JEE Main 2025 — 2 Apr Shift 1 (Previous Year Paper)

If the system of linear equations $3x+y+\beta z=3$, $2x+\alpha y-z=-3$, $x+2y+z=4$ has infinitely many solutions, then the value of $22\beta-9\alpha$ is :

1. A.37
2. B.43
3. C.49
4. D.31✓

Correct answer: D

Let z be a complex number such that $|z|=1$. If $\frac{2+k^2z}{k+\bar{z}}=kz$, $k\in\mathbf{R}$, then the maximum distance of $k+ik^2$ from the circle $|z-(1+2i)|=1$ is :

1. A.$\sqrt{3}+1$
2. B.2
3. C.$\sqrt{5}+1$✓
4. D.3

Correct answer: C

If S and S' are the foci of the ellipse $\frac{x^2}{18}+\frac{y^2}{9}=1$ and P be a point on the ellipse, then $\min(SP\cdot S'P)+\max(SP\cdot S'P)$ is equal to :

1. A.$3(6+\sqrt{2})$
2. B.9
3. C.27✓
4. D.$3(1+\sqrt{2})$

Correct answer: C

Let $A=\begin{bmatrix}\alpha & -1\\ 6 & \beta\end{bmatrix}$, $\alpha>0$, such that $\det(A)=0$ and $\alpha+\beta=1$. If I denotes $2\times2$ identity matrix, then the matrix $(I+A)^8$ is :

1. A.$\begin{bmatrix}1025 & -511\\ 2024 & -1024\end{bmatrix}$
2. B.$\begin{bmatrix}257 & -64\\ 514 & -127\end{bmatrix}$
3. C.$\begin{bmatrix}4 & -1\\ 6 & -1\end{bmatrix}$
4. D.$\begin{bmatrix}766 & -255\\ 1530 & -509\end{bmatrix}$✓

Correct answer: D

If $\theta\in[-2\pi, 2\pi]$, then the number of solutions of $2\sqrt{2}\cos^2\theta+(2-\sqrt{6})\cos\theta-\sqrt{3}=0$, is equal to :

1. A.8✓
2. B.10
3. C.6
4. D.12

Correct answer: A

If the function $f(x)=2x^3-9ax^2+12a^2x+1$, where $a>0$, attains its local maximum and local minimum values at p and q, respectively, such that $p^2=q$, then $f(3)$ is equal to :

1. A.37✓
2. B.23
3. C.55
4. D.10

Correct answer: A

If $\vec{a}$ is a nonzero vector such that its projections on the vectors $2\hat{i}-\hat{j}+2\hat{k}$, $\hat{i}+2\hat{j}-2\hat{k}$ and $\hat{k}$ are equal, then a unit vector along $\vec{a}$ is :

1. A.$\frac{1}{\sqrt{155}}(7\hat{i}+9\hat{j}+5\hat{k})$✓
2. B.$\frac{1}{\sqrt{155}}(7\hat{i}+9\hat{j}-5\hat{k})$
3. C.$\frac{1}{\sqrt{155}}(-7\hat{i}+9\hat{j}+5\hat{k})$
4. D.$\frac{1}{\sqrt{155}}(-7\hat{i}+9\hat{j}-5\hat{k})$

Correct answer: A

The term independent of $x$ in the expansion of $\left(\frac{(x+1)}{\left(x^{2/3}+1-x^{1/3}\right)}-\frac{(x-1)}{\left(x-x^{1/2}\right)}\right)^{10}$, $x>1$, is :

1. A.240
2. B.210✓
3. C.150
4. D.120

Correct answer: B

Let the focal chord PQ of the parabola $y^2=4x$ make an angle of 60° with the positive x-axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y-axis at the point $(0, \alpha)$, then $5\alpha^2$ is equal to :

1. A.25
2. B.15✓
3. C.30
4. D.20

Correct answer: B

Let $a\in\mathbf{R}$ and A be a matrix of order $3\times3$ such that $\det(A)=-4$ and $A+I=\begin{bmatrix}1 & a & 1\\ 2 & 1 & 0\\ a & 1 & 2\end{bmatrix}$, where I is the identity matrix of order $3\times3$. If $\det((a+1)\,\mathrm{adj}((a-1)A))$ is $2^m3^n$, $m, n\in\{0, 1, 2, \ldots, 20\}$, then $m+n$ is equal to :

