JEE Main 2023 April 6 Shift 1 Question Paper Out: Download PDF with Solutions for 2025 Preparation

Let \(A = \{x \in \mathbb{R}: |x+3| + |x+4| \le 3\}\),} \[ B = \left\{ x \in \mathbb{R} : 3 \cdot \sum_{r=1}^{\infty} \frac{3^{x-3}}{10^r} < 3^{-3x} \right\}, \] where \([x]\) denotes the greatest integer function. Then,

• (1)   \(A \subset B, A \ne B\)
• (2) \(A \cap B = \phi\)
• (3) \(A = B\)
• (4) \(B \subset C, A \ne B\)

If the system of equations  
x + y + az = b  
2x + 5y + 2z = 6  
x + 2y + 3z = 3  
Has infinitely many solutions, then 2a + 3b is equal to

• (1) 20
• (2) 23
• (3) 25
• (4) 28

The straight lines l₁ and l₂ pass through the origin and trisect the line segment of the line L: 9x + 5y = 45 between the axes. If m₁ and m₂ are the slopes of the lines l₁ and l_2, then the point of intersection of the line y = (m₁ + m₂)x with L lies on

• (1) y-2x=5
• (2) 6x-y=15
• (3) y-x=5
• (4) 6x+y=10

One vertex of a rectangular parallelepiped is at the origin O and the lengths of its edges along x, y and z axes are 3, 4 and 5 units respectively. Let P be the vertex (3, 4, 5). Then the shortest distance between the diagonal OP and an edge parallel to z axis, not passing through O or P is :

• (1) \(\frac{16}{5}\)
• (2) \(\frac{15}{\sqrt{34}}\)
• (3) \(\frac{12}{5}\)
• (4) \(\frac{9}{5}\)

Mean of first 15 numbers is 12 and variance is 14. Mean of next 15 numbers is 14 and variance is a. If variance of all 30 numbers is 13, then a is equal to

• (1) 12
• (2) 14
• (3) 10
• (4) 3

Let \(A=\) [\(a_{ij}\)]\(_{2\times2}\) be a matrix and \(A^2 = I\) where \(a_{ij} \neq0\). If a sum of diagonal elements and b=det(A), then \(3a^2+4b^2\) is

• (1) 10
• (2) 12
• (3) 4
• (4) 8

If 5f(x) + 4f (\(\frac{1}{x}\)) = \(\frac{1}{x}\)+ 3, then \(18\int_{1}^{2}\) f(x)dx is:

• (1)

  10 \(l\)n 3 - 6

• (2)

  5 \(l\)n2 - 6

• (3)

  10 \(l\)n 2 - 6

• (4)

  5 \(l\)n 2 - 3

Let \(I(x) = \int \frac{x^2\left(x\sec^2 x + \tan x\right)}{(x\tan x + 1)^2}\,dx\). If \(I(0) = 0\), then \(I\left(\frac{\pi}{4}\right)\) is equal to :

• (1) \(\log_e \frac{(\pi+4)^2}{32} - \frac{\pi^2}{4(\pi+4)}\)
• (2) \(\log_e \frac{(\pi+4)^2}{16} - \frac{\pi^2}{4(\pi+4)}\)
• (3) \(\log_e \frac{(\pi+4)^2}{16} + \frac{\pi^2}{4(\pi+4)}\)
• (4) \(\log_e \frac{(\pi+4)^2}{32} + \frac{\pi^2}{4(\pi+4)}\)

Let \(\vec{a}\) = 2\(\widehat{i}\)+3\(\widehat{j}\)+4\(\widehat{k}\), \(\vec{b}\) = \(\widehat{i}\)-2\(\widehat{j}\)-2\(\widehat{k}\), \(\vec{c}\) = -\(\widehat{i}\)+4\(\widehat{j}\)+3\(\widehat{k}\) and \(\vec{d}\) is a vector perpendicular to \(\vec{b}\) and \(\vec{c}\),  \(\vec{a}\).\(\vec{d}\) = 18, then find |\(\vec{a}\)x\(\vec{d}\)|²

• (1) 720
• (2) 700
• (3) 360
• (4) 300

If \(a_1,a_2,.......a_n\) are in arithmetic progression with common difference \(d>n\), then find limit \(\lim_{n \to \infty}\sqrt{\frac{d}{n}}(\frac{1}{\sqrt{a_1}+\sqrt{a_2}})+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+.......+\frac{1}{\sqrt{a_n}+\sqrt{a_{n-1}}})\) is____.

