JEE Main 2024 — 1 Feb Shift 1 (Previous Year Paper)

Let $S=\{x\in\mathbb{R}:(\sqrt3+\sqrt2)^x+(\sqrt3-\sqrt2)^x=10\}$. Then the number of elements in $S$ is:

1. A.0
2. B.4
3. C.1
4. D.2✓

Correct answer: D

If $5f(x)+4f\left(\frac1x\right)=x^2-2$, $\forall x\ne0$ and $y=9x^2f(x)$, then $y$ is strictly increasing in:

1. A.$\left(-\frac1{\sqrt5},0\right)\cup\left(0,\frac1{\sqrt5}\right)$
2. B.$\left(-\frac1{\sqrt5},0\right)\cup\left(\frac1{\sqrt5},\infty\right)$✓
3. C.$\left(0,\frac1{\sqrt5}\right)\cup\left(\frac1{\sqrt5},\infty\right)$
4. D.$\left(-\infty,\frac1{\sqrt5}\right)\cup\left(0,\frac1{\sqrt5}\right)$

Correct answer: B

Let 3, a, b, c be in A.P. and 3, a – 1, b + 1, c + 9 be in G.P. Then, the arithmetic mean of a, b and c is:

1. A.13
2. B.11✓
3. C.−4
4. D.−1

Correct answer: B

The area enclosed by the curves $xy+4y=16$ and $x+y=6$ is equal to:

1. A.$30-28\log_e2$
2. B.$30-32\log_e2$✓
3. C.$28-30\log_e2$
4. D.$32-30\log_e2$

Correct answer: B

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is:

1. A.$\frac27$✓
2. B.$\frac15$
3. C.$\frac17$
4. D.$\frac25$

Correct answer: A

Let $f:\mathbb{R}\to\mathbb{R}$ and $g:\mathbb{R}\to\mathbb{R}$ be defined as $f(x)=\begin{cases}\log_ex, & x>0\\ e^{-x}, & x\le0\end{cases}$ and $g(x)=\begin{cases}x, & x\ge0\\ e^x, & x<0\end{cases}$. Then, $g\circ f:\mathbb{R}\to\mathbb{R}$ is:

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

Correct answer: A

If $n$ is the number of ways five different employees can sit into four indistinguished offices where any office may have any number of persons including zero, then $n$ is equal to:

1. A.43
2. B.51✓
3. C.47
4. D.53

Correct answer: B

Let $f:\mathbb{R}\to\mathbb{R}$ be defined as: $f(x)=\begin{cases}\frac{a-b\cos2x}{x^2}; & x<0\\ x^2+cx+2; & 0\le x\le1\\ 2x+1; & x>1\end{cases}$ If $f$ is continuous everywhere in $\mathbb{R}$ and $m$ is the number of points where $f$ is NOT differentiable then $m+a+b+c$ equals:

1. A.2✓
2. B.4
3. C.1
4. D.3

Correct answer: A

The value of the integral $\int_0^{\pi/4}\frac{x\,dx}{\sin^4(2x)+\cos^4(2x)}$ equals:

1. A.$\frac{\sqrt2\pi^2}{8}$
2. B.$\frac{\sqrt2\pi^2}{16}$
3. C.$\frac{\sqrt2\pi^2}{64}$
4. D.$\frac{\sqrt2\pi^2}{32}$✓

Correct answer: D

If $A=\begin{bmatrix}\sqrt2&1\\-1&\sqrt2\end{bmatrix}$, $B=\begin{bmatrix}1&0\\1&1\end{bmatrix}$, $C=ABA^T$ and $X=A^TC^2A$, then det X is equal to:

1. A.27
2. B.729✓
3. C.891
4. D.243

Correct answer: B

If the system of equations $2x+3y-z=5$ $x+\alpha y+3z=-4$ $3x-y+\beta z=7$ has infinitely many solutions, then $13\alpha\beta$ is equal to ______.