1. A.15
2. B.17
3. C.14
4. D.16✓

Correct answer: D

Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be 5, 6 and 7 square units respectively. Then the area (in square units) of the $\triangle BCD$ is equal to :

1. A.$7\sqrt{3}$
2. B.12
3. C.$\sqrt{110}$✓
4. D.$\sqrt{340}$

Correct answer: C

The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is equal to :

1. A.1820
2. B.45
3. C.360
4. D.2520✓

Correct answer: D

Let A be the set of all functions $f:\mathbf{Z}\to\mathbf{Z}$ and R be a relation on A such that $R=\{(f, g): f(0)=g(1) \text{ and } f(1)=g(0)\}$. Then R is :

1. A.Reflexive but neither symmetric nor transitive
2. B.Symmetric and transitive but not reflective
3. C.Symmetric but neither reflective nor transitive✓
4. D.Transitive but neither reflexive nor symmetric

Correct answer: C

The largest $n\in\mathbf{N}$ such that $3^n$ divides 50! is :

1. A.21
2. B.22✓
3. C.23
4. D.20

Correct answer: B

Let $P_n=\alpha^n+\beta^n$, $n\in\mathbf{N}$. If $P_{10}=123$, $P_9=76$, $P_8=47$ and $P_1=1$, then the quadratic equation having roots $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ is :

1. A.$x^2-x+1=0$
2. B.$x^2-x-1=0$
3. C.$x^2+x+1=0$
4. D.$x^2+x-1=0$✓

Correct answer: D

Let the vertices Q and R of the triangle PQR lie on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$, QR = 5 and the coordinates of the point P be (0, 2, 3). If the area of the triangle PQR is $\frac{m}{n}$ then :

1. A.$5m-2\sqrt{21}n=0$
2. B.$5m-21\sqrt{2}n=0$
3. C.$2m-5\sqrt{21}n=0$✓
4. D.$m-5\sqrt{21}n=0$

Correct answer: C

For $\alpha, \beta, \gamma\in\mathbf{R}$, if $\lim_{x\to0}\frac{x^2\sin\alpha x+(\gamma-1)e^{x^2}}{\sin2x-\beta x}=3$, then $\beta+\gamma-\alpha$ is equal to :

1. A.6
2. B.-1
3. C.4
4. D.7✓

Correct answer: D

Let $a_1, a_2, a_3, \ldots$ be in an A.P. such that $\sum_{k=1}^{12}a_{2k-1}=-\frac{72}{5}a_1$, $a_1\neq0$. If $\sum_{k=1}^{n}a_k=0$, then n is :

1. A.10
2. B.18
3. C.17
4. D.11✓

Correct answer: D

Let one focus of the hyperbola H: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be at $(\sqrt{10}, 0)$ and the corresponding directrix be $x=\frac{9}{\sqrt{10}}$. If e and $l$ respectively are the eccentricity and the length of the latus rectum of H, then $9(e^2+l)$ is equal to :

1. A.16✓
2. B.15
3. C.12
4. D.14

Correct answer: A

Let $f:\mathbf{R}\to\mathbf{R}$ be a twice differentiable function such that $(\sin x\cos y)(f(2x+2y)-f(2x-2y))=(\cos x\sin y)(f(2x+2y)+f(2x-2y))$, for all $x, y\in\mathbf{R}$. If $f'(0)=\frac{1}{2}$, then the value of $24f''\left(\frac{5\pi}{3}\right)$ is :

1. A.-2
2. B.-3✓
3. C.2
4. D.3

Correct answer: B

Let $f:\mathbf{R}\to\mathbf{R}$ be a thrice differentiable odd function satisfying $f'(x)\ge0$, $f''(x)=f(x)$, $f(0)=0$, $f'(0)=3$. Then $9f(\log_e3)$ is equal to ______.

Correct answer: 36

Three distinct numbers are selected randomly from the set $\{1, 2, 3, \ldots, 40\}$. If the probability, that the selected numbers are in an increasing G.P., is $\frac{m}{n}$, $\gcd(m, n)=1$, then m+n is equal to ______.

Correct answer: 2477

Let $[\cdot]$ denote the greatest integer function. If $\int_0^{e^3}\left[\frac{1}{e^{x-1}}\right]dx=\alpha-\log_e2$, then $\alpha^3$ is equal to ______.

