JEE Main 2024 — 30 Jan Shift 2 (Previous Year Paper)

If $x^2-y^2+2hxy+2gx+2fy+c=0$ is the locus of a point, which moves such that it is always equidistant from the lines $x+2y+7=0$ and $2x-y+8=0$, then the value of $g+c+h-f$ equals.

1. A.14✓
2. B.6
3. C.8
4. D.29

Correct answer: A

Let $f(x)=(x+3)^2(x-2)^3$, $x\in[-4,4]$. If $M$ and $m$ are the maximum and minimum values of $f$, respectively in $[-4,4]$, then the value of $M-m$ is:

1. A.392
2. B.600
3. C.108
4. D.608✓

Correct answer: D

Let $y=f(x)$ be a thrice differentiable function in (−5, 5). Let the tangents to the curve $y=f(x)$ at $(1,f(1))$ and $(3,f(3))$ make angles $\frac\pi6$ and $\frac\pi4$, respectively with positive $x$-axis. If $27\int_1^3\left((f'(t))^2+1\right)f''(t)dt=\alpha+\beta\sqrt3$ where $\alpha,\beta$ are integers, then the value of $\alpha+\beta$ equals.

1. A.36
2. B.−16
3. C.−14
4. D.26✓

Correct answer: D

Let $\vec a=\hat i+\alpha\hat j+\beta\hat k$, $\alpha,\beta\in\mathbb{R}$. Let a vector $\vec b$ be such that the angle between $\vec a$ and $\vec b$ is $\frac\pi4$ and $|\vec b|^2=6$. If $\vec a\cdot\vec b=3\sqrt2$, then the value of $(\alpha^2+\beta^2)|\vec a\times\vec b|^2$ is equal to:

1. A.85
2. B.75
3. C.90✓
4. D.95

Correct answer: C

Let $L_1:\vec r=(\hat i-\hat j+2\hat k)+\lambda(\hat i-\hat j+2\hat k)$, $\lambda\in\mathbb{R}$, $L_2:\vec r=(\hat j-\hat k)+\mu(3\hat i+\hat j+p\hat k)$, $\mu\in\mathbb{R}$, and $L_3:\vec r=\delta(l\hat i+m\hat j+n\hat k)$, $\delta\in\mathbb{R}$ be three lines such that $L_1$ is perpendicular to $L_2$ and $L_3$ is perpendicular to both $L_1$ and $L_2$. Then, the point which lies on $L_3$ is:

1. A.(1, −7, 4)
2. B.(−1, 7, 4)✓
3. C.(−1, −7, 4)
4. D.(1, 7, −4)

Correct answer: B

Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is:

1. A.$\frac19$
2. B.$\frac14$
3. C.$\frac13$✓
4. D.$\frac3{10}$

Correct answer: C

Let $f:\mathbb{R}-\{0\}\to\mathbb{R}$ be a function satisfying $f\left(\frac xy\right)=\frac{f(x)}{f(y)}$ for all $x,y$, $f(y)\ne0$. If $f'(1)=2024$, then:

1. A.$xf'(x)+2024f(x)=0$
2. B.$xf'(x)+f(x)=2024$
3. C.$xf'(x)-2024f(x)=0$✓
4. D.$xf'(x)-2023f(x)=0$

Correct answer: C

Let $R=\begin{pmatrix}x&0&0\\0&y&0\\0&0&z\end{pmatrix}$ be a non-zero $3\times3$ matrix, where $x\sin\theta=y\sin\left(\theta+\frac{2\pi}{3}\right)=z\sin\left(\theta+\frac{4\pi}{3}\right)\ne0$, $\theta\in(0,2\pi)$. For a square matrix $M$, Let trace $(M)$ denote the sum of all the diagonal entries of $M$. Then, among the statements: (I) Trace $(R)=0$ (II) If trace$(\text{adj}(\text{adj}(R)))=0$, then $R$ has exactly one non-zero entry.