The sum of roots of |x² - 8x + 15| - 2x + 7 = 0 is:

• (1) \(11+\sqrt{3}\)
• (2) \(11-\sqrt{3}\)
• (3) \(9+\sqrt{3}\)
• (4) \(9-\sqrt{3}\)

In the expansion of \((2^\frac{1}{4}+3^{-\frac{1}{4}})^n\), the ratio of \(5^{th}\) term from start and \(5^{th}\) term form end is \(\sqrt 6 : 1\) , then find \(3^{rd}\) term

• (1) 30\(\sqrt 3\)
• (2) 60\(\sqrt 3\)
• (3) 30
• (4) 50\(\sqrt 3\)

if \(2x^y+3y^x=20\) then \(\frac{dy}{dx}\) at (2,2) is equal to:

• (1) \(-(\frac{3+log_e4}{ 2+loge_8})\)
• (2) \(-(\frac{3+log_e16}{ 4+loge_8})\)
• (3) \(-(\frac{3+log_e8}{ 2+loge_4 })\)
• (4) \(-(\frac{2+log_e8}{ 3+loge_4})\)

The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + ... is

A pair of dice is rolled 5 times. let getting a total of 5 in a single throw is considered as success. If probability of getting atleast four success is \(\frac{x}{3}\) then x is equal to

• (1) \(\frac{41}{9^{5}}\)
• (2) \(\frac{41}{9^{4}}\)
• (3) \(\frac{123}{9^{5}}\)
• (4) \(\frac{123}{9^{4}}\)

If the equation of the plane passing through the line of intersection of the planes 2x – y + z = 3, 4x– 3y +5z + 9 = 0 and parallel to the line  \(\frac{x+1}{−2} =\frac{ y+3}{4}= \frac{z−2}{5}\) is ax by+cz+6=0. then a + b + c is equal to 

• (1) 12
• (2) 13
• (3) 14
• (4) 15

\(5\^{i}+5\hat{j}+2λ\hat{k},\hat{i}+2\hat{j}+3\hat{k},-2\hat{i}+λ\hat{j}+4\hat{k}\) and \(-\hat{i}+5\hat{j}+6\hat{k}.\) Let the set S = {λ∈ \(\mathbb{R}\) : The points A, B, C and D are coplanar}. Then \(\displaystyle\sum_{λ∈S}^{}(λ+2)^2\) is equal to

• (1) 13
• (2) 25
• (3) 41
• (4) \(\frac{37}{2}\)

From the top A of a vertical wall AB of height 30 m, the angles of depression of the top P and bottom Q of a vertical tower PQ are 15\(^\circ\) and 60\(^\circ\) respectively. B and Q are on the same horizontal level. If C is a point on AB such that CB = 15 m, then the area (in m\(^2\)) of the quadrilateral BCPQ is equal to : 

• (1) \(300(\sqrt{3} - \sqrt{5})\)
• (2) \(300(\sqrt{3} + 1)\)
• (3) \(300(\sqrt{3} - 1)\)
• (4) \(600(\sqrt{3} - 1)\)

Statement (P \(\Rightarrow\) Q) \(\land\) (R \(\Rightarrow\) Q) is logically equivalent to :

• (1) (P \(\lor\) R) \(\Rightarrow\) Q}
• (2) (P \(\Rightarrow\) R) \(\lor\) (Q \(\Rightarrow\) R)}
• (3) (P \(\Rightarrow\) R) \(\land\) (Q \(\Rightarrow\) R)
• (4) (P \(\land\) R) \(\Rightarrow\) Q