1. A.1120✓
2. B.1110
3. C.1220
4. D.1210

Correct answer: A

Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=2x(x+y)^3-x(x+y)-1$, $y(0)=1$. Then, $\left(\frac1{\sqrt2}+y\left(\frac1{\sqrt2}\right)\right)^2$ equal:

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

Correct answer: C

Let $\vec a=-5\hat i+\hat j-3\hat k$, $\vec b=\hat i+2\hat j-4\hat k$ and $\vec c=(((\vec a\times\vec b)\times\hat i)\times\hat i)\times\hat i$. Then $\vec c\cdot(-\hat i+\hat j+\hat k)$ is equal to:

1. A.−15
2. B.−12✓
3. C.−13
4. D.−10

Correct answer: B

Let $C:x^2+y^2=4$ and $C':x^2+y^2-4\lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles C and C' intersect at two distinct points, is $\mathbb{R}-[a,b]$, then the point $(8a+12,16b-20)$ lies on the curve:

1. A.$x^2-4y^2=7$
2. B.$6x^2+y^2=42$✓
3. C.$5x^2-y=-11$
4. D.$x^2+2y^2-5x+6y=3$

Correct answer: B

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, $a>b$ be an ellipse, whose eccentricity is $\frac1{\sqrt2}$ and the length of the latusrectum is $\sqrt{14}$. Then the square of the eccentricity of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is:

1. A.$\frac52$
2. B.3
3. C.$\frac72$
4. D.$\frac32$✓

Correct answer: D

Let $S=\{z\in\mathbb{C}:|z-1|=1$ and $(\sqrt2-1)(z+\bar z)-i(z-\bar z)=2\sqrt2\}$. Let $z_1,z_2\in S$ be such that $|z_1|=\max_{z\in S}|z|$ and $|z_2|=\min_{z\in S}|z|$. Then $|\sqrt2z_1-z_2|^2$ equals:

1. A.4
2. B.2✓
3. C.1
4. D.3

Correct answer: B

If $\tan A=\frac{1}{\sqrt{x(x^2+x+1)}}$, $\tan B=\frac{\sqrt x}{\sqrt{x^2+x+1}}$ and $\tan C=(x^{-3}+x^{-2}+x^{-1})^{1/2}$, $0<A,B,C<\frac\pi2$, then $A+B$ is equal to:

1. A.$C$✓
2. B.$\pi-C$
3. C.$\frac\pi2-C$
4. D.$2\pi-C$

Correct answer: A

Let the median and the mean deviation about the median of 7 observation 170, 125, 230, 190, 210, a, b be 170 and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these 7 observations is:

1. A.28
2. B.30✓
3. C.31
4. D.32

Correct answer: B

If the shortest distance between the lines $\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}$ and $\frac{x-\sqrt3}{1}=\frac{y-1}{-2}=\frac{z-2}{1}$ is 1, then the sum of all possible values of $\lambda$ is:

1. A.$-2\sqrt3$
2. B.0
3. C.$3\sqrt3$
4. D.$2\sqrt3$✓

Correct answer: D

For $0<\theta<\frac\pi2$, if the eccentricity of the hyperbola $x^2-y^2\operatorname{cosec}^2\theta=5$ is $\sqrt7$ times eccentricity of the ellipse $x^2\operatorname{cosec}^2\theta+y^2=5$, then the value of θ is:

1. A.$\frac\pi4$
2. B.$\frac{5\pi}{12}$
3. C.$\frac\pi6$
4. D.$\frac\pi3$✓

Correct answer: D

Let 3, 7, 11, 15, ...., 403 and 2, 5, 8, 11, ...., 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to ______.

Correct answer: 6699

Let the line $L:\sqrt2x+y=\alpha$ pass through the point of the intersection P (in the first quadrant) of the circle $x^2+y^2=3$ and the parabola $x^2=2y$. Let the line L touch two circles $C_1$ and $C_2$ of equal radius $2\sqrt3$. If the centres $Q_1$ and $Q_2$ of the circles $C_1$ and $C_2$ lie on the y-axis, then the square of the area of the triangle $PQ_1Q_2$ is equal to ______.

Correct answer: 72

If $\int_{-\pi/2}^{\pi/2}\frac{8\sqrt2\cos x\,dx}{(1+e^{\sin x})(1+\sin^4x)}=\alpha\pi+\beta\log_e(3+2\sqrt2)$, where α, β are integers, then $\alpha^2+\beta^2$ equals ______.

Correct answer: 8

Let $A=\{1,2,3,\ldots,20\}$. Let $R_1$ and $R_2$ two relation on A such that, $R_1=\{(a,b):b$ is divisible by $a\}$ $R_2=\{(a,b):a$ is an integral multiple of $b\}$ Then, number of elements in $R_1-R_2$ is equal to ______.