1. A.Only (II) is true
2. B.Only (I) is true
3. C.Neither (I) nor (II) is true✓
4. D.Both (I) and (II) are true

Correct answer: C

If $z$ is a complex number, then the number of common roots of the equations $z^{1985}+z^{100}+1=0$ and $z^3+2z^2+2z+1=0$, is equal to:

1. A.1
2. B.0
3. C.2✓
4. D.3

Correct answer: C

Let $a$ and $b$ be two distinct positive real numbers. Let $11^{th}$ term of a GP, whose first term is $a$ and third term is $b$, is equal to $p^{th}$ term of another GP, whose first term is a and fifth term is $b$. Then $p$ is equal to:

1. A.20
2. B.24
3. C.25
4. D.21✓

Correct answer: D

Let $\vec a$ and $\vec b$ be two vectors such that $|\vec b|=1$ and $|\vec b\times\vec a|=2$. Then $|(\vec b\times\vec a)-\vec b|^2$ is equal to:

1. A.5✓
2. B.3
3. C.4
4. D.1

Correct answer: A

Let $f:\mathbb{R}\to\mathbb{R}$ be defined as $f(x)=ae^{2x}+be^x+cx$. If $f(0)=-1$, $f'(\log_e2)=21$ and $\int_0^{\log_e4}(f(x)-cx)dx=\frac{39}{2}$, then the value of $|a+b+c|$ equals.

1. A.10
2. B.8✓
3. C.12
4. D.16

Correct answer: B

Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by $f(x)=\frac{x}{(1+x^4)^{1/4}}$, and $g(x)=f(f(f(f(x))))$. Then, $18\int_0^{\sqrt{2\sqrt5}}x^2g(x)dx$ is equal to:

1. A.42
2. B.39✓
3. C.36
4. D.33

Correct answer: B

Let $P$ be a point on the hyperbola $H:\frac{x^2}{9}-\frac{y^2}{4}=1$, in the first quadrant such that the area of triangle formed by $P$ and the two foci of $H$ is $2\sqrt{13}$. Then, the square of the distance of $P$ from the origin is:

1. A.20
2. B.22✓
3. C.18
4. D.26

Correct answer: B

Let $a$ and $b$ be real constants such that the function $f$ defined by $f(x)=\begin{cases}x^2+3x+a, & x\le1\\ bx+2, & x>1\end{cases}$ be differentiable on $\mathbb{R}$. Then, the value of $\int_{-2}^{2}f(x)dx$ equals.

1. A.17✓
2. B.$\frac{19}{6}$
3. C.$\frac{15}{6}$
4. D.21

Correct answer: A

If the domain of the function $f(x)=\log_e\left(\frac{2x+3}{4x^2+x-3}\right)+\cos^{-1}\left(\frac{2x-1}{x+2}\right)$ is $(\alpha,\beta]$, then the value of $5\beta-4\alpha$ is equal to:

1. A.9
2. B.11
3. C.10
4. D.12✓

Correct answer: D

Let $A(\alpha,0)$ and $B(0,\beta)$ be the points on the line $5x+7y=50$. Let the point $P$ divide the line segment $AB$ internally in the ratio 7 : 3. Let $3x-25=0$ be a directrix of the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the corresponding focus be $S$. If from $S$, the perpendicular on the $x$-axis passes through $P$, then the length of the latus rectum of $E$ is equal to:

1. A.$\frac{32}{9}$
2. B.$\frac{25}{9}$
3. C.$\frac{25}{3}$
4. D.$\frac{32}{5}$✓

Correct answer: D

For $\alpha,\beta\in\left(0,\frac\pi2\right)$, let $3\sin(\alpha+\beta)=2\sin(\alpha-\beta)$ and a real number $k$ be such that $\tan\alpha=k\tan\beta$. Then, the value of $k$ is equal to:

1. A.5
2. B.$\frac23$
3. C.−5✓
4. D.$\frac{-2}{3}$

Correct answer: C

Consider the system of linear equations $x+y+z=5$, $x+2y+\lambda^2z=9$, $x+3y+\lambda z=\mu$, where $\lambda,\mu\in\mathbb{R}$. Then, which of the following statement is NOT correct?

1. A.System is consistent if $\lambda\ne1$ and $\mu=13$
2. B.System has unique solution if $\lambda\ne1$ and $\mu\ne13$✓
3. C.System is inconsistent if $\lambda=1$ and $\mu\ne13$
4. D.System has infinite number of solutions if $\lambda=1$ and $\mu=13$

Correct answer: B

Let $S_n$ be the sum to $n$-terms of an arithmetic progression 3, 7, 11, ....... If $40<\left(\frac{6}{n(n+1)}\sum_{k=1}^nS_k\right)<42$, then $n$ equals ______.