Correct answer: 8

If the area of the region $\{(x, y): |4-x^2|\le y\le x^2, y\le4, x\ge0\}$ is $\left(\frac{80\sqrt{2}}{\alpha}-\beta\right)$, $\alpha, \beta\in\mathbf{N}$, then $\alpha+\beta$ is equal to ______.

Correct answer: 22

The absolute difference between the squares of the radii of the two circles passing through the point $(-9, 4)$ and touching the lines $x+y=3$ and $x-y=3$, is equal to ______.

Correct answer: 768

Match List - I with List - II. List - I: (A) Coefficient of viscosity (B) Intensity of wave (C) Pressure gradient (D) Compressibility. List - II: (I) $[ML^0T^{-3}]$ (II) $[ML^{-2}T^{-2}]$ (III) $[M^{-1}LT^2]$ (IV) $[ML^{-1}T^{-1}]$. Choose the correct answer from the options given below :

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

Correct answer: D

A particle is subjected to two simple harmonic motions as : $x_1=\sqrt{7}\sin5t$ cm and $x_2=2\sqrt{7}\sin\left(5t+\frac{\pi}{3}\right)$ cm where x is displacement and t is time in seconds. The maximum acceleration of the particle is $x\times10^{-2}\ ms^{-2}$. The value of x is :

1. A.175✓
2. B.125
3. C.$25\sqrt{7}$
4. D.$5\sqrt{7}$

Correct answer: A

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object 'O', is : (C is the center of curvature of the spherical surface and R is the radius of curvature)

1. A.0.24 m left to the spherical surface
2. B.0.4 m left to the spherical surface✓
3. C.0.24 m right to the spherical surface
4. D.0.4 m right to the spherical surface

Correct answer: B

The battery of a mobile phone is rated as 4.2 V, 5800 mAh. How much energy is stored in it when fully charged ?

1. A.43.8 kJ
2. B.87.7 kJ✓
3. C.24.4 kJ
4. D.48.7 kJ

Correct answer: B

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m, would be :

1. A.0 rad/s
2. B.30 rad/s
3. C.10 rad/s
4. D.20 rad/s✓

Correct answer: D

Considering Bohr's atomic model for hydrogen atom : (A) the energy of H atom in ground state is same as energy of $He^+$ ion in its first excited state. (B) the energy of H atom in ground state is same as that for $Li^{++}$ ion in its second excited state. (C) the energy of H atom in its ground state is same as that of $He^+$ ion for its ground state. (D) the energy of $He^+$ ion in its first excited state is same as that for $Li^{++}$ ion in its ground state. Choose the correct answer from the options given below :

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

Correct answer: B

The relationship between the magnetic susceptibility ($\chi$) and the magnetic permeability ($\mu$) is given by : ($\mu_0$ is the permeability of free space and $\mu_r$ is relative permeability)

1. A.$\chi=\mu_r+1$
2. B.$\chi=1-\frac{\mu}{\mu_0}$
3. C.$\chi=\frac{\mu}{\mu_0}-1$✓
4. D.$\chi=\frac{\mu_r}{\mu_0}+1$

Correct answer: C

A small bob of mass 100 mg and charge +10 $\mu$C is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density '$\sigma$' as shown in figure. If string subtends an angle of 45° with the sheet at equilibrium the charge density of sheet will be. (Given, $\epsilon_0=8.85\times10^{-12}\ \frac{F}{m}$ and acceleration due to gravity, g = 10 $\frac{m}{s^2}$)

1. A.17.7 $nC/m^2$
2. B.0.885 $nC/m^2$
3. C.885 $nC/m^2$
4. D.1.77 $nC/m^2$✓

Correct answer: D

A river is flowing from west to east direction with speed of 9 km $h^{-1}$. If a boat capable of moving at a maximum speed of 27 km $h^{-1}$ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150° to direction of river flow, then the width of the river is :

1. A.112.5 m✓
2. B.$112.5\times\sqrt{3}$ m
3. C.75 m
4. D.300 m

Correct answer: A

A monochromatic light is incident on a metallic plate having work function $\phi$. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is : (Given : The magnitude of charge of an electron is e and mass is m, h is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

1. A.$\sqrt{2m\left(\frac{hc}{\lambda}-\phi\right)}/eB$
2. B.$2\sqrt{m\left(\frac{hc}{\lambda}-\phi\right)}/eB$
3. C.$\sqrt{m\left(\frac{hc}{\lambda}-\phi\right)}/eB$
4. D.$\sqrt{8m\left(\frac{hc}{\lambda}-\phi\right)}/eB$✓

Correct answer: D

Moment of inertia of a rod of mass 'M' and length 'L' about an axis passing through its center and normal to its length is '$\alpha$'. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :

1. A.$\alpha/4$✓
2. B.$\alpha/8$
3. C.$\alpha/2$
4. D.$\alpha$

Correct answer: A

In an adiabatic process, which of the following statements is true ?

