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

Let a₁, a₂, a₃, …. be a G.P. of increasing positive numbers. Let the sum of its 6^th and 8^th terms be 2 and the product of its 3rd and 5th terms be \(\frac{1}{9}\) .Then 6 (a₂ + a₄) (a₄ + a₆) is equal to

• (1) 2
• (2) \(2\sqrt2\)
• (3) \(3\sqrt3\)
• (4) 3

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

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

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

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

Let \(S=\left\{z∈C : \bar{z}=i(z^2+Re(\bar{z}))\right\}\). Then \(\sum\limits_{z∈S}|z|^2\) is equal to 

• (1)

  \(\frac{5}{2}\)

• (2) 3
• (3)

  \(\frac{7}{2}\)

• (4) 4

If \(\lim\limits_{x\rightarrow0}\frac{e^{ax}-\cos(bx)-\frac{cxe^{-ce}}{2}}{1-\cos(2x)}=17\) ,then 5a² + b² is equal to

• (1) 68
• (2) 64
• (3) 72
• (4) 76

The line, that is coplanar to the line \(\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}\) is

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

The coefficient of x5 in the expansion of \((2x^3 - \frac{1}{3x^2})^5\) is

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

Let \( \alpha, \beta \) be the roots of the equation \( x^2 - \sqrt{2}x + 2 = 0 \), then \( \alpha^{14} + \beta^{14} \) is equal to:

• (1) -256
• (2) -128 
• (3) \(-128\sqrt2\)
• (4) \(-256\sqrt2\)

Let \( (\alpha, \beta) \) be the centroid of the triangle formed by the lines \( 15x - y = 82 \), \( 6x - 5y = -4 \), and \( 9x + 4y = 17 \). Then \( \alpha + 2\beta \) and \( 2\alpha - \beta \) are the roots of the equation:

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

If the system of equations
2x + y - z = 5
2x -5y + λz = μ
x + 2y - 5z = 7
has infinitely many solutions, then (λ + μ)² +  (λ - μ)² is equal to

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

The area of the region \(\left\{(x,y):x^2≤y≤|x^2-4|,y≥1\right\}\) is 

• (1) \(\frac{4}{3}(4\sqrt2-1)\)
• (2) \(\frac{4}{3}(4\sqrt2+1)\)
• (3) \(\frac{3}{4}(4\sqrt2-1)\)
• (4) \(\frac{3}{4}(4\sqrt2+1)\)

The value of \(\frac{e^{-\frac{\pi}{4}}+\int^{\frac{\pi}{4}}_{0}e^{-x}\tan^{50}x\ dx}{\int^{\frac{\pi}{4}}_{0}e^{-x}(\tan^{49}x+\tan^{51}x)dx}\) is

• (1) 25
• (2) 49
• (3) 50
• (4) 51

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

• (1)

  \([0,\pi]\)

• (2)

  \([0,\pi)\)

• (3)

  \([0,2\pi]\)

• (4)

  \([0,2\pi)\)

Let for a triangle ABC,
\(\vec{AB}=-2\hat{i}+\hat{j}+3\hat{k} \)
\(\vec{CB}=α\hat{i}+β\hat{j}+γ\hat{k} \)
\(\vec{CA}=4\hat{i}+3\hat{j}+δ\hat{k} \)
If \(δ>0\) and the area of the triangle ABC is \(5\sqrt6\), then \(\vec{CB}.\vec{CA}\) is equal to

• (1) 60
• (2) 54
• (3) 120
• (4) 108

Let the centre of a circle C be (α, β) 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 (α – β + r) is equal to

• (1) 5
• (2) 6
• (3) 7
• (4) 9

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

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

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

• (1) 9
• (2) 10
• (3) 11
• (4) 12

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 = 0 is

• (1) 6
• (2) 7
• (3) 8
• (4) 9

The statement (p∧ (-q)) v ((~ p) ∧ q) v ((~q)) is equivalent to

• (1) (~ p) v (~q)
• (2) p ∨(~ q)
• (3) (~p) ∨ q
• (4) p ∨ q

The random valuable X follows binomial distribution B (n, p) for which the difference of the mean and the variance is 1. If 2P(X = 2) = 3P(X = 1), then n²P(X > 1) is equal to

• (1) 15
• (2) 16
• (3) 12
• (4) 11

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 _______.

Let A= {–4, –3, –2, 0, 1, 3, 4} and R = {(a, b) ∈ A × A : b = |a| or b² = a + 1} 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_n = \(\int\limits_0^{\pi/2}\) \(\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)\) cosx dx, n ∈ N. Then f₂₁ – f₂₀ is equal to____.

The remainder when 7¹⁰³ is divided by 17, is

Let f(x) = \(\displaystyle\sum_{k=1}^{10} kx^k\) , x ∈ R. If 2f(2) + f(2) = 190(2)ⁿ + 1 then n is equal to____. 

