JEE Main 2023 April 12 Shift 1 Question Paper with Solution PDF- Download Here

Two dice A and B are rolled, Let the numbers obtained on A and B be α and β respectively. If the variance of α - β is \(\frac{p}{q}\), where p and q are coprime, then the sum of the positive divisors of p is equal to

• (1) 31
• (2) 36
• (3) 48
• (4) 72

Let A=\(\begin{bmatrix} 1 & \frac{1}{51} \\ 0 & 1\end{bmatrix}\). If B=\(\begin{bmatrix} 1 & 2 \\ -1 & -1\end{bmatrix}\)A \(\begin{bmatrix} -1 & -2 \\ 1 & 1\end{bmatrix}\), then the sum of all the elements of the matrix \(\sum^{50}_{n=1}B^n\) is equal to

• (1) 50
• (2) 75
• (3) 100
• (4) 125

Let y = y(x), y>0, be a solution curve of the differential equation (1 + x²) dy=y (x–y)dx. If y(0)=1 and y(2√2) , = b then

• (1) \(e β^{ − 1} = e^{-2} ( 3 + 2 √ 2 )\)
• (2) \(e ^3 β^{ − 1} = e ( 3 + 2 √ 2 )\)
• (3) \(e β^{ − 1} = e^{-2} ( 5+ √ 2 )\)
• (4) \(e3 β^{ − 1} = e^{-2} ( 3+ 2√ 2 )\)

Let the lines l₁ :  \(\frac{x+5}{3} =\frac{y+4}{1}=\frac{z−α}{−2}\)  and l₂ :3x+2y+z–2=0=x–3y+2z-13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(-4,-3, 2), then |a| + |b|+|c| is equal to

• (1) 8
• (2) 10
• (3) 12
• (4) 14

The number of five-digit numbers, greater than 40000 and divis ible by 5, which can be formed using the digits 0, 1, 3, 5, 7, and 9 without repetition, is equal to:

• (1) 120
• (2) 132
• (3) 72
• (4) 96

Let C be the circle in the complex plane with centre z₀ =\(\frac{1}{2}\) (1+3i) and radius r = 1. Let z₁ = 1+ i and the complex number z2 be outside the circle C such that |z₁ – z₀| |z₂ – z₀| = 1. If z₀, z₁ and z₂ are collinear, then the smaller value of |z₂|₂ is equal to

• (1) \(\frac{3}{2}\)
• (2) \(\frac{5}{2}\)
• (3) \(\frac{7}{2}\)
• (4) \(\frac{13}{2}\)

If the point \((α ,\frac{7√3}{3}) \)lies on the curve traced by the mid-points of the line segments of the lines x cosθ + y sinθ = 7, θ ∈ (0 , \(\frac{π}{2}\) )  between the coordinates axes, then α is equal to 

• (1) -7
• (2) -7√3
• (3) 7
• (4) 7√3

Let α,β be the roots of the quadratic equation  x²+√6x+3=0. Then  \(\frac{α^23+β^23 + α ^14 + β ^14 }{α ^15 + β ^15 + α 160 + β ^{10}}\)  is equal to

• (1) 9
• (2) 12
• (3) 81
• (4) 729

Let P \((\frac{2√3}{√7},\frac{6}{√7} )\), Q,R and S be four points on the ellipse 9x² + 4y² = 36. Let PQ and RS be mutually perpendicular and pass through the origin. If  \(\frac{1}{ ( P Q )^2}  +\frac{ 1}{ ( R S ) ^2} =\frac{ P }{q}\),  where p and q are coprime, then p + q is equal to

• (1) 137
• (2) 143
• (3) 147
• (4) 157

If the local maximum value of the function f( x )=\((\frac{√3e}{2 sin x} )^{ sin^2x}\) ,\(  x ∈ ( 0,\frac{π}{2} )\),  is \(\frac{k}{e}\), then \((\frac{k}{e})^8+\frac{k^8}{e^5}+k^8 \) is equal to