1. A.Work done by the gas equals the increase in internal energy
2. B.The molar heat capacity is infinite
3. C.The internal energy of the gas decreases as the temperature increases
4. D.The molar heat capacity is zero✓

Correct answer: D

A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is :

1. A.(4d/3, 0, 0)
2. B.(d/3, 0, 0)
3. C.(3d/4, 0, 0)
4. D.(d/4, 0, 0)✓

Correct answer: D

A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is :

1. A.$+45^\circ$
2. B.$-45^\circ$✓
3. C.$-\alpha$
4. D.$-\frac{\alpha}{2}$

Correct answer: B

A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V. For a 400 $\Omega$ resistor connected in series, the zener current is found to be 4 times load current. The load current ($I_L$) and load resistance ($R_L$) are :

1. A.$I_L=0.02$ mA; $R_L=250\ \Omega$
2. B.$I_L=10$ mA; $R_L=500\ \Omega$✓
3. C.$I_L=10$ A; $R_L=0.5\ \Omega$
4. D.$I_L=20$ mA; $R_L=250\ \Omega$

Correct answer: B

A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is :

1. A.10 N✓
2. B.0 (zero)
3. C.20 N
4. D.$10\sqrt{2}$ N

Correct answer: A

The equation for real gas is given by $\left(P+\frac{a}{V^2}\right)(V-b)=RT$, where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of $ab^{-2}$ is equivalent to that of :

1. A.Energy density✓
2. B.Planck's constant
3. C.Strain
4. D.Compressibility

Correct answer: A

Let $B_1$ be the magnitude of magnetic field at center of a circular coil of radius R carrying current I. Let $B_2$ be the magnitude of magnetic field at an axial distance 'x' from the center. For $x:R=3:4$, $\frac{B_2}{B_1}$ is :

1. A.25 : 16
2. B.64 : 125✓
3. C.4 : 5
4. D.16 : 25

Correct answer: B

A light wave is propagating with plane wave fronts of the type $x+y+z=$ constant. The angle made by the direction of wave propagation with the x-axis is :

1. A.$\cos^{-1}\left(\sqrt{\frac{2}{3}}\right)$
2. B.$\cos^{-1}(2/3)$
3. C.$\cos^{-1}\left(\frac{1}{3}\right)$
4. D.$\cos^{-1}\left(\frac{1}{\sqrt{3}}\right)$✓

Correct answer: D

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+\sigma$ and $-2\sigma$. The force experienced by a point charge +q placed at the mid point between two plates will be :

1. A.$\frac{3\sigma q}{4\epsilon_0}$
2. B.$\frac{3\sigma q}{2\epsilon_0}$✓
3. C.$\frac{\sigma q}{2\epsilon_0}$
4. D.$\frac{\sigma q}{4\epsilon_0}$

Correct answer: B

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is 30° in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is ______ $\mu$m.

Correct answer: 6

A steel wire of length 2 m and Young\'s modulus $2.0\times10^{11}\ N\,m^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is ______ $\times10^5$ (in SI units).

Correct answer: 25

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 $cm^2$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $1.5\times10^3\ kg/m^3$. What force one needs to apply on the hinged door so that it does not get opened ? (Acceleration due to gravity = 10 $m/s^2$)

Correct answer: 150

A person travelling on a straight line moves with a uniform velocity $v_1$ for a distance x and with a uniform velocity $v_2$ for the next $\frac{3}{2}x$ distance. The average velocity in this motion is $\frac{50}{7}$ m/s. If $v_1$ is 5 m/s then $v_2$ = ______ m/s.

Correct answer: 10

$\gamma_A$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $\gamma_B$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\frac{\gamma_A}{\gamma_B}=\left(1+\frac{1}{n}\right)$, then the value of n is ______.

