JEE Main 2023 13 April Shift 2 Question Paper with Solution PDF- Download Here

JEE Main 2023 Mathematics Questions with Solutions

Section – A

Question 1:

The area of the region \{(x,y): x^2 \leq y \leq |x^2 - 4|, y \geq 1\ \text{ is:

• (1) \(\frac{3}{4} (4\sqrt{2} + 1) \)
• (2) \(\frac{4}{3} (4\sqrt{2} - 1) \)
• (3) \(\frac{3}{4} (4\sqrt{2} - 1) \)
• (4) \(\frac{4}{3} (4\sqrt{2} + 1) \)

If \[ \lim_{x \to 0} \frac{e^{x} - \cos(bx) - cx}{1 - \cos(2x)} = 2, \]
then \( 5a^2 + b^2 \) is equal to:

• (1) 76
• (2) 72
• (3) 64
• (4) 68

The line, that is coplanar to the line \[ \frac{x+1}{-3} = \frac{y-2}{1} = \frac{z-5}{5}, \]
is:

• (1) \(\frac{x+1}{-3} = \frac{y-2}{2} = \frac{z-5}{5}\)
• (2) \(\frac{x+1}{-3} = \frac{y-2}{-2} = \frac{z-5}{5}\)
• (3) \(\frac{x-1}{-2} = \frac{y-2}{2} = \frac{z-5}{4}\)
• (4) \(\frac{x-1}{-2} = \frac{y-2}{5} = \frac{z-5}{4}\)

The plane, passing through the points \( (0, -1, 2) \) and \( (-1, 2, 1) \) and parallel to the line passing through \( (5,1,-7) \) and \( (1,-1,-1) \), also passes through the point

• (1) \( (0, 5, -2) \)
• (2) \( (-2, 5, 0) \)
• (3) \( (2, 0, 1) \)
• (4) \( (1, -2, 1) \)

Let for a triangle ABC, \[ \overrightarrow{AB} = -2\hat{i} + \hat{j} + 3\hat{k}, \quad \overrightarrow{CB} = \hat{i} + \hat{j} + \hat{k}, \quad \overrightarrow{CA} = 4\hat{i} + 3\hat{j} + 4\hat{k} \]
If \( \lambda \) = 0 and the area of triangle ABC is 5 \sqrt{6, then \( CB \) is equal to:

• (1) 108
• (2) 60
• (3) 54
• (4) 120

Let for \[ A = \begin{pmatrix} 1 & 2 & 3
1 & 2 & 3
1 & 1 & 2 \end{pmatrix}, \quad |A| = 2. \quad If \quad |2 \, adj (2A)| = 32, \quad then \quad 3n + \alpha is equal to: \]

• (1) 10
• (2) 9
• (3) 12
• (4) 11

The range of \( f(x) = 4 \sin \left( \frac{x^2}{x^2 + 1} \right) \) is:

• (1) \( (0, \infty) \)
• (2) \( (0, \pi) \)
• (3) \( [0, 2\pi] \)
• (4) \( [0, \pi] \)

Let \( a_1, a_2, a_3, \dots \) be a G.P. of increasing positive numbers. Let the sum of its 6th and 8th terms be 2 and the product of its 3rd and 5th terms be \( \frac{1}{9} \). Then \( 6a_6 + a_6 a_8 \) is equal to:

• (1) 2
• (2) 3
• (3) \( 3\sqrt{5} \)
• (4) \( 2\sqrt{5} \)

If the system of equations \[ 2x + y = -5
2x - 5y + z = -9
x + 2y - 5z = 7 \]
has infinitely many solutions, then \( (x + y)^2 + (y + z)^2 \) is equal to:

• (1) 904
• (2) 916
• (3) 912
• (4) 920

The statement \[ (p \rightarrow q) \rightarrow (r \rightarrow q) \equiv (p \vee q) \rightarrow (r \vee q) \]
is equivalent to:

• (1) \( p \vee q \)
• (2) \( p \rightarrow (q \rightarrow p) \)
• (3) \( p \vee (q \vee r) \)
• (4) \( p \vee q \rightarrow r \)

Let \( S = \{ z \in \mathbb{C} : z = i(z^2 + Re(z)) \} \). Then \( \sum_{z \in S} |z|^2 \) is equal to:

• (1) \( 4 \)
• (2) \( \frac{7}{2} \)
• (3) \( 3 \)
• (4) \( \frac{5}{2} \)