• (1) e⁵+e⁶+e¹¹
• (2) e³+e⁶+e¹⁰
• (3) e³+e⁵+e¹¹
• (4) e³+e⁶+e¹¹

The area of the region enclosed by the curve y = x³ and its tangent at the point (-1, -1) is

• (1) \(\frac{19}{4}\)
• (2) \(\frac{23}{4}\)
• (3) \(\frac{27}{4}\)
• (4) \(\frac{31}{4}\)

Let D be the domain of the function f(x)=sin⁻¹(\( log_{3 x} (\frac{6+2log_3x}{−5x}\))) If the range of the function g : D → R defined by g ( x ) = x − [ x ] is the greatest integer function), is ( α , β ) , then α ² +\(\frac{ 5}{ β}\) is equal to 

• (1) 45
• (2) 46
• (3) 135
• (4) 136

If \(\frac{1}{n+1}\,{}^nC_n+\frac{1}{n}\,{}^nC_{n-1}+\ldots+\frac{1}{2}\,{}^nC_1+{}^nC_0=\frac{1023}{10}\), then \(n\) is equal to :

• (1) 9
• (2) 6
• (3) 7
• (4) 8

Let be a sequence such that a₁ + a₂ +....+ a_n=\(\frac{n^2+3n}{(n+1) (n+2)}\) If  \(28 ∑^{10}_{k=1} \frac{1}{a_k} =  P _1 P_ 2 P _3 . . . P_ m\) , where p₁, p₂, …..p_m are the first m prime numbers, then m is equal to

• (1) 5
• (2) 6
• (3) 7
• (4) 8

Among the two statements
(S1) : (p ⇒ q)∧(q ∧(~q)) is a contradiction and  
(S2) : (p∧q) v ((~p)∧q) v (p ∧ (~q)) v ((~p) ∧ (~q)) is a tautology 

• (1) both are true
• (2) both are false
• (3) only (S1) is true
• (4) only (S2) is true

Let a, b, c be three distinct real numbers, none equal to one. If the vectors \(a\hat{i}+\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}+c\hat{k}\) are coplanar, then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\) is equal to 

• (1) -1
• (2) 1
• (3) -2
• (4) 2

Let  \(λ∈Z ,→a=λ\^i+\^j =/^ k λ ∈\)  and \(\overrightarrow{ b} = 3 \^i− \^j + 2 \^k\) . be a vector such that  ( \(\overrightarrow{ a}+\overrightarrow{ b}+\overrightarrow{ c}\) ) × \(\overrightarrow{ c}=\overrightarrow{ 0},\overrightarrow{ a}.\overrightarrow{ c}\) and  \(\overrightarrow{ b}.\overrightarrow{ C}=-20\)  Then \( | \overrightarrow{c} + ( λ \^i + \^j + \^k ) |  ^2 \) is equal to

• (1) 46
• (2) 49
• (3) 53
• (4) 62

For the expression \((1-x)^{100}\). Then sum of coefficient of first 50 terms is:

• (1) \(^{99}C_{49}\)
• (2) \(-\frac{^{100}C_{50}}{2}\)
• (3) \(-^{99}C_{49}\)
• (4) \(-^{101}C_{50}\)

Let the plane P : 4x – y + z = 10 be rotated by an angle \(\frac{π}{2}\) about its line of intersection with the plane x + y – z = 4. If α is the distance of the point (2, 3, -4) from the new position of the plane P, then 35α is

• (1) 85
• (2) 90
• (3) 105
• (4) 126

Given A, B, C represents angles of a  ⃤ AB and cosA + 2 cosB + cosC = 2 and AB = 3 and BC = 7 then cosA – cosC is?

• (1) \(-\frac{10}{7}\)
• (2) \(\frac{10}{7}\)
• (3) \(\frac{5}{7}\)
• (4) \(-\frac{5}{7}\)

let D_k=\(\begin{vmatrix} 1 & 2k& 2k-1\\ n & n^2+n+2 & n^2\\ n & n^2+n & n^2+n+2 \end{vmatrix}\) if \(∑^n_{ k=1}\) D_k=96, Then n is equal to

Let the digits a, b, c be in A.P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?