For x ∈ (–1, 1], the number of solutions of the equation sin^-1x = 2 tan^-1 x is equal to____

If y=y(x) is the solution of the differential equation \(\frac{dy}{dx}+\frac{4x}{(x^2-1)}y=\frac{x+2}{(x^2-1)^{\frac{5}{2}}},x>1\) such that \(y(2)=\frac{2}{9}\log_e(2+\sqrt3)\ \text{and}\ y(\sqrt2)=\alpha\log_e(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}∈\N,\) then αβγ is equal to

Let [α] denote the greatest integer ≤ α. Then \([\sqrt1] + [ \sqrt 2 ] + [ \sqrt3 ] + . . . + [ \sqrt120 ] [\sqrt1 ] + [ \sqrt2 ] + [ \sqrt3 ] + . . . + [ 120 ]\)  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 foci of a hyperbola are (±2,0) and its eccentricity is \(\frac{3}{2}\) . A tangent, perpendicular to the line 2x + 3y = 6, 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 |6a| + |5b| is equal to_____.

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

• (1) 5 m/s
• (2) 10 m/s
• (3) 25 m/s
• (4) 50 m/s

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. 
In the light of above statements, choose the most appropriate answer from the option given below:

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

In the equation \(\bigg[X + {\frac{a}{Y^2}}\bigg] [Y - b] = RT\), 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) Energy
• (2) Pressure gradient
• (3) Impulse
• (4) Coefficient of viscosity

The initial pressure and volume of an ideal gas are P₀ and V₀. The final pressure of the gas when the gas is suddenly compressed to volume \(\frac{V_0}{4}\) will be(Given γ = ratio of specific heats at constant pressure and at constant volume)

• (1) \(P_0\)
• (2) \(4P_0\)
• (3) \(P_0(4)^y\)
• (4) \(P_0(4)^{\frac{1}{y}}\)

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

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

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are \( \rho \) and \( \frac{\rho}{3} \) respectively. The ratio of acceleration due to gravity at their surfaces (i.e. \( g_A : g_B \)) will be:

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

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) positive y-axis
• (2) negative y-axis
• (3) positive z-axis
• (4) at 45° angle from positive y-axis

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

• (1) 10.3 μC
• (2) 4.8 μC
• (3) 7.2 μC
• (4) 12 μC

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) 2:1
• (2) 9:4
• (3) 9:1
• (4) 25:9

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 373K is approximately

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

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

• (1)
• (2)
• (3)
• (4)

A 10 μC charge is divided into two equal parts and kept at 1 cm distance. Find repulsion between charges?

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

Given below are two statements:
Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. 
Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.
In the light of above statements, choose the correct answer from the options given below :

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

• (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

An electron is moving along positive x direction in xy plane, magnetic field points in negative z direction, then the force due to magnetic field on electron points in the direction 

• (1) j
• (2) -j
• (3) k
• (4) -k

A particle is performing S.H.M whose distance from mean position varies as \(x = Asin(wt)\). Find the position of the particle from the mean position, where kinetic energy and potential energy is equal.

• (1) \(\frac{A}{2}\)
• (2) \(\frac{A}{\sqrt2}\)
• (3) \(\frac{A}{2\sqrt2}\)
• (4) \(\frac{A}{4}\)

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 train B is 54 km/h, then the length of train B is:

• (1) 100 m 
• (2) 320 m 
• (3) 200 m 
• (4) 400 m 

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

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

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

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

Three point charges q, –2q and 2q are placed on x-axis at a distance x = 0, x = \(\frac{3}{ 4}\) R and x = R respectively from origin as shown. If q = 2 × 10^-6 C and R = 2 cm, the magnitude of net force experienced by the charge –2q is ________ 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 n × 10^-4 eV. The value of n is____.[Assume the atom to be stationary during the absorption and emission process](Take h = 6.6 x 10^-34 js and c = 3 x 10⁸ m/s)

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 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 as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is (Take g = 10 ms^-2).

Two plates A and B have thermal conductivities 84 \(Wm^{-1}K^{-1}\) and 126 \(Wm^{-1}K^{-1}\) respectively. They have 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 °C and 0 ºC respectively, then the temperature of the surface of contact in steady state is ________°C.

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 ______g.

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross- sectional area 24 cm². The two ends of the wire are connected to a resistor. The total resistance in the circuit is 129. If an externally applied uniform magnetic field in the core along its axis changes from 1.5 T in one direction to 1.5 T in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ________mC.

In the circuit shown, the energy stored in the capacitor is \( n \, \mu \text{J} \). The value of \( n \) is: 

 

A bi-convex lens of focal length 10 cm is cut perpendicularly to principal axis. 
Find Power (in D) of new lens.

A car accelerates from rest to \( u \, \text{m/s} \). The energy spent in this process is \( E \, \text{J} \). The energy required to accelerate the car from \( u \, \text{m/s} \) to \( 2u \, \text{m/s} \) is \( nE \, \text{J} \). The value of \( n \) is.

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

• (1)
• (2)
• (3)
• (4)

In the wet tests for identification of various cations by precipitation, which transition element cation doesn't belong to group IV in qualitative inorganic analysis ?