Correct answer: 46

Let the line of the shortest distance between the lines $L_1:\vec r=(\hat i+2\hat j+3\hat k)+\lambda(\hat i-\hat j+\hat k)$ and $L_2:\vec r=(4\hat i+5\hat j+6\hat k)+\mu(\hat i+\hat j-\hat k)$ intersect $L_1$ and $L_2$ at P and Q respectively. If $(\alpha,\beta,\gamma)$ is the mid point of the line segment PQ, then $2(\alpha+\beta+\gamma)$ is equal to ______.

Correct answer: 21

If the coefficient of $x^{30}$ in the expansion of $\left(1+\frac1x\right)^6(1+x^2)^7(1-x^3)^8$; $x\ne0$ is α, then |α| equals ______.

Correct answer: 678

Let $P=\{z\in\mathbb{C}:|z+2-3i|\le1\}$ and $Q=\{z\in\mathbb{C}:z(1+i)+\bar z(1-i)\le-8\}$. Let in $P\cap Q$, $|z-3+2i|$ be maximum and minimum at $z_1$ and $z_2$ respectively. If $|z_1|^2+2|z_2|^2=\alpha+\beta\sqrt2$, where α, β integers, then α + β equals ______.

Correct answer: 36

The number of elements in the set $S=\{(x,y,z):x,y,z\in\mathbb{Z},\ x+2y+3z=42,\ x,y,z\ge0\}$ equals ______.

Correct answer: 169

If $x=x(t)$ is the solution of the differential equation $(t+1)dx=(2x+(t+1)^4)dt$, $x(0)=2$, then, $x(1)$ equals ______.

Correct answer: 14

Let $\{x\}$ denote the fractional part of x and $f(x)=\frac{\cos^{-1}(1-\{x\}^2)\sin^{-1}(1-\{x\})}{\{x\}-\{x\}^3}$, $x\ne0$. If L and R respectively denotes the left hand limit and the right hand limit of $f(x)$ at $x=0$, then $\frac{32}{\pi^2}(L^2+R^2)$ is equal to ______.

Correct answer: 18

A galvanometer has a resistance of 50Ω and it allows maximum current of 5 mA. It can be converted into voltmeter to measure upto 100 V by connecting in series a resistor of resistance:

1. A.5975Ω
2. B.20050Ω
3. C.19500Ω
4. D.19950Ω✓

Correct answer: D

In the given circuit if the power rating of Zener diode is 10 mW, the value of series resistance $R_s$ to regulate the input unregulated supply is:

1. A.$\frac37$ kΩ✓
2. B.10 Ω
3. C.1 kΩ
4. D.10 kΩ

Correct answer: A

In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be:

1. A.reduced by $\frac14L$
2. B.reduced by $\frac34L$✓
3. C.increased to 4 L
4. D.increased by 2 L

Correct answer: B

The dimensional formula of angular impulse is:

1. A.$[ML^{-2}T^{-1}]$
2. B.$[ML^2T^{-2}]$
3. C.$[ML^2T^{-1}]$✓
4. D.$[MLT^{-1}]$

Correct answer: C

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is $g=\pi^2$ m/s², then the length of the second's pendulums at a height h = 2R from the surface of earth will be:

1. A.$\frac49$ m
2. B.$\frac29$ m
3. C.$\frac19$ m✓
4. D.$\frac89$ m

Correct answer: C

The de-Broglie wavelengths of a proton and an α particle are λ and 2λ respectively. The ratio of the velocities of proton and α particle will be:

1. A.8 : 1✓
2. B.4 : 1
3. C.1 : 2
4. D.1 : 8

Correct answer: A

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04, the acceleration of the system in m s$^{-2}$ is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):

1. A.3
2. B.1.2
3. C.4
4. D.2✓

Correct answer: D

A ball of mass 0.5 kg is attached to a string of length 50 cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N. The maximum possible value of angular velocity of the ball in rad/s is:

1. A.1000
2. B.1600
3. C.40✓
4. D.20

Correct answer: C

Two moles a monoatomic gas is mixed with six moles of diatomic gas. The molar specific heat of the mixture at constant volume is:

1. A.$\frac74R$
2. B.$\frac94R$✓
3. C.$\frac32R$
4. D.$\frac52R$

Correct answer: B

A parallel plate capacitor has a capacitance C = 200 pF. It is connected to 230 V ac supply with an angular frequency 300 rad/s. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are:

1. A.1.38 μA and 1.38 μA
2. B.13.8 μA and 138 μA
3. C.14.3 μA and 143 μA
4. D.13.8 μA and 13.8 μA✓

Correct answer: D

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly:

1. A.13.6 eV
2. B.1.9 eV
3. C.12.1 eV✓
4. D.1.5 eV

Correct answer: C

The pressure and volume of an ideal gas are related as $PV^{3/2}=K$ (constant). The work done when the gas is taken from state $A(P_1,V_1,T_1)$ to state $B(P_2,V_2,T_2)$ is:

1. A.$2(P_2\sqrt{V_2}-P_1\sqrt{V_1})$
2. B.$2(P_1V_1-P_2V_2)$✓
3. C.$2(P_2V_2-P_1V_1)$
4. D.$2(\sqrt{P_1}V_1-\sqrt{P_2}V_2)$

Correct answer: B

The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as $r=(0.35\pm0.05)$ cm, $R=(100\pm10)$ ohm, $l=(15\pm0.2)$ cm. The percentage error in resistivity of the material of the wire is:

1. A.35.6%
2. B.37.3%
3. C.39.9%✓
4. D.25.6%

Correct answer: C

A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle θ to the horizontal, the maximum height attained by it is equal to 4R. The angle of projection θ is then given by:

1. A.$\sin^{-1}\left[\frac{\pi^2R}{2gT^2}\right]^{1/2}$
2. B.$\sin^{-1}\left[\frac{2gT^2}{\pi^2R}\right]^{1/2}$✓
3. C.$\cos^{-1}\left[\frac{2gT^2}{\pi^2R}\right]^{1/2}$
4. D.$\cos^{-1}\left[\frac{\pi R}{2gT^2}\right]^{1/2}$

Correct answer: B

A monochromatic light of wavelength 6000 Å is incident on the single slit of width 0.01 mm. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm, the linear width of the central maximum is:

1. A.120 mm
2. B.12 mm
3. C.60 mm
4. D.24 mm✓

Correct answer: D

10 divisions on the main scale of a vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is:

1. A.$\frac5{11}$✓
2. B.$\frac{10}{11}$
3. C.$\frac12$
4. D.$\frac{50}{11}$

Correct answer: A

With rise in temperature, the Young's modulus of elasticity:

1. A.increases
2. B.changes erratically
3. C.decreases✓
4. D.remains unchanged

Correct answer: C

A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass $10^{-2}$ kg moving with a speed of $2\times10^2$ m/s. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is: [Use : g = 10 m/s²]

1. A.0.30 m
2. B.0.40 m
3. C.0.20 m✓
4. D.0.35 m

Correct answer: C

The reading in the ideal voltmeter (V) shown in the given circuit diagram is:

1. A.0 V✓
2. B.3 V
3. C.5 V
4. D.10 V

Correct answer: A

Two identical capacitors have same capacitance C. One of them is charged to the potential V and other to the potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is:

1. A.$\frac34CV^2$
2. B.$\frac14CV^2$✓
3. C.$\frac12CV^2$
4. D.$2CV^2$

Correct answer: B

A particle is moving in one dimension (along x axis) under the action of a variable force. It's initial position was 16 m right of origin. The variation of its position (x) with time (t) is given as $x=-3t^3+18t^2+16t$, where x is in m and t is in s. The velocity of the particle when its acceleration becomes zero is ______ m/s.

Correct answer: 52

A tuning fork resonates with a sonometer wire of length 1 m stretched with tension of 6 N. When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ______ Hz.

Correct answer: 6

A plane is in level flight at constant speed and each of its two wings has an area of 40 m². If the speed of the air is 180 km/h over the lower wing surface and 252 km/h over the upper wing surface, the mass of the plane is ______ kg. [Take air density to be 1 kg m$^{-3}$ and g = 10 m s$^{-2}$]

Correct answer: 9600

A regular polygon of 6 sides is formed by bending a wire of length 4π meter. If an electric current of $4\pi\sqrt3$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x\times10^{-7}$ T. The value of x is ______.