If ²ⁿC₃ : ⁿC₃ = 10, then \(\frac{n^{2}+3n}{n^{2}-3n+4}\) is equal to

Let y = y(x) be a solution of the differential equation (x cos x)dy +(xy sin x + y cos x – l)dx = 0, 0 < x < \(\frac{π}{2}\). If\(\frac{π}{3}y(\frac{π}{3})=\sqrt3\), then \(| \frac{π}{6 }y“( \frac{π}{6})+2 y'( \frac{π}{6})| \) is equal to______.

If the area of the region \( S={(x,y) : 2y-y^2 ≤ x^2 ≤ 2y, x ≥ y}\) is equal to \(\frac{ n+2}{n+1}−\frac{π}{n−1}\), then the natural number n is equal to _____.

Let the point (p, p+1) lie inside the region \(E = \{(x,y):3-x≤y≤\sqrt{9-x^2}, 0 ≤ x ≤ 3\} \)If the set of all values of p is the interval (a,b). then b2 + b - a2 is equal to_____

Let a∈ Z and [t] be the greatest integer t. Then the number of points, where the function f(x)=[a+13 sin x], x ∈ (0, π) is not differentiable, is ____

Let A = {1, 2, 3, 4,.....10} and B = {0, 1, 2, 3, 4}. The number of elements in the relation R = {(a, b) ∈ A × A: 2(a – b)2 + 3(a – b) ∈ B} is______.

A circle passing through the point P\(( \alpha , \beta )\) in the first quadrant touches the two coordinate axes at the points A and B. The point P is above the line AB. The point Q on the line segment AB is the foot of perpendicular from P on AB. If PQ is equal to 11 units, then value of \(( \alpha \beta )\)  is ___

The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is______ 

Let the tangent to the curve x² + 2x – 4y + 9 = 0 at the point P(1, 3) on it meet the y-axis at A. Let the line passing through P and parallel to the line x – 3y = 6 meet the parabola y² = 4x at B. If B lies on the line 2x – 3y = 8. then (AB)² is equal to___

The coefficient of \(x^{18}\) in the expansion of \(\left(x^4 - \frac{1}{x^3}\right)^{15}\) is ________

Let the image of the point \(P(1, 2, 3)\) in the plane \(2x - y + z = 9\) be \(Q\). If the coordinates of the point \(R\) are \((6, 10, 7)\), then the square of the area of the triangle \(PQR\) is ___________.

A particle is moving with constant speed in a circular path. When the particle turns by an angle \(90\degree\) , the ratio of instantaneous velocity to its average velocity is \(π : x\sqrt2\). The value of x will be -

• (1) 7
• (2) 2
• (3) 1
• (4) 5

The induced emf can be produced in a coil by
A. moving the coil with uniform speed inside uniform magnetic field 
B. moving the coil with non uniform speed inside uniform magnetic field 
C. rotating the coil inside the uniform magnetic field 
D. changing the area of the coil inside the uniform magnetic field 
Choose the correct answer from the options given below :

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

Name the logic gate equivalent to the diagram attached

• (1) NOR
• (2) OR
• (3) NAND
• (4) AND

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Range is maximum at θ = 45º.
Reason (R): Range is maximum when sin (2θ) = 1.
In the light of the above statements, choose the correct answer from the options given below:

• (1) Both assertion (A) and reason (R) are true & reason (R) is the correct explanation of assertion.
• (2) Both assertion (A) and reason (R) are true but reason (R is not correct explanation of assertion.
• (3) Assertion (A) is true and reason (R) is false.
• (4) Assertion (A) is false and reason (R) is false.