Let \( \alpha, \beta \) be the roots of the equation \( x^2 - \sqrt{5}x + 2 = 0 \). Then \( \alpha^4 + \beta^4 \) is equal to:

• (1) \( -64 \)
• (2) \( -128 \)
• (3) \( 64 \)
• (4) \( -256 \)

Let \( |a| = 2, |b| = 3 \) and the angle between the vectors \( a \) and \( b \) be \( \frac{\pi}{4} \). Then \( |a + 2b| \times |2a - 3b| \) is equal to:

• (1) 482
• (2) 841
• (3) 882
• (4) 441

The value of \[ \int_{0}^{\frac{\pi}{4}} \frac{e^x}{(e^x + \tan^2 x)} \, dx \]
is:

• (1) 25
• (2) 51
• (3) 50
• (4) 49

The coefficient of \( x^2 \) in the expansion of \[ \left( 2x^2 - \frac{1}{3x^3} \right)^5 \]
is:

• (1) \( \frac{80}{9} \)
• (2) 8
• (3) 9
• (4) \( \frac{26}{3} \)

The random variable X follows binomial distribution B (n, p), for which the difference of the mean and the variance is 1. If \[ 1^{2}P(X = x) - 2P(X = 3X - 1), \quad then \quad np(X)^{2} is equal to \]

• (1) 16
• (2) 11
• (3) 12
• (4) 15

Let the centre of a circle C be (\alpha, \beta) and its radius r < 8. Let \(3x + 4y - 24\) and \(3x - 4y - 32\) be two tangents and \(4x + 3y = 1\) be a normal to C. Then the value of (\alpha - \beta) is equal to:

• (1) 5
• (2) 6
• (3) 7
• (4) 9

Let N be the foot of perpendicular from the point P(1, -2, 3) on the line passing through the points (4, 5, 8) and (1, -7, -5). Then the distance of N from the plane \( 2x - 2y + z = 5 \) is:

• (1) 6
• (2) 7
• (3) 9
• (4) 8

All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written in a dictionary with serial numbers. The serial number of the word MONDAY is:

• (1) 328
• (2) 327
• (3) 324
• (4) 326

Let \( \alpha, \beta \) be the centroid of the triangle formed by the lines \( 15x + y = 82 \), \( 6x - 5y = -4 \), and \( 9x + 4y = 17 \). Then at \( \alpha \) and \( \beta \) are the roots of the equation:

• (1) \( x^2 - 13x + 42 = 0 \)
• (2) \( x^2 - 10x + 25 = 0 \)
• (3) \( x^2 - 7x + 12 = 0 \)
• (4) \( x^2 - 14x + 48 = 0 \)

Section – B

Question 21:

Let \( A = \{-4, -3, 2, 0, 1, 3, 4\} \) and \( R = \{(a, b) : a \in A, b = |a| or a = b\} \) be a relation on \( A \). Then the minimum number of elements that must be added to the relation \( R \) so that it becomes reflexive and symmetric, is:

Let \( f = \left( \sum_{k=1}^{\infty} \sin^k x \right) \left( \sum_{k-1} \sin^k x \right) \cos x dx \in N \). Then \( f_{11} \) is equal to:

If \( y = y(x) \) is the solution of the differential equation \[ \frac{dy}{dx} = \frac{4x}{(x - 1)^{2}} - \frac{x^2 - 2}{(x - 1)^{3}} such that y(2) = \frac{2}{9} \log_2 \left( 2 + \sqrt{5} \right) \]
and \( y(x) = \alpha \log \left( \sqrt{x + \beta} \right) + \gamma \cdot \sqrt{x} - \frac{1}{x} \), then \( \alpha \beta \gamma \) is equal to:

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is:

The remainder, when \(7^{110}\) is divided by 17, is \underline{\hspace{3cm.

Let \( f(x) = \sum_{k=1}^{\infty} x^k \), where \( x \in \mathbb{R} \) and \( f(2) = 119 \). Then \( f(2) - f(1) \) is equal to _______________.

For \( x \in (-1, 1) \), the number of solutions of the equation \( \sin x = 2 \tan x \) is equal to_______________.

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is \hspace{3cm}.