Correct answer: 72

The current in a conductor is expressed as $I=3t^2+4t^3$, where I is in Ampere and t is in second. The amount of electric charge that flows through a section of the conductor during t = 1s to t = 2s is ______ C.

Correct answer: 22

The distance between object and its 3 times magnified virtual image as produced by a convex lens is 20 cm. The focal length of the lens used is ______ cm.

Correct answer: 15

The identical spheres each of mass 2 M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 4 m each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4\sqrt2}{x}$, where the value of x is ______.

Correct answer: 3

A rectangular loop of sides 12 cm and 5 cm, with its sides parallel to the x-axis and y-axis respectively, moves with a velocity of 5 cm/s in the positive x axis direction, in a space containing a variable magnetic field in the positive z direction. The field has a gradient of $10^{-3}$ T/cm along the negative x direction and it is decreasing with time at the rate of $10^{-3}$ T/s. If the resistance of the loop is 6 mΩ, the power dissipated by the loop as heat is ______ $\times10^{-9}$ W.

Correct answer: 216

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where x is ______.

Correct answer: 27

Two identical charged spheres are suspended by strings of equal lengths. The string make an angle θ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is 1.5 g/cc, the dielectric constant of water will be ______. [Take density of water = 1 g/cc]

Correct answer: 3

Which of the following compound will most easily be attacked by an electrophile?

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

Correct answer: A

In case of isoelectronic species the size of $\text{F}^-$, Ne and $\text{Na}^+$ is affected by:

1. A.None of the factors because their size is the same
2. B.Electron-electron interaction in the outer orbitals
3. C.Principal quantum number (n)
4. D.Nuclear charge (z)✓

Correct answer: D

Which of the following reactions are disproportionation reactions? (A) $\text{Cu}^+\to\text{Cu}^{2+}+\text{Cu}$ (B) $3\text{MnO}_4^{2-}+4\text{H}^+\to2\text{MnO}_4^-+\text{MnO}_2+2\text{H}_2\text{O}$ (C) $2\text{KMnO}_4\to\text{K}_2\text{MnO}_4+\text{MnO}_2+\text{O}_2$ (D) $2\text{MnO}_4^-+3\text{Mn}^{2+}+2\text{H}_2\text{O}\to5\text{MnO}_2+4\text{H}^+$ Choose the correct answer from the options given below:

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

Correct answer: C

We have three aqueous solutions of NaCl labelled as 'A', 'B' and 'C' with concentration 0.1 M, 0.01 M, 0.001 M, respectively. The value of van't Hoff factor (i) for these solutions will be in the order:

1. A.$i_A<i_C<i_B$
2. B.$i_A<i_B<i_C$✓
3. C.$i_A>i_B>i_C$
4. D.$i_A=i_B=i_C$

Correct answer: B

Match List-I with List-II. List-I (Reactions): (A) $\text{CH}_3(\text{CH}_2)_5\text{COOC}_2\text{H}_5\to\text{CH}_3(\text{CH}_2)_5\text{CHO}$; (B) $\text{C}_6\text{H}_5\text{COC}_6\text{H}_5\to\text{C}_6\text{H}_5\text{CH}_2\text{C}_6\text{H}_5$; (C) $\text{C}_6\text{H}_5\text{CHO}\to\text{C}_6\text{H}_5\text{CH(OH)CH}_3$; (D) $\text{CH}_3\text{COCH}_2\text{COOC}_2\text{H}_5\to\text{CH}_3\text{CH(OH)CH}_2\text{COOC}_2\text{H}_5$ List-II (Reagents): (I) $\text{CH}_3\text{MgBr}$, $\text{H}_2\text{O}$; (II) Zn(Hg) and conc. HCl; (III) $\text{NaBH}_4$, $\text{H}^+$; (IV) DIBAL-H, $\text{H}_2\text{O}$ Choose the correct answer from the options given below:

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

Correct answer: A

Ionic reactions with organic compounds proceed through: (A) homolytic bond cleavage (B) heterolytic bond cleavage (C) free radical formation (D) primary free radical (E) secondary free radical Choose the correct answer from the options given below:

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

Correct answer: D

In acidic medium, $\text{K}_2\text{Cr}_2\text{O}_7$ shows oxidising action as represented in the half reaction: $\text{Cr}_2\text{O}_7^{2-}+X\text{H}^++Y\text{e}^-\to2A+Z\text{H}_2\text{O}$. X, Y, Z and A respectively are:

1. A.8, 6, 4 and $\text{Cr}_2\text{O}_3$
2. B.8, 4, 6 and $\text{Cr}_2\text{O}_3$
3. C.14, 6, 7 and $\text{Cr}^{3+}$✓
4. D.14, 7, 6 and $\text{Cr}^{3+}$

Correct answer: C

Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following:

1. A.q = 0, ΔT < 0, w ≠ 0
2. B.q = 0, ΔT = 0, w = 0✓
3. C.q = 0, ΔT ≠ 0, w = 0
4. D.q ≠ 0, ΔT = 0, w = 0

Correct answer: B

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Haloalkanes react with KCN to form alkyl cyanides as a main product while with AgCN form isocyanide as the main product. Reason (R) : KCN and AgCN both are highly ionic compounds. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Both (A) and (R) are correct and (R) is the correct explanation of (A)
2. B.(A) is not correct (R) is correct
3. C.Both (A) and (R) are correct but (R) is not the correct explanation of (A)
4. D.(A) is correct (R) is not correct✓

Correct answer: D

Given below are two statements: Statement (I) : A solution of $[\text{Ni(H}_2\text{O)}_6]^{2+}$ is green in colour. Statement (II) : A solution of $[\text{Ni(CN)}_4]^{2-}$ is colourless. 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.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) : Potassium hydrogen phthalate is primary standard for standardisation of sodium hydroxide solution. Statement (II) : In this titration phenolphthalein can be used as indicator. 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 incorrect
2. B.Statement I is incorrect but Statement II is correct
3. C.Statement I is correct but Statement II is incorrect
4. D.Both Statement I and Statement II are correct✓

Correct answer: D

Given below are two statements: Statement (I) : The $\text{NH}_2$ group in aniline is ortho and para directing and powerful activating group. Statement (II) : Aniline does not undergo Friedel-Craft's reaction (alkylation and acylation). 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 incorrect but Statement II is correct
3. C.Statement I is correct but Statement II is incorrect
4. D.Both Statement I and Statement II are incorrect

Correct answer: A

Which of the following complex is homoleptic?

1. A.$[\text{Fe(NH}_3)_4\text{Cl}_2]^+$
2. B.$[\text{Ni(CN)}_4]^{2-}$✓
3. C.$[\text{Co(NH}_3)_4\text{Cl}_2]^+$
4. D.$[\text{Ni(NH}_3)_2\text{Cl}_2]$

Correct answer: B

Given below are two statements: Statement (I) : Aminobenzene and aniline are same organic compounds. Statement (II) : Aminobenzene and aniline are different organic compounds. In the light of the above statements, choose the most appropriate answer from the options given below:

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

Correct answer: A

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : $\text{PH}_3$ has lower boiling point the $\text{NH}_3$. Reason (R) : In liquid state $\text{NH}_3$ molecules are associated through vander Waal's forces, but $\text{PH}_3$ molecules are associated through hydrogen bonding. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Both (A) and (R) are correct and (R) is the correct explanation of (A)
2. B.Both (A) and (R) are correct but (R) is not the correct explanation of (A)
3. C.(A) is correct (R) is not correct✓
4. D.(A) is not correct (R) is correct

Correct answer: C

In Kjeldahl's method for estimation of nitrogen, $\text{CuSO}_4$ acts as:

1. A.reducing agent
2. B.hydrolysis agent
3. C.catalytic agent✓
4. D.oxidizing agent

Correct answer: C

If one strand of a DNA has the sequence ATGCTTCA, sequence of the bases in complementary stand is:

1. A.GTACTTAC
2. B.TACGAAGT✓
3. C.CATTAGCT
4. D.ATGCGACT

Correct answer: B

Identify A and B in the following sequence of reaction: Toluene $\xrightarrow{\text{Cl}_2/h\nu}$ A $\xrightarrow{\text{H}_2\text{O},\ 373\text{ K}}$ B

1. A.A = benzoyl chloride, B = benzaldehyde
2. B.A = benzal chloride ($\text{C}_6\text{H}_5\text{CHCl}_2$), B = benzoic acid
3. C.A = benzyl chloride, B = benzaldehyde
4. D.A = benzal chloride ($\text{C}_6\text{H}_5\text{CHCl}_2$), B = benzaldehyde✓

Correct answer: D