Correct answer: 3

On complete combustion 1.0 g of an organic compound (X) gave 1.46 g of $CO_2$ and 0.567 g of $H_2O$. The empirical formula mass of compound (X) is ______ g. (Given molar mass in g $mol^{-1}$ C : 12, H : 1, O : 16)

1. A.15
2. B.45
3. C.30✓
4. D.60

Correct answer: C

$CaCO_3(s)+2HCl(aq)\to CaCl_2(aq)+CO_2(g)+H_2O(l)$. Consider the above reaction, what mass of $CaCl_2$ will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of $CaCO_3$ ? (Given : Molar mass of Ca, C, O, H and Cl are 40, 12, 16, 1 and 35.5 g $mol^{-1}$, respectively)

1. A.2.636 g
2. B.5.272 g
3. C.3.908 g
4. D.10.545 g✓

Correct answer: D

According to Bohr's model of hydrogen atom, which of the following statement is incorrect ?

1. A.Radius of $4^{th}$ orbit is four times larger than that of $2^{nd}$ orbit
2. B.Radius of $3^{rd}$ orbit is nine times larger than that of $1^{st}$ orbit
3. C.Radius of $8^{th}$ orbit is four times larger than that of $4^{th}$ orbit
4. D.Radius of $6^{th}$ orbit is three times larger than that of $4^{th}$ orbit✓

Correct answer: D

Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?

1. A.$dU\neq0$
2. B.$dw\neq0$
3. C.The pressure in the vessel B before opening the stopcock is zero✓
4. D.$dq\neq0$

Correct answer: C

Consider the following compound (X): $\overset{I}{H}-C\equiv C-\overset{II}{CH_2}-\overset{III}{CH}(CH_3)-\overset{IV}{CH_3}$. The most stable and least stable carbon radicals, respectively, produced by homolytic cleavage of corresponding C–H bond are :

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

Correct answer: A

Given below are two statements : Statement (I) : In octahedral complexes, when $\Delta_o<P$ high spin complexes are formed. When $\Delta_o>P$ low spin complexes are formed. Statement (II) : In tetrahedral complexes because of $\Delta_t<P$, low spin complexes are rarely formed. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Correct answer: D

Among $SO_2$, $NF_3$, $NH_3$, $XeF_2$, $ClF_3$ and $SF_4$, the hybridization of the molecule with non-zero dipole moment and highest number of lone-pairs of electrons on the central atom is :

1. A.$sp^3d^2$
2. B.$dsp^2$
3. C.$sp^3d$✓
4. D.$sp^3$

Correct answer: C

Designate whether each of the following compounds is aromatic or not aromatic. (a) cyclopentadienyl anion (b) cyclopentadienyl cation (c) cyclobutadiene dication (cyclobutene ring carrying + charges on the two sp$^2$ carbons) (d) cyclobutadiene dianion (cyclobutene ring carrying − charges on the two carbons) (e) cycloheptatrienyl (tropylium) cation (f) cyclooctatetraene (g) cyclobutadiene (h) cyclopropenyl cation

1. A.a, b, c, d aromatic and e, f, g, h not aromatic
2. B.b, e, f, g aromatic and a, c, d, h not aromatic
3. C.e, g aromatic and a, b, c, d, f, h not aromatic
4. D.a, c, d, e, h aromatic and b, f, g not aromatic✓

Correct answer: D

Given below are two statements : Statement (I) : The metallic radius of Al is less than that of Ga. Statement (II) : The ionic radius of $Al^{3+}$ is less than that of $Ga^{3+}$. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Correct answer: A

A molecule with the formula $AX_4Y$ has all it\'s elements from p-block. Element A is rarest, monoatomic, non-radioactive from its group and has the lowest ionization enthalpy value among A, X and Y. Elements X and Y have first and second highest electronegativity values respectively among all the known elements. The shape of the molecule is :

1. A.Octahedral
2. B.Pentagonal planar
3. C.Trigonal bipyramidal
4. D.Square pyramidal✓

Correct answer: D

The property/properties that show irregularity in first four elements of group-17 is/are : (A) Covalent radius (B) Electron affinity (C) Ionic radius (D) First ionization energy. Choose the correct answer from the options given below :

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

Correct answer: C

Consider the following molecules : (p) $CH_3-CH_2-CO-Cl$ (q) $CH_3-CH_2-CO-O-CO-CH_3$ (r) $CH_3-CH_2-CO-O-CH_2-CH_3$ (s) $CH_3-CH_2-CO-NH_2$. The correct order of rate of hydrolysis is :

1. A.p > q > r > s✓
2. B.p > r > q > s
3. C.r > q > p > s
4. D.q > p > r > s

Correct answer: A

A solution is made by mixing one mole of volatile liquid A with 3 moles of volatile liquid B. The vapour pressure of pure A is 200 mm Hg and that of the solution is 500 mm Hg. The vapour pressure of pure B and the least volatile component of the solution, respectively, are :

1. A.600 mm Hg, B
2. B.600 mm Hg, A✓
3. C.1400 mm Hg, A
4. D.1400 mm Hg, B

Correct answer: B

Which of the following graph correctly represents the plots of $K_H$ at 1 bar for gases in water versus temperature?