A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W. The rate at which internal energy of the system increase is

• (1) 500 W
• (2) 600 W
• (3) 800 W
• (4) 1200 W

A small ball of mass M and density \(\rho\) is dropped in a viscous liquid of density \(\rho_0\). After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

• (1) \(F=Mg(1+\frac{\rho_0}{\rho})\)
• (2) \(F=Mg(1+\frac{\rho}{\rho_0})\)
• (3) \(F=Mg(1-\frac{\rho_0}{\rho})\)
• (4) \(F=Mg(1±\rho\rho_0)\)

A small block of mass 100 g is tied to a spring of spring constant 7.5 N/m and length 20 cm. The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 rad/s about point A, then tension in the spring is-

• (1) 0.75N
• (2) 1.5N
• (3) 0.25N
• (4) 0.50N

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion (A): Earth has atmosphere and moon doesn’t Reason (R): escape speed on moon is less than that Earth. In the light of the above statements, choose the correct answer from the options given below

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

The kinetic energy of an electron, α-particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron (λe) α-particle (λα) and the proton (λp) are as follows :

• (1) λα > λp > λe
• (2) λα = λp > λe
• (3) λα = λp < λe
• (4) λα < λp < λe

A monochromatic light wave with wavelength \(λ_1\) and frequency \(v_1\) in air enters another medium. If the angle of incidence and angle of refraction at the interface are 45° and 30° respectively, then the wavelength \(λ_2\) and frequency \(v_2\) of the refracted wave are : 

• (1) \(λ_2 = 1/√2 λ_1, v_2 = v_1\)
• (2) \(λ_2 = λ_1 , v_2 = 1/√2 v_1\)
• (3) \(λ_2 = λ_1, v_2 = √2v_1\)
• (4) \(λ_2 = √2λ_1 , v_2 = v_1\)

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

• (1) zero in the region r < a and inversely proportional to r in the region r > a
• (2) inversely proportional to r in the region r < a and uniform throughout in the region r > a
• (3) directly proportional to r in the region r < a and inversely proportional to r in the region r > a
• (4) uniform in the region r < a and inversely proportional to distance r from the axis, in the region r > a

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:

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

A mass \(m\) is attached to two springs as shown in the figure. The spring constants of the two springs are \(K_1\) and \(K_2\). For the frictionless surface, the time period of oscillation of mass \(m\) is:

• (1) \(2 \pi \sqrt{\frac{m}{K_1-K_2}}\)
• (2) \(\frac{1}{2 \pi} \sqrt{\frac{K_1-K_2}{m}}\)
• (3) \(\frac{1}{2 \pi} \sqrt{\frac{K_1+K_2}{m}}\)
• (4) \(2 \pi \sqrt{\frac{m}{K_1+K_2}}\)

Two resistances are given as \(R_1=(10 ±0.5) Ω\) and \(R_2= (15±0.5) Ω\). The percentage error in the measurement of equivalent resistance when they are connected in parallel is -

• (1) 2.33
• (2) 4.33
• (3) 5.33
• (4) 6.33

For the plane electromagnetic wave given by \(E = E_o sin (ωt-kx)\) and \(B = B_o sin ( ωt-kx)\), the ratio of average electric energy density to average magnetic energy density is

• (1) 2
• (2) 1/2
• (3) 1
• (4) 4

The resistivity (\(\rho\)) of semiconductor varies with temperature. Which of the following curve represents the correct behavior

• (1)

• (2)

• (3)

• (4)

• (1) A
• (2) D
• (3) C
• (4) B

The number of air molecules per cm³ increased from 3 × 10¹⁹ to 12 × 10¹⁹. The ratio of collision frequency of air molecules before and after the increase in the number respectively is :

• (1) 0.25
• (2) 0.75
• (3) 1.25
• (4) 0.50

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the entre (O) of shell can be graphically represented as –

• (1)

• (2)

• (3)

• (4)

By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21% ?

