ______ J, respectively. (Take $g=10\ \mathrm{m/s^2}$)

1. A.$\frac{5\sqrt{50}}{\pi}$ and $8\times10^{-3}$✓
2. B.$\frac{5\sqrt{50}}{\pi}$ and 8
3. C.$10\sqrt{50}$ and $2\times10^{-3}$
4. D.$\frac{5\sqrt{50}}{\pi}$ and $16\times10^{-3}$

Correct answer: A

The electric potential as a function of $x$, $y$ is given by $V=5(x^2-y^2)$ V. The electric field at a point $(2,3)$ m is ______ V/m.

1. A.$\left(-20\hat i+30\hat j\right)$✓
2. B.$\left(20\hat i-30\hat j\right)$
3. C.$\left(20\hat i+45\hat j\right)$
4. D.$\left(-4\hat i+6\hat j\right)$

Correct answer: A

A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm. The magnetic field at the mid point between the two wires is ______ $\mu$T. ($\frac{\mu_0}{4\pi}=10^{-7}\ \mathrm{N/A^2}$)

1. A.30
2. B.300✓
3. C.150
4. D.0.0

Correct answer: B

A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as $B=0.4\sin(300t)$ Tesla. The normal to the plane of loop makes an angle of 60° with the field. The maximum induced emf produced in the loop is ______ mV.

1. A.12
2. B.18
3. C.21
4. D.24✓

Correct answer: D

A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha\times10^{-7}$ J. The value of $\alpha$ is ______. (combined capacitance of spheres is 200 pF)

1. A.5
2. B.$\frac52$✓
3. C.$\frac72$
4. D.$\frac92$

Correct answer: B

The energy released if hydrogen atoms are combined to form ${}^4_2He$ is ______ MeV. (Take binding energies per nucleon of ${}^2_1H$ and ${}^4_2He$ as 1.1 MeV and 7.2 MeV, respectively)

1. A.6.1
2. B.24.4✓
3. C.26.6
4. D.5

Correct answer: B

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is ______.

1. A.1.5
2. B.$\sqrt3$
3. C.$\sqrt2$✓
4. D.1.65

Correct answer: C

Refer to the logic circuit given below. For two inputs ($A=1, B=1$) and ($A=0, B=1$), output (Y) will be ______.

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

Correct answer: C

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is ______ m/s. Assume pulley is massless and string is light and inextensible. (Take $g=10\ \mathrm{m/s^2}$)

1. A.7.74✓
2. B.7.20
3. C.6.55
4. D.4.50

Correct answer: A

A block takes $t$ time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time $\frac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\frac{\alpha}{100}\right)$. The value of $\alpha$ is ______.

Correct answer: 75

The de Broglie wavelength for an electron accelerated through the potential difference of $V_1$ volt is $\lambda_1$. When the potential difference is changed to $V_2$ volt, the associated de Broglie wavelength is increased by 50%. If $(V_1/V_2)=(9/\alpha)$, then the value of $\alpha$ is ______.

Correct answer: 4

A moving coil of galvanometer when shunted with 2 $\Omega$ resistance gives a full scale deflection for a current of 500 mA. When a resistance of 470 $\Omega$ is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is ______ $\Omega$.

Correct answer: 50

Two cells of emfs 1 V and 2 V and internal resistance 2 $\Omega$ and 1 $\Omega$, respectively connected in parallel, gave a current of 1 A through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be $\frac{\alpha}{5}$ A. The value of $\alpha$ is ______.

Correct answer: 3

A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is ______ cm.

Correct answer: 10

Which of the following contain the same number of atoms ? (Given : Molar mass in g $\mathrm{mol^{-1}}$ of H, He, O and S are 1, 4, 16 and 32 respectively) A. 2 g of $\mathrm{O_2}$ gas B. 4 g of $\mathrm{SO_2}$ gas C. 1400 mL of $\mathrm{O_2}$ at STP D. 0.05 L of He at STP E. 0.0625 mol of $\mathrm{H_2}$ gas. Choose the correct answer from the options given below :

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

Correct answer: D

The Bohr radius of a hydrogen like species is 70.53 pm. The species and the stationary state (n) are respectively (Given : Hydrogen atom Bohr radius is 52.9 pm)