The foci of a hyperbola are \( (\pm 2, 0) \) and its eccentricity is \( \frac{3}{2} \). A tangent, perpendicular to the line \( 2x + 3y - 6 = 0 \), is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the \( x \)- and \( y \)-axes are \( a \) and \( b \) respectively, then \( |a| + |b| \) is equal to \underline{\hspace{3cm.

Let \( [\alpha] \) denote the greatest integer \( \leq \alpha \). Then \( [\sqrt{1}] + [\sqrt{2}] + [\sqrt{3}] + \dots + [\sqrt{20}] \) is equal to \underline{\hspace{3cm.

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then the length of train B is:

• (1) 120 m
• (2) 200 m
• (3) 320 m
• (4) 80 m

The output from a NAND gate having inputs A and B given below will be,

• (1)
• (2)
• (3)
• (4)

The distance travelled by an object in time t is given by \( s = (2.5)t^2 \). The instantaneous speed of the object at \( t = 5 \) sec will be:
 

• (1) 25 m/s
• (2) 12.5 m/s
• (3) 5 m/s
• (4) 62.5 m/s

In a Young's double slits experiment, the ratio of amplitude of light coming from slits is \( 2 : 1 \). The ratio of the maximum to minimum intensity in the interference pattern is:
 

• (1) 9 : 1
• (2) 9 : 4
• (3) 2 : 1
• (4) 25 : 9

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170.
Reason R: Nuclear force is short ranged.

• (1) Both A and R are true but R is NOT the correct explanation of A
• (2) Both A and R are true and R is the correct explanation of A
• (3) A is true but R is false
• (4) A is false but R is true

Two planets A and B of radii R and 1.5R have densities \( \rho \) and \( \rho/2 \) respectively. The ratio of acceleration due to gravity at the surface of B to A is:

• (1) 2 : 3
• (2) 2 : 1
• (3) 4 : 3
• (4) 3 : 4

The mean free path of molecules of a certain gas at STP is 1500d, where d is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 K is approximately:

• (1) 750d
• (2) 1500d
• (3) 1098d
• (4) 2049d

To radiate an EM signal of wavelength \( \lambda \) with high efficiency, the antennas should have a minimum size equal to:

• (1) \( \lambda \)
• (2) \( \frac{\lambda}{2} \)
• (3) \( 2\lambda \)
• (4) \( \frac{\lambda}{4} \)

A particle executes SHM of amplitude A. The distance from the mean position when its kinetic energy is equal to its potential energy is:

• (1) \( \sqrt{2}A \)
• (2) \( \frac{1}{2} A \)
• (3) \( \frac{1}{\sqrt{2}}A \)
• (4) \( 2A \)

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z axis and magnetic field is along the positive x-axis. Then the direction of propagation of electromagnetic wave is:

• (1) negative y-axis
• (2) at 45\(^\circ\) angle from positive y-axis
• (3) positive y-axis
• (4) positive z-axis

Given below are two statements:
Statement I: Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.
Statement II: Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.

• (1) Both Statement I and Statement II are true
• (2) Both Statement I and Statement II are false
• (3) Statement I is true but Statement II is false
• (4) Statement I is false but Statement II is true

Given below are two statements:
Statement I: For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.
Statement II: Escape velocity is independent of the radius of the planet.

• (1) Both Statement I and Statement II are correct
• (2) Statement I is correct but Statement II is incorrect
• (3) Statement I is incorrect but Statement II is correct
• (4) Both Statement I and Statement II are incorrect

A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity of 0.2 rad/s. The centripetal force acting on the vehicle is:

• (1) 2800 N
• (2) 560 N
• (3) 2240 N
• (4) 14 N

A 10 \(\mu\)C charge is divided into two parts and placed at 1 cm distance so that the repulsive force between them is maximum. The charges of the two parts are:

• (1) 7 \(\mu\)C, 3 \(\mu\)C
• (2) 8 \(\mu\)C, 2 \(\mu\)C
• (3) 9 \(\mu\)C, 1 \(\mu\)C
• (4) 5 \(\mu\)C, 5 \(\mu\)C

In the equation \( [ x + \frac{a}{y} ] [ Y - b ] = RT \), where \( X \) is pressure, \( Y \) is volume, \( R \) is universal gas constant and \( T \) is temperature. The physical quantity equivalent to the ratio \( \frac{a}{b} \) is:

• (1) Coefficient of viscosity
• (2) Energy
• (3) Impulse
• (4) Pressure gradient

An electron is moving along the positive x-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then

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

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: A spherical body of radius \( (5 \pm 0.1) \) mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4%.