• (1) 12%
• (2) 15%
• (3) 14%
• (4) 10%

The radius of fifth orbit of the Li++ is __________ × 10^-12 m.
Take : radius of hydrogen atom = 0.51 Å

Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is __________ \(× 10^{-3} \)kg-\(m^2\)

A steel rod bas a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young's modulus of steel is 2.0 × \(10^{11}\) N/m\(^2\). The longitudinal strain produced in the wire is _______ × \(10^{-5}\)

Two identical circular wires of radius 20 cm and carrying current \(\sqrt2 \)A are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is _________ × 10^{-8} T.
 

A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of 30o with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water surface in centimeters is (n-w = 4/3) ____________

A particle of mass 10 g moves in a straight line with retardation 2x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is \((10/x)^{-n}\)J. The value of n will be ____________

The length of a metallic wire is increased by 20% and its area of cross section is reduced by 4%. The percentage change in resistance of the metallic wire is ______

A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant K = 4. The thickness of the dielectric material is x, where x < d. Let C1 and C2 be the capacitance of the system for \(x =\) \(\frac{1}{3}d\) and \(x=\frac{2}{3}d\), respectively. If C₁ = 2μF, the value of C₂ is _______ μF.

An ideal transformer with purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 V. The average rate of energy consumption in the houses served by the transformer is 60 kW. The value of resistive load (Rs) required in the secondary circuit will be ________ mΩ.

A person driving car at a constant speed of 15 m/s is approaching a vertical wall. The person notices a change of 40 Hz in the frequency of his car’s horn upon reflection from the wall. The frequency of horn is ____ Hz.

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R 
Assertion: Magnetic moment of [Fe(H2O)6]3+ is 5.92 BM and that of [Fe(CN)6]3– is 1.73 BM 
Reason: Oxidation state of Fe in both the complexes is +3. 
In the light of the above statements, choose the correct answer from the options given below

• (1) Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
• (2) Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
• (3) Reason is correct but Assertion is not correct
• (4) Reason is incorrect but Reason is correct

The standard electrode potential of M^+/M in aqueous solution does not depend on

• (1) Sublimation of a solid metal
• (2) Ionisation of a gaseous metal atom
• (3) Ionisation of a solid metal atom
• (4) Hydration of a gaseous metal ion

CH₃CH₂-Br \(\overrightarrow{Acetone}^{NaI}\) CH₃-CH₂-I+NaBr
Which of the following statement is correct ? 

• (1) Acetic acid solvent can take in above reaction. 
• (2) NaI is soluble in acetone but NaBr is precipitate in acetone
• (3) NaI is precipitated in acetone but NaBr is soluble in acetone 
• (4) When acetone is taken in solvent transition state is highly polar

the major product A and B from the the following reaction are

• (1)
• (2)
• (3)
• (4)

• (1) A & B
• (2) B only
• (3) A & D
• (4) B & D

Predict expression from α in terms of \(K_{eq}\) and concentration C : 

\(A_2 B_3(aq) \leftrightharpoons 2{A_3} (aq)+3B_{{2-}}(aq)\)

• (1) \(\left(\frac{{K_{eq}}}{{108C^4}}\right)^{\frac{1}{5}}\)
• (2) \((\frac{K_{eq}}{5C^4})^\frac{1}{5}\)
• (3) \((\frac{4K_{eq}}{5C^4})^\frac{1}{5}\)
• (4) \((\frac{9K_{eq}}{108C^4})^\frac{1}{5}\)

The difference between electron gain enthalpies will be maximum between

• (1) Ne and F
• (2) Ne and Cl
• (3) Ar and Cl
• (4) Ar and F

The major product formed in the following reaction is

• (1)
• (2)
• (3)
• (4)

• (1)

  i\(\to\)c, ii\(\to\)d, iii\(\to\)b, iv\(\to\)a

• (2)

  i\(\to\)d, ii\(\to\)c, iii\(\to\)b, iv\(\to\)a

• (3)

  i\(\to\)c, ii\(\to\)d, iii\(\to\)a, iv\(\to\)b

• (4)

  i\(\to\)c, ii\(\to\)b, iii\(\to\)d, iv\(\to\)a

Compound P is neutral. Q gives effervescence with NaHCO₃ while R reacts with Hinsbergs reagent to give solid soluble in NaOH. Compound P is

• (1)
• (2)
• (3)
• (4)

Which one among the following metals is the weakest reducing agent?