Correct answer: 9

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections: A, B and C. A students is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C 6 questions, then the total number of ways a student can select 15 questions is ______.

Correct answer: 11376

Consider two circles $C_1:x^2+y^2=25$ and $C_2:(x-\alpha)^2+y^2=16$, where $\alpha\in(5,9)$. Let the angle between the two radii (one to each circle) drawn from one of the intersection points of $C_1$ and $C_2$ be $\sin^{-1}\left(\frac{\sqrt{63}}{8}\right)$. If the length of common chord of $C_1$ and $C_2$ is $\beta$, then the value of $(\alpha\beta)^2$ equals ______.

Correct answer: 1575

The variance $\sigma^2$ of the data | $x_i$ | 0 | 1 | 5 | 6 | 10 | 12 | 17 | | $f_i$ | 3 | 2 | 3 | 2 | 6 | 3 | 3 | is ______.

Correct answer: 29

Let a line passing through the point (−1, 2, 3) intersects the lines $L_1:\frac{x-1}{3}=\frac{y-2}{2}=\frac{z+1}{-2}$ at $M(\alpha,\beta,\gamma)$ and $L_2:\frac{x+2}{-3}=\frac{y-2}{-2}=\frac{z-1}{4}$ at $N(a,b,c)$. Then, the value of $\frac{(\alpha+\beta+\gamma)^2}{(a+b+c)^2}$ equals ______.

Correct answer: 196

The number of symmetric relations defined on the set {1, 2, 3, 4} which are not reflexive is ______.

Correct answer: 960

Let $Y=Y(X)$ be a curve lying in the first quadrant such that the area enclosed by the line $Y-y=Y'(x)(X-x)$ and the co-ordinate axes, where $(x,y)$ is any point on the curve, is always $\frac{-y^2}{2Y'(x)}+1$, $Y'(x)\ne0$. If $Y(1)=1$, then $12Y(2)$ equals ______.

Correct answer: 20

The area of the region enclosed by the parabola $(y-2)^2=x-1$, the line $x-2y+4=0$ and the positive coordinate axes is ______.

Correct answer: 5

The number of real solutions of the equation $x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0$ is ______.

Correct answer: 1

Let $\alpha=\sum_{k=0}^{n}\left(\frac{\left({}^nC_k\right)^2}{k+1}\right)$ and $\beta=\sum_{k=0}^{n-1}\left(\frac{{}^nC_k\,{}^nC_{k+1}}{k+2}\right)$. If $5\alpha=6\beta$, then $n$ equals ______.

Correct answer: 10

A block of mass $m$ is placed on a surface having vertical cross section given by $y=\frac{x^2}{4}$. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

1. A.$\frac13$ m
2. B.$\frac12$ m
3. C.$\frac16$ m
4. D.$\frac14$ m✓

Correct answer: D

If a nuclear fission reaction of an isotope of mass $M$, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $\Delta M$ will be:

1. A.$c\sqrt{\frac{2\Delta M}{M}}$✓
2. B.$\frac{\Delta Mc^2}{3}$
3. C.$c\sqrt{\frac{3\Delta M}{M}}$
4. D.$\sqrt{\frac{2c\Delta M}{M}}$

Correct answer: A

A beam of unpolarized light of intensity $I_0$ passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45° relative to that of A. The intensity of emergent light is:

1. A.$I_0$
2. B.$\frac{I_0}{8}$
3. C.$\frac{I_0}{2}$
4. D.$\frac{I_0}{4}$✓

Correct answer: D

If the total energy transferred to a surface in time $t$ is $6.48\times10^5$ J, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

1. A.$2.16\times10^{-3}$ kg m/s✓
2. B.$4.32\times10^{-3}$ kg m/s
3. C.$1.58\times10^{-3}$ kg m/s
4. D.$2.46\times10^{-3}$ kg m/s

Correct answer: A

A particle of charge '−q' and mass 'm' moves in a circle of radius 'r' around an infinitely long line charge of linear charge density '+λ'. Then time period will be given as: (Consider k as Coulomb's constant)

1. A.$T=\frac{1}{2\pi}\sqrt{\frac{2k\lambda q}{m}}$
2. B.$T=2\pi r\sqrt{\frac{m}{2k\lambda q}}$✓
3. C.$T=\frac{1}{2\pi r}\sqrt{\frac{m}{2k\lambda q}}$
4. D.$T^2=\frac{4\pi^2m}{2k\lambda q}r^3$

Correct answer: B

If mass is written as $m=kc^PG^{-1/2}h^{1/2}$ then the value of P will be: (Constants have their usual meaning with k a dimensionless constant).