Reason R: The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.

• (1) Both A and R are true but R is NOT the correct explanation of A
• (2) Both A and R are true and R is the correct explanation of A
• (3) A is false but R is true
• (4) A is true but R is false

The initial pressure and volume of an ideal gas are \(P_1\) and \(V_1\). The final pressure of the gas when the gas is suddenly compressed to volume \( \frac{V_1}{4} \) will be:

• (1) \(P_1 \left( \frac{V_1}{4} \right)^\gamma \)
• (2) \(4 P_1\)
• (3) \(P_0\)
• (4) \(P_1 \left( \frac{V_1}{4} \right)^{\gamma-1}\)

In the network shown below, the charge accumulated in the capacitor in steady state will be:

• (1) 4.8 \muC
• (2) 12 \muC
• (3) 7.2 \muC
• (4) 10.3 \muC

Section – B

Question 51:

In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass \(m\) is attached, the string vibrates with fundamental frequency of 50 Hz. The value of \(m\) is \underline{\hspace{3cm g

• (1) 25 g
• (2) 40 g
• (3) 50 g
• (4) 60 g

\textbf{Two plates A and B have thermal conductivities \(84 \, \text{W/m·K}\) and \(126 \, \text{W/m·K}\) respectively. They have the same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at \(100^\circ \text{C}\) and \(0^\circ \text{C}\) respectively, then the temperature of the surface of contact in steady state is \underline{\hspace{3cm}} \(^\circ \text{C}\).}

• (1) 40°C
• (2) 50°C
• (3) 60°C
• (4) 70°C

In the circuit shown below, the energy stored in the capacitor is \(3 \, \mu J\). The value of \(n\) is ______________.

• (1) 75
• (2) 100
• (3) 125
• (4) 150

A light rope is wound around a hollow cylinder of mass \(5 \, kg\) and radius \(70 \, cm\). The rope is pulled with a force of \(52.5 \, N\). The angular acceleration of the cylinder will be \underline{\hspace{3cm rad/s\(^2\)

• (1) 1.5 rad/s\(^2\)
• (2) 5 rad/s\(^2\)
• (3) 10 rad/s\(^2\)
• (4) 15 rad/s\(^2\)

A straight wire AB of mass \(40 \, g\) and length \(50 \, cm\) is suspended by a pair of flexible leads in uniform magnetic field of magnitude \(0.40 \, T\). The magnitude of the current required in the wire to remove the tension in the supporting leads is \underline{\hspace{3cm A. (Take \(g = 10 \, m/s^2\))

• (1) 1.5 A
• (2) 2 A
• (3) 3 A
• (4) 4 A

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area \(24 \, cm^2\). The two ends of the wire are connected to a resistor. The total resistance in the circuit is \(12 \, \Omega\). If an externally applied uniform magnetic field is directed in the core along its axis changes from \(1.5 \, T\) in the opposite direction to \(1.5 \, T\) in the same direction, the charge flowing through a point in the circuit during the change of magnetic field is _____________ mC.

• (1) 6 mC
• (2) 12 mC
• (3) 15 mC
• (4) 20 mC

Three point charges \(q = -2q\) and \(2q\) are placed on x-axis at a distance \(x = 0\), \(x = \frac{2}{3} R\) and \(x = R\) respectively from origin as shown. If \(q = 2 \times 10^{-4} \, C\) and \(R = 2 \, cm\), the magnitude of net force experienced by the charge \(-2q\) is \underline{\hspace{3cm N.

• (1) 5440 N
• (2) 54400 N
• (3) 5400 N
• (4) 440 N

An atom absorbs a photon of wavelength \(500 \, nm\) and emits another photon of wavelength \(600 \, nm\). The net energy absorbed by the atom in this process is \(3 \times 10^{-4}\) eV. The value of \(h\) is \underline{\hspace{3cm.

• (1) \(6.6 \times 10^{-34} \, J\)
• (2) \(6.6 \times 10^{-31} \, J\)
• (3) \(4.12 \times 10^{-34} \, J\)
• (4) \(4.12 \times 10^{-32} \, J\)

A car accelerates from rest to \(2 \, m/s\). The energy spent in this process is \(E_1\). The energy required to accelerate the car from \(1 \, m/s\) to \(2 \, m/s\) is \(E_2\). The value of \(E_1\) is \underline{\hspace{3cm.