• (1) \(Z n^{2+}\)
• (2) \(Fe ^{3+}\)
• (3) \(Ni ^{2+}\)
• (4) \(Co ^{2+}\)

Compound A from the following reaction sequence is 

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

The total number of stereoisomers for the complex [Cr(ox)₂Clbr]³- (where oxalate) is:

• (1) 2
• (2) 4
• (3) 3
• (4) 1

Major product of the following reaction is

• (1)

• (2)

• (3)

• (4)

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

• (1) asparagine
• (2) arginine
• (3) histidine
• (4) lysine

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

• (1) [Co(en)₃]³⁺
• (2) [Co(H₂O)₆]²⁺
• (3) [Zn(H₂O)₆]²⁺
• (4) [Ni(H₂O₆]²⁺

Given below are two statements: 
Statement I: SO\(_2\) and H\(_2\)O both possess V-shaped structures. 
Statement II: The bond angle of SO\(_2\) is less than that of H\(_2\)O. In the light of the above statements, choose the most appropriate answer from the options given below:

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

The covalency and oxidation state respectively of boron in [BF₄]^-, are

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

Given below are two statements:
Statement I: Tropolone is an aromatic compound and has 8л electrons. 
Statement II: electrons of >C = O group in tropolone is involved in aromaticity. 
In the light of the above statements, choose the correct answer from the options given below

• (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

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

Given below are two statements: one is labeled as Assertion (A) and the other is labeled as Reason (R).
Assertion (A): Acidic nature follows the order:

Reason (R): F is a better electron-withdrawing group than Cl
In the light of the above statements, write the detailed answer:

• (1) (A) and (R) both are correct and (R) is the correct explanation of (A) 
• (2) (A) and (R) both are correct, but (R) is not the correct explanation of (A) 
• (3) (A) is correct but (R) is not correct 
• (4) (A) is incorrect but (R) is correct 

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

• (1) Br^- and I^- only
• (2) CI^- Br^- and I^- only
• (3) I^- only
• (4) Br^- only

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

better method for preparation of bef₂ among the following is

• (1) \(B e+ F_ 2\,\,\ \underrightarrow{\triangle} \,\,B e F _2\)
• (2) \(( N H _4 ) _2 B e F_ 4\,\,\ \underrightarrow{\triangle} \,\,B e F _2\)
• (3) \(B eO+C+ F_ 2\,\,\ \underrightarrow{\triangle} \,\,B e F _2\)
• (4) \(B eH_2+F_ 2\,\,\ \underrightarrow{\triangle} \,\,B e F _2\)

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. 
In the light of the above statements, choose the most appropriate answer from the options given below

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

Which of the following are the Green house gases?
A. Water vapour 
B. Ozone 
C. 1₂ 
D. Molecular hydrogen 
Choose the most appropriate answer from the options given below

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

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 directions when the size of particles is large enough. 
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) Both A and R are correct but R is NOT the correct explanation of A
• (3) A is true but R is false
• (4) A is false but R is true

Given below are two statements related to Ellingham diagram:
Statement-I: Ellingham diagrams can be constructed for formation of oxides, sulfides and halides of metals. 
Statement-II : It consists of plots of ΔfH° vs T for formation of oxides of elements. 
In the light of the above statements, choose the most appropriate answer from the options given below

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

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

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

A(g) → 2B(g) + C(g) is a 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 ___mm Hg. (Nearest integer)

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____
(Given: Molar mass AgBr=188g mol^-1)

See the following chemical reaction: \[ \text{Cr}_2\text{O}_7^{2-} + \text{XH}^+ + \text{6Fe}^{2+} \rightarrow \text{YCr}^{3+} + \text{6Fe}^{3+} + \text{ZH}_2\text{O}. \] The sum of \(X\), \(Y\), and \(Z\) is _____.

1g of a carbonate (M₂CO₃) on treatment with excess HCl produces 0.01 mol of CO₂ .The molar mass of M₂CO₃ is g mol^-1. (Nearest integer)

The orbital angular momentum of an electron in 3s orbital is  \(\frac{xh}{2π}\) The value of x is___.

By weight, 23% NaCl and 19.5% MgCl₂ are present in salt water. The degree of dissociation of both salts is 100%. Find the average boiling point of salt water (inºC). (Kb = 0.52 K kg mol^–1) (Nearest integer)

At 298 K, the standard reduction potential for Cu²⁺/Cu electrode is 0.34 V. 
Given: Ksp Cu(OH)2 = 1 × 10^-20 
Take \(\frac{2.303RT}{F}\)= 0.059V 
The reduction potential at pH = 14 for the above couple is (-)x x 10^-2 V. 
The value of x 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____ x 10^-2 (Nearest integer) 
Given: pKa (CH₃COOH) = 4.76 
log 2 = 0.30 
log 3 = 0.48

If the formula of borax is \(Na_2B_4Ox(OH)y.zH_2O\) , Find the value of x + y + z. 

Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of 4 Å. The radius of sodium atom is __________ × 10⁻¹ Å (Nearest integer)