Two circles in the first quadrant of radii r₁ and r₂ touch the coordinate axes. Each of them cuts off an intercept of 2 units with the line x + y = 2. Then \(r^2_1+r_2^2– r_1r_2\) is equal to_____.

A fair n (n>1) faces die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is \(\frac{n}{9}\), then n is equal to_____.

If \(∫^{0.15}_{-0.15 }|100x^2-1|dx=\frac{k}{3000,}\)  then k is equal to____.

The number of relations, on the set {1,2,3} containing (1,2) and (2,3), which are reflexive and transitive but not symmetric, is______

Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x) = |[x] |+\(\sqrt{x -[x] }\)is discontinuous is _____.

Positive numbers a₁, a_2, .... a₅ are in geometric progression. Their mean and variance are \(\frac{31}{10}\) and \(\frac{m}{n}\) respectively. The mean of the reciprocals is \(\frac{31}{40}\), then m + n is?

• (1) 209
• (2) 211
• (3) 113
• (4) 429

Let I(x) = \(∫√\frac{x+7}{x} dx\) and I (9) = 12 + 7 loge 7. If I (1) = α + 7 loge (1 + 2√2), then α4 is equal to_____.

Let the plane x + 3y – 2z + 6 = 0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is \((α,β,\frac{6}{7}),\) then 98(α + β)² is equal to___.

A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be

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

Given below are two statements:
Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance. 
Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.  
In the light of given 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

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

Given below are two statement : one is labelled as Assertion A and the other is labelled as Reason R.  
Assertion A : EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology.  
Reason R : Infrared EM waves are more energetic than microwaves, (used in Radar)  
In the light of given statements, choose the correct answer from the options given below:  

• (1) Both A and R true and R is the correct explanation of A
• (2) Both A and R 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

The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.

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

Suppose a situation in which two planets orbits around the sun in the same orbit. If the mass of plant 1 is twice the mass of planet 2, then what do they have same?

• (1) Potential energy
• (2) Kinetic energy
• (3) Total energy
• (4) Velocity

Three force F₁ = 10N, F₂ = 8 N, F₃ = 6N are acting on a particle of mass 5 kg. The forces F₂ and F₃ are applied perpendicular so that particle remains at rest. If the force F₁ is removed, then the acceleration of the particle is

• (1) 2 ms^-2
• (2) 7 ms^-2
• (3) 4.8 ms^-2
• (4) 0.5 ms^-2

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. when viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is

• (1) \(\frac{6}{5}\)
• (2) \(\frac{2}{3}\)
• (3) \(\frac{4}{3}\)
• (4) \(\frac{3}{2}\)

A proton and an α-particle are accelerated from rest by 2V and 4V potentials, respectively. The ratio of their de-Broglie wavelength is

• (1) 2:1
• (2) 4:1
• (3) 8:1
• (4) 16:1

Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R.  
Assertion A : If an electric dipole of dipole moment 30 x 10-5 Cm is enclosed by a closed surface, the net flux coming out of the surface will by zero.
Reason R : Electric dipole consists of two equal and opposite charges. 
In the light of 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 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

Given below are two statements:  
Statement I : The diamagnetic property depends on temperature.  
Statement II : The included magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field.  
In the light of given statement, 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 correct but Statement II is false.
• (4) Statement I is incorrect but Statement II is true

A wire of resistance 160 Ω is melted and drawn in wire of one-fourth of its length. The new resistance of the wire will be

• (1) 10 Ω
• (2) 16 Ω
• (3) 40 Ω
• (4) 640 Ω

A particle is thrown vertically upward with initial velocity of 150 m/s. Find the ratio of its speed at t = 3 seconds and t = 5 seconds. is \(\frac{x+1}{x}\) the value of x is___. (take g = 10 m/s2)

• (1) 5
• (2) 6
• (3) 10
• (4) -5

If the r.m.s speed of chlorine molecule is \(490\ \mathrm{m/s}\) at \(27^{\circ}\mathrm{C}\), the r.m.s speed of argon molecules at the same temperature will be (Atomic mass of argon \(= 39.9\ \mathrm{u}\), molecular mass of chlorine \(= 70.9\ \mathrm{u}\))