1. A.$\frac12$✓
2. B.$\frac{-1}{3}$
3. C.$\frac13$
4. D.2

Correct answer: A

If 50 Vernier divisions are equal to 49 main scale division of a traveling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of traveling microscope is:

1. A.0.1 mm
2. B.0.1 cm
3. C.0.01 cm
4. D.0.01 mm✓

Correct answer: D

In the given circuit, the voltage across load resistance $(R_L)$ is:

1. A.14.00 V
2. B.8.75 V✓
3. C.9.00 V
4. D.8.50 V

Correct answer: B

If three moles of monoatomic gas $\left(\gamma=\frac53\right)$ is mixed with two moles of a diatomic gas $\left(\gamma=\frac75\right)$, the value of adiabatic exponent γ for the mixture is:

1. A.1.35
2. B.1.40
3. C.1.52✓
4. D.1.75

Correct answer: C

For the photoelectric effect, the maximum kinetic energy $(E_k)$ of the photoelectrons is plotted against the frequency (ν) of the incident photons as shown in figure. The slope of the graph gives

1. A.Ratio of Planck's constant to electric charge
2. B.Planck's constant✓
3. C.Work function of the metal
4. D.Charge of electron

Correct answer: B

Choose the correct statement for processes A & B shown in figure.

1. A.$\frac{T^\gamma}{P^{\gamma-1}}=k$ for process A and $PV=k$ for process B.
2. B.$PV=k$ for process B and A.
3. C.$\frac{P^{\gamma-1}}{T^\gamma}=k$ for process B and $T=k$ for process A.
4. D.$PV^\gamma=k$ for process B and $PV=k$ for process A.✓

Correct answer: D

Projectiles A and B are thrown at angles of 45° and 60° with vertical respectively from top of a 400 m high tower. If their range and times of flight are same, the ratio of their speeds of projection $v_A:v_B$ is: [Take $g=10$ m s$^{-2}$]

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

Correct answer: C

A block of ice at −10°C is slowly heated and converted to steam at 100°C. Which of the following curves represent the phenomenon qualitatively:

1. A.Temperature rises, stays constant, rises, then stays constant (two plateaus, second longer)✓
2. B.Temperature rises, a plateau, then rises steeply (one plateau)
3. C.Plateau at the start, rise, plateau, rise
4. D.Rise, plateau, rise (single plateau)

Correct answer: A

Three block A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure. The tension $T_1$ and $T_2$ in the string are respectively:

1. A.60 N, 80 N
2. B.40 N, 64 N✓
3. C.80 N, 100 N
4. D.88 N, 96 N

Correct answer: B

An electron revolving in $n^{th}$ Bohr orbit has magnetic moment $\mu_n$. If $\mu_n\propto n^x$, the value of $x$ is:

1. A.3
2. B.0
3. C.1✓
4. D.2

Correct answer: C

A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60° by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is: [$g=10$ m/s²]

1. A.10 J
2. B.$5\times10^3$ J
3. C.5 J✓
4. D.$5\sqrt3$ J

Correct answer: C

When a potential difference V is applied across a wire of resistance R, it dissipate energy at a rate W. If the wire is cut into two halve and these halve are connected mutually parallel across the same supply, the energy dissipation rate will become:

1. A.4W✓
2. B.$\frac14W$
3. C.$\frac12W$
4. D.2W

Correct answer: A

Escape velocity of a body from earth is 11.2 km/s. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is:

1. A.4.2 km/s
2. B.8.4 km/s
3. C.11.2 km/s
4. D.7.9 km/s✓

Correct answer: D

An alternating voltage $V(t)=220\sin100\pi t$ volt is applied to a purely resistive load of 50 Ω. The time taken for the current to rise from half of the peak value to the peak value is:

1. A.5 ms
2. B.3.3 ms✓
3. C.7.2 ms
4. D.2.2 ms

Correct answer: B

Match List I with List II. List-I: A. Gauss's law of magnetostatics; B. Faraday's law of electro magnetic induction; C. Ampere's Law; D. Gauss's law of electrostatics List-II: I. $\oint\vec E\cdot d\vec a=\frac1{\epsilon_0}\int\rho dV$; II. $\oint\vec B\cdot d\vec a=0$; III. $\oint\vec E\cdot d\vec l=\frac{-d}{dt}\int\vec B\cdot d\vec a$; IV. $\oint\vec B\cdot d\vec l=\mu_0I$ Choose the correct answer from the options given below:

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

Correct answer: A

In an experiment to measure the focal length (f) of a convex lens, the magnitude of object distance (x) and the image distance (y) are measured with reference to the focal point of the lens. The y-x plot is shown in figure. The focal length of the lens is ______ cm.

Correct answer: 20

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillation will be ______ s. [take $g=\pi^2$ m s$^{-2}$]

Correct answer: 8

A big drop is formed by coalescing 1000 small identical drops of water. If $E_1$ be the total surface energy of 1000 small drops of water and $E_2$ be the surface energy of single big drop of water, then $E_1:E_2$ is $x:1$ where $x=$ ______.

Correct answer: 10

Two resistance of 100 Ω and 200 Ω are connected in series with a battery of 4 V and negligible internal resistance. A voltmeter is used to measure voltage across 100 Ω resistance, which give reading as 1 V. The resistance of voltmeter must be ______ Ω.

Correct answer: 200

A vector has magnitude same as that of $\vec A=3\hat i+4\hat j$ and is parallel to $\vec B=4\hat i+3\hat j$. The $x$ and $y$ components of this vector in first quadrant are $x$ and 3 respectively were $x=$ ______.

Correct answer: 4

A power transmission line feeds input power at 2.3 kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V by the transformer. The current in the primary of the transformer is 5A and it efficiency is 90%. The winding of transformer is made of copper. The output current of transformer is ______ A.

Correct answer: 45

A point source is emitting sound waves of intensity $16\times10^{-8}$ W m$^{-2}$ at the origin. The difference in intensity (magnitude only) at two points located at a distance of 2 m and 4 m from the origin respectively will be ______ $\times10^{-8}$ W m$^{-2}$.

Correct answer: 3

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 37° with each other. When suspended in a liquid of density 0.7 g/cm³, the angle remains same. If density of material of the sphere is 1.4 g/cm³, the dielectric constant of the liquid is ______ $\left(\tan37^\circ=\frac34\right)$.

Correct answer: 2

The current of 5A flows in a square loop of side 1 m is placed in air. The magnetic field at the centre of the loop is $X\sqrt2\times10^{-7}$ T. The value of X is ______.

Correct answer: 40

Two discs of moment of inertia $I_1=4$ kg m² and $I_2=2$ kg m², about their central axes & normal to their planes, rotating with angular speeds 10 rad/s & 4 rad/s respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is ______ J.

Correct answer: 24

Salicylaldehyde is synthesized from phenol, when reacted with.

1. A.$\text{HCCl}_3$, NaOH✓
2. B.Formyl chloride (HCOCl), NaOH
3. C.$\text{CCl}_4$, NaOH
4. D.$\text{CO}_2$, NaOH

Correct answer: A

Given below are two statements: Statement – I: High concentration of strong nucleophilic reagent with secondary alkyl halide which do not have bulky substituents will follow $S_N2$ mechanism. Statement – II: A secondary alkyl halide when treated with a large excess of ethanol follows $S_N1$ mechanism. In the light of the above statements, choose the most appropriate from the options given below:

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

Correct answer: C

Reduction potential of ion are given below: $\text{ClO}_4^-$ $E^\circ=1.19$ V; $\text{IO}_4^-$ $E^\circ=1.65$ V; $\text{BrO}_4^-$ $E^\circ=1.74$ V. The correct order of their oxidizing power is:

1. A.$\text{BrO}_4^->\text{ClO}_4^->\text{IO}_4^-$
2. B.$\text{BrO}_4^->\text{IO}_4^->\text{ClO}_4^-$✓
3. C.$\text{ClO}_4^->\text{IO}_4^->\text{BrO}_4^-$
4. D.$\text{IO}_4^->\text{BrO}_4^->\text{ClO}_4^-$