1. A.$\mathrm{Li^{2+}}$, 3
2. B.$\mathrm{He^+}$, 3
3. C.$\mathrm{He^+}$, 2
4. D.$\mathrm{Li^{2+}}$, 2✓

Correct answer: D

Given below are two statements : Statement I : The number of compounds among $\mathrm{SO_2, SO_3, SF_4, SF_6}$ and $\mathrm{H_2S}$ in which sulphur does not obey the Octet rule is 3. Statement II : Among $[\mathrm{H_2O, ClF_3, SF_4}]$, $[\mathrm{NH_3, BrF_5, SF_4}]$, $[\mathrm{BrF_5, ClF_3, XeF_4}]$ and $[\mathrm{XeF_4, ClF_3, H_2O}]$, the number of sets in which all the molecules have one lone pair of electrons on the central atom is 1. 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: D

Match List - I with List - II. Given $V_1$ and $V_2$ are initial and final volumes respectively. List - I (Isothermal process) : A. Reversible expansion B. Free expansion C. Irreversible Compression D. Cyclic reversible. List - II (Expression) : I. $q=0$ II. $q=nRT\ln\frac{V_2}{V_1}$ III. $w=-p_{ext}(V_1-V_2)$ IV. $\frac{q_{rev}}{T}=0$. Choose the correct answer from the options given below :

1. A.A-II, B-III, C-I, D-IV
2. B.A-II, B-I, C-IV, D-III
3. C.A-II, B-I, C-III, D-IV✓
4. D.A-I, B-II, C-III, D-IV

Correct answer: C

Given below are two statements : A semi-permeable membrane separates Chamber 1 (18 g glucose in 100 mL aqueous solution) from Chamber 2 (30 g glucose in 250 mL aqueous solution). Statement I : $\mathrm{H_2O}$ molecules move from the chamber 1 to chamber 2. Statement II : The osmotic pressure of a solution prepared by dissolving 50 mg of potassium sulphate (molar mass = 174 g/mol) in 2 L of water (at 27 °C) is 0.0107 bar. (Given: R = 0.083 $\mathrm{dm^3}$ bar $\mathrm{K^{-1}mol^{-1}}$ and assume complete dissociation of electrolyte) 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: D

Given is a concentrated solution of a weak electrolyte $\mathrm{A_xB_y}$ of concentration 'c' and dissociation constant 'K'. The degree of dissociation is given by :

1. A.$\left[K\times c^{x+y-1}x^xy^y\right]^{x+y}$
2. B.$\left(\frac{K}{c^{x+y-1}x^xy^y}\right)^{\frac{1}{x+y}}$✓
3. C.$\left(\frac{c^{x+y-1}x^xy^y}{K}\right)^{x+y}$
4. D.$\left(\frac{c^{x+y-1}x^xy^y}{K}\right)^{\frac{1}{x+y}}$

Correct answer: B

For a general redox reaction Anode: $\mathrm{Red_1\rightarrow Ox_1^{n_1+}+n_1e^-}$; Cathode: $\mathrm{Ox_2+n_2e^-\rightarrow Red_2^{n_2-}}$. Which of the following statement is incorrect ?

1. A.The overall reaction can be written as $\mathrm{n_2Red_1+n_1Ox_2\rightleftharpoons n_2Ox_1^{n_1+}+n_1Red_2^{n_2-}}$
2. B.The electrons do not appear in the overall reaction because electrons produced at the anode are consumed at the cathode.
3. C.The graph of $\frac{(E-E^\circ)}{RT/F}$ vs $\log_{10}Q$ is a set of straight lines through the origin with slope $\propto\frac1n$ (steepest for n = 1, then n = 2, n = 3), where n is the number of electrons transferred in redox reaction.
4. D.If the reaction is carried out reversibly, the electrical work done is equal to the ratio of charge and potential difference through which charge is moved.✓

Correct answer: D

In a period, the first ionisation enthalpy of the element at extreme left and the negative electron gain enthalpy of the extreme right element, except noble gases, are respectively.