• (1) \(451.7\ \mathrm{m/s}\)
• (2) \(751.7\ \mathrm{m/s}\)
• (3) \(551.7\ \mathrm{m/s}\)
• (4) \(651.7\ \mathrm{m/s}\)

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be

• (1) 1
• (2) 2
• (3) 3
• (4) 4

Given below are two statements :  
Statement I : When the frequency of an a.c. source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.  
Statement II : In a series LCR circuit, the value of power factor at resonance is one. 
In the light of given statements, choose the most appropriate 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 correct but Statement II is false.
• (4) Statement I is incorrect but Statement II is true.

In an n-p-n common emitter (CE) transistor the collector current changes from 5 mA to 16 mA for the change in base current from 100 μA and 200 μA, respectively. The current gain of transistor is______.

• (1) 0.9
• (2) 9
• (3) 110
• (4) 210

An engine operating between the boiling and freezing points of water will have 
A. efficiency more than 27%  
B. efficiency less than the efficiency a Carnot engine operating between the same two temperatures.  
C. efficiency equal to 27%  
D. efficiency less than 27% 

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

an body cools down from 80°C to 60°C in 5 minutes The temperature pf the surrounding is 20°C. The time taken to cool from 60°C to 40°C is

• (1) \(\frac{25}{3}s\)
• (2) 500 s
• (3) 450 s
• (4) 420 s

The amplitude of 15sin(1000πt) is modulated by 10sin(4πt) signal. The amplitude modulated signal contains frequency(ies) of
(A) 500 Hz 
(B) 2 Hz  
(C) 250 Hz  
(D) 498 Hz  
(E) 502 Hz 
Choose the correct answer from the options given below: 

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

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____KJ. [The coefficient of friction between tyre of bus and road is 0.04].

64 identical balls made of conducting material each having a potential of 10 mV are joined to form a bigger ball. The potential of a bigger ball is?

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is \(\frac{x}{5}\). The value of x is____.

The current flowing through a conductor connected across a source is 2A and 1.2 A at 0°C and 100°C respectively. The current flowing through the conductor at 50°C will be ______x10² mA.

Glycerine of density 1.25 × 10³ kg m^-3 is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is 10 cm2 and 5 cm2 and pressure drop across its length is 3 Nm^-2. The rate of flow of glycerine through the pipe is x x10^-5 m3 s^-1. The value of x is____.

Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at cm from the first lens.

For a certain organ pipe, the first three resonance frequencies are in the ratio of 1:3:5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 ms^-1 the length of the organ pipe is ___ m.

A common example of alpha decay is 
 

A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. Somehow, the radus of the loop starts expanding at a constant rate of 1 mm/s. The magnitude of induced emf in the loop at an instant when the radius of the loop is 2 cm will be ___μV

A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip 30°. The number of oscillations per minute become 10 at another place Q of 60° dip. The ratio of the total magnetic field at the two places respectively is \(\frac{4}{√x}\) The value of x is 

Given below are two statements :
Statement I: Boron is extremely hard indicating its high lattice energy 
Statement II: Boron has highest melting and boiling point compared to its other group members. 
In the light of the above statements, choose the most appropriate answer from the options given below :

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

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

The two products formed in above reaction are

• (1) Butanoic acid and acetic acid
• (2) Butanal and acetaldehyde
• (3) Butanoic acid and acetaldehyde
• (4) Butanal and acetic acid

The bond order and magnetic property of acetylide ion are same as that of

• (1) \(O^+_2\)
• (2) \(N^+_2\)
• (3) \(NO^+\)
• (4) \(O^-_2\)

A in the above reaction is:

• (1)
• (2)
• (3)
• (4)

Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: 5f electrons can participate in bonding to a far greater extent than 4f electrons 
Reason R: 5f orbitals are not as buried as 4f orbitals 
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