• (1) 1 J
• (2) 2 J
• (3) 3 J
• (4) 4 J

The major product for the following reaction is :

\(HS-CN \xrightarrow{} HO-C = NH CN \)

• (1) (A)
• (2) (B)
• (3) (C)
• (4) (D)

Correct Answer:(4) (D)
View Solution

In the wet tests for detection of various cations by precipitation, Ba\(^{2+}\) cations are detected by obtaining precipitate of :

• (1) Ba(OAc)\(_2\)
• (2) BaCO\(_3\)
• (3) BaSO\(_4\)
• (4) Ba(ox) : Barium oxalate

Compound A from the following reaction sequence is:

The reaction sequence:

• (1) Phenol
• (2) Benzoic Acid
• (3) Aniline
• (4) Salicylic Acid

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Isotopes of hydrogen have almost same chemical properties, but difference in their rates of reaction.

Reason R: Isotopes of hydrogen have different enthalpy of bond dissociation.

• (1) A is not correct but R is correct
• (2) Both A and R are correct but R is NOT the correct explanation of A
• (3) Both A and R are correct and R is the correct explanation of A
• (4) A is correct but R is not correct

Given below are statements related to Ellingham diagram:

Statement I: Ellingham diagram can be constructed for oxides, sulphides and halides of metals.

Statement II: It consists of plots of \( \Delta H_f^\circ \) vs formation of oxides of elements.

• (1) Statement I is correct but Statement II is incorrect
• (2) Statement I is incorrect but Statement II is correct
• (3) Both Statement I and Statement II are incorrect
• (4) Both Statement I and Statement II are correct

Better method for preparation of \(BeF_2\), among the following is:

• (1) BeH\(_4\) + F\(_2 \xrightarrow{} \) BeF\(_2\)
• (2) Be + F\(_2 \xrightarrow{} \) BeF\(_2\)
• (3) (NH\(_3\))\(_2\)BeF\(_4 \xrightarrow{} \) BeF\(_2\)
• (4) BeO + C + F\(_2 \xrightarrow{} \) BeF\(_2\)

Identify the correct order of standard enthalpy of formation of sodium halides.

• (1) NaCl < NaBr < NaI < NaCl
• (2) NaF < NaCl < NaBr < NaI
• (3) NaCl < NaF < NaBr < NaI
• (4) NaI < NaBr < NaCl < NaF

Which of the following complexes will exhibit maximum attraction to an applied magnetic field?

• (1) [Zn(H\(_2\)O)\(_6\)]\(^{2+}\)
• (2) [Ni(H\(_2\)O)\(_6\)]\(^{2+}\)
• (3) [Co(en)\(_3\)]\(^{3+}\)
• (4) [Ni(H\(_2\)O)\(_6\)]\(^{2+}\)

The correct group of halide ions which can be oxidized by oxygen in acidic medium is

• (1) Cl\(^-\), Br\(^-\) and I\(^-\) only
• (2) Br\(^-\) only
• (3) Br\(^-\) and I\(^-\) only
• (4) I\(^-\) only

The total number of stereoisomers for the complex [Cr(ox)\(_3\)]\(^{3+}\) (where ox = oxalate) is:

• (1) 3
• (2) 1
• (3) 4
• (4) 2

Match List I with List II
I - Bromo propene is reacted with reagents in List I to give product in List II.

LIST I                                                               LIST II
Reagent                                                         Product                                                                                                  

• (1) KOH (alc)                                                  Nitrite
• (2) KCN (alc)                                                  Ester
• (3) AgNO\(_3\)                                               Alkene
• (4) H\(_2\)CO\(_3\)                                      Nitralkane

The covalency and oxidation state respectively of boron in [BF\(_3\)] are:

• (1) 3 and 5
• (2) 4 and 3
• (3) 4 and 4
• (4) 3 and 4

What happens when methane undergoes combustion in systems A and B respectively?