1. A.lowest and lowest
2. B.highest and lowest
3. C.lowest and highest✓
4. D.highest and highest

Correct answer: C

Given below are two statements : Statement I : $\mathrm{F_2O<H_2O<Cl_2O}$ is the correct trend in terms of bond angle. Statement II : $\mathrm{SiF_4, SnF_4}$ and $\mathrm{PbF_4}$ are ionic in nature. 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: C

The correct order of first ($\Delta_iH_1$) and second ($\Delta_iH_2$) ionisation enthalpy values of Cr and Mn are : A. $\Delta_iH_1$ : Cr > Mn B. $\Delta_iH_2$ : Cr > Mn C. $\Delta_iH_1$ : Mn > Cr D. $\Delta_iH_2$ : Mn > Cr. Choose the correct answer from the options given below :

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

Correct answer: B

Which of the following sequences of hybridisation, geometry and magnetic nature are correct for the given coordination compounds ? A. $\mathrm{[NiCl_4]^{2-}}$ $-$ $sp^3$, tetrahedral, paramagnetic B. $\mathrm{[Ni(NH_3)_6]^{2+}}$ $-$ $sp^3d^2$, octahedral, paramagnetic C. $\mathrm{[Ni(CO)_4]}$ $-$ $sp^3$, tetrahedral, paramagnetic D. $\mathrm{[Ni(CN)_4]^{2-}}$ $-$ $dsp^2$, square planar, diamagnetic. Choose the correct answer from the options given below :

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

Correct answer: D

Given below are two statements : Statement I : A mixture of $\mathrm{C_{12}H_{22}O_{11}}$ (sugar) and NaCl can be separated by dissolving sugar in alcohol, due to differential solubility. Statement II : Rose essence from rose petals is seperated by steam distillation due to its high volatility and insolubility in $\mathrm{H_2O}$. 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

Shown below is the structure of methyl acetate with three different $\alpha$, $\beta$ and $\gamma$ carbon - oxygen bonds: $\mathrm{H_3C-C(=O)-O-CH_3}$, where $\alpha$ is the C=O bond, $\beta$ is the (acyl C)$-$O single bond and $\gamma$ is the O$-\mathrm{CH_3}$ bond. The correct order of bond lengths of these bonds is :

1. A.$\alpha>\beta>\gamma$
2. B.$\alpha<\beta<\gamma$✓
3. C.$\alpha=\beta=\gamma$
4. D.$\alpha<\beta=\gamma$

Correct answer: B

'x' is the product which is obtained by the hydrolysis of prop-1-yne in the presence of mercuric sulphate under dilute acidic medium at 333 K. 'y' is the product which is obtained by the reaction of ethane nitrile with methyl magnesium bromide in dry ether followed by hydrolysis. IUPAC name of product obtained from 'x' and 'y' in the presence of barium hydroxide followed by heating is :

1. A.2-Methylpent-4-en-3-one
2. B.4-Methylpent-3-en-2-one✓
3. C.4-Methylpent-1-ene
4. D.2-Methylpent-3-one

Correct answer: B

An optically active alkyl bromide $\mathrm{C_4H_9Br}$, reacts with ethanolic KOH to form major compound [A] which reacts with bromine to give compound [B]. Compound [B] reacts with ethanolic KOH and sodamide to give compound [C]. One molecule of water adds to compound [C] on warming with mercuric sulphate and dilute sulphuric acid at 333 K to form compound [D]. The functional group in compound D will be confirmed by :

1. A.Haloform test✓
2. B.Lucas test
3. C.Silver mirror test
4. D.Benedict test

Correct answer: A

Consider the following reaction. Benzyl phenyl ether ($\mathrm{C_6H_5-O-CH_2-C_6H_5}$) + HI $\rightarrow$ Product. Statement I : In the above reaction, product formed will be a mixture of benzyl alcohol and iodobenzene. Statement II : In the above reaction, the $\mathrm{-O-CH_2-}$ bond is cleaved to give the product. 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: D

Consider the following organic reaction sequence. Choose the final product (X) from the following (consider the major product in all intermediate reactions): Propanoic acid ($\mathrm{CH_3CH_2COOH}$) $\xrightarrow{\mathrm{(i)\ NH_3/\Delta;\ (ii)\ NaOH/Br_2;\ (iii)\ HNO_2/H_2O,\ 0^\circ C;\ (iv)\ C_6H_5N_2Cl,\ 0^\circ C}}$ (X) Major Product