A metal chloride contains 55.0% of chlorine by weight. 100 mL vapours of the metal chloride at STP weigh 0.57 g. The molecular formula of the metal chloride is (Given: Atomic mass of chlorine is 35.5u)

• (1) MCL
• (2) MCL₂
• (3) MCL₃
• (4) MCL₄

Correct statements for the given reaction are:

A. Compound 'B' is aromatic 
B. The completion of above reaction is very slow 
C. 'A' shows tautomerism 
D. The bond lengths C-C in compound B are found to be same 
Choose the correct answer from the options given below

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

The incorrect statement regarding the reaction given below is

• (1) The product 'B' formed in the above reaction is p-nitroso compound at low temperature.
• (2) The reaction occurs at low temperature
• (3) The electrophile involved in the reaction is NO⁺
• (4) 'B' is N-nitroso ammonium compound

For lead storage battery pick the the correct statements.
A. During charging of battery, PbSO4 on anode is converted into PbO2 
B. During charging of battery, PbSO4 on cathode is converted into PbO2 
C. Lead storage battery, consists of grid of lead packed with PbO2 as anode 
D. Lead storage battery has ~ 38% solution of sulphuric acid as an electrolyte 
Choose the correct answer from the options given below:

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

Given below are two statements :
Statement I: SbCI, is more covalent than SbCI3
Statement II: The higher oxides of halogens also tend to be more stable than the lower ones. 
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

In the following reaction

A is

• (1)
• (2)
• (3)
• (4)

The major products ‘P’ formed in the following sequence of reaction is

• (1)
• (2)
• (3)
• (4)

The density of the alkali metals is in the order:

• (1) K<Na<Rb<Cs
• (2) Na<K<Cs<Rb
• (3) K<Cs<Na<Rb
• (4) NavRb<K<Cs

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

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: In the Ellingham diagram, a sharp change in slope of the line is observed for Mg → MgO at ~ 1120°C 
Reason R: There is a large change of entropy associated with the change of state. 
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

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

Four gases A, B, C and D have critical temperatures 5.3, 33.2, 126.0 and 154.3K respectively. For their adsorption on fixed amount of charcoal, the correct order is :

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

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

Consider the following reaction sequence: \([CaCl_2 + Na_2CO_3 → X+Y] → Z\)

• (1) X: CaCO₃, Y: NaCI, Z: NCI
• (2) X: CaO, Y: NaCI + CO₂, Z: KCl
• (3) X: CaO, Y: NaCI + CO₂, Z: NaCI
• (4) X: CaCO₃, Y: NaCI, Z: KCI

In an oligopeptide named Alanylglycylphenyl alanyl isoleucine, the number of sp² hybridised carbons is_____.

80 mole percent of MgCl₂ is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of M_gCl₂ at 38°C is ____mm Hg. (Nearest integer)
Given : Vapour pressure of water at 38°C is 50 mm Hg.

Three organic compounds A, B and C were allowed to run in thin layer chromatography using hexane and gave the following result (see figure). The R_f value of the most polar compound is ____ x 10^-2.

The value of x compound ‘D’ is

The mass of NH3 produced when 131.8 kg of cyclohexanecarbaldehyde undergoes Tollen's test is ___ kg. (Nearest Integer)
Molar Mass of C = 12g/mol 
N = 14g/mol 
0 = 16g/mol

The reaction 2NO + Br2 → 2NOBr 
takes places through the mechanism given below : 
NO + Br2 ⇔ NOBr2 (fast)  
NOBr2 + NO → 2NOBr (slow) 
The overall order of the reaction is_____.

pH of 1 litre of HCL solution is 1. How much water (in litres) is added to make pH=2?

One mole of an ideal gas at 350K is in a 2.0 L vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from 2.0L to 3.0L against a constant pressure of 4 atm. The change in entropy of the surroundings (ΔS) is JK (Nearest integer) Given: R = 8.314 J K^-1 Mol^-1.

At 600K, the root mean square (rms) speed of gas X (molar mass = 40) is equal to the most probable speed of gas Y at 90K. The molar mass of the gas Y is ____ g mol^-1. (Nearest integer)