• (1) System A: Temperature remains same \quad System B: Temperature rises
• (2) System A: Temperature falls \quad System B: Temperature rises
• (3) System A: Temperature falls \quad System B: Temperature remains same
• (4) System A: Temperature rises \quad System B: Temperature remains same

The naturally occurring amino acid that contains only one basic functional group in its chemical structure is:

• (1) Histidine
• (2) Lysine
• (3) Aspartic acid
• (4) Arginine

Given below are two statements:
Statement I: SO\(_2\) and H\(_2\)O both possess V-shaped structure.
Statement II: The bond angle of SO\(_2\) is less than that of H\(_2\)O

• (1) Both Statements I and Statement II are incorrect
• (2) Both Statement I is correct but Statement II is incorrect
• (3) Statement I is correct but Statement II is incorrect
• (4) Statement I is incorrect but Statement II is correct

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The diameter of colloidal particles in solution should not be much smaller than wavelength of light to show Tyndall effect.
Reason R: The light scatters in all direction when the size of particles is large enough.

• (1) Both A and R are correct but R is NOT the correct explanation of A
• (2) Both A and R are correct and R is the correct explanation of A
• (3) A is false but R is true
• (4) A is correct but R is false

Match List I with List II

List I                                                                                          List II
(A) Weak intermolecular forces of attraction   (I) Hexamethylenediamine + adipic acid
(B) Hydrogen bonding                                       (II) AlEt\(_3\) + TiCl\(_4\)
(C) Heavily branched polymer                          (III) 2-chloro-1, 3-butadiene
(D) High density polymer                                  (IV) Phenol + formaldehyde
Choose the correct answer from the options given below:

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

Given below are two statements:
Statement I: Tropolone is an aromatic compound and has 8\(\pi\) electrons.
Statement II: The bond angle of C=O group in tropolone is involved in aromaticity.

• (1) Statement I is false but Statement II is true
• (2) Statement I is true but Statement II is false
• (3) Both Statement I and Statement II are true
• (4) Both Statement I and Statement II are false

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Order of acidic nature of the following compounds is A \(>\) B \(>\) C.



Reason R: Fluoro is a stronger electron withdrawing group than Chloro group.

In the light of the above statements, choose the correct answer from the options given below:

• (1) Both A and R are correct and R is the correct explanation of A
• (2) A is false but R is true
• (3) Both A and R are correct but R is NOT the correct explanation of A
• (4) A is true but R is false

Section – B

Question 81:

If the formula of Borax is Na\(_2\)B\(_4\)O\(_7\).(OH)\(_2\), then x + y + z = ?

The formula of borax is Na\(_2\)B\(_4\)O\(_7\).(OH)\(_2\)
 

Question 82:

Sea water contains 29.29% NaCl and 19% MgCl\(_2\) by weight of solution. The normal boiling point of the sea water is:

20 mL of 0.1 M NaOH is added to 50 mL of 0.1 M acetic acid solution. The pH of the resulting solution is:

At 298 K, the standard reduction potential for Cu\(^{2+}\)/Cu electrode is 0.034 V. Given: K\(_a\), Cu(OH)\(_2\) = 1 × 10\(^{-9}\). The reduction potential at pH = 14 for the above couple is (X) × 10\(^{-7}\). The value of X is:

Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of 4 Å. The radius of sodium atom is \hspace{3cm} × 10\(^{-10}\) Å (Nearest integer)
 

• (1) 17
• (2) 1.732
• (3) 1.4
• (4) 1.0

A (g) \(\rightarrow\) 2B (g) + C (g) is first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be \underline{\hspace{3cm mm Hg.
 

• (1) 2200 mm Hg
• (2) 2400 mm Hg
• (3) 1800 mm Hg
• (4) 2000 mm Hg

1g of a carbonate (M\(_2\)CO\(_3\)) on treatment with excess HCl produces 0.01 mol of CO\(_2\). The molar mass of M\(_2\)CO\(_3\) is \underline{\hspace{3cm g/mol (Nearest integer).
 

• (1) 100 g/mol
• (2) 200 g/mol
• (3) 250 g/mol
• (4) 300 g/mol

0.400 g of an organic compound (X) gave 0.376 g of AgBr in Carius method for estimation of bromine. % of bromine in the compound (X) is:
 

• (1) 40%
• (2) 60%
• (3) 70%
• (4) 80%

The orbital angular momentum of an electron in a 3s orbital is \( \frac{x h}{2\pi} \). The value of \( x \) is ___ (nearest integer).

See the following chemical reaction: \[ Cr_2O_7^{2-} + XH^+ + 6Fe^{2+} \rightarrow YCr^{3+} + 6Fe^{3+} + ZH_2O \]
The sum of \( X \), \( Y \) and \( Z \) is ___ .