Correct answer: B

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R: Assertion A: $\text{H}_2\text{Te}$ is more acidic than $\text{H}_2\text{S}$. Reason R: Bond dissociation enthalpy of $\text{H}_2\text{Te}$ is lower than $\text{H}_2\text{S}$. In the light of the above statements, choose the most appropriate from the options given below:

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

Correct answer: D

The solution from the following with highest depression in freezing point/lowest freezing point is:

1. A.180 g of acetic acid dissolved in water✓
2. B.180 g of glucose dissolved in water
3. C.180 g of acetic acid dissolved in benzene
4. D.180 g of benzoic acid dissolved in benzene

Correct answer: A

If a substance 'A' dissolves in solution of a mixture of 'B' and 'C' with their respective number of moles as $n_A$, $n_B$ and $n_C$, Mole fraction of C in the solution is:

1. A.$\frac{n_C}{n_A\times n_B\times n_C}$
2. B.$\frac{n_C}{n_A-n_B-n_C}$
3. C.$\frac{n_B}{n_A+n_B}$
4. D.$\frac{n_C}{n_A+n_B+n_C}$✓

Correct answer: D

Given below are two statements: Statement-I: Along the period, the chemical reactivity of the element gradually increases from group 1 to group 18. Statement-II: The nature of oxides formed by group 1 elements is basic while that of group 17 elements is acidic. In the light of the above statements, choose the most appropriate from the options given below:

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

Correct answer: B

Which among the following purification methods is based on the principle of "Solubility" in two different solvents?

1. A.Distillation
2. B.Differential Extraction✓
3. C.Column Chromatography
4. D.Sublimation

Correct answer: B

Given below are two statement: Statement-I: Since Fluorine is more electronegative than nitrogen, the net dipole moment of $\text{NF}_3$ is greater than $\text{NH}_3$. Statement-II: In $\text{NH}_3$, the orbital dipole due to lone pair and the dipole moment of NH bonds are in opposite direction, but in $\text{NF}_3$ the orbital dipole due to lone pair and dipole moment of N – F bonds are in same direction. In the light of the above statements, choose the most appropriate from the options given below:

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

Correct answer: C

The coordination geometry around the manganese in decacarbonyldimanganese (0) is:

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

Correct answer: B

Alkaline oxidative fusion of $\text{MnO}_2$ gives "A" which on electrolytic oxidation in alkaline solution produces B. A and B respectively are

1. A.$\text{Mn}_2\text{O}_7$ and $\text{MnO}_4^-$
2. B.$\text{MnO}_4^{2-}$ and $\text{Mn}_2\text{O}_7$
3. C.$\text{MnO}_4^{2-}$ and $\text{MnO}_4^-$✓
4. D.$\text{Mn}_2\text{O}_3$ and $\text{MnO}_4^{2-}$

Correct answer: C

The correct stability order of carbocations is:

1. A.$(\text{CH}_3)_3\overset{+}{\text{C}}>(\text{CH}_3)_2\overset{+}{\text{C}}\text{H}>\text{CH}_3\overset{+}{\text{C}}\text{H}_2>\overset{+}{\text{C}}\text{H}_3$✓
2. B.$(\text{CH}_3)_3\overset{+}{\text{C}}>\text{CH}_3\overset{+}{\text{C}}\text{H}_2>(\text{CH}_3)_2\overset{+}{\text{C}}\text{H}>\overset{+}{\text{C}}\text{H}_3$
3. C.$\overset{+}{\text{C}}\text{H}_3>\text{CH}_3\overset{+}{\text{C}}\text{H}_2>(\text{CH}_3)_2\overset{+}{\text{C}}\text{H}>(\text{CH}_3)_3\text{C}^+$
4. D.$\overset{+}{\text{C}}\text{H}_3>(\text{CH}_3)_2\overset{+}{\text{C}}\text{H}>\text{CH}_3\overset{+}{\text{C}}\text{H}_2>(\text{CH}_3)_3\overset{+}{\text{C}}$

Correct answer: A

The products A and B formed in the following reaction scheme are respectively Benzene $\xrightarrow{\text{(i) conc. HNO}_3/\text{conc. H}_2\text{SO}_4,\ 323-333\text{ K; (ii) Sn/HCl}}$ A $\xrightarrow{\text{(i) NaNO}_2\text{, HCl, 273–278 K; (ii) Phenol}}$ B