1. A.Graph: straight lines rising from the origin, steepest labelled $O_2$, then $N_2$, lowest He
2. B.Graph: curves rising to a maximum then falling, highest He, then $N_2$, lowest $CH_4$✓
3. C.Graph: U-shaped curves (falling then rising steeply), top He, then $N_2$, lowest $O_2$
4. D.Graph: curves rising to a maximum then falling, highest $O_2$, then $N_2$, lowest He

Correct answer: B

An optically active alkyl halide $C_4H_9Br$ [A] reacts with hot KOH dissolved in ethanol and forms alkene [B] as major product which reacts with bromine to give dibromide [C]. The compound [C] is converted into a gas [D] upon reacting with alcoholic $NaNH_2$. During hydration 18 gram of water is added to 1 mole of gas [D] on warming with mercuric sulphate and dilute acid at 333 K to form compound [E]. The IUPAC name of compound [E] is :

1. A.Butan-2-one✓
2. B.Butan-2-ol
3. C.Butan-1-al
4. D.But-2-yne

Correct answer: A

Given below are two statements : Statement (I) : Vanillin (4-hydroxy-3-methoxybenzaldehyde) will react with NaOH and also with Tollen's reagent. Statement (II) : Vanillin will undergo self aldol condensation very easily. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Correct answer: B

Choose the correct tests with respective observations. (A) $CuSO_4$ (acidified with acetic acid) + $K_4[Fe(CN)_6]\to$ Chocolate brown precipitate. (B) $FeCl_3+K_4[Fe(CN)_6]\to$ Prussian blue precipitate. (C) $ZnCl_2+K_4[Fe(CN)_6]$, neutralised with $NH_4OH\to$ White or bluish white precipitate. (D) $MgCl_2+K_4[Fe(CN)_6]\to$ Blue precipitate. (E) $BaCl_2+K_4[Fe(CN)_6]$, neutralised with NaOH $\to$ White precipitate. Choose the correct answer from the options given below :

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

Correct answer: D

Identify the correct statement among the following :

1. A.All naturally occurring amino acids are optically active.
2. B.Amino acid, cysteine can easily undergo dimerisation due to the presence of free SH group.✓
3. C.All naturally occurring amino acids except glycine contain one chiral centre.
4. D.Glutamic acid is the only amino acid that contains a −COOH group at the side chain.

Correct answer: B

The correct order of basic nature in aqueous solution for the bases $NH_3$, $H_2N-NH_2$, $CH_3CH_2NH_2$, $(CH_3CH_2)_2NH$ and $(CH_3CH_2)_3N$ is :

1. A.$NH_3<H_2N-NH_2<(CH_3CH_2)_3N<CH_3CH_2NH_2<(CH_3CH_2)_2NH$
2. B.$NH_2-NH_2<NH_3<CH_3CH_2NH_2<(CH_3CH_2)_3N<(CH_3CH_2)_2NH$✓
3. C.$NH_3<H_2N-NH_2<CH_3CH_2NH_2<(CH_3CH_2)_2NH<(CH_3CH_2)_3N$
4. D.$H_2N-NH_2<NH_3<(CH_3CH_2)_3N<CH_3CH_2NH_2<(CH_3CH_2)_2NH$

Correct answer: B

If equal volumes of $AB_2$ and XY (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $AY_2$ at 300 K ? (Given $K_{sp}$ (at 300 K) for $AY_2=5.2\times10^{-7}$)

1. A.$3.6\times10^{-3}$ M $AB_2$, $5.0\times10^{-4}$ M XY
2. B.$2.0\times10^{-4}$ M $AB_2$, $0.8\times10^{-3}$ M XY
3. C.$2.0\times10^{-2}$ M $AB_2$, $2.0\times10^{-2}$ M XY✓
4. D.$1.5\times10^{-4}$ M $AB_2$, $1.5\times10^{-3}$ M XY