• (1) \(Rb\)
• (2) \(Na\)
• (3) \(Li\)
• (4) \(K\)

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

Polymer which is named as orlon is:

• (1) Polyamide
• (2) Polyacrylonitrile
• (3) Polycarbonate
• (4) Polyethene

• (1)

  i\(\to\)c, ii\(\to\)d, iii\(\to\)a, iv\(\to\)b

• (2)

  i\(\to\)c, ii\(\to\)d, iii\(\to\)b, iv\(\to\)a

• (3)

  i\(\to\)d, ii\(\to\)c, iii\(\to\)b, iv\(\to\)a

• (4)

  i\(\to\)c, ii\(\to\)b, iii\(\to\)d, iv\(\to\)a

Which compound is added to cement to increase its setting time?

• (1) Gypsum
• (2) Lime stone
• (3) Clay
• (4) Calcium carbonate

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Radius of H⁺ is 1.5 × 10^–3 pm
Reason (R) : H⁺ cannot exist independently
In the light of the above statements, write the detailed answer:

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

A binary compound has Y-atoms forming FCC unit cell and another type of X-atoms occupying \(\frac{1}{3}\)^rd of tetrahedral voids. Find out the molecular formula of the compound

 

Photochemical smog found mainly in 

• (1) Industrial area
• (2) Marshy place
• (3) Hilly area of Himachal
• (4) Cold humid climate 

How many bromo products are formed when ethane is reacted with excess of Br₂ on heating?

The wavelength of an electron of kinetic energy \(4.50 \times 10^{-29}\) J is ___________ \(\times 10^{-5}\) m. (Nearest integer)
Given : mass of electron is \(9 \times 10^{-31}\) kg, \(h = 6.6 \times 10^{-34}\) J s

The number of species from the following which have square pyramidal structure is___
\(PF_5, BrF^− _4 4 − , IF_5\) ; \(BrF_5, XeOF_4, ICl ^−_ 4\)

Consider the graph of Gibbs free energy G vs Extent of reaction. The number of statement/s from the following which are true with respect to points (a), (b) and (c) is…

A. Reaction is spontaneous at (a) and (b)  
B. Reaction is at equilibrium at point (b) and nonspontaneous at point (c)  
C. Reaction is spontaneous at (a) and nonspontaneous at (c)  
D. Reaction is non-spontaneous at (a) and (b)

Determine the amount of urea (NH₂CONH₂) to be added in 1000 g of water to decrease its vapour presssure by 25%. 
Given: Molar mass of N. C. O and H are 14. 12. 16 and 1 2 mol^-1 respectively.

The value of \(log_{10}K\) for a reaction A ⇋ B is

(Given,

 \(\Delta H^{\circ}_{298K}\) = –54.67 kJ \(mol^{-1}\)

 \(\Delta H^{\circ}_{298K}\) = 10 kJ \(mol^{-1}\)

 and R = 8.314 J \(K^{-1}mol^{-1}\)

 2.303 × 8.314 × 298 = 5705) 

Number of ambidentate ligands in given complex [M(en)(SCN)4] : 

How many moles of \(Ba_3(PO_4)_2\) will be formed by the reaction of \(5\) moles of \(BaCl_2\) and \(3\) moles of \(Na_3(PO_4)\).

Oxidation number of Mo in Ammonophosphomolybdate

For the adsorption of hydrogen on platinum, the activation energy is 30 kJ mol^-1 and for the adsorption of hydrogen on nickel, the activation energy is 41.4 kJ mol^-1 . The logarithm of the ratio of the rates of chemisorption on equal areas of the metals at 300 K is ……… (Nearest integer) Given: ln 10 = 2. 3  R = 8.3 JK^-1 mol^-1