1. A.Benzene✓
2. B.Phenol
3. C.Propanol
4. D.Chlorobenzene

Correct answer: A

The number of compounds from the following which can undergo reaction with $\mathrm{Br_2}$/KOH (alcoholic) to give respective products and these respective products can also be obtained separately by Gabriel phthalimide reaction is : $\mathrm{C_6H_5CONH_2}$, $\mathrm{C_6H_5CH_2CONH_2}$, $\mathrm{CH_3CONH_2}$, $\mathrm{C_6H_{11}CONHCH_2CH_3}$, $\mathrm{(CH_3)_3CCONHCH_3}$, $\mathrm{C_6H_{11}CONH_2}$

1. A.5
2. B.4
3. C.3✓
4. D.6

Correct answer: C

Consider the following reactions. Total number of electrons in the $\pi$ bonds and lone pair of electrons in the product (X) is : Glucose $\mathrm{CHO-(CHOH)_4-CH_2OH}$ $\xrightarrow{\mathrm{(i)\ HI,\ \Delta;\ (ii)\ V_2O_5/10-20\ atm/773\ K;\ (iii)\ Benzoyl\ chloride/Anhyd.\ AlCl_3}}$ (X) Major product

1. A.12
2. B.16
3. C.14
4. D.18✓

Correct answer: D

Treatment of a gas 'X' with a freshly prepared ferrous sulphate solution gives a compound 'Y' as a brown ring. The compounds X and Y are.

1. A.NO and $\mathrm{[Fe(NO)]SO_4}$✓
2. B.$\mathrm{NO_2}$ and $\mathrm{[Fe(NO_2)]SO_4}$
3. C.$\mathrm{N_2O}$ and $\mathrm{[Fe(N_2O)]SO_4}$
4. D.$\mathrm{N_2O_4}$ and $\mathrm{[Fe(N_2O_4)]SO_4}$

Correct answer: A

An excess of $\mathrm{AgNO_3}$ is added to 100 mL of a 0.05 M solution of tetraaquadichloridochromium (III) chloride. The number of moles of AgCl precipitated will be ______ $\times10^{-3}$. (Nearest integer)

Correct answer: 5

An alkane (Y) requires 8 moles of oxygen for complete combustion and on chlorination with $\mathrm{Cl_2}/h\nu$, (Y) gives only one monochlorinated product (Z). The total number of primary carbon atoms in (Y) is ______.

Correct answer: 4

500 mL of 0.2 M $\mathrm{MnO_4^-}$ solution in basic medium when mixed with 500 mL of 1.5 M KI solution, oxidises iodide ions to liberate molecular iodine. This liberated iodine is then titrated with a standard $x$ M thiosulphate solution in presence of starch till the end point. If 300 mL of thiosulphate was consumed, then the value of $x$ is ______.

Correct answer: 1

In a closed flask at 600 K, one mole of $\mathrm{X_2Y_4(g)}$ attains equilibrium as given below : $\mathrm{X_2Y_4(g)\rightleftharpoons2XY_2(g)}$. At equilibrium, 75% $\mathrm{X_2Y_4(g)}$ was dissociated and the total pressure is 1 atm. The magnitude of $\Delta_rG^\ominus$ (in kJ $\mathrm{mol^{-1}}$) at this temperature is ______. (Nearest Integer) (Given : R = 8.3 J $\mathrm{mol^{-1}K^{-1}}$; ln 10 = 2.3, log 2 = 0.3, log 3 = 0.48, log 5 = 0.69, log 7 = 0.84)

Correct answer: 8

Decomposition of a hydrocarbon follows the equation $k=(5.5\times10^{11}\ \mathrm{s^{-1}})\,e^{\frac{-28000\ K}{T}}$. The activation energy of reaction is ______ kJ $\mathrm{mol^{-1}}$. (Nearest Integer) Given : R = 8.3 J $\mathrm{K^{-1}mol^{-1}}$

Correct answer: 232